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Hence_RR ,_, our_APPGE new_JJ continuous_JJ age-period-cohort_JJ model_NN1 predicts_VVZ alarmingly_RR low_JJ future_JJ fertility_NN1 for_IF the_AT US_NP1 (_( as_RG well_RR as_CSA for_IF Italy_NP1 )_) ._. 
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In_II the_AT case_NN1 that_CST the_AT indices_NN2 are_VBR independent_JJ ,_, the_AT insurance_NN1 portfolio_NN1 can_VM not_XX be_VBI hedged_VVN with_IW the_AT bonds_NN2 ._. 
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Active_JJ power_NN1 flow_NN1 loss_NN1 APFL_NN1 (_( 0_MC <_FO APFL_VV0 <_FO 1_MC1 )_) ,_, the_AT reduction_NN1 ratio_NN1 of_IO active_JJ power_NN1 flow_NN1 before_II and_CC after_II grid_NN1 fault_NN1 ,_, the_AT formula_NN1 is_VBZ as_CSA follows_VVZ :_: (_( 5_MC )_) <equation>where_FO Pni_NN1 is_VBZ the_AT active_JJ power_NN1 of_IO the_AT load_NN1 station_NN1 i_ZZ1 under_II normal_JJ operating_NN1 conditions_NN2 of_IO the_AT grid_NN1 ,_, and_CC Pdi_NP1 is_VBZ that_CST after_CS grid_NN1 failure_NN1 ._. 
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In_II dynamic_JJ terms_NN2 ,_, this_DD1 is_VBZ interpreted_VVN as_II a_AT1 non_FU trivial_JJ relation_NN1 ,_, or_CC an_AT1 absence_NN1 of_IO any_DD simple_JJ one_PN1 ,_, between_II the_AT initial_JJ state_NN1 and_CC the_AT quenched_JJ one_PN1 ._. 
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Instead_RR ,_, we_PPIS2 simulate_VV0 a_AT1 neural_JJ spiking_NN1 sequence_NN1 as_II a_AT1 bootstrap_NN1 sample_NN1 based_VVN on_II the_AT original_JJ intensity_NN1 estimation_NN1 ._. 
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However_RR ,_, the_AT local_JJ sub-network_NN1 and_CC the_AT estimated_JJ parameters_NN2 corresponding_VVG to_II them_PPHO2 provide_VV0 useful_JJ some_DD insights_NN2 ,_, in_II this_DD1 study_NN1 ,_, on_II the_AT relationship_NN1 between_II nodes_NN2 ,_, overlapping_VVG communities_NN2 ,_, their_APPGE proportions_NN2 of_IO belonging_VVG communities_NN2 ,_, and_CC characteristic_JJ topics_NN2 within_II each_DD1 community_NN1 ._. 
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Despite_II not_XX having_VHG run_VVN all_DB methods_NN2 on_II the_AT same_DA machine_NN1 ,_, the_AT comparison_NN1 of_IO space_NN1 usages_NN2 for_IF each_DD1 data_NN structure_NN1 will_VM nevertheless_RR be_VBI accurate_JJ ;_; results_NN2 regarding_II execution_NN1 times_NNT2 will_VM certainly_RR be_VBI machine-dependent_JJ but_CCB orders_NN2 of_IO magnitudes_NN2 are_VBR expected_VVN to_TO be_VBI roughly_RR preserved_VVN ._. 
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To_TO improve_VVI local_JJ alignments_NN2 ,_, the_AT structure–weight_NN1 is_VBZ strongly_RR decreased_VVN compared_VVN to_II the_AT optimal_JJ weight_NN1 for_IF global_JJ alignment_NN1 (_( which_DDQ is_VBZ nearly_RR the_AT same_DA as_CSA the_AT default_NN1 weight_NN1 )_) ._. 
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These_DD2 offences_NN2 broadly_RR span_VV0 the_AT classification_NN1 of_IO criminal_JJ activity_NN1 often_RR employed_VVN in_II the_AT literature_NN1 ._. 
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Second_MD ,_, we_PPIS2 derive_VV0 a_AT1 joint_JJ estimator_NN1 of_IO Sobol_NN1 '_NULL indices_NN2 ,_, its_APPGE consistency_NN1 and_CC its_APPGE asymptotic_JJ distribution_NN1 ,_, and_CC third_MD ,_, we_PPIS2 demonstrate_VV0 the_AT applicability_NN1 of_IO these_DD2 results_NN2 by_II31 means_II32 of_II33 numerical_JJ tests_NN2 ._. 
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This_DD1 could_VM be_VBI due_JJ in_RR21 part_RR22 to_II seasonality_NN1 ,_, but_CCB there_EX could_VM also_RR be_VBI some_DD truly_RR non-Markovian_JJ character_NN1 to_II the_AT true_JJ process_NN1 ._. 
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We_PPIS2 use_VV0 intermediate_JJ distributions_NN2 (_( as_CSA described_VVN in_II Sect._NP1 2.4.1_MC )_) ,_, using_VVG geometric_JJ annealing_NN1 ,_, in_II all_DB of_IO our_APPGE algorithms_NN2 ,_, making_VVG use_NN1 of_IO the_AT adaptive_JJ method_NN1 from_II Sect._NP1 2.4.2_MC to_TO choose_VVI how_RRQ to_TO place_VVI these_DD2 distributions_NN2 ._. 
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For_IF 8-state_JJ prediction_NN1 ,_, the_AT plots_NN2 look_VV0 roughly_RR the_AT same_DA for_IF both_DB2 Figures_NN2 3_MC and_CC 4_MC ._. 
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Note_VV0 that_CST the_AT block_NN1 structure_NN1 does_VDZ not_XX depend_VVI on_II the_AT infinite_JJ sites_NN2 assumption_NN1 (_( perfect_JJ phylogeny_NN1 model_NN1 )_) or_CC any_DD specific_JJ evolutionary_JJ model_NN1 (_( Supplementary_JJ Material_NN1 S1_FO )_) ._. 
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So_RR ,_, when_CS the_AT number_NN1 of_IO explanatory_JJ variables_NN2 increases_VVZ then_RT the_AT performance_NN1 of_IO ML_NNU estimator_NN1 is_VBZ poor_JJ as_II compare_VV0 to_II GRR_NP1 estimators_NN2 ._. 
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Specifically_RR ,_, the_AT L2_FO based_VVN tests_NN2 H_ZZ1 &H;_NULL Boot_NN1 and_CC E_ZZ1 &H;_NULL Boot_VV0 perform_VV0 better_RRR than_CSN the_AT L∞based_FO test_VV0 Jirak_NP1 ._. 
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We_PPIS2 found_VVD numerically_RR rt_NNU (_( q_ZZ1 =_FO 103_MC )_) 0.98_MC ,_, rt_NNU (_( q_ZZ1 =_FO 104_MC )_) 0.94_MC ,_, rt_NNU (_( q_ZZ1 =_FO 105_MC )_) 0.92_MC ,_, rt_NNU (_( q_ZZ1 =_FO 106_MC )_) 0.90_MC and_CC rt_NNU (_( q_ZZ1 =_FO 109_MC )_) 0.87_MC ._. 
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The_AT uniformity_NN1 of_IO the_AT level_NN1 over_II P0_FO guarantees_VVZ that_CST such_DA distortions_NN2 do_VD0 not_XX occur_VVI or_CC ,_, at_RR21 least_RR22 ,_, vanish_VV0 in_II large_JJ samples_NN2 ._. 
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Hence_RR for_IF large_JJ experiments_NN2 and_CC Monte_NP1 Carlo_NP1 sample_NN1 sizes_NN2 ,_, the_AT computational_JJ complexity_NN1 of_IO the_AT precomputation_NN1 is_VBZ essentially_RR fixed_VVN ,_, and_CC the_AT complexity_NN1 of_IO the_AT approximation_NN1 within_II the_AT optimization_NN1 becomes_VVZ O_ZZ1 (_( nN2_NNU (_( B+B_FO )_) )_) ._. 
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The_AT numerical_JJ simulations_NN2 are_VBR conducted_VVN on_II two-layer_JJ Erdos–Renyi_JJ random_JJ networks_NN2 with_IW n=50_FO nodes_NN2 and_CC p=0.1_FO ._. 
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While_CS iterations_NN2 add_VV0 to_II the_AT computational_JJ complexity_NN1 of_IO the_AT procedure_NN1 ,_, a_AT1 more_RGR serious_JJ issue_NN1 is_VBZ that_DD1 of_IO convergence_NN1 ._. 
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Suppose_VV0 that_CST the_AT n-variate_JJ random_JJ variable_NN1 <equation>_FO follows_VVZ a_AT1 multivariate_JJ normal_JJ distribution_NN1 with_IW mean_JJ vector_NN1 <equation>_FO and_CC variance-covariance_JJ matrix_NN1 <equation>_FO :_: that_REX21 is_REX22 ,_, In_II this_DD1 section_NN1 ,_, we_PPIS2 provide_VV0 an_AT1 empirical_JJ analysis_NN1 of_IO feedback_NN1 effects_NN2 within_II order_NN1 book_NN1 dynamics_NN ._. 
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The_AT aim_NN1 of_IO this_DD1 paper_NN1 is_VBZ precisely_RR to_TO shed_VVI light_NN1 on_II this_DD1 question_NN1 ._. 
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To_TO see_VVI this_DD1 ,_, consider_VV0 the_AT expectation_NN1 of_IO s_ZZ1 ,_, h_ZZ1 ,_, i.e._REX ,_, This_DD1 leads_VVZ to_II the_AT question_NN1 of_IO what_DDQ effect_VV0 CBT_NP1 has_VHZ on_II unemployment_NN1 ._. 
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The_AT question_NN1 of_IO learning_VVG discrete_JJ graphical_JJ models_NN2 is_VBZ also_RR important_JJ ,_, but_CCB it_PPH1 is_VBZ not_XX yet_RR clear_JJ how_RRQ the_AT present_JJ work_NN1 can_VM be_VBI extended_VVN to_II such_DA models_NN2 ._. 
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The_AT aim_NN1 of_IO our_APPGE study_NN1 is_VBZ to_TO obtain_VVI the_AT exact_JJ asymptotics_NN1 of_IO the_AT exit_NN1 probability_NN1 in_II this_DD1 now_RT classical_JJ framework_NN1 under_II the_AT weakest_JJT conditions_NN2 ._. 
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This_DD1 can_VM be_VBI achieved_VVN using_VVG 2_MC statistics_NN which_DDQ requires_VVZ :_: Gaussian_JJ residuals_NN2 (_( an_AT1 assumption_NN1 )_) ;_; scaling_NN1 of_IO residuals_NN2 to_II unit_NN1 variance_NN1 (_( requiring_VVG knowledge_NN1 of_IO error_NN1 size_NN1 )_) ;_; and_CC knowledge_NN1 of_IO the_AT number_NN1 of_IO degrees-of-freedom_NN2 (_( d.f._NNU )_) remaining_VVG after_II parameter_NN1 estimation_NN1 (_( which_DDQ can_VM also_RR correct_VVI for_IF residual_JJ correlations_NN2 )_) ._. 
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Consequently_RR ,_, the_AT whole-space_JJ estimate_NN1 (_( 3.3_MC )_) is_VBZ an_AT1 immediate_JJ consequence_NN1 of_IO Proposition_NN1 6.9_MC ._. 
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The_AT German_JJ Federal_JJ Statistical_JJ Office_NN1 is_VBZ currently_RR exploring_VVG new_JJ ways_NN2 of_IO integrating_VVG German_JJ social_JJ statistics_NN within_II the_AT major_JJ survey_NN1 ,_, the_AT German_JJ Mikrozensus_NN1 (_( MZ_NP1 )_) which_DDQ is_VBZ a_AT1 1%_NNU sample_NN1 of_IO the_AT population_NN1 in_II Germany_NP1 ._. 
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It_PPH1 is_VBZ therefore_RR important_JJ to_TO identify_VVI them_PPHO2 prior_II21 to_II22 modelling_NN1 and_CC performing_VVG data_NN analysis_NN1 ._. 
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The_AT insets_NN2 show_VV0 the_AT corresponding_JJ critical_JJ exponent_NN1 ._. 
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Spatial_JJ variability_NN1 is_VBZ quantified_VVN by_II the_AT kriging_JJ variance_NN1 given_VVN by_II (_( 10_MC )_) of_IO the_AT supplemental_JJ material_NN1 ,_, and_CC an_AT1 under-appreciated_JJ property_NN1 is_VBZ that_CST the_AT kriging_JJ covariances_NN2 are_VBR also_RR available_JJ ._. 
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We_PPIS2 consider_VV0 the_AT HJB_NP1 equation_NN1 formally_RR associated_VVN to_II the_AT value_NN1 function_NN1 <equation>_FO ,_, that_REX21 is_REX22 ,_, In_II the_AT example_NN1 study_NN1 ,_, it_PPH1 is_VBZ remarkable_JJ how_RRQ the_AT peptide_NN1 data_NN tally_VV0 with_IW the_AT manual_JJ analysisboth_NN1 in_II the_AT identification_NN1 of_IO the_AT discriminatory_JJ peptide_NN1 markers_NN2 and_CC the_AT final_JJ assignment_NN1 of_IO taxon_NN1 to_TO sample_VVI ._. 
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The_AT corresponding_JJ optimal_JJ transaction_NN1 volume_NN1 in_II this_DD1 state_NN1 is_VBZ chosen_VVN as_II a_AT1 maximiser_NN1 for_IF <equation>_FO ._. 
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Campbell_NP1 (_( 2013_MC )_) examines_VVZ the_AT historical_JJ backgrounds_NN2 for_IF the_AT formation_NN1 and_CC breakup_NN1 of_IO each_DD1 individual_JJ currency_NN1 union_NN1 and_CC notices_VVZ that_CST factors_NN2 like_II war_NN1 and_CC decolonization_NN1 should_VM be_VBI controlled_VVN for_IF ._. 
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For_IF our_APPGE illustrative_JJ example_NN1 ,_, we_PPIS2 choose_VV0 to_TO model_VVI SPS_NN2 score_VV0 because_CS it_PPH1 was_VBDZ a_AT1 known_JJ quantity_NN1 ._. 
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Selecting_VVG k-mers_NN2 with_IW the_AT Miniception_NN1 is_VBZ as_RG efficient_JJ as_CSA a_AT1 selecting_VVG k-mers_NN2 with_IW a_AT1 random_JJ minimizer_NN1 using_VVG a_AT1 hash_NN1 function_NN1 ,_, and_CC does_VDZ not_XX require_VVI any_DD additional_JJ storage_NN1 ._. 
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For_IF each_DD1 task_NN1 ,_, we_PPIS2 trained_VVD a_AT1 k-nearest_JJT neighbours_NN2 (_( kNN_NNU )_) regressor_NN1 model_NN1 ._. 
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This_DD1 speedup_NN1 is_VBZ achieved_VVN by_II employing_VVG a_AT1 divide-and-conquer_VV0 strategy_NN1 ,_, where_CS we_PPIS2 break_VV0 the_AT problem_NN1 of_IO recovering_VVG a_AT1 K-sparse_JJ signal_NN1 into_II K-many_DA2 smaller_JJR problems_NN2 of_IO recovering_VVG 1-sparse_JJ signal_NN1 ,_, and_CC solve_VV0 each_DD1 1-sparse_JJ problem_NN1 efficiently_RR ,_, and_CC combine_VV0 the_AT solutions_NN2 to_II each_DD1 of_IO them_PPHO2 to_TO recover_VVI the_AT original_JJ signal_NN1 ._. 
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Each_DD1 of_IO those_DD2 algorithms_NN2 relies_VVZ on_II one_MC1 or_CC more_DAR parameter_NN1 ,_, and_CC the_AT specific_JJ choice_NN1 of_IO parameters_NN2 employed_VVN in_II this_DD1 section_NN1 is_VBZ given_VVN in_II Sect_NP1 ._. 
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C_NP1 for_IF each_DD1 algorithm_NN1 ._. 
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Assume_VV0 further_RRR that_CST the_AT bounded_VVN uniformly_RR ._. 
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Table_NN1 3_MC reports_NN2 coefficient_NN1 estimates_NN2 of_IO Regression_NN1 (_( 5_MC )_) ._. 
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In_RR21 particular_RR22 ,_, they_PPHS2 find_VV0 that_CST the_AT program_NN1 increases_VVZ the_AT present_JJ discounted_JJ value_NN1 of_IO participant_NN1 earnings_NN2 by_II $121_NNU using_VVG a_AT1 3%_NNU discount_NN1 rate_NN1 ._. 
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For_IF both_DB2 panels_NN2 ,_, in_II Columns_NN2 1–4_MCMC we_PPIS2 report_VV0 the_AT regressions_NN2 of_IO NEIO_NP1 and_CC NSR_NP1 components_NN2 to_II the_AT high-yield_NN1 (_( HY_NP1 )_) and_CC investment-grade_NN1 (_( IG_NP1 )_) categories_NN2 on_II their_APPGE lags_NN2 and_CC past_JJ cumulative_JJ returns_NN2 on_II high-yield_JJ bond_NN1 index_NN1 returns_NN2 (_( HYRET_NP1 )_) and_CC Baa-rated_JJ bond_NN1 index_NN1 returns_NN2 (_( BaaRET_NP1 )_) ._. 
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Due_II21 to_II22 the_AT scaling_NN1 property_NN1 of_IO urban_JJ form_NN1 and_CC city-size_JJ distributions_NN2 ,_, we_PPIS2 can_VM utilize_VVI the_AT method_NN1 of_IO proof_NN1 by_II contradiction_NN1 (_( reduction_NN1 to_II absurdity_NN1 )_) to_TO prove_VVI the_AT relation_NN1 between_II the_AT scaling_NN1 exponent_NN1 of_IO Zipf_NP1 distribution_NN1 q_ZZ1 and_CC urbanization_NN1 level_NN1 L._NP1 This_DD1 is_VBZ the_AT consequence_NN1 of_IO the_AT strong_JJ increase_NN1 in_RP with_IW W._NP1 Since_CS the_AT work_NN1 of_IO Bachelier_NP1 in_II 1900_MC ,_, Brownian_JJ motion_NN1 (_( abbreviated_VVN BM_NP1 )_) is_VBZ a_AT1 basic_JJ model_NN1 for_IF financial_JJ time_NNT1 series_NN ._. 
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Find_VV0 the_AT maximizer_NN1 <equation>_FO of_IO the_AT optimization_NN1 problem_NN1 with_IW objective_JJ function_NN1 <equation>_FO and_CC admissible_JJ set_NN1 <equation>_FO ,_, i.e._REX ,_, We_PPIS2 refer_VV0 to_II for_IF some_DD results_NN2 on_II the_AT un-rotated_VVN infinitely_RR deep_JJ wall_NN1 ._. 
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For_IF each_DD1 month_NNT1 ,_, we_PPIS2 estimate_VV0 the_AT fund_NN1 confidence_NN1 set_NN1 (_( FCS_NP2 )_) of_IO superior_JJ funds_NN2 and_CC construct_VV0 a_AT1 portfolio_NN1 of_IO the_AT funds_NN2 identified_VVN to_TO be_VBI superior_JJ ._. 
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This_DD1 involves_VVZ simulating_VVG the_AT Brownian_JJ motion_NN1 independently_RR of_IO a_AT1 Poisson_NP1 process_NN1 with_IW rate_NN1 K._NP1 Each_DD1 event_NN1 of_IO the_AT Poisson_NP1 process_NN1 is_VBZ a_AT1 potential_JJ death_NN1 event_NN1 ,_, and_CC an_AT1 appropriate_JJ Bernoulli_JJ variable_NN1 then_RT determines_VVZ whether_CSW31 or_CSW32 not_CSW33 the_AT death_NN1 occurs_VVZ ._. 
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To_TO further_RRR test_VVI the_AT clinical_JJ efficiency_NN1 of_IO top-ranked_JJ drug_NN1 candidates_NN2 ,_, we_PPIS2 performed_VVD retrospective_JJ case–control_NN1 studies_NN2 using_VVG patients_NN2 '_NULL EHRs_VVZ data_NN ._. 
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For_IF some_DD applications_NN2 ,_, however_RR ,_, such_II21 as_II22 historical_JJ counts_NN2 of_IO natural_JJ hazards_NN2 (_( Stoner_NP1 2018_MC )_) ,_, it_PPH1 is_VBZ often_RR impractical_JJ and_CC even_RR impossible_JJ to_TO obtain_VVI completely_RR observed_VVN data_NN ._. 
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Current_JJ technologies_NN2 for_IF single-cell_JJ transcriptomics_NN2 allow_VV0 thousands_NNO2 of_IO cells_NN2 to_TO be_VBI analyzed_VVN in_II a_AT1 single_JJ experiment_NN1 ._. 
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This_DD1 simple_JJ model_NN1 provides_VVZ a_AT1 clear_JJ picture_NN1 of_IO thermalization_NN1 and_CC its_APPGE connection_NN1 with_IW dynamical_JJ instability_NN1 triggered_VVD by_II driving_VVG the_AT system_NN1 periodically_RR ._. 
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In_RR21 particular_RR22 ,_, our_APPGE setup_NN1 allows_VVZ for_IF the_AT use_NN1 of_IO gradient_NN1 estimators_NN2 &lsqb;_( such_II21 as_II22 finite-difference_JJ schemes_NN2 (_( Nesterov_NP1 and_CC Spokoiny_NP1 2011_MC )_) or_CC nudging_VVG steps_NN2 (_( Akyildiz_NP1 and_CC Míguez_NP1 2020_MC )_) &rsqb;_) in_II the_AT jittering_JJ kernel_NN1 to_TO accelerate_VVI the_AT propagation_NN1 of_IO samples_NN2 into_II lower-cost_JJ regions_NN2 ._. 
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For_IF this_DD1 example_NN1 we_PPIS2 choose_VV0 a_AT1 more_RGR aggressive_JJ set_NN1 of_IO scalings_NN2 =_FO (_( 3/9,4/9,5/9,6/9,7/9,8/9_MF )_) ._. 
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We_PPIS2 can_VM use_VVI them_PPHO2 to_TO explore_VVI alternative_JJ reasons_NN2 that_CST θ_NULL might_VM differ_VVI between_II individuals_NN2 and_CC how_RRQ these_DD2 differences_NN2 in_II θ_NULL interact_VV0 with_IW our_APPGE main_JJ treatment_NN1 effects_NN2 ._. 
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The_AT same_DA conclusion_NN1 can_VM be_VBI obtained_VVN from_II Table_NN1 4_MC when_CS estimating_VVG the_AT Laplace_NP1 transform_VV0 of_IO the_AT time_NNT1 to_TO ruin_VVI ._. 
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However_RRQV equation_NN1 (_( 17_MC )_) is_VBZ to_TO be_VBI solved_VVN in_II the_AT bounded_JJ domain_NN1 ._. 
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When_CS adapted_VVN to_II bounded_JJ domains_NN2 ,_, the_AT different_JJ definitions_NN2 of_IO the_AT fractional_JJ Laplacian_JJ in_RR21 general_RR22 do_VD0 not_XX any_RR21 longer_RR22 coincide_VVI and_CC this_DD1 is_VBZ both_RR a_AT1 problem_NN1 for_IF applications_NN2 and_CC a_AT1 challenge_NN1 for_IF mathematical_JJ research_NN1 which_DDQ is_VBZ currently_RR subject_NN1 of_IO intense_JJ work_NN1 &lsqb;_( 27_MC &rsqb;_) ._. 
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When_CS combined_VVN with_IW our_APPGE previous_JJ cost_NN1 components_NN2 ,_, we_PPIS2 find_VV0 that_CST each_DD1 marginal_JJ FIU_NN1 admission_NN1 has_VHZ a_AT1 net_NN1 cost_VVN of_IO $24,445_NNU ._. 
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The_AT agents_NN2 of_IO each_DD1 community_NN1 respectively_RR formed_VVD their_APPGE scale-free_JJ networks_NN2 ,_, then_RT every_AT1 bypassing_JJ agent_NN1 of_IO the_AT blockaded_JJ community_NN1 connected_VVN to_II several_DA2 agents_NN2 in_II the_AT blockade-free_JJ community_NN1 according_II21 to_II22 the_AT number_NN1 of_IO its_APPGE existing_JJ neighbors_NN2 ._. 
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In_II the_AT ranges_NN2 of_IO r_ZZ1 very_RG close_JJ to_II and_CC enclosing_VVG 1,2,3_MC ,_, (_( i.e._REX ,_, around_II 0=1,12,13_FO ,_, with_II31 reference_II32 to_II33 1=1_FO )_) the_AT trajectories_NN2 are_VBR '_NULL singly_RR modulated_VVN '_NULL with_IW the_AT frequency_NN1 of_IO the_AT drive_NN1 field_NN1 F(t)_NNU ,_, Fig._NN1 1(e)_FO ._. 
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The_AT increase_NN1 of_IO isolation_NN1 (_( up_II21 to_II22 a_AT1 lockdown_NN1 )_) shows_VVZ to_TO be_VBI the_AT best_JJT option_NN1 to_TO keep_VVI the_AT situation_NN1 under_II the_AT healthcare_NN1 system_NN1 capacity_NN1 ,_, aside_II21 from_II22 ensuring_VVG a_AT1 faster_JJR decrease_NN1 of_IO new_JJ case_NN1 occurrences_NN2 (_( months_NNT2 of_IO difference_NN1 )_) ,_, and_CC a_AT1 significantly_RR smaller_JJR death_NN1 toll_NN1 (_( average_NN1 of_IO 87,000_MC )_) ._. 
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Single-cell_JJ RNA_NN1 sequencing_NN1 (_( scRNA-seq_FW )_) has_VHZ been_VBN extensively_RR used_VVN in_II the_AT past_JJ few_DA2 years_NNT2 to_TO analyze_VVI intercellular_JJ communication_NN1 in_II tissues_NN2 (_( see_VV0 e.g._REX Bonnardel_NP1 et_RA21 al._RA22 ,_, 2019_MC ;_; Camp_NP1 et_RA21 al._RA22 ,_, 2017_MC ;_; Caruso_NP1 et_RA21 al._RA22 ,_, 2019_MC ;_; Cohen_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Halpern_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Kumar_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Puram_NP1 et_RA21 al._RA22 ,_, 2017_MC ;_; Schiebinger_NP1 et_RA21 al._RA22 ,_, 2019_MC ;_; Sheikh_NN1 et_RA21 al._RA22 ,_, 2019_MC ;_; Skelly_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Vento-Tormo_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Wang_NP1 ,_, 2020_MC ;_; Zepp_NP1 et_RA21 al._RA22 ,_, 2017_MC ;_; Zhou_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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The_AT distortion_NN1 risk_NN1 measure_NN1 of_IO X_ZZ1 is_VBZ defined_VVN as_CSA g(X)=∞0g_NN1 (_( SX_NP1 (_( x_ZZ1 )_) )_) dx_MC ,_, where_CS the_AT distortion_NN1 function_NN1 g_ZZ1 :_: &lsqb;_( 0,1_MC &rsqb;_) →_NULL &lsqb;_( 0,1_MC &rsqb;_) is_VBZ non-decreasing_JJ and_CC satisfies_VVZ g(0)=0_FO and_CC g(1)=1_FO (_( Denuit_NP1 et_RA21 al._RA22 ,_, 2006_MC )_) ._. 
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This_DD1 probability_NN1 density_NN1 has_VHZ a_AT1 non-trivial_JJ spatial_JJ structure_NN1 (_( figure_NN1 5_MC )_) ._. 
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Here_RL ,_, the_AT indicator_NN1 constant_JJ u_ZZ1 ,_, v_ZZ1 takes_VVZ the_AT value_NN1 1_MC1 if_CS the_AT edge_NN1 (_( u_ZZ1 ,_, v_ZZ1 )_) ∈Gp_FO ,_, and_CC 0_MC otherwise_RR ._. 
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The_AT map_NN1 structure_NN1 mirrors_NN2 that_DD1 of_IO analogous_JJ maps_NN2 of_IO experimental_JJ fitness_NN1 measurements_NN2 (_( Bandaru_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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We_PPIS2 also_RR compare_VV0 the_AT MVPFs_NP1 of_IO cash_NN1 transfers_NN2 to_II those_DD2 of_IO in-kind_NN1 transfers_NN2 ,_, testing_VVG the_AT applicability_NN1 of_IO the_AT Atkinson-Stiglitz_NP1 theorem_NN1 (_( Atkinson_NP1 and_CC Stiglitz_NP1 1976_MC ;_; Hylland_NP1 and_CC Zeckhauser_NP1 1981_MC )_) ._. 
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<s>
Methods_NN2 based_VVN on_II the_AT actual_JJ observed_JJ time_NNT1 series_NN (_( Coppi_NP1 and_CC D_ZZ1 '_NULL Urso_NP1 2002_MC ,_, 2003_MC ,_, 2006_MC ;_; Coppi_NP1 et_RA21 al_RA22 ._. 
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2010_MC ;_; D_NP1 '_NULL Urso_NP1 2004_MC ,_, 2005_MC ;_; D_NP1 '_NULL Urso_NP1 and_CC De_NP1 Giovanni_NP1 2008_MC ;_; D_NP1 '_NULL Urso_NP1 et_RA21 al_RA22 ._. 
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2018_MC )_) ._. 
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<s>
As_CS31 long_CS32 as_CS33 a_AT1 general_JJ solution_NN1 of_IO (_( 21_MC )_) exists_VVZ and_CC is_VBZ known_VVN ,_, the_AT equation_NN1 <equation>_FO that_DD1 characterises_VVZ the_AT extrema_NN1 of_IO the_AT large_JJ deviation_NN1 function_NN1 I_PPIS1 can_VM always_RR be_VBI used_VVN to_TO determine_VVI the_AT stationary_JJ densities_NN2 for_IF which_DDQ I_ZZ1 is_VBZ minimal_JJ (_( <equation>_FO )_) ._. 
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A_AT1 significant_JJ deviation_NN1 exists_VVZ between_II reported_JJ and_CC calculated_VVD confirmed_JJ cases_NN2 even_RR before_II the_AT start_NN1 of_IO the_AT second_MD wave_NN1 ._. 
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<s>
Consider_VV0 the_AT system_NN1 :_: <equation>_FO ,_, where_CS p_ZZ1 is_VBZ an_AT1 mn×1_FO vector_NN1 ._. 
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<s>
Given_VVN the_AT gradual_JJ ,_, dynamic_JJ nature_NN1 of_IO wealth_NN1 accumulation_NN1 ,_, it_PPH1 would_VM be_VBI difficult_JJ (_( or_CC impossible_JJ )_) to_TO capture_VVI the_AT long-run_JJ effects_NN2 without_IW a_AT1 parametric_JJ model_NN1 ._. 
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<s>
From_II Theorem_NN1 4.11_MC ,_, we_PPIS2 know_VV0 that_CST we_PPIS2 have_VH0 <equation>_FO for_IF all_DB <equation>_FO ._. 
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<s>
This_DD1 is_VBZ consistent_JJ with_IW the_AT previous_JJ discussion_NN1 ,_, since_CS must_VM imply_VVI that_DD1 for_IF n_ZZ1 >_FO N._NNU Values_NN2 from_II simulations_NN2 are_VBR also_RR presented_VVN with_IW data_NN points_NN2 ._. 
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<s>
The_AT server_NN1 can_VM be_VBI flexibly_RR queried_VVN with_IW three_MC types_NN2 of_IO input_NN1 :_: (_( I_ZZ1 )_) a_AT1 list_NN1 of_IO chemicals_NN2 (_( or_CC targets_NN2 )_) for_IF chemogenomics-like_JJ screening_NN1 in_II silico_NN1 (_( Fig._NN1 1A_FO )_) ;_; (_( II_MC )_) one_MC1 or_CC more_DAR pairs_NN2 of_IO chemicals_NN2 to_TO be_VBI administered_VVN in_II combination_NN1 for_IF polypharmacological_JJ purposes_NN2 (_( Supplementary_JJ Fig_NN1 ._. 
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<s>
S4_FO )_) ;_; and_CC (_( III_MC )_) a_AT1 single_JJ chemical_NN1 and/or_CC a_AT1 single_JJ target_NN1 to_TO be_VBI characterized_VVN (_( Supplementary_JJ Fig_NN1 ._. 
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<s>
S4_FO )_) ._. 
</s>
<s>
We_PPIS2 are_VBR ,_, especially_RR Katarzyna_NP1 ,_, afraid_JJ that_CST we_PPIS2 missed_VVD some_DD papers_NN2 ,_, maybe_RR even_RR very_RG interesting_JJ ones_NN2 ,_, and_CC if_CS so_RR we_PPIS2 really_RR apologize_VV0 for_IF that_DD1 ._. 
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<s>
By_II analyzing_VVG the_AT similarity_NN1 of_IO the_AT GRALL_NN1 compounds_VVZ with_IW the_AT fraction_NN1 of_IO ligands_NN2 annotated_VVN at_II Level_NN1 1_MC1 or_CC 2_MC (_( structural_JJ biology_NN1 )_) ,_, we_PPIS2 found_VVD that_CST a_AT1 Tanimoto_NN1 coefficient_NN1 (_( Tc_NP1 )_) of_IO 0.4_MC used_VVD as_II a_AT1 distance_NN1 threshold_NN1 between_II Morgan_NP1 fingerprints_NN2 is_VBZ appropriate_JJ to_II group_NN1 congeneric_JJ compounds_NN2 that_CST exert_VV0 comparable_JJ modulation_NN1 at_II GlyR_NP1 ._. 
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<s>
Therefore_RR ,_, compounds_VVZ with_IW a_AT1 maximal_JJ pair-wise_RR Tc_NP1 >_FO 0.4_MC relative_II21 to_II22 ligands_NN2 in_II Level_NN1 1_MC1 to_II 4_MC were_VBDR annotated_VVN to_II the_AT same_DA binding_JJ site_NN1 with_IW a_AT1 level_NN1 of_IO confidence_NN1 5_MC ._. 
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<s>
This_DD1 is_VBZ computed_VVN using_VVG only_RR experimentally_RR verified_VVN annotations_NN2 on_II proteins_NN2 in_II UniProtKB/Swiss-Prot_NP1 (_( The_AT UniProt_NN1 Consortium_NN1 ,_, 2017_MC ,_, 2018_MC )_) ._. 
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<s>
From_II the_AT data_NN comparison_NN1 of_IO Table_NN1 4_MC ,_, it_PPH1 is_VBZ not_XX difficult_JJ to_TO find_VVI that_CST the_AT small_JJ world_NN1 network_NN1 has_VHZ better_JJR ability_NN1 to_TO resist_VVI deliberate_JJ attacks_NN2 than_CSN the_AT scale-free_JJ network_NN1 ._. 
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<s>
Rather_RR ,_, it_PPH1 may_VM be_VBI because_CS the_AT pattern_NN1 of_IO measurement_NN1 errors_NN2 in_II each_DD1 dataset_NN1 is_VBZ independent_JJ of_IO regressors_NN2 ,_, such_CS21 that_CS22 it_PPH1 has_VHZ negligible_JJ effects_NN2 on_II empirical_JJ results_NN2 for_IF the_AT sample_NN1 ._. 
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<s>
Generalized_JJ latent_JJ variable_NN1 models_NN2 are_VBR built_VVN up_RP from_II (_( i_ZZ1 )_) linear_JJ predictors_NN2 ;_; (_( ii_MC )_) Generalized_JJ Linear_JJ Model_NN1 (_( GLM_NP1 )_) links_NN2 and_CC exponential_NN1 family_NN1 distributions_NN2 ;_; and_CC (_( iii_MC )_) conditional_JJ independence_NN1 relations_NN2 ._. 
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<s>
Authors_NN2 would_VM like_VVI to_TO thank_VVI Prof._NNB A._NP1 Baroni_NN1 of_IO the_AT Campania_NP1 University_NN1 "_" Luigi_NP1 Vanvitelli_NP1 "_" (_( Italy_NP1 )_) for_IF kindly_RR providing_VVG us_PPIO2 the_AT Skin_NN1 lesions_NN2 data_NN set_VV0 ._. 
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<s>
On_II the_AT flip_NN1 side_NN1 ,_, we_PPIS2 have_VH0 explored_VVN adding_VVG the_AT response_NN1 vector_NN1 as_II an_AT1 input_NN1 matrix_NN1 in_II the_AT setting_NN1 of_IO multiple_JJ datasets_NN2 integration_NN1 ._. 
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The_AT rationale_NN1 is_VBZ demonstrated_VVN by_II Fig._NN1 2_MC ._. 
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<s>
We_PPIS2 assume_VV0 that_CST the_AT reader_NN1 is_VBZ familiar_JJ with_IW the_AT elementary_JJ results_NN2 of_IO the_AT Malliavin_NP1 calculus_NN1 as_CSA given_VVN ,_, for_REX21 instance_REX22 ,_, in_II Nualart_NP1 &lsqb;_( 16_MC &rsqb;_) ._. 
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The_AT possibility_NN1 of_IO obtaining_VVG net_JJ particle_NN1 transport_NN1 in_II periodic_JJ potentials_NN2 without_IW application_NN1 of_IO any_DD obvious_JJ bias_NN1 in_II presence_NN1 of_IO noise_NN1 has_VHZ been_VBN a_AT1 subject_NN1 of_IO study_NN1 over_II the_AT last_MD few_DA2 decades_NNT2 mainly_RR inspired_VVN by_II biological_JJ investigations_NN2 ._. 
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<s>
Entropy_NN1 curves_NN2 are_VBR not_XX shown_VVN here_RL ,_, because_CS they_PPHS2 do_VD0 not_XX exhibit_VVI any_DD striking_JJ monotonic_JJ feature_NN1 of_IO interest_NN1 ._. 
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<s>
Second_MD ,_, instead_II21 of_II22 specifying_VVG a_AT1 single_JJ baseline_NN1 response_NN1 model_NN1 ,_, one_PN1 may_VM consider_VVI multiple_JJ baseline_NN1 response_NN1 models_NN2 ,_, and_CC obtain_VV0 consistency_NN1 when_CS one_MC1 of_IO the_AT specified_JJ baseline_NN1 response_NN1 models_NN2 is_VBZ correct_JJ ._. 
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<s>
VLDA_NP1 achieved_VVD comparatively_RR good_JJ classification_NN1 error_NN1 performance_NN1 under_II the_AT independence_NN1 (_( average_JJ rank_NN1 =6.3=6.3_FO )_) and_CC local_JJ AR(1)_FO correlation_NN1 structures_NN2 (_( average_JJ rank_NN1 =5.5=5.5_FO )_) ._. 
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<s>
We_PPIS2 used_VVD both_RR the_AT guide_NN1 function_NN1 with_IW the_AT exact_JJ covariance_NN1 as_CSA in_II (_( 25_MC )_) and_CC the_AT guide_NN1 function_NN1 with_IW diagonal_JJ covariance_NN1 as_CSA in_II (_( 26_MC )_) ._. 
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<s>
The_AT integer-valued_JJ GARCH_NN1 model_NN1 is_VBZ commonly_RR used_VVN in_II modeling_VVG time_NNT1 series_NN of_IO counts_NN2 ._. 
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<s>
The_AT second_MD quantity_NN1 ,_, <equation>_FO ,_, is_VBZ based_VVN on_II employing_VVG the_AT nuclear_JJ norm_NN1 regularization_NN1 procedure_NN1 on_II the_AT full_JJ set_NN1 of_IO observations_NN2 ._. 
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<s>
We_PPIS2 see_VV0 that_CST an_AT1 unexpected_JJ third_MD component_NN1 is_VBZ obtained_VVN as_II a_AT1 q-Gaussian_JJ with_IW different_JJ q_ZZ1 values_NN2 for_IF (_( K_ZZ1 =_FO 0.2_MC ,_, z_ZZ1 =_FO 3_MC )_) ,_, (_( K_ZZ1 =_FO 0.6_MC ,_, z_ZZ1 =_FO 3_MC )_) ,_, and_CC (_( K_ZZ1 =_FO 0.6_MC ,_, z_ZZ1 =_FO 4_MC )_) cases_NN2 ._. 
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<s>
The_AT coefficients_NN2 of_IO interest_NN1 are_VBR β_NULL 1_MC1 ,_, which_DDQ captures_VVZ the_AT average_JJ incremental_JJ effect_NN1 of_IO the_AT covenant_NN1 violation_NN1 on_II resource_NN1 utilization_NN1 at_II the_AT establishments_NN2 with_IW the_AT attribute_NN1 of_IO interest_NN1 ,_, and_CC β_NULL 2_MC ,_, which_DDQ captures_VVZ the_AT effect_NN1 on_II other_JJ establishments_NN2 within_II the_AT same_DA firm_NN1 ._. 
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<s>
Our_APPGE theoretical_JJ analysis_NN1 illustrates_VVZ that_CST |_NULL LOALO_NP1 |_NULL →_NULL 0_MC with_IW overwhelming_JJ probability_NN1 ,_, when_CS n_ZZ1 ,_, p_ZZ1 →_NULL ∞_FO ,_, where_CS the_AT dimension_NN1 p_NN1 of_IO the_AT feature_NN1 vectors_NN2 may_VM be_VBI comparable_JJ with_IW or_CC even_RR greater_JJR than_CSN the_AT number_NN1 of_IO observations_NN2 ,_, n_ZZ1 ._. 
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<s>
Despite_II the_AT high_JJ dimensionality_NN1 of_IO the_AT problem_NN1 ,_, our_APPGE theoretical_JJ results_NN2 do_VD0 not_XX require_VVI any_DD sparsity_NN1 assumption_NN1 on_II the_AT vector_NN1 of_IO regression_NN1 coefficients_NN2 ._. 
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<s>
Therefore_RR ,_, N∞_FO ,_, δ_FO (_( c_ZZ1 )_) ≥_FO N∞_FO ,_, 0_MC (_( c_ZZ1 δ_FO )_) =_FO ∞_FO ._. 
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But_CCB the_AT collision-avoidance_JJ algorithm_NN1 from_II intelligent_JJ robot_NN1 does_VDZ not_XX allow_VVI any_DD collision_NN1 ._. 
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<s>
In_II other_JJ words_NN2 ,_, the_AT insurer_NN1 is_VBZ more_DAR risk_NN1 averse_JJ than_CSN the_AT reinsurer_NN1 and_CC has_VHZ a_AT1 natural_JJ demand_NN1 for_IF reinsurance_NN1 protection_NN1 ._. 
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<s>
Traditional_JJ modelling_NN1 approaches_NN2 have_VH0 difficulty_NN1 in_II handling_VVG censored_JJ patient_JJ samples_NN2 as_CSA they_PPHS2 do_VD0 not_XX have_VHI a_AT1 specific_JJ time_NNT1 point_NN1 of_IO death_NN1 ._. 
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<s>
First_MD ,_, we_PPIS2 define_VV0 a_AT1 subsumption_NN1 relation_NN1 between_II sequences_NN2 of_IO elements_NN2 in_II GO_VV0 ,_, where_CS an_AT1 element_NN1 can_VM be_VBI a_AT1 word_NN1 or_CC a_AT1 GO_NN1 concept_NN1 ._. 
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<s>
In_II these_DD2 Cases_NN2 class_NN1 attendance_NN1 and_CC the_AT individual_JJ study_NN1 are_VBR random_JJ ._. 
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<s>
For_IF the_AT same_DA reason_NN1 ,_, in_II the_AT synthetic_JJ data_NN design_NN1 ,_, increasing_JJ correlation_NN1 strength_NN1 leads_VVZ to_II higher_JJR predictive_JJ error_NN1 when_RRQ blocks_NN2 contain_VV0 more_DAR than_CSN one_MC1 signal_NN1 (_( see_VV0 second_NNT1 and_CC fourth_MD columns_NN2 of_IO Fig._NN1 7_MC )_) ._. 
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<s>
This_DD1 could_VM significantly_RR affect_VVI the_AT residual_JJ lifetime_NNT1 of_IO the_AT remaining_JJ component_NN1 ,_, eventually_RR shortening_VVG it_PPH1 ._. 
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<s>
Assertion_NN1 (_( b_ZZ1 )_) implies_VVZ that_CST the_AT test_NN1 based_VVN on_II (_( 5_MC )_) is_VBZ consistent_JJ with_II31 respect_II32 to_II33 the_AT different_JJ effects_NN2 alternative_NN1 in_II (_( 2_MC )_) ,_, i.e._REX ,_, (_( 9_MC )_) holds_VVZ true_JJ ._. 
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<s>
Since_CS HISAT2_FO and_CC vg_NNU have_VH0 graph_NN1 alignment_NN1 capabilities_NN2 ,_, we_PPIS2 also_RR built_VVN graph-genome_JJ indexes_NN2 for_IF both_DB2 using_VVG the_AT 6.2_MC million_NNO SNPs_NP2 and_CC indels_VVZ from_II the_AT 1000_MC Genomes_NN2 Phase_NN1 3_MC call_NN1 set_VVN with_IW allele_NN1 frequency_NN1 at_RR21 least_RR22 10%_NNU (_( Lowy-Gallego_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ._. 
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<s>
One_MC1 can_VM clearly_RR observe_VVI that_CST the_AT entropy_NN1 of_IO Japan_NP1 '_NULL s_ZZ1 city-size_JJ distribution_NN1 is_VBZ decreasing_VVG sharply_RR over_II the_AT years_NNT2 ;_; it_PPH1 signifies_VVZ that_CST the_AT larger_JJR cities_NN2 are_VBR becoming_VVG even_RR larger_JJR and_CC smaller_JJR cities_NN2 are_VBR becoming_VVG even_RR smaller_JJR in_RR21 general_RR22 ._. 
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<s>
We_PPIS2 intentionally_RR keep_VV0 our_APPGE discussion_NN1 broad_JJ so_CS21 that_CS22 our_APPGE results_NN2 are_VBR relevant_JJ for_IF a_AT1 wide_JJ range_NN1 of_IO low_JJ rank_NN1 estimation_NN1 problems_NN2 ,_, e.g._REX low_JJ rank_NN1 matrix_NN1 completion_NN1 or_CC factor_NN1 analysis_NN1 ._. 
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<s>
Assume_VV0 <equation>_FO so_CS that_DD1 starting_NN1 from_II <equation>_FO ,_, we_PPIS2 have_VH0 <equation>_FO a.s_NNU ._. 
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<s>
for_IF all_DB <equation>_FO (_( cf._VV0 Dividend_NN1 strategy_NN1 in_II insurance_NN1 risk_NN1 theory_NN1 was_VBDZ first_MD proposed_VVN by_II Finetti_NP1 (_( 1957_MC )_) in_II the_AT binomial_JJ risk_NN1 model_NN1 ,_, and_CC since_II then_RT dividend_NN1 problems_NN2 have_VH0 been_VBN widely_RR studied_VVN under_II various_JJ risk_NN1 models_NN2 ._. 
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<s>
In_II our_APPGE model_NN1 ,_, the_AT measured_JJ log_NN1 TFP_NP1 equals_VVZ <equation>_FO ,_, where_CS the_AT component_NN1 <equation>_FO is_VBZ the_AT efficiency_NN1 of_IO capital_NN1 reallocation_NN1 ._. 
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<s>
In_II these_DD2 methods_NN2 ,_, each_DD1 jth_MD instrument_NN1 contributes_VVZ a_AT1 separate_JJ IV_MC estimate_VV0 β_NULL Yj/_JJ β_NULL Xj_NP1 of_IO the_AT causal_JJ effect_NN1 of_IO X_ZZ1 on_II Y._NP1 None_PN beats_VVZ the_AT other_JJ two_MC uniformly_RR for_IF all_DB n_ZZ1 and_CC all_DB significance_NN1 levels_NN2 (_( see_VV0 Figure_NN1 2_MC )_) ,_, but_CCB the_AT last_MD is_VBZ often_RR the_AT winner_NN1 ,_, hence_RR the_AT simpler_JJR statement_NN1 of_IO Section_NN1 2_MC ._. 
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<s>
Because_CS the_AT software_NN1 automatically_RR identifies_VVZ the_AT most_RGT appropriate_JJ number_NN1 of_IO clusters_NN2 ,_, it_PPH1 can_VM be_VBI simultaneously_RR applied_VVN to_II many_DA2 datasets_NN2 ,_, without_IW the_AT requirement_NN1 for_IF the_AT user_NN1 to_TO specify_VVI ._. 
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<s>
To_TO build_VVI and_CC train_VVI models_NN2 with_IW CellNOpt_NP1 ,_, CNORprob_NP1 and_CC CNORode_VV0 without_IW coding_NN1 ,_, we_PPIS2 offer_VV0 an_AT1 interactive_JJ R-Shiny_JJ application_NN1 (_( Supplementary_JJ Text_NN1 S6_FO )_) ._. 
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<s>
Of_RR21 course_RR22 ,_, we_PPIS2 can_VM also_RR observe_VVI that_CST the_AT SPA_NN1 value_NN1 in_II Section_NN1 4.3.2_MC is_VBZ significantly_RR lower_JJR than_CSN that_DD1 in_II Section_NN1 4.3.1_MC ._. 
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In_II other_JJ words_NN2 ,_, only_RR export_VV0 revenues_NN2 reported_VVN in_II income_NN1 statements_NN2 of_IO firms_NN2 are_VBR considered_VVN as_II a_AT1 "_" natural_JJ hedge_NN1 "_" for_IF companies_NN2 that_CST have_VH0 FX-denominated_JJ debt_NN1 ._. 
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<s>
The_AT following_JJ theorem_NN1 shows_VVZ the_AT asymptotic_JJ distribution_NN1 of_IO the_AT Wald_NN1 statistic_NN1 if_CS yt_NN1 is_VBZ a_AT1 stochastic_JJ trend_NN1 ._. 
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Online_JJ Appendix_NN1 Figure_NN1 A.1_FO shows_VVZ a_AT1 corresponding_JJ plot_NN1 for_IF the_AT HHI_NN1 ._. 
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<s>
Under_II Assumption_NN1 1_MC1 and_CC for_IF all_DB sufficiently_RR small_JJ >0h>0_FO ,_, The_AT prior_JJ distribution_NN1 has_VHZ the_AT form_NN1 ?_FO N_ZZ1 (_( 0,100_MC )_) ,_, p_ZZ1 (_( β_NULL γ_NULL |_NULL γ_NULL )_) ?_FO N_ZZ1 (_( 0_MC ,_, I_ZZ1 )_) ,_, γ_NULL j?i.i.d_FO ._. 
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Three_MC states_NN2 are_VBR found_VVN in_II the_AT space–time_NNT1 diagram_NN1 ._. 
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<s>
The_AT right_JJ panel_NN1 includes_VVZ also_RR the_AT marginal_JJ prior_JJ density_NN1 (_( dashed_JJ line_NN1 )_) for_IF the_AT τ_NULL m_ZZ1 ._. 
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<s>
Here_RL we_PPIS2 present_VV0 the_AT R-optimal_JJ designs_NN2 for_IF estimating_VVG the_AT coefficients_NN2 <equation>_FO and_CC <equation>_FO that_CST correspond_VV0 to_II the_AT intercept_VV0 and_CC the_AT term_NN1 <equation>_FO ._. 
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<s>
As_CSA displayed_VVN in_II the_AT right_JJ hand_NN1 side_NN1 panel_NN1 of_IO Fig._NN1 4_MC ,_, both_DB2 the_AT distance_NN1 covariance_NN1 <equation>_FO and_CC Wilks_NP1 '_NULL Lambda_NN1 <equation>_FO perform_VV0 poorly_RR under_RG Cauchy_JJ marginals_NN2 in_II31 terms_II32 of_II33 power_NN1 ._. 
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The_AT dotted_JJ lines_NN2 ,_, representing_VVG the_AT 95%_NNU confidence_NN1 interval_NN1 ,_, were_VBDR obtained_VVN as_CSA follows_VVZ ._. 
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<s>
Stocks_NN2 are_VBR ranked_VVN by_II the_AT average_NN1 daily_RR traded_VVN value_NN1 (_( in_II units_NN2 of_IO <equation>_FO of_IO the_AT local_JJ currency_NN1 ,_, the_AT Swedish_JJ krona_NNU1 )_) ,_, which_DDQ can_VM be_VBI considered_VVN as_II an_AT1 indicator_NN1 of_IO liquidity_NN1 ._. 
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<s>
Optimal_JJ risk_NN1 sharing_VVG between_II insurance_NN1 and_CC reinsurance_NN1 companies_NN2 has_VHZ been_VBN considered_VVN by_II various_JJ authors_NN2 ._. 
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However_RR ,_, among_II the_AT PDMP-based_JJ MCMC_NP1 algorithms_NN2 ,_, CS_NP2 outperforms_VVZ both_RR ZS_NP2 and_CC BPS_NP2 ._. 
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In_II the_AT second_MD part_NN1 of_IO this_DD1 paper_NN1 we_PPIS2 apply_VV0 perturbation_NN1 techniques_NN2 to_II the_AT capital_NN1 requirements_NN2 when_RRQ asset_NN1 volatility_NN1 becomes_VVZ small_JJ ._. 
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<s>
Student_NN1 '_NULL s_ZZ1 t_ZZ1 distribution_NN1 has_VHZ an_AT1 appeal_NN1 of_IO being_VBG underpinned_VVN by_II a_AT1 simple_JJ multiplicative_JJ (_( continuous_JJ GARCH_NN1 )_) stochastic_JJ volatility_NN1 model_NN1 &lsqb;_( 7_MC &rsqb;_) ,_, which_DDQ leads_VVZ to_II an_AT1 Inverse_JJ Gamma_NN1 (_( IGa_NN1 )_) steady-state_JJ distribution_NN1 for_IF the_AT variance_NN1 of_IO the_AT volatility_NN1 &lsqb;_( 6_MC &rsqb;_) ,_, &lsqb;_( 8_MC &rsqb;_) ,_, &lsqb;_( 9_MC &rsqb;_) ,_, &lsqb;_( 10_MC &rsqb;_) ._. 
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We_PPIS2 use_VV0 a_AT1 conservative_JJ weighting_NN1 factor_NN1 ,_, w_ZZ1 ,_, to_TO denote_VVI the_AT importance_NN1 of_IO the_AT experimental_JJ annotation_NN1 (_( manually_RR reviewed_VVN )_) in_II which_DDQ w_ZZ1 is_VBZ an_AT1 integer_NN1 number_NN1 and_CC w≥1_FO ._. 
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<s>
For_REX21 instance_REX22 ,_, as_II an_AT1 extension_NN1 of_IO the_AT Erlang_NNU risk_NN1 model_NN1 ,_, Albrecher_NP1 et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 2_MC &rsqb;_) transformed_VVD the_AT integral_JJ equation_NN1 for_IF the_AT function_NN1 into_II an_AT1 integro-differential_JJ equation_NN1 whenever_RRQV the_AT inter-arrival_JJ time_NNT1 distributions_NN2 have_VH0 rational_JJ Laplace_NP1 transforms_VVZ ._. 
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<s>
From_II what_DDQ we_PPIS2 observed_VVD ,_, TinGa_NP1 seems_VVZ to_TO be_VBI a_AT1 good_JJ trade-off_NN1 between_II Slingshot_NP1 ,_, which_DDQ is_VBZ a_AT1 method_NN1 that_CST performs_VVZ optimally_RR on_II simple_JJ trajectory_NN1 types_NN2 such_II21 as_II22 linear_JJ or_CC bifurcating_VVG trajectories_NN2 ,_, and_CC PAGA_NP1 and_CC Monocle_NP1 3_MC ,_, which_DDQ perform_VV0 best_RRT on_II graphs_NN2 and_CC trees_NN2 but_CCB tend_VV0 to_TO return_VVI too_RG complex_JJ topologies_NN2 when_CS facing_VVG simple_JJ trajectories_NN2 ._. 
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<s>
A_AT1 strategy_NN1 that_CST selects_VVZ stocks_NN2 based_VVN on_II their_APPGE average_JJ same-month_JJ returns_NN2 earns_VVZ an_AT1 average_JJ return_NN1 of_IO 1.03%_FO per_II month_NNT1 (_( t-value_NN1 =_FO 7.19_MC )_) ,_, and_CC this_DD1 strategy_NN1 '_NULL s_ZZ1 alpha_NN1 from_II the_AT Carhart_NP1 (_( 1997_MC )_) four-factor_JJ model_NN1 augmented_VVN with_IW the_AT long-term_JJ reversals_NN2 factor_NN1 is_VBZ 1.09%_FO (_( t-value_NN1 =_FO 7.19_MC )_) ._. 
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Condition_NN1 (_( i_ZZ1 )_) of_IO Theorem_NN1 4.1_MC is_VBZ a_AT1 drift_NN1 restriction_NN1 for_IF the_AT Ibor_NN1 rate_NN1 process_NN1 ._. 
</s>
<s>
The_AT two_MC groups_NN2 have_VH0 different_JJ laws_NN2 for_IF connecting_VVG with_IW other_JJ groups_NN2 :_: the_AT blockaded_JJ group_NN1 forbids_VVZ its_APPGE agents_NN2 to_TO communicate_VVI with_IW the_AT blockade-free_JJ group_NN1 ,_, but_CCB the_AT blockade-free_JJ group_NN1 does_VDZ not_XX forbid_VVI communication_NN1 with_IW the_AT blockaded_JJ group_NN1 ._. 
</s>
<s>
Each_DD1 color_NN1 represents_VVZ a_AT1 different_JJ coarse-graining_JJ scale_NN1 τ_NULL in_II equation_NN1 ,_, and_CC as_CSA this_DD1 scale_NN1 grows_VVZ ,_, convergence_NN1 to_II the_AT continuous_JJ becomes_VVZ faster_RRR ._. 
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<s>
However_RR ,_, one_MC1 downside_NN1 is_VBZ that_CST the_AT derivative_NN1 of_IO a_AT1 stationary_JJ GP_NN1 is_VBZ no_RR21 longer_RR22 stationary_JJ in_RR21 general_RR22 ,_, and_CC thus_RR sampling_VVG from_II the_AT joint_JJ Gaussian_JJ prior_JJ of_IO (_( (_( 0_MC )_) ,_, (_( 0_MC )_) ,_, ,_, (_( )_) )_) (_( f(0)_FO ,_, f(u0)_FO ,_, ,_, f(uN)_NN1 )_) can_VM not_XX take_VVI advantage_NN1 of_IO the_AT embedding_NN1 techniques_NN2 for_IF a_AT1 stationary_JJ GP_NN1 ._. 
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<s>
Even_RR Seurat_VV0 ,_, which_DDQ is_VBZ fast_JJ on_II smaller_JJR datasets_NN2 ,_, takes_VVZ over_II 1.5h_FO on_II a_AT1 68K_FO scRNA-seq_FW dataset_NN1 of_IO 1000_MC genes_NN2 &lsqb;_( when_CS bypassing_VVG preliminary_JJ principal_JJ component_NN1 analysis_NN1 (_( PCA_NP1 )_) &rsqb;_) and_CC often_RR runs_VVZ into_II memory_NN1 allocation_NN1 errors_NN2 ._. 
</s>
<s>
Let_VV0 <equation>_FO be_VBI the_AT regular_JJ grid_NN1 of_IO cubes_NN2 ._. 
</s>
<s>
Wi_NN2 ._. 
</s>
<s>
Some_DD of_IO the_AT cubes_NN2 Wi_NN1 may_VM not_XX contain_VVI enough_DD fibre_NN1 voxels_VVZ to_TO obtain_VVI a_AT1 reliable_JJ estimate_NN1 of_IO the_AT local_JJ fibre_NN1 direction_NN1 wi_NN2 ._. 
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<s>
Given_VVN the_AT spatial_JJ nature_NN1 of_IO the_AT problem_NN1 ,_, the_AT design_NN1 matrix_NN1 X_ZZ1 is_VBZ very_RG sparse_JJ ,_, which_DDQ fails_VVZ to_TO satisfy_VVI the_AT dense_JJ Gaussian_JJ design_NN1 assumption_NN1 that_CST we_PPIS2 made_VVD in_II theorem_NN1 3_MC ._. 
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<s>
The_AT analysis_NN1 covers_VVZ option-type_JJ contracts_NN2 (_( longevity_NN1 caplets_NN2 and_CC floorlets_NN2 )_) ,_, geared_VVD longevity_NN1 bonds_NN2 ,_, longevity-spread_JJ bonds_NN2 ,_, S-forwards_NN2 and_CC longevity_NN1 swaps_NN2 ._. 
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<s>
As_CSA reported_VVN in_II Table_NN1 10_MC ,_, the_AT five_MC respective_JJ coefficients_NN2 on_II the_AT common_JJ ownership_NN1 measures_NN2 are_VBR insignificant_JJ ._. 
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<s>
So_RR ,_, adding_VVG a_AT1 global_JJ DSED_JJ γ_NULL component_NN1 significantly_RR improves_VVZ performance_NN1 in_II this_DD1 sparser_JJR graph_NN1 (_( Table_NN1 4_MC )_) ._. 
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<s>
Smaller_JJR misclassification_NN1 rates_NN2 and_CC larger_JJR value_NN1 functions_NN2 indicate_VV0 better_JJR performance_NN1 ._. 
</s>
<s>
These_DD2 normalized_JJ B-factors_NN2 can_VM be_VBI applied_VVN to_II any_DD protein_NN1 sequences_NN2 without_IW crystallographic_JJ data_NN for_IF flexibility_NN1 prediction_NN1 ,_, e.g._REX as_CSA implemented_VVN in_II Biopython_NP1 ._. 
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<s>
To_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, this_DD1 is_VBZ the_AT first_MD framework_NN1 based_VVN on_II nonparametric_JJ link_NN1 functions_NN2 to_TO directly_RR model_VVI the_AT conditional_JJ quantile_JJ function_NN1 for_IF a_AT1 given_JJ functional_JJ covariate_NN1 ._. 
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<s>
Thus_RR ,_, we_PPIS2 propose_VV0 a_AT1 novel_JJ link_NN1 prediction_NN1 method_NN1 called_VVN global_JJ and_CC local_JJ integrated_JJ diffusion_NN1 embedding_NN1 (_( GLIDE_NN1 )_) ._. 
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<s>
These_DD2 results_NN2 show_VV0 that_CST complex_JJ queries_NN2 ,_, such_II21 as_II22 2_MC ,_, are_VBR also_RR vulnerable_JJ to_II the_AT dependency_NN1 between_II the_AT tuples_NN2 in_II the_AT dataset_NN1 ._. 
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<s>
The_AT top_JJ left_JJ and_CC central_JJ plots_NN2 show_VV0 posterior_JJ densities_NN2 for_IF 0_MC and_CC 1_MC1 ,_, indicating_VVG substantial_JJ learning_NN1 of_IO these_DD2 parameters_NN2 compared_VVN to_II the_AT flat_JJ priors_NN2 also_RR shown_VVN ._. 
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<s>
For_IF this_DD1 ,_, we_PPIS2 fix_VV0 an_AT1 arbitrary_JJ initial_JJ datum_NN1 <equation>_FO ._. 
</s>
<s>
The_AT benchmark_NN1 assesses_VVZ the_AT complexity_NN1 of_IO scenarios_NN2 and_CC can_VM serve_VVI as_II a_AT1 standardization_NN1 of_IO scenarios_NN2 of_IO various_JJ difficulty_NN1 ._. 
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<s>
We_PPIS2 assume_VV0 the_AT changepoints_NN2 correspond_VV0 to_II abrupt_JJ changes_NN2 in_II the_AT location_NN1 ,_, that_DD1 is_VBZ mean_JJ ,_, median_NN1 ,_, or_CC other_JJ quantile_JJ ,_, of_IO the_AT data_NN ._. 
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<s>
Moreover_RR ,_, empirical_JJ log-likelihood_JJ ratio_NN1 for_IF the_AT nonparametric_JJ part_NN1 is_VBZ also_RR investigated_VVN ._. 
</s>
<s>
BC=positive_FO regulation_NN1 of_IO acute_JJ inflammatory_JJ response_NN1 (_( GO:0002675_FO )_) is_VBZ also_RR a_AT1 GO_NN1 concept_NN1 ,_, which_DDQ is_VBZ a_AT1 subtype_NN1 of_IO A_ZZ1 and_CC B_ZZ1 as_RR21 well_RR22 ._. 
</s>
<s>
The_AT system_NN1 energy_NN1 profiles_NN2 of_IO SCW_NP1 for_IF both_DB2 models_NN2 are_VBR presented_VVN in_II Fig._NN1 9_NN1 (_( a_AT1 and_CC b_ZZ1 )_) as_II the_AT function_NN1 of_IO field_NN1 strength_NN1 ._. 
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<s>
It_PPH1 was_VBDZ empirically_RR demonstrated_VVN in_II Tomita_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2017_MC )_) that_CST in_II situations_NN2 where_RRQ the_AT signal_NN1 is_VBZ contained_VVN in_II a_AT1 subspace_NN1 that_CST is_VBZ small_JJ relative_II21 to_II22 the_AT dimensionality_NN1 of_IO the_AT feature_NN1 space_NN1 ,_, random_JJ rotation_NN1 ensembles_NN2 tend_VV0 to_TO underperform_VVI ordinary_JJ random_JJ forests_NN2 ._. 
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<s>
Panel_NN1 (_( a_ZZ1 )_) of_IO Fig._NN1 10_MC shows_VVZ the_AT VaR_NN1 levels_NN2 calculated_VVN in_II the_AT multiple-curve_JJ approach_NN1 and_CC in_II the_AT (_( pre-crisis_NN1 )_) single_JJ curve_NN1 approach_NN1 ._. 
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<s>
This_DD1 provides_VVZ a_AT1 useful_JJ illustration_NN1 for_IF the_AT comparison_NN1 among_II specific_JJ traits_NN2 located_VVN in_II space_NN1 ._. 
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<s>
We_PPIS2 next_MD evaluate_VV0 the_AT ability_NN1 of_IO beta_NN1 to_TO explain_VVI the_AT difference_NN1 between_II day_NNT1 and_CC night_NNT1 returns_NN2 for_IF individual_JJ stocks_NN2 ._. 
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<s>
This_DD1 in_II an_AT1 important_JJ part_NN1 of_IO the_AT statistical_JJ production_NN1 process_NN1 ,_, which_DDQ is_VBZ done_VDN by_II Official_JJ Statistics_NN ._. 
</s>
<s>
Let<equation>be_FO as_CSA in_II Theorem_NN1 2.4and_FO another_DD1 solution_NN1 to_II the_AT SPDE_NP1 (_( 2.3_MC )_) belonging_VVG to_II the_AT Definition2.3_FO ._. 
</s>
<s>
In_II31 addition_II32 to_II33 this_DD1 information_NN1 ,_, diagnosis_NN1 month_NNT1 and_CC year_NNT1 were_VBDR recorded_VVN along_II21 with_II22 the_AT FIPS_NP2 county_NN1 code_NN1 for_IF each_DD1 woman_NN1 ._. 
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<s>
Thus_RR ,_, the_AT computational_JJ complexity_NN1 of_IO IWMM_NP1 is_VBZ smaller_JJR than_CSN even_RR the_AT simplest_JJT single-proposal_JJ adaptive_JJ importance_NN1 sampling_NN1 methods_NN2 ._. 
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<s>
This_DD1 makes_VVZ inference_NN1 for_IF this_DD1 type_NN1 of_IO models_NN2 complicated_VVD which_DDQ in_II turn_NN1 makes_VVZ a_AT1 thorough_JJ analysis_NN1 for_IF model_NN1 selection_NN1 and_CC parameter_NN1 inference_NN1 difficult_JJ ._. 
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<s>
Treating_VVG the_AT embeddings_NN2 X_ZZ1 and_CC X_ZZ1 as_CSA independent_JJ ,_, each_DD1 is_VBZ modelled_VVN separately_RR using_VVG the_AT same_DA Gaussian_JJ structure_NN1 and_CC prior_JJ distributions_NN2 (_( 1_MC1 )_) ,_, except_II21 for_II22 three_MC parameters_NN2 which_DDQ are_VBR initially_RR assumed_VVN common_JJ to_II both_DB2 embeddings_NN2 :_: the_AT latent_JJ dimension_NN1 d_ZZ1 ,_, the_AT number_NN1 of_IO communities_NN2 K_ZZ1 and_CC the_AT vector_NN1 of_IO node_NN1 assignments_NN2 to_II those_DD2 communities_NN2 ,_, zz_UH ._. 
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<s>
It_PPH1 also_RR lists_VVZ time-series_JJ averages_NN2 of_IO the_AT monthly_JJ correlations_NN2 between_II the_AT characteristic_NN1 and_CC the_AT mispricing_JJ signal_NN1 ._. 
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<s>
Then_RT we_PPIS2 run_VV0 the_AT algorithm_NN1 on_II the_AT two_MC networks_NN2 respectively_RR ._. 
</s>
<s>
In_II total_NN1 ,_, k2_FO has_VHZ 8976_MC entries_NN2 from_II 36_MC different_JJ ncRNA_NN1 families_NN2 ._. 
</s>
<s>
While_CS we_PPIS2 consider_VV0 quite_RG general_JJ (_( unstructured_JJ )_) settings_NN2 ,_, one_MC1 other_JJ major_JJ motivation_NN1 for_IF this_DD1 work_NN1 is_VBZ to_TO be_VBI able_JK to_TO monitor_VVI pairs_NN2 of_IO structured_JJ multivariate_JJ time-series_JJ models_NN2 such_II21 as_II22 VAR_NP1 or_CC GARCH_VV0 models_NN2 ,_, over_II time_NNT1 ._. 
</s>
<s>
This_DD1 model_NN1 is_VBZ adopted_VVN bearing_VVG in_II mind_NN1 that_CST the_AT unclassified_JJ features_NN2 of_IO many_DA2 datasets_NN2 tend_VV0 to_TO fall_VVI in_II regions_NN2 of_IO overlap_NN1 of_IO the_AT classes_NN2 in_II the_AT feature_NN1 space_NN1 ._. 
</s>
<s>
The_AT identifiability_NN1 relationships_NN2 among_II the_AT six_MC parameters_NN2 associated_VVN with_IW node_NN1 4_MC are_VBR more_RGR complex_JJ ._. 
</s>
<s>
This_DD1 work_NN1 is_VBZ supported_VVN in_RR21 part_RR22 by_II National_JJ Institutes_NN2 of_IO Health_NN1 (_( R01_FO GM076485_FO to_II D.H.M._NP1 )_) and_CC National_JJ Science_NN1 Foundation_NN1 (_( IIS-1817231_MC to_II L.H._NP1 )_) ._. 
</s>
<s>
In_II other_JJ words_NN2 ,_, there_EX is_VBZ no_AT panacea_NN1 clustering_NN1 method_NN1 to_TO be_VBI useful_JJ for_IF all_DB cases_NN2 ._. 
</s>
<s>
Table_NN1 1_MC1 reports_VVZ the_AT empirical_JJ results_NN2 ._. 
</s>
<s>
Following_VVG this_DD1 principle_NN1 ,_, four_MC outlier_JJR types_NN2 are_VBR commonly_RR considered_VVN in_II the_AT time_NNT1 series_NN literature_NN1 ,_, namely_REX Additive_NP1 Outliers_NP1 (_( AO_NP1 )_) ,_, Transitory_JJ Change_NN1 (_( TC_NP1 )_) outliers_NN2 ,_, Level_JJ Shift_NN1 (_( LS_NP2 )_) outliers_NN2 and_CC Innovative_JJ Outliers_NP1 (_( IO_NP1 )_) (_( see_VV0 Tsay_NN1 1986_MC ;_; Pe?a_NP1 2011_MC ,_, among_II others_NN2 )_) ._. 
</s>
<s>
Using_VVG accounting-based_JJ replicating_JJ portfolios_NN2 ,_, we_PPIS2 first_MD assign_VV0 fair_JJ values_NN2 to_II more_DAR than_CSN 25,000_MC firms_NN2 from_II 36_MC countries_NN2 in_II the_AT 1993–2016_MCMC sample_NN1 period_NN1 ._. 
</s>
<s>
The_AT existing_JJ change_NN1 point_NN1 literature_NN1 usually_RR falls_VVZ into_II two_MC main_JJ categories_NN2 :_: the_AT change_NN1 point_NN1 detection_NN1 and_CC the_AT change_NN1 point_NN1 estimation_NN1 ._. 
</s>
<s>
However_RR ,_, the_AT penalty_NN1 for_IF doing_VDG this_DD1 is_VBZ an_AT1 increase_NN1 in_II the_AT expected_JJ computational_JJ cost_NN1 by_II a_AT1 factor_NN1 of_IO /KX/KXtherefore_FU it_PPH1 is_VBZ reasonable_JJ to_TO expect_VVI to_TO have_VHI a_AT1 larger_JJR number_NN1 of_IO potential_JJ death_NN1 events_NN2 ,_, each_DD1 of_IO which_DDQ will_VM have_VHI a_AT1 smaller_JJR acceptance_NN1 probability_NN1 ._. 
</s>
<s>
First_MD ,_, a_AT1 proposal_NN1 Y_ZZ1 is_VBZ drawn_VVN from_II a_AT1 proposal_NN1 kernel_NN1 ,_, and_CC second_NNT1 ,_, the_AT proposal_NN1 is_VBZ accepted_VVN as_CSA (_( +1_MC )_) X(i+1)_FO with_IW a_AT1 certain_JJ probability_NN1 ._. 
</s>
<s>
In_II summary_NN1 ,_, Supplementary_JJ Videos_NN2 S1–S3_VV0 demonstrate_VV0 how_RRQ to_TO use_VVI the_AT morphology_NN1 visualization_NN1 module_NN1 interactively_RR ._. 
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<s>
Yet_RR ,_, the_AT rates_NN2 of_IO convergence_NN1 are_VBR slower_RRR than_CSN those_DD2 of_IO Theorem_NN1 6_MC ._. 
</s>
<s>
There_EX is_VBZ a_AT1 large_JJ literature_NN1 in_II optimal_JJ policy_NN1 design_NN1 focused_VVN on_II improving_JJ efficiency_NN1 by_II targeting_VVG the_AT right_JJ subset_NN1 of_IO individuals_NN2 ._. 
</s>
<s>
Domestic_JJ prices_NN2 are_VBR negatively_RR related_VVN to_II nominal_JJ exchange_NN1 rates_NN2 (_( relative_JJ prices_NN2 of_IO the_AT domestic_JJ currency_NN1 )_) ,_, because_CS domestic_JJ inflation_NN1 is_VBZ likely_JJ to_TO be_VBI associated_VVN with_IW depreciation_NN1 of_IO the_AT home_NN1 currency_NN1 ._. 
</s>
<s>
We_PPIS2 implemented_VVD all_DB the_AT algorithms_NN2 in_II the_AT open-source_JJ python_NN1 toolbox_NN1 pyABC_NN1 (_( https_NNU :_: ,_, Klinger_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ,_, which_DDQ offers_VVZ a_AT1 state-of-the-art_JJ implementation_NN1 of_IO ABC-SMC_NN1 ._. 
</s>
<s>
For_IF each_DD1 set_NN1 (_( Zj1_FO ,_, ,_, ZjM_NP1 )_) ,_, j=1_FO ,_, ,_, J_ZZ1 ,_, the_AT single_JJ variable_NN1 which_DDQ is_VBZ equal_JJ to_II 1_MC1 can_VM be_VBI sampled_VVN from_II a_AT1 discrete_JJ distribution_NN1 ._. 
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<s>
By_RT21 now_RT22 ,_, there_EX is_VBZ an_AT1 extensive_JJ literature_NN1 on_II trend-following_NN1 ,_, including_II backtests_NN2 of_IO its_APPGE performance_NN1 more_RRR than_CSN a_AT1 century_NNT1 into_II the_AT past_NN1 &lsqb;_( 13_MC &rsqb;_) ,_, &lsqb;_( 14_MC &rsqb;_) ,_, and_CC efforts_NN2 to_TO optimize_VVI trend-following_JJ strategies_NN2 by_II machine_NN1 learning_NN1 methods_NN2 &lsqb;_( 15_MC &rsqb;_) ._. 
</s>
<s>
Figure_NN1 2_MC also_RR shows_VVZ the_AT accuracy_NN1 achieved_VVN by_II methods_NN2 whose_DDQGE Q3_FO or_CC Q8_FO accuracies_NN2 intersect_VV0 the_AT respective_JJ curve_NN1 ._. 
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<s>
While_CS the_AT first_MD scenario_NN1 is_VBZ common_JJ to_II every_AT1 classifier_NN1 ,_, the_AT second_MD scenario_NN1 is_VBZ crucial_JJ in_II clinical_JJ settings_NN2 ,_, particularly_RR in_II the_AT case_NN1 of_IO performing_VVG antimicrobial_JJ resistance_NN1 predictions_NN2 :_: samples_NN2 collected_VVN from_II infected_JJ patients_NN2 are_VBR not_XX guaranteed_VVN to_TO follow_VVI the_AT same_DA distribution_NN1 that_CST was_VBDZ used_VVN for_IF training_NN1 ,_, as_CSA an_AT1 infection_NN1 could_VM potentially_RR come_VVI from_II a_AT1 bacterial_JJ strain_NN1 not_XX included_VVN in_II the_AT training_NN1 data_NN ,_, e.g._REX from_II a_AT1 strain_NN1 that_CST was_VBDZ picked_VVN up_RP during_II travelling_NN1 ._. 
</s>
<s>
The_AT truncation_NN1 radius_NN1 of_IO 1_MC1 nm_FU was_VBDZ applied_VVN to_II real-space_JJ Ewald_NN1 interactions_NN2 and_CC van_NP1 der_NP1 Walls_NP1 interactions_NN2 ._. 
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<s>
We_PPIS2 demonstrate_VV0 through_II several_DA2 simulated_JJ and_CC real_JJ examples_NN2 that_CST semiBSL_NN1 can_VM offer_VVI significantly_RR improved_VVN posterior_JJ approximations_NN2 compared_VVN to_II BSL_NN1 ._. 
</s>
<s>
If_CS a_AT1 portfolio_NN1 consists_VVZ of_IO many_DA2 independent_JJ and_CC identical_JJ risks_NN2 ,_, the_AT law_NN1 of_IO large_JJ numbers_NN2 implies_VVZ that_CST each_DD1 customer_NN1 will_VM have_VHI to_TO cover_VVI approximately_RR the_AT expected_JJ value_NN1 of_IO a_AT1 single_JJ risk_NN1 ._. 
</s>
<s>
In_II this_DD1 case_NN1 ,_, the_AT interactions_NN2 between_II the_AT searching_JJ protein_NN1 and_CC non-specific_JJ sites_NN2 on_II the_AT DNA_NN1 are_VBR very_RG weak_JJ (_( jumping_JJ regime_NN1 )_) ._. 
</s>
<s>
The_AT synchronization_NN1 pattern_NN1 of_IO a_AT1 fully_RR connected_VVN competing_JJ Kuramoto_NN1 model_NN1 with_IW a_AT1 uniform_JJ intrinsic_JJ frequency_NN1 distribution_NN1 g()_ZZ1 was_VBDZ recently_RR considered_VVN ._. 
</s>
<s>
For_IF a_AT1 half-filled_JJ repulsive_JJ Hubbard_NN1 model_NN1 with_IW a_AT1 minimal_JJ defined_VVN on_II the_AT Kagome_NN1 lattice_NN1 ,_, the_AT optimal_JJ flux_NN1 patterns_NN2 for_IF its_APPGE free_JJ energy_NN1 F_ZZ1 at_II any_DD finite_JJ temperature_NN1 are_VBR ±/2_FU in_II each_DD1 triangle_NN1 and_CC 0_MC or_CC in_II each_DD1 hexagon_NN1 ._. 
</s>
<s>
Columns_NN2 4_MC and_CC 5_MC of_IO Table_NN1 4_MC (_( i.e._REX ,_, =5_FO )_) reports_VVZ the_AT optimal_JJ scheme_NN1 designs_NN2 under_II the_AT default_NN1 parameter_NN1 values_NN2 for_IF the_AT entry_NN1 cohort_NN1 ._. 
</s>
<s>
The_AT time_NNT1 complexity_NN1 of_IO the_AT search_NN1 in_II PRSSA_NP1 is_VBZ proportional_JJ to_II the_AT number_NN1 of_IO species_NN ,_, i.e._REX O(N)_II ._. 
</s>
<s>
In_II a_AT1 context_NN1 of_IO error_NN1 correction_NN1 models_NN2 with_IW Granger_NP1 causality_NN1 tests_NN2 ,_, they_PPHS2 show_VV0 that_CST in_II both_DB2 the_AT short_JJ and_CC the_AT long_JJ runs_NN2 ,_, GDP_NN1 growth_NN1 directly_RR influences_VVZ FDI_NP1 ,_, while_CS growth_NN1 in_II local_JJ infrastructure_NN1 and_CC local_JJ investment_NN1 has_VHZ indirect_JJ but_CCB not_XX direct_JJ influence_NN1 ._. 
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<s>
This_DD1 research_NN1 focuses_VVZ on_II the_AT economic_JJ performance_NN1 instead_II21 of_II22 the_AT safety_NN1 aspect_NN1 to_TO maximize_VVI the_AT discounted_JJ total_JJ dividend_NN1 payment_NN1 until_CS ruin_NN1 ._. 
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<s>
Second_MD ,_, condition_NN1 (_( ii_MC )_) is_VBZ a_AT1 generalisation_NN1 of_IO the_AT well-known_JJ HJM_NP1 drift_NN1 condition_NN1 ._. 
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<s>
For_IF a_AT1 pure_JJ condition_NN1 in_II our_APPGE benchmark_NN1 data_NN ,_, qmin=0.9_FO and_CC qmax=1.0_FO were_VBDR used_VVN ._. 
</s>
<s>
In_II contrast_NN1 ,_, the_AT second_MD type_NN1 (_( VFDI_NP1 )_) is_VBZ explained_VVN by_II using_VVG the_AT factor–proportions_NN2 hypothesis_NN1 which_DDQ accounts_VVZ for_IF the_AT existence_NN1 of_IO vertically_RR integrated_JJ firms_NN2 with_IW geofigureically_RR fragmented_JJ production_NN1 (_( Faeth_NP1 2009_MC )_) ._. 
</s>
<s>
They_PPHS2 are_VBR labeled_VVN CEM1_FO and_CC CEM2_FO due_II21 to_II22 the_AT different_JJ loading_NN1 rate_NN1 that_CST has_VHZ been_VBN applied_VVN in_II each_DD1 case_NN1 ._. 
</s>
<s>
Instrumental_JJ variable_NN1 (_( IV_MC )_) analysis_NN1 is_VBZ an_AT1 increasingly_RR popular_JJ tool_NN1 for_IF inferring_VVG the_AT effect_NN1 of_IO an_AT1 exposure_NN1 on_II an_AT1 outcome_NN1 ,_, as_CSA witnessed_VVN by_II the_AT growing_JJ number_NN1 of_IO IV_MC applications_NN2 in_II epidemiology_NN1 ,_, for_REX21 instance_REX22 ._. 
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<s>
Remark_VV0 Remark_NN1 2_MC ._. 
</s>
<s>
The_AT quantity_NN1 1(0)_FO γ_NULL 1(0)_FO is_VBZ the_AT leading_JJ term_NN1 of_IO the_AT bias_NN1 of_IO the_AT profile_NN1 score_NN1 in_II linear_JJ exponential_NN1 models_NN2 in_II the_AT pfixed_JJ asymptotic_JJ regime_NN1 (_( McCullagh_NP1 and_CC Tibshirani_NP1 (_( 1990_MC )_) ,_, section_NN1 3_MC )_) ._. 
</s>
<s>
The_AT above_JJ integral_JJ can_VM be_VBI computed_VVN exactly_RR ,_, and_CC yields_NN2 ,_, Then_RT <equation>_FO and_CC (_( 4.5_MC )_) holds_VVZ (_( if_CS <equation>_FO ,_, the_AT limit_NN1 is_VBZ <equation>_FO )_) ._. 
</s>
<s>
This_DD1 last_MD observation_NN1 is_VBZ especially_RR robust_JJ for_IF either_RR small_JJ or_CC large_JJ ,_, as_CSA can_VM be_VBI seen_VVN in_II section_NN1 of_IO the_AT supplementary_JJ material_NN1 ,_, in_II which_DDQ analogous_JJ plots_NN2 for_IF different_JJ couples_NN2 of_IO values_NN2 (_( ,_, )_) are_VBR presented_VVN ._. 
</s>
<s>
Moreover_RR ,_, the_AT proof_NN1 of_IO Theorem_NN1 3.17_MC actually_RR shows_VVZ that_CST if_CS both_DB2 tuples_NN2 of_IO measures_NN2 are_VBR conditionally_RR atomless_JJ ,_, the_AT above_JJ condition_NN1 is_VBZ not_XX only_RR necessary_JJ ,_, but_CCB also_RR sufficient_JJ to_TO guarantee_VVI the_AT existence_NN1 of_IO a_AT1 bijection_NN1 linking_VVG <equation>_FO to_II <equation>_FO ._. 
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<s>
In_BCL21 order_BCL22 to_TO motivate_VVI the_AT design_NN1 of_IO the_AT SA_NP1 proposal_NN1 in_II Sect._NP1 3.2_MC ,_, consider_VV0 the_AT behaviour_NN1 of_IO the_AT function_NN1 gi_NN2 depicted_VVD exemplarily_RR in_II Fig._NN1 3_MC for_IF a_AT1 p-value_JJ pi_NN1 below_RL (_( left_JJ )_) and_CC above_RL (_( right_RR )_) the_AT testing_NN1 threshold_NN1 =1/5000=1/5000_FU ._. 
</s>
<s>
Iterated_JJ filtering_NN1 runs_VVZ a_AT1 sequence_NN1 of_IO particle_NN1 filter_NN1 on_II the_AT augmented_JJ space_NN1 comprising_VVG the_AT latent_JJ variable_NN1 and_CC the_AT parameter_NN1 ,_, where_CS the_AT parameters_NN2 are_VBR subject_II21 to_II22 random_JJ perturbations_NN2 at_II each_DD1 time_NNT1 point_NN1 ._. 
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<s>
Generally_RR ,_, the_AT proposed_JJ method_NN1 COGDAG_NN1 shows_VVZ significantly_RR better_JJR performance_NN1 in_II TPR_NP1 and_CC FPR_NP1 ._. 
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<s>
Moreover_RR ,_, there_EX is_VBZ no_AT prescribed_JJ form_NN1 of_IO stationarity_NN1 assumed_VVN within_II the_AT panel_NN1 ._. 
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<s>
Taking_VVG a_AT1 statistical_JJ viewpoint_NN1 emphasizes_VVZ the_AT first_MD two_MC moments_NN2 of_IO the_AT prediction_NN1 error_NN1 ,_, X-X_MC ._. 
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<s>
The_AT evaluated_VVN numerical_JJ values_NN2 of_IO (_( s_ZZ1 )_) ,_, for_IF each_DD1 particular_JJ s_ZZ1 (_( 0.3_MC ≤_FO s_ZZ1 ≤_FO 5_MC )_) ,_, are_VBR given_VVN in_II table_NN1 1_MC1 ._. 
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<s>
It_PPH1 is_VBZ therefore_RR important_JJ to_TO have_VHI a_AT1 good_JJ solution_NN1 ranking_NN1 approach_NN1 ._. 
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<s>
This_DD1 article_NN1 complements_VVZ this_DD1 conventional_JJ wisdom_NN1 by_II showing_VVG that_CST such_DA central–local_JJ alignment_NN1 might_VM break_VVI down_RP in_II the_AT presence_NN1 of_IO imperfect_JJ performance_NN1 monitoring_NN1 ._. 
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<s>
As_CSA expected_VVN ,_, the_AT critical_JJ risk_NN1 increases_VVZ with_IW f_ZZ1 ,_, indicating_VVG that_CST the_AT social_JJ protection_NN1 factor_NN1 allows_VVZ for_IF high-r_JJ agents_NN2 to_TO stay_VVI with_IW w>0_FO even_RR for_IF long_JJ times_NNT2 after_II equilibrium_NN1 ._. 
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<s>
As_CSA denoted_VVN by_II AR-FastBioseq_NN1 in_II Figure_NN1 4_MC ,_, we_PPIS2 compared_VVD this_DD1 approach_NN1 with_IW the_AT original_JJ AffinityRegression_NN1 and_CC our_APPGE ProbeRating_NN1 ._. 
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<s>
The_AT articles_NN2 closest_RRT in_II spirit_NN1 to_II ours_PPGE are_VBR &lsqb;_( 1_MC1 ,_, 18_MC ,_, 26_MC &rsqb;_) ._. 
</s>
<s>
We_PPIS2 approximate_VV0 <equation>_FO by_II <equation>_FO by_II using_VVG a_AT1 regression_NN1 Monte_NP1 Carlo_NP1 (_( RMC_NP1 )_) algorithm_NN1 ,_, where_CS <equation>_FO is_VBZ the_AT number_NN1 of_IO Monte_NP1 Carlo_NP1 paths_NN2 ._. 
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<s>
The_AT sixth_MD set_NN1 of_IO bars_NN2 controls_VVZ for_IF total_JJ wealth_NN1 (_( including_II the_AT component_NN1 not_XX captured_VVN by_II the_AT Census/ACS_FU wealth_NN1 proxies_NN2 )_) by_II using_VVG information_NN1 from_II the_AT SCF_NP1 ,_, following_VVG the_AT method_NN1 described_VVN in_II Online_JJ Appendix_NN1 F._NP1 The_AT seventh_MD set_NN1 of_IO bars_NN2 includes_VVZ fixed_JJ effects_NN2 for_IF the_AT tract_NN1 in_II which_DDQ the_AT child_NN1 grew_VVD up_RP (_( defined_VVN as_II the_AT first_MD nonmissing_JJ tract_NN1 of_IO their_APPGE parents_NN2 )_) ._. 
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<s>
In_II our_APPGE model_NN1 we_PPIS2 envisage_VV0 two_MC broad_JJ motives_NN2 for_IF participationboth_NN1 the_AT consumption_NN1 of_IO spiritual_JJ activities_NN2 as_CSA such_DA and_CC the_AT purchase_NN1 of_IO insurance_NN1 against_II various_JJ shocks_NN2 ,_, and_CC our_APPGE survey_NN1 evidence_NN1 indicates_VVZ that_CST both_DB2 of_IO these_DD2 motives_NN2 matter_VV0 ._. 
</s>
<s>
One_MC1 potential_JJ concern_NN1 with_IW this_DD1 strategy_NN1 is_VBZ that_DD1 destination_NN1 municipality_NN1 exposure_NN1 is_VBZ correlated_VVN with_IW other_JJ contemporaneous_JJ shocks_NN2 that_CST might_VM have_VHI contributed_VVN to_II the_AT increase_NN1 in_II the_AT share_NN1 of_IO nonagricultural_JJ lending_NN1 during_II this_DD1 period_NN1 ._. 
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<s>
Then_RT ,_, its_APPGE local_JJ domain_NN1 Bj_NP1 and_CC boundary_NN1 blocks_NN2 =±_FO (_( +1_MC )_) j=j±_FO (_( L+1_FO )_) have_VH0 no_AT intersection_NN1 with_IW the_AT ones_NN2 of_IO i_ZZ1 ._. 
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<s>
We_PPIS2 would_VM like_VVI to_TO thank_VVI the_AT Editor_NN1 and_CC Referees_NN2 very_RG much_DA1 for_IF their_APPGE constructive_JJ comments_NN2 ,_, which_DDQ significantly_RR helped_VVD us_PPIO2 to_TO improve_VVI the_AT manuscript_NN1 ._. 
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<s>
M.M.B_NP1 ._. 
</s>
<s>
is_VBZ a_AT1 post-doctoral_JJ researcher_NN1 in_II the_AT Democritus_JJ University_NN1 of_IO Thrace_NP1 ._. 
</s>
<s>
The_AT third_MD term_NN1 describes_VVZ the_AT rate_NN1 at_II which_DDQ node_NN1 i_ZZ1 will_VM be_VBI infected_VVN by_II contagion_NN1 c_ZZ1 if_CS it_PPH1 is_VBZ susceptible_JJ ._. 
</s>
<s>
For_IF all_DB models_NN2 ,_, our_APPGE estimation_NN1 algorithm_NN1 was_VBDZ run_VVN for_IF 20,000_MC iterations_NN2 ,_, 5000_MC of_IO which_DDQ were_VBDR used_VVN as_CSA burn_NN1 in_RP ,_, and_CC the_AT hyperparameters_NN2 were_VBDR chosen_VVN as_CSA s=40_FO ,_, =0.05_FO and_CC s=0.01_FO ._. 
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<s>
We_PPIS2 also_RR show_VV0 that_CST agricultural_JJ productivity_NN1 growth_NN1 had_VHD a_AT1 limited_JJ impact_NN1 on_II migration_NN1 ,_, indicating_VVG that_CST the_AT reallocation_NN1 of_IO labor_NN1 primarily_RR occurred_VVD within_II the_AT local_JJ labor_NN1 market_NN1 ._. 
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<s>
Even_RR at_II these_DD2 medium-term_JJ frequencies_NN2 ,_, we_PPIS2 do_VD0 not_XX observe_VVI downward_JJ pressure_NN1 on_II before-duty_JJ unit_NN1 values_NN2 in_II31 response_II32 to_II33 the_AT tariff_NN1 changes_NN2 ._. 
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<s>
Model_VV0 dependent_JJ constructions_NN2 of_IO the_AT guide_NN1 function_NN1 have_VH0 been_VBN proposed_VVN for_IF specific_JJ latent_JJ processes_NN2 ,_, such_II21 as_II22 perfectly_RR observed_VVN diffusion_NN1 processes_NN2 (_( Lin_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
2010_MC )_) or_CC stochastically_RR generated_VVN graph_NN1 models_NN2 (_( Bloem-Reddy_NP1 and_CC Orbanz_NP1 2018_MC )_) ._. 
</s>
<s>
That_REX21 is_REX22 ,_, (_( 10_MC )_) Ye_PPY →_NULL ,_, k=1_FO ,_, if_CS the_AT kth_NNU RNBRW_NP1 returns_VVZ e_ZZ1 as_II the_AT retracing_JJ edge_NN1 ,_, 0_MC ,_, otherwise_RR ._. 
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<s>
Accounting_VVG for_IF multiple_JJ trees_NN2 elucidates_VVZ the_AT consequences_NN2 of_IO non-uniqueness_NN1 of_IO solutions_NN2 on_II spatial_JJ clonal_JJ composition_NN1 and_CC distribution_NN1 ._. 
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<s>
We_PPIS2 observe_VV0 counties_NN2 in_II Nevada_NP1 and_CC the_AT Dakotas_NP2 which_DDQ have_VH0 seen_VVN large_JJ increases_NN2 in_II their_APPGE mortality_NN1 rates_NN2 between_II the_AT years_NNT2 2000_MC and_CC 2010_MC ,_, and_CC regions_NN2 in_II eastern_JJ Texas_NP1 and_CC Alabama_NP1 ,_, which_DDQ have_VH0 consistently_RR seen_VVN increases_NN2 in_II mortality_NN1 over_II each_DD1 of_IO these_DD2 decades_NNT2 ._. 
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<s>
Given_CS21 that_CS22 PBMC16k_FO is_VBZ the_AT only_JJ available_JJ cell-hashed_JJ CITE-seq_FW dataset_NN1 ,_, we_PPIS2 focus_VV0 the_AT evaluation_NN1 of_IO CITE-sort_NN1 over_II the_AT PBMC16k_FO dataset_NN1 ._. 
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<s>
However_RR ,_, existing_JJ methods_NN2 do_VD0 not_XX consider_VVI the_AT case_NN1 of_IO informative_JJ missing_JJ values_NN2 which_DDQ are_VBR widely_RR encountered_VVN in_II practice_NN1 ._. 
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<s>
The_AT symbols_NN2 correspond_VV0 to_II the_AT predicted_JJ response_NN1 equation_NN1 (_( 74_MC )_) measured_VVD in_II the_AT unperturbed_JJ system_NN1 ,_, while_CS the_AT solid_JJ lines_NN2 corresponds_VVZ to_TO direct_VVI measurement_NN1 of_IO susceptibility_NN1 in_II the_AT presence_NN1 of_IO a_AT1 perturbation_NN1 of_IO strength_NN1 =_FO 0.1_MC ._. 
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<s>
The_AT GAS_NN1 backed_VVD CoVaR_NP1 measure_NN1 has_VHZ several_DA2 advantages_NN2 ._. 
</s>
<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 examine_VV0 the_AT empirical_JJ performance_NN1 of_IO our_APPGE proposed_JJ methods_NN2 in_II31 terms_II32 of_II33 size_NN1 and_CC power_NN1 ,_, and_CC compare_VV0 them_PPHO2 with_IW several_DA2 existing_JJ state_NN1 of_IO the_AT art_NN1 techniques_NN2 ._. 
</s>
<s>
These_DD2 journals_NN2 have_VH0 been_VBN gaining_VVG ground_NN1 and_CC importance_NN1 over_II the_AT last_MD years_NNT2 in_II the_AT financial_JJ networks_NN2 field_NN1 ._. 
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<s>
The_AT motion_NN1 of_IO a_AT1 random_JJ system_NN1 depends_VVZ on_II the_AT interaction_NN1 between_II the_AT deterministic_JJ parts_NN2 of_IO the_AT system_NN1 and_CC the_AT random_JJ forces_NN2 &lsqb;_( 54_MC &rsqb;_) ._. 
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<s>
We_PPIS2 demonstrate_VV0 that_CST the_AT GIRF_NN1 methodology_NN1 can_VM enable_VVI likelihood-based_JJ inference_NN1 on_II a_AT1 spatiotemporal_JJ mechanistic_JJ model_NN1 addressing_VVG a_AT1 scientific_JJ application_NN1 ._. 
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<s>
Figure_NN1 6_MC shows_VVZ that_CST the_AT marginal_JJ posteriors_NN2 estimated_VVD using_VVG CSGVA_NP1 are_VBR quite_RG close_JJ to_II that_DD1 of_IO MCMC_NP1 ,_, while_CS GVA_NP1 underestimated_VVD the_AT posterior_JJ variance_NN1 of_IO and_CC quite_RG severely_RR ._. 
</s>
<s>
Moreover_RR ,_, it_PPH1 is_VBZ not_XX immediately_RR apparent_JJ that_CST a_AT1 weighted_JJ generalization_NN1 retains_VVZ the_AT combinatorial_JJ properties_NN2 of_IO the_AT CNT_NP1 model_NN1 that_CST enable_VV0 its_APPGE efficient_JJ computation_NN1 ._. 
</s>
<s>
This_DD1 dataset_NN1 includes_VVZ ultra-low_JJ coverage_NN1 (_( ≈_NULL 0.5×_FO )_) whole-genome_JJ sequencing_NN1 of_IO 90_MC cells_NN2 from_II two_MC different_JJ time_NNT1 points_VVZ :_: 46_MC pre-treatment_JJ cells_NN2 and_CC 44_MC post-treatment_JJ cells_NN2 ._. 
</s>
<s>
As_CSA seen_VVN in_II Table_NN1 1_MC1 ,_, around_RG 70%_NNU of_IO doctorate_NN1 recipients_NN2 ,_, both_RR citizens_NN2 and_CC foreign-born_NN1 ,_, have_VH0 definite_JJ postgraduation_NN1 plans_NN2 (_( for_IF employment_NN1 ,_, study_NN1 ,_, or_CC postdoctoral_JJ training_NN1 )_) ._. 
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<s>
Secondly_RR ,_, the_AT median_NN1 largely_RR deviates_VVZ from_II the_AT mean_JJ when_CS the_AT data_NN is_VBZ highly_RR skewed_VVN ._. 
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<s>
We_PPIS2 treat_VV0 the_AT inter-donation_JJ interval_NN1 as_II a_AT1 nominal_JJ variable_NN1 with_IW three_MC categories_NN2 ._. 
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<s>
Fig._NN1 7_MC shows_VVZ the_AT density_NN1 profile_NN1 at_II t=104s_FO corresponding_VVG to_II Fig._NN1 6_MC ._. 
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<s>
Third_MD ,_, the_AT key_JJ observation_NN1 that_CST the_AT In(s)_NNU2 obey_VV0 '_NULL a_AT1 strange_JJ reduction_NN1 rule_NN1 '_NULL &lsqb;_( 43_MC &rsqb;_) ,_, i.e._REX ,_, We_PPIS2 discuss_VV0 conditions_NN2 under_II which_DDQ there_EX exists_VVZ a_AT1 representative_JJ agent_NN1 ._. 
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<s>
Thanks_II21 to_II22 Lemma_NN1 4.12_MC and_CC Proposition_NN1 4.13_MC ,_, we_PPIS2 have_VH0 that_DD1 <equation>_FO ._. 
</s>
<s>
Geofigureical_JJ agglomeration_NN1 ,_, topofigurey_NN1 factor_NN1 ,_, and_CC neighbors_NN2 '_NULL Log_VV0 income_NN1 p.c._NNU are_VBR used_JJ to_II measure_NN1 spatial_JJ effects_NN2 ._. 
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<s>
In_II this_DD1 subsection_NN1 ,_, we_PPIS2 shall_VM use_VVI the_AT COS_NP2 method_NN1 to_TO approximate_VVI the_AT function_NN1 V_ZZ1 (_( u_ZZ1 ;_; b_ZZ1 )_) ._. 
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<s>
The_AT cross-sectional_JJ impact_NN1 of_IO the_AT shock_NN1 on_II ATM_NN1 withdrawals_NN2 is_VBZ concentrated_VVN in_II December_NPM1 2016_MC but_CCB remains_VVZ through_II June_NPM1 2017_MC ._. 
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<s>
When_CS there_EX is_VBZ no_AT missing_JJ value_NN1 ,_, we_PPIS2 compute_VV0 the_AT truncated_JJ SVD_NP1 U_NP1 δ_NULL VT_NP1 of_IO the_AT scaled_JJ genotype_NN1 matrix_NN1 of_IO diploid_JJ individuals_NN2 Gi_NN1 ,_, j=Gi_FO ,_, j2fj2fj(1fj)_FO ,_, where_CS Gi_NN1 ,_, j_ZZ1 is_VBZ the_AT allele_NN1 count_NN1 (_( genotype_NN1 )_) of_IO individual_JJ i_ZZ1 and_CC variant_NN1 j_ZZ1 ,_, and_CC fj_NNU is_VBZ the_AT estimated_JJ allele_NN1 frequency_NN1 of_IO variant_NN1 j_ZZ1 (_( 2fj_FO is_VBZ the_AT mean_JJ allele_NN1 count_NN1 of_IO variant_NN1 j_ZZ1 )_) ._. 
</s>
<s>
Using_VVG GenBank_NP1 (_( Benson_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) and_CC RefSeq_NP1 (_( Haft_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) repositories_NN2 as_II an_AT1 example_NN1 ,_, we_PPIS2 see_VV0 an_AT1 exponential_NN1 data_NN growth_NN1 (_( Supplementary_JJ Fig_NN1 ._. 
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<s>
S1_FO )_) ._. 
</s>
<s>
The_AT main_JJ drawback_NN1 of_IO these_DD2 methods_NN2 is_VBZ their_APPGE inability_NN1 to_TO control_VVI for_IF heterogeneity_NN1 in_II unobservable_JJ growth_NN1 potential_NN1 ._. 
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<s>
We_PPIS2 report_VV0 the_AT mean_JJ and_CC variance_NN1 of_IO these_DD2 metrics_NN2 calculated_VVN from_II our_APPGE nested_JJ cross_NN1 validation_NN1 ._. 
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<s>
One_PN1 must_VM rather_RR apply_VVI (_( some_DD form_NN1 of_IO )_) local_JJ alignment_NN1 ._. 
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<s>
Neglecting_VVG the_AT network_NN1 structure_NN1 of_IO the_AT model_NN1 and_CC working_VVG only_RR with_IW the_AT compartment_NN1 model_NN1 can_VM lead_VVI to_II completely_RR different_JJ results_NN2 concerning_II how_RRQ the_AT infected_JJ populations_NN2 evolve_VV0 in_II time_NNT1 ._. 
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<s>
In_II our_APPGE framework_NN1 ,_, the_AT same_DA <equation>_FO satisfies_VVZ <equation>_FO ,_, which_DDQ is_VBZ still_RR universally_RR measurable_JJ and_CC <equation>-polar_FO ._. 
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<s>
Simulated_JJ velocities_NN2 of_IO the_AT starting_NN1 process_NN1 from_II a_AT1 traffic_NN1 signal_NN1 ._. 
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<s>
Thus_RR ,_, both_DB2 of_IO them_PPHO2 are_VBR inadequate_JJ for_IF diagnosis-specific_JJ identification_NN1 ._. 
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<s>
We_PPIS2 consider_VV0 a_AT1 probability_NN1 space_NN1 <equation>_FO with_IW a_AT1 filtration_NN1 <equation>_FO satisfying_VVG the_AT usual_JJ conditions_NN2 ,_, where_CS <equation>_FO represents_VVZ a_AT1 fixed_JJ time_NNT1 horizon_NN1 ._. 
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<s>
I_PPIS1 do_VD0 not_XX detect_VVI statistically_RR significant_JJ effects_NN2 on_II student_NN1 outcomes_NN2 of_IO literature_NN1 teacher_NN1 stereotypes_NN2 ._. 
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<s>
Indeed_RR ,_, only_RR the_AT sandwichbased_JJ test_NN1 provided_VVD a_AT1 pvalue_NN1 below_RG 0.05_MC ,_, but_CCB this_DD1 test_NN1 is_VBZ often_RR anticonservative_JJ ,_, as_CSA discussed_VVN in_II Section_NN1 5.1_MC ._. 
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<s>
The_AT scenarios_NN2 were_VBDR generated_VVN to_TO address_VVI spurious_JJ inferences_NN2 related_VVN to_II (_( i_ZZ1 )_) detrending_VVG methods_NN2 ;_; (_( ii_MC )_) inappropriate_JJ choice_NN1 of_IO filtering_VVG bands_NN2 ;_; (_( iii_MC )_) original_JJ fluctuations_NN2 ,_, their_APPGE levels_NN2 and_CC spectral_JJ densities_NN2 ;_; and_CC (_( iv_MC )_) the_AT cross-correlation_JJ structure_NN1 ._. 
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<s>
The_AT column_NN1 labeled_VVD "_" C_NP1 "_" gives_VVZ average_JJ number_NN1 of_IO correct_JJ zeros_MC2 and_CC column_NN1 labeled_VVD "_" I_PPIS1 "_" gives_VVZ the_AT average_JJ number_NN1 of_IO incorrect_JJ zeros_MC2 ._. 
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<s>
This_DD1 table_NN1 uses_VVZ online_JJ job_NN1 vacancy_NN1 data_NN from_II Burning_JJ Glass_NN1 Technologies_NN2 (_( BG_NP1 )_) to_TO calculate_VVI the_AT rate_NN1 of_IO skill_NN1 change_NN1 between_II 2007_MC and_CC 2019_MC for_IF each_DD1 three-digit_JJ SOC_NN1 code_NN1 ._. 
</s>
<s>
The_AT relationship_NN1 between_II the_AT OEF_NN1 liquidation_NN1 rate_NN1 and_CC the_AT liquidation_NN1 line_NN1 under_II different_JJ variable_NN1 combinations_NN2 is_VBZ shown_VVN in_II Fig._NN1 11_MC ._. 
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<s>
Moreover_RR ,_, they_PPHS2 are_VBR anisotropic_JJ and_CC do_VD0 not_XX satisfy_VVI an_AT1 action-reaction_JJ principle_NN1 ._. 
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<s>
Detailed_JJ description_NN1 of_IO each_DD1 method_NN1 and_CC results_NN2 are_VBR provided_VVN in_II the_AT Supplementary_JJ Method_NN1 S1_FO ._. 
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<s>
We_PPIS2 demonstrate_VV0 that_CST optimal_JJ model_NN1 averaging_NN1 can_VM be_VBI successfully_RR incorporated_VVN into_II '_NULL super_JJ learning_NN1 '_NULL ,_, a_AT1 recently_RR proposed_JJ data_NN adaptive_JJ approach_NN1 which_DDQ combines_VVZ several_DA2 learners_NN2 to_TO improve_VVI predictive_JJ performance_NN1 ._. 
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<s>
We_PPIS2 consider_VV0 ∈100,200_FO ,_, ,_, 10,000N∈100,200_FO ,_, ,_, 10,000_MC ,_, with_IW each_DD1 computation_NN1 replicated_VVN =10,000R=10,000_FO times_NNT2 ._. 
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<s>
We_PPIS2 will_VM further_RRR study_VVI on_II shrinking_VVG the_AT time-varying_JJ conditional_JJ covariance_NN1 matrix_NN1 in_II a_AT1 future_JJ project_NN1 ._. 
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<s>
The_AT alternative_JJ options_NN2 led_VVN to_II slightly_RR different_JJ interpretations_NN2 of_IO the_AT temporal_JJ frailty_NN1 ._. 
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We_PPIS2 conclude_VV0 with_IW an_AT1 example_NN1 cast_VVN in_II the_AT single_JJ stock/single_JJ stochastic_JJ factor_NN1 case_NN1 ._. 
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<s>
Although_CS other_JJ weighting_NN1 functions_NN2 are_VBR possible_JJ our_APPGE choice_NN1 is_VBZ limited_VVN by_II application_NN1 of_IO a_AT1 functional_JJ central_JJ limit_NN1 theorem_NN1 in_II H?lder_NP1 spaces_NN2 ._. 
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<s>
Three_MC safety_NN1 evaluation_NN1 indicators_NN2 are_VBR used_JJ to_II measure_NN1 the_AT safety_NN1 performance_NN1 of_IO the_AT models_NN2 due_II21 to_II22 the_AT car-following_JJ models_NN2 can_VM not_XX be_VBI directly_RR used_VVN to_TO evaluate_VVI the_AT safety_NN1 of_IO vehicles_NN2 :_: time_NNT1 to_II collision_NN1 (_( TTC_NP1 )_) ,_, time_NNT1 exposed_JJ time-to-collision_NN1 (_( TET_NP1 )_) ,_, and_CC time_NNT1 integrated_JJ time-to-collision_NN1 (_( TIT_NP1 )_) ._. 
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<s>
Existence_NN1 is_VBZ no_RR21 longer_RR22 a_AT1 trivial_JJ issue_NN1 ,_, and_CC it_PPH1 has_VHZ to_TO be_VBI studied_VVN before_II one_PN1 could_VM discuss_VVI optimality_NN1 ._. 
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<s>
In_RR21 addition_RR22 using_VVG MICE_NN2 leads_VVZ to_II more_RGR biased_JJ results_NN2 than_CSN using_VVG the_AT survey_NN1 areas_NN2 only_RR (_( e.g._REX bias_NN1 ranging_VVG from_II 0.04_MC to_II 0.10_MC )_) and_CC is_VBZ also_RR characterized_VVN by_II a_AT1 much_RR larger_JJR uncertainty_NN1 (_( CI_FO width_NN1 ranging_VVG from_II 0.107_MC to_II 0.132_MC )_) ._. 
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<s>
For_REX21 example_REX22 in_II the_AT snippet_NN1 below_RL ,_, the_AT first_MD query_NN1 returns_VVZ all_DB intervals_NN2 from_II the_AT file_NN1 whereas_CS the_AT second_MD uses_VVZ a_AT1 zoom_NN1 level_NN1 (_( if_CS available_JJ )_) and/or_CC summarizes_VVZ the_AT data_NN to_II 1000_MC bins_NN2 ._. 
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Moreover_RR ,_, the_AT investor_NN1 might_VM want_VVI to_TO alter_VVI the_AT terminal_JJ time_NNT1 itself_PPX1 ._. 
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<s>
Equivalently_RR ,_, a_AT1 standardized_JJ version_NN1 det_NN1 (_( cov_NN1 (_( )_) )_) 1/S_FU ,_, where_CS S_ZZ1 is_VBZ the_AT number_NN1 of_IO components_NN2 of_IO ,_, represents_VVZ a_AT1 geometric_JJ average_JJ variance_NN1 of_IO the_AT s_ZZ1 ,_, adjusted_VVN for_IF their_APPGE covariance_NN1 ._. 
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<s>
In_II this_DD1 paper_NN1 ,_, two_MC possible_JJ covariatesthe_NN1 past_II economic_JJ growth_NN1 and_CC inflationare_NN1 attempted_VVD ._. 
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<s>
The_AT ad_JJ21 hoc_JJ22 developed_JJ algorithm_NN1 has_VHZ proven_VVN to_TO be_VBI fairly_RR efficient_JJ ,_, except_CS in_II high-dimensional_JJ settings_NN2 (_( e.g._REX the_AT eight-part_JJ composition_NN1 estimated_VVN in_II Sect._NP1 6_MC )_) ._. 
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<s>
We_PPIS2 suppose_VV0 that_CST in_II the_AT financial_JJ market_NN1 ,_, there_EX exists_VVZ an_AT1 insurance_NN1 company_NN1 with_IW an_AT1 aggregate_JJ insurance_NN1 liability_NN1 corresponding_VVG to_II a_AT1 liability_NN1 cash_NN1 flow_NN1 given_VVN by_II the_AT <equation>-adapted_FO stochastic_JJ process_NN1 <equation>_FO ,_, the_AT original_JJ liability_NN1 cash_NN1 flow_NN1 ._. 
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<s>
If_CS instead_RR one_MC1 of_IO the_AT tracer_NN1 hop_NN1 times_NNT2 ,_, τ_NULL p_ZZ1 or_CC τ_NULL q_ZZ1 ,_, was_VBDZ the_AT smallest_JJT ,_, the_AT tracer_NN1 would_VM hop_VVI to_II the_AT right/left_NN1 neighboring_VVG site_NN1 if_CS that_DD1 site_NN1 was_VBDZ vacant_JJ ._. 
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<s>
In_II the_AT study_NN1 of_IO optimal_JJ transport_NN1 ,_, one_PN1 typically_RR looks_VVZ at_II an_AT1 optimal_JJ transport_NN1 for_IF one_MC1 pair_NN of_IO measures_NN2 ._. 
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<s>
The_AT first_MD measure_NN1 is_VBZ less_RGR conservative_JJ and_CC is_VBZ always_RR smaller_JJR than_CSN the_AT second_NNT1 ._. 
</s>
<s>
Based_VVN on_II incremental_JJ error_NN1 rates_NN2 ,_, multiple_JJ classifications_NN2 for_IF each_DD1 read_VVN are_VBR filtered_VVN out_RP and_CC only_RR the_AT best_JJT ones_NN2 are_VBR selected_VVN ._. 
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Namely_REX ,_, if_CS the_AT issuance_NN1 of_IO MC_NN1 CoCos_NP2 with_IW <equation>_FO is_VBZ not_XX possible_JJ ,_, type_NN1 H_ZZ1 issues_VVZ a_AT1 PWD_NP1 CoCo_NP1 with_IW <equation>_FO ._. 
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The_AT key_JJ concept_NN1 underlying_JJ BIRD_NN1 is_VBZ that_CST doublets_NN2 can_VM be_VBI identified_VVN by_II a_AT1 signal_NN1 derived_VVN from_II the_AT shift_NN1 toward_II higher_JJR BAR_NN1 (_( see_VV0 Section_NN1 2_MC )_) ._. 
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For_IF realistic_JJ applications_NN2 of_IO the_AT valuation_NN1 framework_NN1 considered_VVN here_RL ,_, it_PPH1 is_VBZ reasonable_JJ to_TO put_VVI further_JJR restrictions_NN2 on_II the_AT set_NN1 of_IO allowed_JJ replicating_JJ portfolios_NN2 ._. 
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This_DD1 is_VBZ particularly_RR important_JJ given_VVN the_AT rapid_JJ pace_NN1 at_II which_DDQ new_JJ ,_, refined_JJ algorithms_NN2 for_IF cellular_JJ communication_NN1 are_VBR being_VBG developed_VVN and_CC holds_VVZ true_JJ irrespective_II21 of_II22 the_AT kind_NN1 of_IO data_NN used_VMK to_TO infer_VVI communication_NN1 ,_, including_VVG ,_, for_REX21 instance_REX22 ,_, single-cell_JJ proteomics_NN1 data_NN (_( Labib_NP1 and_CC Kelley_NP1 ,_, 2020_MC )_) ,_, which_DDQ can_VM be_VBI even_RR more_RGR informative_JJ on_II cellular_JJ communication_NN1 than_CSN RNA-seq_FW ._. 
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Note_VV0 the_AT change_NN1 in_II the_AT grouping_NN1 of_IO cases_NN2 in_II the_AT noiseless_JJ and_CC the_AT noisier_JJR scenario_NN1 ._. 
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We_PPIS2 show_VV0 that_DD1 variant_NN1 and_CC haplotype_VV0 features_NN2 selected_VVN by_II HAPLEXR_NP1 are_VBR smaller_JJR in_II size_NN1 than_CSN competing_JJ methods_NN2 (_( and_CC thus_RR more_RGR interpretable_JJ )_) and_CC are_VBR significantly_RR enriched_VVN in_II functional_JJ annotations_NN2 related_VVN to_II gene_NN1 regulation_NN1 ._. 
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The_AT data_NN consist_VV0 of_IO two_MC sets_NN2 of_IO scRNA-seq_FW :_: 104_MC cells_NN2 (_( 22_MC PCR_NP1 cycles_NN2 )_) and_CC 59_MC cells_NN2 (_( 12_MC PCR_NP1 cycles_NN2 )_) ._. 
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The_AT regulator_NN1 might_VM need_VVI to_TO support_VVI small-_JJ and_CC mid-sized_JJ companies_NN2 ,_, who_PNQS are_VBR interested_JJ in_II taking_VVG advantage_NN1 of_IO such_DA models_NN2 by_II reducing_VVG the_AT costs_NN2 ,_, for_REX21 example_REX22 ,_, by_II providing_VVG basic_JJ technical_JJ documents_NN2 and_CC tools_NN2 ._. 
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At_RR21 large_RR22 δt_FO ,_, the_AT ISFs_NP2 become_VV0 scattered_VVN due_II21 to_II22 image_NN1 de-correlation_NN1 ._. 
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In_II practice_NN1 ,_, interpretation_NN1 revolves_VVZ around_II the_AT posterior_JJ topic_NN1 memberships_NN2 ,_, P_ZZ1 (_( zd=k_NNU |_NULL (_( wdn_NNU )_) )_) ,_, and_CC probabilities_NN2 ,_, P_ZZ1 (_( β_NULL kv_NNU |_NULL (_( wdn_NNU )_) )_) ._. 
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We_PPIS2 illustrate_VV0 these_DD2 effects_NN2 in_II Panels_NN2 D_ZZ1 and_CC E_ZZ1 of_IO Fig._NN1 1_MC1 ._. 
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We_PPIS2 have_VH0 given_VVN analytical_JJ arguments_NN2 in_II that_DD1 indeed_RR the_AT plateau_NN1 value_NN1 of_IO mn_NNU is_VBZ exactly_RR equal_JJ to_II 1at_FO γ_NULL d_ZZ1 for_IF the_AT uniform_JJ measure_NN1 ,_, our_APPGE numerical_JJ results_NN2 suggest_VV0 that_CST this_DD1 remains_VVZ true_JJ when_CS ,_, even_CS21 if_CS22 we_PPIS2 do_VD0 not_XX have_VHI analytical_JJ support_NN1 for_IF this_DD1 assumption_NN1 in_II the_AT general_JJ case_NN1 ._. 
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We_PPIS2 re-examine_VV0 the_AT influence_NN1 of_IO the_AT inflation_NN1 and_CC unemployment_NN1 rates_NN2 on_II the_AT size_NN1 distribution_NN1 of_IO income_NN1 among_II US_NP1 families_NN2 using_VVG 16_MC years_NNT2 of_IO additional_JJ data_NN (_( 1995–2010_MCMC )_) not_XX available_JJ in_II previous_JJ studies_NN2 ,_, including_II the_AT deepest_JJT recession_NN1 since_CS World_NN1 War_NN1 II_MC ._. 
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Overall_RR ,_, allocation_NN1 (_( B_ZZ1 )_) proved_VVD to_TO be_VBI the_AT easiest_JJT to_TO classify_VVI using_VVG both_DB2 the_AT (_( MC_NNU )_) 3_MC and_CC MCMC_NP1 algorithms_NN2 ,_, with_IW almost_RR 100%_NNU correct_JJ classification_NN1 rates_NN2 in_II all_DB cases_NN2 ._. 
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One_MC1 of_IO the_AT basic_JJ assumptions_NN2 in_II this_DD1 model_NN1 is_VBZ assuming_VVG appropriate_JJ risks_NN2 for_IF all_DB units_NN2 ._. 
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This_DD1 uses_VVZ the_AT fact_NN1 that_CST <equation>_FO is_VBZ indeed_RR an_AT1 <equation>-local_FO martingale_NN1 since_CS <equation>_FO is_VBZ an_AT1 martingale_NN1 ,_, hence_RR continuous_JJ ,_, not_XX jumping_VVG to_TO zero_VVI ._. 
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Guarniero_NP1 et_RA21 al_RA22 ._. 
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(_( 2017_MC )_) proposed_VVD a_AT1 method_NN1 for_IF estimating_VVG the_AT exact_JJ guide_NN1 function_NN1 (_( )_) =_FO (_( :_: |_NULL )_) n(xn)=p_NNU (_( yn:N_VV0 |_NULL xn_FO )_) in_II a_AT1 backward_JJ direction_NN1 =_FO ,_, 1_MC1 ,_, ,_, 1n=N_FO ,_, N1_FO ,_, ,_, 1_MC1 ,_, using_VVG parametric_JJ fitting_NN1 to_II mixtures_NN2 of_IO normals_NN2 ._. 
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Our_APPGE aim_NN1 here_RL is_VBZ twofold_RR :_: (_( 1_MC1 )_) we_PPIS2 want_VV0 to_TO evaluate_VVI the_AT performance_NN1 of_IO the_AT actual_JJ estimator_NN1 (_( 32_MC )_) when_CS it_PPH1 is_VBZ not_XX influenced_VVN by_II a_AT1 plug-in_JJ intensity_NN1 estimator_NN1 ,_, and_CC (_( 2_MC )_) we_PPIS2 want_VV0 to_TO study_VVI if_CS (_( 32_MC )_) manages_VVZ to_TO capture_VVI the_AT behaviour_NN1 of_IO a_AT1 Poisson_NP1 process_NN1 ,_, since_CS Poisson_NP1 processes_NN2 are_VBR currently_RR the_AT only_JJ models_NN2 for_IF which_DDQ we_PPIS2 actually_RR know_VV0 the_AT theoretical_JJ value_NN1 of_IO the_AT J-function_NN1 and_CC ,_, in_RR21 addition_RR22 ,_, Poisson_NP1 processes_NN2 are_VBR the_AT model_NN1 representing_VVG complete_JJ spatial_JJ randomness_NN1 ._. 
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We_PPIS2 find_VV0 that_CST the_AT test_NN1 leads_VVZ to_II the_AT same_DA result_NN1 as_CSA that_DD1 with_IW the_AT best_JJT fit_JJ model_NN1 at_II the_AT base_NN1 level_NN1 ,_, implying_VVG that_CST the_AT independence_NN1 structure_NN1 is_VBZ overall_RR the_AT best_JJT fit_JJ for_IF the_AT top-level_JJ aggregation_NN1 in_II this_DD1 empirical_JJ case_NN1 ._. 
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While_CS for_IF e=1_FO edge_NN1 density_NN1 and_CC cluster_VV0 count_NN1 perform_VV0 better_JJR overall_NN1 ,_, for_IF weak_JJ signals_NN2 (_( second_MD column_NN1 )_) connectivity_NN1 has_VHZ a_AT1 slight_JJ advantage_NN1 over_II them_PPHO2 for_IF 〈_NULL k_ZZ1 〉_NULL <9_FO ._. 
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Then_RT ,_, using_VVG results_NN2 from_II Demidenko_NP1 (_( 2004_MC )_) and_CC Wang_NP1 and_CC Heckman_NP1 (_( 2009_MC )_) ,_, on_II identifiability_NN1 in_II normal_JJ mixed_JJ models_NN2 ,_, it_PPH1 follows_VVZ the_AT identifiability_NN1 of_IO the_AT elliptical_JJ linear_JJ mixed_JJ models_NN2 with_IW measurement_NN1 error_NN1 (_( 4_MC )_) ._. 
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I_PPIS1 investigate_VV0 the_AT effect_NN1 of_IO teacher_NN1 bias_NN1 by_II estimating_VVG equation_NN1 (_( 2_MC )_) directly_RR ,_, comparing_VVG students_NN2 of_IO the_AT same_DA gender_NN1 within_II the_AT same_DA school_NN1 and_CC cohort_NN1 but_CCB assigned_VVN to_II different_JJ classes_NN2 ._. 
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At_II this_DD1 time_NNT1 ,_, one_PN1 has_VHZ an_AT1 abrupt_JJ change_NN1 in_II the_AT stimulus_NN1 and_CC for_IF t>t1_FO one_MC1 observes_VVZ another_DD1 important_JJ feature_NN1 of_IO the_AT SDNN_NP1 ,_, namely_REX ,_, a_AT1 decrease_NN1 in_II m(t)_NNU ,_, together_RL with_IW a_AT1 growth_NN1 in_II m(t)_NNU ._. 
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This_DD1 shows_VVZ the_AT "_" only_JJ if_CS "_" part_NN1 ._. 
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The_AT third_MD tracking_JJ algorithm_NN1 implemented_VVN for_IF model_NN1 (_( 5.1_MC )_) –_- (_( 5.3_MC )_) is_VBZ the_AT conventional_JJ BPF_NP1 ._. 
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Phylogeny-based_JJ methods_NN2 that_CST assume_VV0 that_CST the_AT transmission_NN1 events_NN2 coincide_VV0 with_IW the_AT branching_JJ events_NN2 in_II the_AT phylogeny_NN1 are_VBR therefore_RR only_RR applicable_JJ in_II the_AT context_NN1 of_IO pathogens_NN2 with_IW low_JJ mutation_NN1 rates_NN2 ,_, short_JJ incubation_NN1 times_NNT2 and_CC acute_JJ infections_NN2 (_( Cottam_NP1 et_RA21 al._RA22 ,_, 2008_MC ;_; Harris_NP1 et_RA21 al._RA22 ,_, 2010_MC ;_; Leitner_NP1 et_RA21 al._RA22 ,_, 1996_MC ;_; Ypma_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ._. 
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LOAD_NN1 had_VHD the_AT lowest_JJT MSE_NN1 ,_, MSEEff_NP1 ,_, in_II all_DB except_II eight_MC cases_NN2 ._. 
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In_II turn_NN1 ,_, those_DD2 ten_MC tribes_NN2 would_VM make_VVI up_RP the_AT population_NN1 of_IO the_AT 500_MC members_NN2 of_IO the_AT Boule_NN1 ._. 
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Footnote_VV0 6_MC Among_II non-participants_NN2 ,_, only_RR nearest_JJT neighbors_NN2 were_VBDR contacted_VVN for_IF the_AT survey_NN1 ._. 
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There_EX are_VBR some_DD notable_JJ differences_NN2 in_II the_AT cyclical_JJ performance_NN1 of_IO the_AT different_JJ groups_NN2 ._. 
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The_AT resulting_JJ MDS_NN2 plot_VV0 in_II Fig._NN1 15_MC ,_, with_IW an_AT1 associated_JJ stress_NN1 value_NN1 of_IO 4.275%_FO ,_, allows_VVZ us_PPIO2 to_TO visually_RR inspect_VVI the_AT proximity_NN1 between_II the_AT time_NNT1 series_NN in_II31 terms_II32 of_II33 the_AT QAF-distance_NN1 ._. 
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The_AT obtained_VVN efficiency_NN1 is_VBZ compared_VVN with_IW (_( i_ZZ1 )_) the_AT Curzon–Ahlborn_NP1 bound_VVD ,_, (_( ii_MC )_) the_AT efficiency_NN1 for_IF the_AT engine_NN1 with_IW instantaneous_JJ '_NULL adiabatic_JJ '_NULL branches_NN2 developed_VVD in_RP ,_, ,_, and_CC (_( iii_MC )_) the_AT efficiency_NN1 obtained_VVN for_IF large_JJ dissipation_NN1 in_II the_AT recent_JJ proposal_NN1 ,_, using_VVG a_AT1 fast_JJ forward_JJ approach_NN1 ,_, to_TO build_VVI a_AT1 Carnot-like_JJ engine_NN1 ,_, ._. 
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Specifically_RR ,_, Naim_NP1 and_CC Gildea_NP1 (_( 2012_MC )_) showed_VVD that_CST in_II the_AT presence_NN1 of_IO overlaps_NN2 between_II clusters_NN2 ,_, the_AT condition_NN1 number_NN1 associated_VVN with_IW EM_FU increases_NN2 (_( the_AT convergence_NN1 rate_NN1 decreases_VVZ )_) as_II the_AT imbalance_NN1 in_II mixing_VVG coefficients_NN2 increases_NN2 ;_; hence_RR a_AT1 slower_JJR convergence_NN1 of_IO the_AT EM_FU algorithm_NN1 ._. 
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Here_RL ,_, we_PPIS2 consider_VV0 only_RR the_AT discount_NN1 curve_NN1 and_CC the_AT two_MC risky_JJ curves_NN2 with_IW 3_MC month_NNT1 and_CC 6_MC month_NNT1 tenors_NN2 in_BCL21 order_BCL22 to_TO have_VHI a_AT1 longer_JJR time_NNT1 period_NN1 of_IO data_NN which_DDQ ranges_VVZ from_II 05/09/2005_MF to_II 08/03/2017_MF ._. 
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The_AT model_NN1 contains_VVZ a_AT1 single_JJ mean_JJ parameter_NN1 <equation>_FO and_CC standard_JJ deviation_NN1 (_( SD_NP1 )_) parameter_NN1 <equation>_FO which_DDQ we_PPIS2 assume_VV0 to_TO be_VBI known_VVN and_CC ,_, without_IW loss_NN1 of_IO generality_NN1 ,_, equal_JJ to_II 1_MC1 ._. 
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Both_RR simulations_NN2 and_CC proof-of-principle_JJ real_JJ data_NN application_NN1 confirmed_VVD that_CST the_AT mutational_JJ features_NN2 captured_VVN by_II MutSpace_NP1 are_VBR capable_JJ of_IO stratifying_VVG cancer_NN1 subtypes_NN2 ._. 
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Both_RR oscillatory_JJ and_CC temporally_RR gradated_JJ activity_NN1 has_VHZ been_VBN observed_VVN in_II transcript_NN1 levels_NN2 (_( Kim_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) ._. 
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After_CS middle_JJ school_NN1 ,_, students_NN2 self-select_JJ into_II three_MC different_JJ tracks_NN2 :_: academic-oriented_JJ (_( "_" liceo_NN1 "_" )_) ,_, technical_JJ ,_, and_CC vocational_JJ high_JJ school_NN1 ._. 
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In_II this_DD1 section_NN1 ,_, we_PPIS2 characterise_VV0 absence_NN1 of_IO arbitrage_NN1 in_II a_AT1 multiple_JJ curve_NN1 financial_JJ market_NN1 ._. 
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Indeed_RR Glynn_NP1 and_CC Rhee_NP1 (_( 2014_MC )_) did_VDD not_XX apply_VVI their_APPGE methodology_NN1 to_II the_AT MCMC_NP1 setting_NN1 ._. 
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On_II the_AT one_MC1 hand_NN1 ,_, <equation>_FO in_II (_( 2.5_MC )_) can_VM be_VBI interpreted_VVN as_II the_AT dividends_NN2 arising_VVG from_II the_AT financial_JJ investment_NN1 adjusted_VVN by_II the_AT demofigureic_JJ risk_NN1 –_- notice_VV0 that_CST an_AT1 individual_JJ with_IW high_JJ subjective_JJ mortality_NN1 force_NN1 is_VBZ less_RGR likely_JJ to_TO annuitise_VVI and_CC would_VM rather_RR enjoy_VVI the_AT return_NN1 on_II a_AT1 financial_JJ investment_NN1 ;_; on_II the_AT other_JJ hand_NN1 ,_, <equation>_FO is_VBZ closely_RR related_VVN to_II the_AT risk_NN1 premium_NN1 of_IO the_AT financial_JJ investment_NN1 ._. 
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Our_APPGE case_NN1 studies_NN2 have_VH0 demonstrated_VVN numerous_JJ advantages_NN2 of_IO this_DD1 algorithm_NN1 ._. 
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Therefore_RR ,_, other_JJ researchers_NN2 improved_VVD the_AT model_NN1 over_II the_AT years_NNT2 ,_, adding_VVG new_JJ constraints_NN2 to_TO approximate_VVI the_AT simulation_NN1 to_II real_JJ scenarios_NN2 ._. 
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Thus_RR ,_, to_TO consider_VVI a_AT1 balanced_JJ dataset_NN1 ,_, our_APPGE effective_JJ sample_NN1 spans_VVZ the_AT period_NN1 between_II the_AT first_MD quarter_NN1 of_IO 2000_MC to_II the_AT last_MD quarter_NN1 of_IO 2015_MC for_IF all_DB the_AT nineteen_MC countries_NN2 of_IO the_AT EA_NP1 but_CCB Cyprus_NP1 ._. 
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Finally_RR ,_, inspired_VVN by_II theorem_NN1 1_MC1 of_IO Shah_NP1 and_CC Samworth_NP1 (_( 2013_MC )_) ,_, we_PPIS2 also_RR specialize_VV0 our_APPGE result_NN1 to_TO produce_VVI a_AT1 bagindependent_JJ false_JJ discovery_NN1 bound_VVD that_DD1 is_VBZ valid_JJ for_IF any_DD B2_FO ._. 
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The_AT minimizer_NN1 of_IO the_AT tuning_NN1 parameter_NN1 <equation>_FO can_VM be_VBI obtained_VVN by_II a_AT1 grid_NN1 search_NN1 ._. 
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Parallelization_NN1 is_VBZ possible_JJ in_II the_AT parameterization_NN1 level_NN1 as_RR21 well_RR22 ,_, using_VVG the_AT argument_NN1 parallelModels_NN2 ._. 
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The_AT natural_JJ gas_NN1 sector_NN1 has_VHZ undergone_VVN major_JJ regulatory_JJ and_CC technological_JJ changes_NN2 ._. 
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This_DD1 latter_DA consists_VVZ on_II a_AT1 basic_JJ process_NN1 of_IO chemical_JJ reduction_NN1 of_IO nitrogen_NN1 oxides_NN2 (_( NONOx_NP1 )_) to_II diatomic_JJ nitrogen_NN1 (_( N2N2_FO )_) and_CC water_NN1 (_( H2OH2O_FO )_) by_II the_AT reaction_NN1 of_IO NONOx_NP1 and_CC ammonia_NN1 NH3NH3_FO ._. 
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The_AT exclusion_NN1 of_IO SAVs_NP2 with_IW 0-stars_NN2 helped_VVN improve_VVI the_AT accuracy_NN1 (_( blue_JJ curve_NN1 in_II Fig._NN1 1C_FO )_) ._. 
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The_AT procedure_NN1 is_VBZ summarized_VVN in_II Algorithm_NN1 2_MC ._. 
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The_AT two_MC main_JJ findings_NN2 from_II this_DD1 simulation_NN1 experiment_NN1 can_VM be_VBI summarized_VVN as_CSA follows_VVZ ._. 
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Briefly_RR ,_, we_PPIS2 downloaded_VVD the_AT gene_NN1 annotations_NN2 (_( hg19_FO )_) and_CC corresponding_JJ reference_NN1 sequences_NN2 of_IO 2794_MC mature_JJ miRNA_NN1 in_II human_NN1 from_II miRbase_NN1 (_( v21_FO )_) ._. 
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Figure_NN1 2_MC shows_VVZ the_AT bivariate_JJ scatterplot_NN1 of_IO posterior_JJ samples_NN2 using_VVG BSL_NN1 ,_, semiBSL_NN1 and_CC EES_NP1 ._. 
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A_AT1 random_JJ sample_NN1 of_IO potentially_RR missing_VVG is-a_VBZ relations_NN2 is_VBZ selected_VVN and_CC evaluated_VVN by_II two_MC domain_NN1 experts_NN2 (_( authors_NN2 EWH_NN1 and_CC HNBM_NP1 )_) ._. 
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While_CS this_DD1 analysis_NN1 provides_VVZ us_PPIO2 with_IW information_NN1 concerning_II the_AT significance_NN1 and_CC the_AT direction_NN1 of_IO the_AT impact_NN1 of_IO one_MC1 variable_NN1 on_II another_DD1 ,_, the_AT neutrality_NN1 tests_NN2 only_RR give_VV0 an_AT1 imperfect_JJ picture_NN1 on_II how_RRQ a_AT1 shock_NN1 evolves_VVZ over_II time_NNT1 ._. 
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The_AT above_JJ model_NN1 and_CC approaches_NN2 are_VBR based_VVN on_II the_AT assumption_NN1 of_IO the_AT covariates_NN2 being_VBG low-dimensional_JJ ._. 
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For_IF <equation>_FO ,_, a_AT1 single_JJ power-law_NN1 increase_NN1 is_VBZ observed_VVN ._. 
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Table_NN1 9_MC ,_, Table_NN1 10_MC show_VV0 the_AT SPA_NN1 test_NN1 results_NN2 obtained_VVN after_II 10,000_MC bootstrap_NN1 simulations_NN2 ._. 
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To_TO illustrate_VVI this_DD1 heterogeneity_NN1 ,_, we_PPIS2 plot_VV0 isoquants_NN2 representing_VVG the_AT set_NN1 of_IO colleges_NN2 that_CST have_VH0 mobility_NN1 rates_NN2 at_II the_AT 10th_MD percentile_NN1 (_( 0.9%_FO )_) ,_, median_NN1 (_( 1.6%_FO )_) ,_, and_CC 90th_MD percentile_NN1 (_( 3.5%_FO )_) of_IO the_AT enrollment-weighted_JJ distribution_NN1 across_II colleges_NN2 ._. 
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In_II this_DD1 case_NN1 ,_, a_AT1 regression_NN1 requires_VVZ at_RR21 least_RR22 two_MC explanatory_JJ variables_NN2 with_IW unit_NN1 roots_VVZ that_CST could_VM nullify_VVI each_PPX221 other_PPX222 and_CC allow_VV0 the_AT residuals_NN2 to_TO exhibit_VVI a_AT1 stationary_JJ process_NN1 ._. 
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Grouping_NN1 helps_VVZ in_II contact_NN1 and_CC interaction_NN1 between_II countries_NN2 within_II the_AT group_NN1 and_CC is_VBZ in_II the_AT interests_NN2 of_IO major_JJ countries_NN2 ._. 
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During_II the_AT conversion_NN1 from_II free_JJ flow_NN1 to_II synchronous_JJ flow_NN1 ,_, due_II21 to_II22 the_AT interactions_NN2 between_II vehicles_NN2 ,_, the_AT velocities_NN2 of_IO vehicles_NN2 changes_NN2 within_II a_AT1 great_JJ range_NN1 ,_, which_DDQ leads_VVZ to_II a_AT1 significant_JJ velocity_NN1 difference_NN1 between_II vehicles_NN2 in_II the_AT system_NN1 ._. 
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Yet_RR ,_, this_DD1 does_VDZ not_XX allow_VVI capturing_VVG frequency_NN1 properly_RR ._. 
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After_CS a_AT1 first_MD signal_NN1 detection_NN1 step_NN1 (_( see_VV0 Supplementary_JJ Section_NN1 '_NULL Signal_NN1 extraction_NN1 from_II mzDB_NNU files_NN2 '_NULL )_) ,_, the_AT algorithm_NN1 associates_VVZ the_AT chromatographic_JJ peaks_NN2 detected_VVN with_IW validated_JJ PSMs_NP1 ,_, first_MD by_II retrieving_VVG the_AT corresponding_JJ MS/MS_NN1 spectra_NN2 acquired_VVN during_II the_AT peptide_NN1 elution_NN1 (_( i.e._REX within_II the_AT detected_JJ chromatogram_NN1 boundaries_NN2 )_) ,_, and_CC then_RT by_II matching_VVG the_AT precursor_NN1 m/z_ZZ1 value_NN1 of_IO these_DD2 spectra_NN2 to_II the_AT chromatographic_JJ peak_NN1 m/z_ZZ1 value_NN1 (_( see_VV0 Supplementary_JJ Section_NN1 '_NULL PSM_NP1 assignment_NN1 and_CC deisotoping_VVG '_NULL )_) ._. 
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The_AT main_JJ computational_JJ bottleneck_NN1 of_IO our_APPGE algorithm_NN1 is_VBZ a_AT1 low-rank_NN1 SVD_NP1 of_IO a_AT1 structured_JJ matrix_NN1 ,_, which_DDQ is_VBZ performed_VVN using_VVG a_AT1 block_NN1 QR-stylized_NN1 strategy_NN1 that_CST makes_VVZ effective_JJ use_NN1 of_IO singular_JJ subspace_NN1 warm-start_NN1 information_NN1 across_II iterations_NN2 ._. 
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We_PPIS2 are_VBR grateful_JJ to_II Institute_NN1 for_IF Plasma_NP1 Research_NN1 of_IO Kharazmi_JJ University_NN1 for_IF all_DB their_APPGE kindness_NN1 and_CC help_VV0 in_II31 terms_II32 of_II33 providing_VVG us_PPIO2 with_IW their_APPGE super_JJ computer_NN1 and_CC facilities_NN2 ._. 
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The_AT estimated_JJ coefficient_NN1 associated_VVN with_IW the_AT Gini_NN1 before_II taxes_NN2 and_CC transfers_NN2 remains_VVZ positive_JJ and_CC statistically_RR significant_JJ (_( <equation>_FO ,_, robust_JJ standard_JJ error_NN1 of_IO 0.178_MC )_) ,_, while_CS the_AT point_NN1 estimate_NN1 associated_VVN with_IW the_AT Gini_NN1 after_II taxes_NN2 and_CC transfers_NN2 is_VBZ small_JJ and_CC statistically_RR insignificant_JJ (_( <equation>_FO ,_, robust_JJ standard_JJ error_NN1 of_IO 0.222_MC )_) ._. 
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<s>
More_RGR specifically_RR ,_, let_VV0 <equation>_FO stand_VVI for_IF the_AT distance_NN1 between_II the_AT distribution_NN1 function_NN1 H_ZZ1 of_IO <equation>_FO and_CC the_AT conditional_JJ distribution_NN1 function_NN1 <equation>_FO of_IO <equation>_FO given_VVN <equation>_FO (_( where_CS <equation>_FO for_IF any_DD non-decreasing_JJ function_NN1 g_ZZ1 )_) ._. 
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<s>
Then_RT ,_, if_CS <equation>_FO satisfies_VVZ (_( 1_MC1 )_) ,_, the_AT distribution_NN1 of_IO <equation>_FO is_VBZ either_RR Gaussian_JJ or_CC symmetric_JJ ,_, and_CC <equation>_FO and_CC <equation>_FO as_CSA <equation>_FO for_IF some_DD <equation>_FO ,_, we_PPIS2 have_VH0 <equation>_FO with_IW probability_NN1 1_MC1 as_CSA <equation>_FO ._. 
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<s>
For_IF the_AT second_MD term_NN1 ,_, we_PPIS2 assume_VV0 <equation>_FO ,_, <equation>_FO for_IF <equation>_FO and_CC one_MC1 <equation>_FO say_VV0 <equation>_FO is_VBZ t_ZZ1 and_CC <equation>_FO for_IF <equation>_FO ._. 
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<s>
Although_CS HaploMerger2_FO can_VM also_RR link_VVI adjacent_JJ contigs_NN2 using_VVG overlap_NN1 information_NN1 after_II purging_VVG ,_, our_APPGE tests_NN2 suggest_VV0 that_CST it_PPH1 makes_VVZ false_JJ joins_NN2 ,_, perhaps_RR because_CS it_PPH1 does_VDZ not_XX use_VVI read_VV0 depth_NN1 to_TO distinguish_VVI haplotypic_JJ duplication_NN1 from_II repeat_NN1 duplication_NN1 ._. 
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<s>
Kananga_NN1 is_VBZ a_AT1 city_NN1 of_IO roughly_RR 1_MC1 million_NNO and_CC the_AT capital_NN1 of_IO Kasa?_JJ Central_JJ province_NN1 ._. 
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<s>
The_AT expected_JJ multipopulation_NN1 SFS_NN2 under_II a_AT1 given_JJ demographic_JJ model_NN1 can_VM be_VBI efficiently_RR computed_VVN when_CS the_AT populations_NN2 in_II the_AT model_NN1 are_VBR related_VVN by_II a_AT1 tree_NN1 ,_, scaling_VVG to_II hundreds_NNO2 of_IO populations_NN2 ._. 
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<s>
As_CSA stated_VVN earlier_RRR ,_, Pedroni_NP1 '_NULL s_ZZ1 tests_NN2 rely_VV0 on_II the_AT assumption_NN1 that_CST there_EX is_VBZ no_AT cross-unit_JJ correlation_NN1 in_II the_AT data_NN ._. 
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<s>
In_II Fig._NN1 2_MC we_PPIS2 present_VV0 the_AT evolution_NN1 of_IO ki(t)_NN1 for_IF different_JJ p_ZZ1 ,_, corresponding_VVG to_II three_MC different_JJ power-law_NN1 distribution_NN1 respectively_RR (_( normal_JJ ,_, single_JJ and_CC reversed_VVN )_) ._. 
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<s>
We_PPIS2 do_VD0 so_RR because_CS one_PN1 could_VM claim_VVI that_DD1 ,_, for_REX21 instance_REX22 ,_, a_AT1 sign_NN1 restriction_NN1 that_CST forces_NN2 bank_VV0 loans_NN2 to_TO decrease_VVI in_II the_AT same_DA month_NNT1 that_CST the_AT interest_NN1 rate_NN1 increases_NN2 is_VBZ a_AT1 very_RG stringent_JJ requirement_NN1 ._. 
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<s>
Suppose_VV0 that_CST the_AT Poisson_NP1 intensity_NN1 for_IF the_AT claim_NN1 number_NN1 process_NN1 and_CC the_AT distribution_NN1 for_IF the_AT individual_JJ claim_NN1 sizes_NN2 are_VBR both_RR unknown_JJ ._. 
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<s>
In_II the_AT other_JJ cases_NN2 the_AT chain_NN1 of_IO potentials_NN2 is_VBZ semitransparent_JJ ._. 
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<s>
For_IF a_AT1 more_RGR detailed_JJ dissertation_NN1 ,_, see_VV0 Pesarin_NP1 (_( 2001_MC )_) and_CC Pesarin_NP1 and_CC Salmaso_NP1 (_( 2010_MC )_) ._. 
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<s>
There_RL ,_, we_PPIS2 compare_VV0 two_MC methods_NN2 for_IF entropy_NN1 estimation_NN1 :_: plug-in_JJ and_CC nearest_JJT neighbor_NN1 statistics_NN ._. 
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<s>
Comparison_NN1 of_IO different_JJ bounds_NN2 under_II Transformed_JJ Gamma_NN1 Distribution_NN1 in_II31 terms_II32 of_II33 difference_NN1 from_II MC_NN1 estimate_NN1 for_IF r_ZZ1 =_FO 0_MC ._. 
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<s>
Using_VVG Preqin_NN1 data_NN ,_, we_PPIS2 construct_VV0 a_AT1 sample_NN1 of_IO 24,000_MC VC_NN1 and_CC growth_NN1 equity_NN1 (_( to_II which_DDQ we_PPIS2 refer_VV0 together_RL as_CSA VC_NN1 for_IF simplicity_NN1 )_) investments_NN2 by_II about_RG 3500_MC investors_NN2 over_II the_AT period_NN1 1995–2014_MCMC ._. 
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<s>
Under_II Gaussian_JJ errors_NN2 ,_, this_DD1 paper_NN1 derives_VVZ the_AT detailed_JJ proof_NN1 of_IO the_AT theoretical_JJ results_NN2 including_II consistency_NN1 and_CC asymptotic_JJ normality_NN1 of_IO the_AT QMLE_NN1 ,_, hence_RR it_PPH1 solves_VVZ the_AT conjectures_NN2 in_II Hansen_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( J_ZZ1 Appl_NP1 Econ_NP1 27:877–906_MCMC ,_, 2012_MC )_) ._. 
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<s>
In_II contrast_NN1 ,_, reference-free_JJ binning_NN1 tools_NN2 operate_VV0 without_IW the_AT use_NN1 of_IO reference_NN1 databases_NN2 ._. 
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<s>
After_CS about_RG forty_MC years_NNT2 of_IO extraordinarily_RR rapid_JJ economic_JJ growth_NN1 ,_, China_NP1 is_VBZ facing_VVG the_AT most_RGT severe_JJ environmental_JJ degradation_NN1 in_II its_APPGE history_NN1 ._. 
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<s>
The_AT fraction_NN1 of_IO a_AT1 fund_NN1 '_NULL s_ZZ1 total_JJ AUM_NN1 held_VVN in_II cash_NN1 may_VM impact_VVI the_AT choice_NN1 of_IO the_AT equity_NN1 portfolio_NN1 '_NULL s_ZZ1 liquidity_NN1 ._. 
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<s>
In_II this_DD1 article_NN1 ,_, we_PPIS2 introduce_VV0 TinGa_NP1 ,_, a_AT1 fast_JJ and_CC flexible_JJ TI_JJ method_NN1 ._. 
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<s>
Here_RL we_PPIS2 use_VV0 0=0.04ε0=0.04_FO and_CC obtain_VV0 =9._FO m=9_FO ._. 
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<s>
A_AT1 similar_JJ quantity_NN1 tBG_NNU is_VBZ defined_VVN for_IF network_NN1 BG_NP1 ._. 
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<s>
According_II21 to_II22 the_AT properties_NN2 of_IO generating_JJ function_NN1 &lsqb;_( 37_MC &rsqb;_) ,_, we_PPIS2 have(10)<equation>_FO ,_, k<1if_FO p≥_FO ,_, and_CC Gi(1)_FO is_VBZ actually_RR the_AT probability_NN1 that_CST finite_JJ messages_NN2 will_VM be_VBI received_VVN after_II user_NN1 i_ZZ1 generates_VVZ a_AT1 message_NN1 ._. 
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<s>
If_CS there_EX are_VBR multiple_JJ change_NN1 points_NN2 ,_, though_CS it_PPH1 is_VBZ not_XX investigated_VVN in_II this_DD1 paper_NN1 ,_, the_AT binary_JJ segmentation_NN1 method_NN1 can_VM be_VBI used_VVN ._. 
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<s>
This_DD1 action_NN1 removes_VVZ all_DB information_NN1 saved_VVN for_IF the_AT corresponding_JJ user_NN1 in_II the_AT database_NN1 ._. 
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<s>
Next_MD ,_, we_PPIS2 show_VV0 how_RRQ the_AT weighted_JJ CND_NP1 helps_NN2 recover_VVI cell_NN1 populations_NN2 in_II tumors_NN2 using_VVG noisy_JJ CNPs_NP1 derived_VVN from_II low-coverage_JJ single-cell_JJ DNA_NN1 sequencing_NN1 data_NN (_( Section_NN1 3.2_MC )_) ._. 
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<s>
First_MD ,_, the_AT nonlinear_JJ time-varying_JJ factor_NN1 model_NN1 proposed_VVN by_II Phillips_NP1 and_CC Sul_NP1 (_( 2007_MC ,_, 2009_MC )_) will_VM be_VBI employed_VVN to_TO identify_VVI the_AT convergence_NN1 patterns_NN2 in_II this_DD1 paper_NN1 ._. 
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<s>
An_AT1 exome_NN1 study_NN1 of_IO the_AT former_DA therefore_RR could_VM be_VBI expected_VVN to_TO result_VVI in_II a_AT1 higher_JJR yield_NN1 of_IO statistically_RR significant_JJ findings_NN2 ,_, given_VVN a_AT1 moderately_RR sized_VVN sample_NN1 ._. 
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<s>
While_CS market_NN1 integration_NN1 brings_VVZ new_JJ buyers_NN2 for_IF the_AT domestic_JJ asset_NN1 ,_, i.e._REX ,_, capital_NN1 inflows_NN2 ,_, it_PPH1 also_RR leads_VVZ domestic_JJ investors_NN2 to_TO buy_VVI foreign_JJ assets_NN2 –_- capital_NN1 outflows_NN2 –_- which_DDQ make_VV0 the_AT effect_NN1 of_IO flows_NN2 ambiguous_JJ ._. 
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<s>
Note_VV0 that_CST ,_, due_II21 to_II22 the_AT scale-free_JJ nature_NN1 of_IO the_AT human_JJ interactome_NN1 ,_, few_DA2 nodes_NN2 have_VH0 high_JJ degrees_NN2 ._. 
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<s>
Figure_NN1 V_MC plots_NN2 the_AT time-varying_JJ estimated_JJ coefficients_NN2 on<equation>_FO and_CC 90%_NNU confidence_NN1 intervals_NN2 when_RRQ the_AT outcome_NN1 variable_NN1 is_VBZ the_AT log_NN1 of_IO deposits_NN2 in_II local_JJ bank_NN1 branches_NN2 ._. 
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<s>
This_DD1 large_JJ number_NN1 of_IO layers_NN2 is_VBZ a_AT1 consequence_NN1 of_IO the_AT fact_NN1 that_CST we_PPIS2 did_VDD not_XX use_VVI any_DD of_IO the_AT conventional_JJ architecture_NN1 (_( Jaderberg_NP1 et_RA21 al._RA22 ,_, 2015_MC ;_; Krizhevsky_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) and_CC hence_RR needed_VVN to_TO use_VVI the_AT Lambda_NN1 functions_NN2 in_II Keras_NP2 to_TO represent_VVI some_DD of_IO the_AT activation_NN1 functions_NN2 and_CC PWM_NP1 convolutions_NN2 ._. 
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<s>
However_RR ,_, for_IF bosons_NN2 a_AT1 particle_NN1 source_NN1 and_CC sink_VV0 behave_VV0 in_II a_AT1 dramatically_RR different_JJ way_NN1 ._. 
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<s>
For_IF the_AT bth_NNU bootstrap_NN1 sample_NN1 of_IO the_AT mth_NNU imputed_JJ dataset_NN1 ,_, estimate_VV0 θ_NULL using_VVG the_AT complete_JJ data_NN point_NN1 estimator_NN1 ,_, giving_VVG ,_, ._. 
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<s>
the_AT mean-reverting_JJ models_NN2 (_( for_IF BP_NP1 it_PPH1 can_VM be_VBI obtained_VVN by_II integration_NN1 with_IW (_( 5_MC )_) ,_, find_VV0 E&lsqb;vtvt+_FO τ_NULL &rsqb;_) we_PPIS2 use_VV0 (_( 17_MC )_) to_II &rsqb;_) which_DDQ yields_VVZ &lsqb;_( 32_MC &rsqb;_) (_( 27_MC )_) <equation>_FO τ_NULL =0_FO ._. 
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<s>
In_II this_DD1 section_NN1 ,_, I_PPIS1 do_VD0 not_XX control_VVI other_JJ gravity_NN1 variables_NN2 including_II common_JJ language_NN1 ,_, common_JJ history_NN1 of_IO colonies_NN2 ,_, free_JJ trade_NN1 agreements_NN2 ._. 
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Relative_JJ performance_NN1 of_IO methods_NN2 agrees_VVZ well_RR with_IW the_AT synthetic_JJ independence_NN1 design_NN1 (_( Figs_NN2 ._. 
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S13_FO and_CC S14_FO )_) ._. 
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Therefore_RR ,_, since_CS <equation>_FO is_VBZ strictly_RR convex_JJ and_CC decreasing_VVG around_RG 0_MC ,_, its_APPGE minimum_NN1 must_VM be_VBI achieved_VVN on_II the_AT positive_JJ line_NN1 ,_, i.e._REX ,_, <equation>_FO ._. 
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<s>
A_AT1 step-wise_JJ optimization_NN1 is_VBZ applied_VVN in_II this_DD1 paper_NN1 ,_, which_DDQ provides_VVZ an_AT1 implementable_JJ way_NN1 to_TO deal_VVI with_IW the_AT multiple-objective_JJ optimization_NN1 problem_NN1 ._. 
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<s>
We_PPIS2 fit_VV0 all_DB models_NN2 to_II the_AT full_JJ data_NN set_VV0 ,_, and_CC report_VV0 the_AT number_NN1 of_IO leave-one-out_NN1 folds_NN2 where_RRQ the_AT k_ZZ1 diagnostic_JJ value_NN1 is_VBZ above_II 0.7_MC when_CS using_VVG the_AT full_JJ data_NN posterior_NN1 directly_RR as_II a_AT1 proposal_NN1 distribution_NN1 ._. 
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<s>
The_AT paper_NN1 is_VBZ organized_VVN as_CSA follows_VVZ ._. 
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<s>
We_PPIS2 start_VV0 the_AT analysis_NN1 on_II November_NPM1 5_MC ,_, 2012_MC to_TO allow_VVI for_IF some_DD delay_NN1 in_II the_AT notification_NN1 of_IO short_JJ positions_NN2 ,_, due_II21 to_II22 a_AT1 statutory_JJ holiday_NN1 in_II some_DD federal_JJ states_NN2 ._. 
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<s>
We_PPIS2 observe_VV0 that_CST the_AT split_JJ transformation_NN1 has_VHZ the_AT effect_NN1 of_IO moving_VVG the_AT parameters_NN2 to_II initial_JJ values_NN2 that_CST are_VBR more_RGR appropriate_JJ for_IF exploring_VVG the_AT posterior_NN1 on_II two_MC components_NN2 ._. 
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The_AT lognormal_JJ probability_NN1 density_NN1 with_IW parameters_NN2 <equation>_FO and_CC <equation>_FO is_VBZ used_VVN here_RL ._. 
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<s>
Ikeda_NP1 and_CC Kubokawa_NP1 (_( 2016_MC )_) considered_VVD a_AT1 general_JJ class_NN1 of_IO weighted_JJ estimators_NN2 including_II linear_JJ combinations_NN2 of_IO the_AT sample_NN1 covariance_NN1 matrix_NN1 and_CC the_AT model-based_JJ estimators_NN2 under_II the_AT factor_NN1 model_NN1 ,_, and_CC linear_JJ shrinkage_NN1 estimators_NN2 without_IW factors_NN2 as_CSA special_JJ cases_NN2 ._. 
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<s>
One_PN1 can_VM therefore_RR easily_RR extend_VVI this_DD1 approach_NN1 for_IF computing_VVG tight_JJ bounds_NN2 for_IF other_JJ mortality_NN1 and_CC longevity_NN1 linked_JJ securities_NN2 ._. 
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As_CSA it_PPH1 is_VBZ evident_JJ ,_, depending_II21 on_II22 the_AT plasma_NN1 parameters_NN2 such_II21 as_II22 temperature_NN1 and_CC concentration_NN1 of_IO positive_JJ ions_NN2 and_CC electron_NN1 species_NN ,_, compressive_JJ and_CC rarefactive_JJ IADLs_NN2 can_VM be_VBI formed_VVN in_II a_AT1 warm_JJ plasma_NN1 consisting_VVG of_IO two_MC types_NN2 of_IO electrons_NN2 each_DD1 described_VVN by_II a_AT1 Maxwellian_JJ distribution_NN1 ._. 
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<s>
What_DDQ are_VBR the_AT possible_JJ distributions_NN2 of_IO <equation>_FO under_II <equation>_FO ?_? 
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<s>
We_PPIS2 compared_VVD our_APPGE approach_NN1 to_TO trendsceek_VVI and_CC found_VVD similar_JJ genes_NN2 (_( see_VVI Supplementary_JJ Fig_NN1 ._. 
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<s>
S6_FO )_) in_II a_AT1 considerably_RR shorter_JJR running_JJ time_NNT1 :_: our_APPGE method_NN1 took_VVD 6.5s_NNU ,_, whereas_CS trendsceek_NN1 needed_JJ 1080s_MC2 (_( run_NN1 times_NNT2 measured_VVN on_II a_AT1 single_JJ 2.0GHz_FO CPU_NN1 core_NN1 )_) ._. 
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Our_APPGE article_NN1 makes_VVZ two_MC important_JJ contributions_NN2 ._. 
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<s>
This_DD1 is_VBZ the_AT algorithmic_JJ challenge_NN1 that_CST we_PPIS2 tackle_VV0 in_II CRISPRLand_NP1 using_VVG a_AT1 divide-and-conquer_VV0 strategy_NN1 ._. 
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<s>
Immediate_JJ applications_NN2 include_VV0 ,_, first-passage_JJ properties_NN2 ,_, super-diffusive_JJ fluctuations_NN2 for_IF anomalous_JJ transport_NN1 ,_, representation_NN1 by_II the_AT means_NN of_IO fractional_JJ equations_NN2 ,_, large_JJ deviation_NN1 properties_NN2 and_CC many_DA2 more_DAR ._. 
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<s>
The_AT only_JJ expensive_JJ matrix_NN1 operation_NN1 of_IO 1212212221_MC can_VM be_VBI performed_VVN once_RR outside_II the_AT MCMC_NP1 loop_NN1 and_CC reused_VVD ._. 
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<s>
The_AT extra_JJ factor_NN1 reduces_VVZ to_II 1_MC1 for_IF the_AT Fused_JJ Lasso_NN1 and_CC to_II 2pj_FO when_RRQ all_DB pairwise_RR differences_NN2 are_VBR regularized_VVN ._. 
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<s>
Moreover_RR ,_, with_II31 respect_II32 to_II33 the_AT selection_NN1 of_IO parameter_NN1 c_ZZ1 ,_, we_PPIS2 observe_VV0 that_CST selecting_VVG bigger_JJR c_ZZ1 may_VM cause_VVI the_AT characteristics_NN2 of_IO users/items_NN2 to_TO be_VBI not_XX obvious_JJ and_CC increase_VV0 the_AT amount_NN1 of_IO calculation_NN1 ._. 
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<s>
Each_DD1 month_NNT1 '_NULL s_ZZ1 quintiles_NN2 are_VBR determined_VVN from_II sorts_NN2 of_IO firms_NN2 with_IW nonmissing_VVG values_NN2 for_IF all_DB characteristics_NN2 ._. 
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<s>
Using_VVG this_DD1 triangulation_NN1 ,_, the_AT proportion_NN1 of_IO elements_NN2 in_II 11_MC which_DDQ have_VH0 a_AT1 data_NN footprint_VV0 size_NN1 in_II the_AT single_JJ digits_NN2 is_VBZ 92%_NNU ._. 
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<s>
This_DD1 will_VM be_VBI the_AT case_NN1 throughout_II the_AT article_NN1 unless_CS specified_VVN ._. 
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<s>
Together_RL ,_, these_DD2 results_NN2 suggest_VV0 that_CST firms_NN2 discriminate_VV0 in_II31 favor_II32 of_II33 high_JJ sales_NN workers_NN2 by_II applying_VVG a_AT1 lower_JJR promotion_NN1 threshold_NN1 for_IF expected_JJ managerial_JJ quality_NN1 ,_, leading_VVG marginally_RR promoted_VVN high_JJ sales_NN workers_NN2 to_TO be_VBI worse_JJR managers_NN2 ._. 
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<s>
We_PPIS2 found_VVD a_AT1 figure_NN1 of_IO 0.19_MC which_DDQ is_VBZ closer_JJR to_II the_AT one_PN1 reported_VVN by_II Abraham_NP1 et_RA21 al_RA22 ._. 
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(_( 2009_MC )_) ._. 
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<s>
The_AT determination_NN1 of_IO whether_CSW a_AT1 given_JJ tuple_NN1 of_IO distributions_NN2 is_VBZ jointly_RR mixable_JJ is_VBZ a_AT1 highly_RR non-trivial_JJ task_NN1 ._. 
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<s>
The_AT results_NN2 demonstrate_VV0 that_CST the_AT non-negativity_JJ constraints_NN2 introduce_VV0 slight_JJ gains_NN2 at_II the_AT most_RGT disaggregated_JJ level_NN1 ,_, but_CCB slight_JJ losses_NN2 at_II the_AT aggregated_JJ levels_NN2 ._. 
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<s>
See_VV0 Fig._NN1 2_MC for_IF a_AT1 visual_JJ illustration_NN1 ._. 
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We_PPIS2 now_RT turn_VV0 to_TO solve_VVI these_DD2 equation_NN1 order_NN1 by_II order_NN1 ._. 
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<s>
Although_CS mathematical_JJ models_NN2 have_VH0 been_VBN successfully_RR made_VVN for_IF scan-based_JJ worms_NN2 ,_, they_PPHS2 are_VBR difficult_JJ to_TO make_VVI for_IF topology-based_JJ worms_NN2 because_CS such_DA models_NN2 must_VM not_XX have_VHI the_AT homogeneous_JJ assumption_NN1 ._. 
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<s>
Currently_RR ,_, we_PPIS2 are_VBR using_VVG terms_NN2 and_CC search_NN1 volume_NN1 indices_NN2 that_CST have_VH0 been_VBN proposed_VVN by_II previous_JJ authors_NN2 and_CC studies_NN2 ._. 
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<s>
For_REX21 example_REX22 ,_, respiratory_JJ traces_NN2 obtained_VVN from_II a_AT1 plethysmograph_NN1 used_VVN on_II rodents_NN2 in_II experimental_JJ sleep_NN1 apnea_NN1 research_NN1 exhibit_VV0 many_DA2 abrupt_JJ changes_NN2 in_II their_APPGE periodic_JJ components_NN2 as_II the_AT rat_NN1 naturally_RR changes_VVZ their_APPGE breathing_NN1 pattern_NN1 in_II the_AT course_NN1 of_IO its_APPGE sleep-wake_JJ activities_NN2 (_( Han_NP1 et_RA21 al_RA22 ._. 
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<s>
2002_MC ;_; Nakamura_NP1 ,_, Fukuda_NP1 ,_, and_CC Kuwaki_NP1 2003_MC )_) ._. 
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<s>
We_PPIS2 consider_VV0 ,_, for_IF >0t>0_FO ,_, the_AT nonlinear_JJ stochastic_JJ dissipative_JJ Hamiltonian_JJ dynamical_JJ system_NN1 represented_VVN by_II the_AT following_JJ nonlinear_JJ ISDE_NN1 ,_, If_CS ,_, the_AT SAW_NN1 is_VBZ pruned_VVN (_( killed_VVN )_) with_IW the_AT probability_NN1 1/2_MF ._. 
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<s>
Furthermore_RR ,_, Table_NN1 10_MC summarizes_VVZ the_AT descriptive_JJ statistics_NN of_IO key_JJ variables_NN2 by_II group_NN1 ._. 
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<s>
The_AT integration_NN1 of_IO different_JJ insights_NN2 coming_VVG from_II complementary_JJ methods_NN2 provides_VVZ the_AT analyst_NN1 with_IW a_AT1 detailed_JJ picture_NN1 of_IO the_AT model_NN1 at_II hand_NN1 ._. 
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<s>
We_PPIS2 took_VVD the_AT price_NN1 indexes_NN2 for_IF these_DD2 six_MC nondurables_NN2 and_CC services_NN2 as_CSA their_APPGE prices_NN2 ._. 
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<s>
It_PPH1 should_VM be_VBI noted_VVN that_CST if_CS the_AT parameter_NN1 values_NN2 of_IO two_MC systems_NN2 differ_VV0 too_RG much_DA1 ,_, the_AT found_VVN periodic_JJ orbit_NN1 may_VM no_RR21 longer_RR22 be_VBI smooth_JJ nor_CC convergent_JJ ._. 
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<s>
Let_VV0 <equation>_FO ,_, for_IF <equation>_FO ,_, be_VBI the_AT Gumbel_NP1 distribution_NN1 ._. 
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The_AT sample_NN1 period_NN1 is_VBZ 2017:1_MC to_II 2019:4_MC ._. 
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<s>
Because_CS the_AT exchangeability_NN1 is_VBZ satisfied_VVN after_II every_AT1 iteration_NN1 of_IO IBSS_NP1 ,_, and_CC not_XX just_RR at_II convergence_NN1 ,_, the_AT result_NN1 is_VBZ not_XX sensitive_JJ to_II stopping_VVG criteria_NN2 ._. 
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<s>
Considering_CS21 that_CS22 luggage_NN1 does_VDZ affect_VVI dpw_NNU on_II both_DB2 sides_NN2 ,_, dpw_NNU of_IO W2_FO ,_, W3_FO ,_, R2_FO and_CC R3_FO on_II the_AT left_JJ and_CC right_NN1 are_VBR plotted_VVN in_II figure_NN1 11_MC ._. 
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<s>
The_AT equation_NN1 shows_VVZ that_CST for_IF there_RL to_TO be_VBI a_AT1 nonzero_NN1 score_NN1 between_II two_MC nodes_NN2 p_ZZ1 and_CC q_ZZ1 ,_, there_EX must_VM be_VBI at_RR21 least_RR22 a_AT1 pair_NN of_IO nodes_NN2 u_ZZ1 and_CC v_ZZ1 connecting_JJ p_ZZ1 and_CC q_ZZ1 ._. 
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<s>
The_AT positivity_NN1 of_IO <equation>_FO in_II Assumption_NN1 4.3_MC rules_NN2 out_RP the_AT cases_NN2 when_RRQ <equation>_FO or_CC <equation>_FO (_( see_VV0 point_NN1 (_( a_ZZ1 )_) of_IO Remark_NN1 4.1_MC )_) ._. 
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<s>
This_DD1 second_NNT1 scenario_NN1 can_VM be_VBI modeled_VVN as_CSA follows_VVZ ._. 
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<s>
However_RR ,_, the_AT second_MD factor_NN1 (_( Productive_JJ capacity_NN1 )_) and_CC the_AT third_MD one_PN1 (_( Competitivenes_NP1 and_CC agglomeration_NN1 )_) appear_VV0 to_TO be_VBI non-significant_JJ ._. 
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<s>
For_IF the_AT purpose_NN1 of_IO operon_NN1 detection_NN1 ,_, small_JJ values_NN2 of_IO k_ZZ1 and_CC ?_ZZ1 make_VV0 sense_NN1 ._. 
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<s>
Panel_NN1 A_ZZ1 plots_NN2 intent-to-treat_NN1 (_( ITT_NP1 )_) and_CC treatment-on-the-treated_NN1 (_( TOT_NN1 )_) estimates_VVZ for_IF medical_JJ spending_NN1 ._. 
</s>
<s>
The_AT temporal_JJ behaviour_NN1 of_IO the_AT equilibrium_NN1 fluctuations_NN2 of_IO the_AT current_NN1 has_VHZ been_VBN studied_VVN in_II reference_NN1 &lsqb;_( 38_MC &rsqb;_) ._. 
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<s>
Corollary_NN1 3.4_MC suggests_VVZ that_CST the_AT insured_VVN should_VM always_RR fully_RR retain_VVI the_AT risk_NN1 below_II the_AT level_NN1 <equation>_FO ,_, regardless_RR of_IO the_AT dependence_NN1 structure_NN1 between_II <equation>_FO and_CC <equation>_FO ._. 
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<s>
Looking_VVG at_II the_AT number_NN1 of_IO studies_NN2 which_DDQ quantify_VV0 trade_NN1 effects_NN2 of_IO currency_NN1 unions_NN2 ,_, it_PPH1 might_VM not_XX be_VBI exaggerated_VVN to_TO say_VVI that_CST the_AT trade_NN1 effects_NN2 of_IO currency_NN1 unions_NN2 or_CC of_IO the_AT European_JJ Monetary_JJ Union_NN1 are_VBR an_AT1 "_" over_NN1 researched_VVN "_" topic_NN1 ._. 
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<s>
There_EX is_VBZ no_AT external_JJ field_NN1 applied_VVD ._. 
</s>
<s>
First_MD ,_, it_PPH1 provides_VVZ clear_JJ derivations_NN2 for_IF the_AT MLEs_NP2 and_CC LSEs_NP2 of_IO the_AT q-Weibull_JJ parameters_NN2 and_CC compares_VVZ their_APPGE performance_NN1 through_II a_AT1 simulation_NN1 study_NN1 ._. 
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<s>
The_AT PS_NN1 Relaxed_VVD Lasso_NP1 and_CC the_AT MIMI_JJ model_NN1 have_VH0 the_AT smallest_JJT Log-Score_NP1 compared_VVD with_IW the_AT other_JJ methods_NN2 ._. 
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<s>
Denote_VV0 N(t)_NN1 as_II a_AT1 stochastic_JJ Poisson_NP1 process_NN1 with_IW intensity_NN1 k1(t)_FO and_CC zii=1∞_FO as_CSA independent_JJ identically_RR distributed_VVN (_( iid_NN1 )_) insurance_NN1 claims_NN2 ._. 
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<s>
The_AT initial_JJ attempt_NN1 to_TO evaluate_VVI the_AT quality_NN1 of_IO ETR_NN1 assemblies_NN2 was_VBDZ centromere-specific_JJ (_( Bzikadze_NP1 and_CC Pevzner_NP1 ,_, 2019_MC )_) and_CC has_VHZ not_XX resulted_VVN in_II a_AT1 general_JJ quality_NN1 assessment_NN1 tool_NN1 for_IF ETR_NN1 assemblies_NN2 ._. 
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<s>
We_PPIS2 thank_VV0 Tal_NP1 Agranov_NP1 for_IF the_AT critical_JJ reading_NN1 of_IO the_AT paper_NN1 ._. 
</s>
<s>
A_AT1 variety_NN1 of_IO models_NN2 have_VH0 been_VBN compared_VVN for_IF the_AT conditional_JJ intensity_NN1 of_IO arrivals_NN2 of_IO computer_NN1 network_NN1 traffic_NN1 events_NN2 ._. 
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<s>
The_AT NI_NP1 is_VBZ a_AT1 special_JJ case_NN1 of_IO general_JJ bilevel_NN1 problems_NN2 ._. 
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<s>
An_AT1 extensive_JJ number_NN1 of_IO short-read_JJ alignment_NN1 techniques_NN2 and_CC tools_NN2 have_VH0 been_VBN introduced_VVN to_TO address_VVI this_DD1 challenge_NN1 emphasizing_VVG different_JJ aspects_NN2 of_IO the_AT process_NN1 (_( Fonseca_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ._. 
</s>
<s>
When_CS mixing_VVG parameter_NN1 0.6_MC ≤_FO ≤_FO 0.7_MC ,_, our_APPGE method_NN1 has_VHZ significantly_RR better_JJR performance_NN1 than_CSN the_AT original_JJ methods_NN2 ._. 
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<s>
A_AT1 condition_NN1 requiring_VVG the_AT presence_NN1 of_IO an_AT1 InterPro_NN1 signature_NN1 is_VBZ the_AT normal_JJ starting_NN1 point_NN1 for_IF preparing_VVG a_AT1 rule_NN1 ._. 
</s>
<s>
We_PPIS2 record_VV0 MSEs_NN2 from_II the_AT 0th_FO iteration_NN1 (_( i.e._REX ,_, initialization_NN1 stage_NN1 )_) and_CC set_VV0 the_AT sketch_NN1 dimension_NN1 to_TO be_VBI m_NNU at_II every_AT1 iteration_NN1 ._. 
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<s>
As_CSA reported_VVN in_II the_AT Internet_NN1 Appendix_NN1 ,_, insignificant_JJ coefficients_NN2 are_VBR the_AT most_RGT frequent_JJ outcome_NN1 ,_, with_IW significant_JJ coefficients_NN2 split_VVN between_II positive_JJ and_CC negative_JJ ,_, suggesting_VVG that_CST the_AT lack_NN1 of_IO a_AT1 relation_NN1 between_II average_JJ profitability_NN1 and_CC common_JJ ownership_NN1 is_VBZ not_XX due_II21 to_II22 heterogeneous_JJ effects_NN2 within_II industries_NN2 ._. 
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<s>
Given_VVN the_AT vital_JJ role_NN1 played_VVN by_II financial_JJ institutions_NN2 in_II mitigating_JJ problems_NN2 associated_VVN with_IW information_NN1 asymmetry_NN1 and_CC agency_NN1 costs_NN2 and_CC in_II easing_VVG the_AT firms_NN2 '_NULL access_VV0 to_II capital_NN1 ,_, corporate_JJ debt_NN1 levels_NN2 are_VBR expected_VVN to_TO increase_VVI with_IW financial_JJ development_NN1 (_( Leland_NP1 and_CC Pyle_NP1 1977_MC ;_; Diamond_NN1 1984_MC )_) ._. 
</s>
<s>
Additionally_RR ,_, the_AT time_NNT1 evolution_NN1 of_IO the_AT 11_MC industry_NN1 sectors_NN2 is_VBZ not_XX necessarily_RR the_AT same_DA ._. 
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<s>
In_II the_AT figure_NN1 ,_, together_RL with_IW the_AT spectrum_NN1 of_IO the_AT ladder_NN1 ,_, we_PPIS2 report_VV0 the_AT numerically_RR calculated_VVN spectrum_NN1 of_IO the_AT XXZ_NP1 spin-chain_NN1 in_II a_AT1 staggered_JJ field_NN1 which_DDQ is_VBZ a_AT1 mean_JJ field_NN1 description_NN1 of_IO the_AT ladder_NN1 ._. 
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<s>
To_TO estimate_VVI China_NP1 '_NULL s_ZZ1 provincial_JJ physical_JJ capital_NN1 stock_NN1 ,_, we_PPIS2 use_VV0 the_AT perpetual_JJ inventory_NN1 method_NN1 ;_; for_IF more_DAR details_NN2 ,_, see_VV0 Zhang_NP1 (_( 2008_MC )_) ._. 
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<s>
Fig._NN1 7_MC Results_NN2 from_II the_AT designs_NN2 under_II the_AT 0-1_MCMC model_NN1 selection_NN1 loss_NN1 with_IW n=7_FO placentas_NN2 in_II Section_NN1 5_MC ._. 
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<s>
The_AT difficulty_NN1 in_II pricing_JJ MLS_NNU2 '_NULL s_ZZ1 stems_VVZ from_II the_AT fact_NN1 that_CST the_AT MLS_NNU2 market_NN1 is_VBZ incomplete_JJ as_II the_AT underlying_JJ mortality_NN1 rates_NN2 are_VBR usually_RR untradeable_JJ in_II financial_JJ markets_NN2 ._. 
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<s>
However_RR ,_, in_II other_JJ settings_NN2 this_DD1 extension_NN1 may_VM be_VBI more_RGR important_JJ ._. 
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<s>
In_II the_AT remainder_NN1 ,_, we_PPIS2 will_VM make_VVI repeatedly_RR use_NN1 of_IO the_AT following_JJ assumption_NN1 ,_, which_DDQ ,_, to_TO improve_VVI the_AT readability_NN1 of_IO the_AT paper_NN1 ,_, will_VM be_VBI referred_VVN as_CSA (_( A_ZZ1 )_) ._. 
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<s>
Many_DA2 CF_VV0 algorithms_NN2 associate_VV0 a_AT1 user/an_FU item_NN1 with_IW one_MC1 of_IO subgroups_NN2 by_II explicit_JJ or_CC implicit_JJ features_NN2 ._. 
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<s>
We_PPIS2 note_VV0 that_CST the_AT numerical_JJ efficiency_NN1 of_IO Algorithm_NN1 5_MC ,_, as_II31 well_II32 as_II33 that_DD1 of_IO the_AT original_JJ NUTS_NN2 algorithm_NN1 ,_, can_VM be_VBI improved_VVN by_II tuning_VVG the_AT covariance_NN1 C_ZZ1 (_( see_VV0 the_AT numerical_JJ results_NN2 in_II Sect._NP1 4.3_MC )_) ._. 
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<s>
We_PPIS2 apply_VV0 the_AT following_JJ data_NN filters_NN2 ._. 
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<s>
The_AT study_NN1 found_VVD that_CST the_AT free_JJ velocity_NN1 is_VBZ 1.4_MC and_CC 1.7_MC m_ZZ1 s1_FO for_IF the_AT bending_NN1 walking_NN1 and_CC normal_JJ walking_NN1 ,_, respectively_RR ,_, while_CS it_PPH1 was_VBDZ about_RG 0.73_MC m_ZZ1 s1_FO for_IF crawling_VVG ._. 
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<s>
Tables_NN2 4_MC and_CC 5_MC show_VV0 the_AT performance_NN1 of_IO a_AT1 set_NN1 of_IO baseline_NN1 classifiers_NN2 (_( SVM_NP1 ,_, GPR_NP1 ,_, KNN-5_MC )_) and_CC the_AT various_JJ rotation_NN1 variants_NN2 after_II adding_VVG noise_NN1 dimensions_NN2 to_II the_AT data_NN sets_VVZ IRIS_NP1 and_CC IONO_NP1 ._. 
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<s>
In_II Figure_NN1 4d_NNU ,_, we_PPIS2 examine_VV0 the_AT effect_NN1 of_IO pre-treatment_JJ sexual_JJ function_NN1 level_NN1 on_II recovery_NN1 shape_NN1 by_II stratifying_VVG those_DD2 curves_NN2 by_II age_NN1 ._. 
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<s>
EvoLSTM_NP1 is_VBZ trained_VVN from_II a_AT1 set_NN1 of_IO pairs_NN2 of_IO aligned_JJ ancestral/descendant_FU sequences_NN2 ._. 
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Among_II the_AT three_MC CIs_NN2 ,_, the_AT asymptotic_JJ CI_NN1 is_VBZ the_AT narrowest_JJT ._. 
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<s>
To_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, the_AT effect_NN1 of_IO relative_JJ sample_NN1 sizes_NN2 on_II the_AT efficiency_NN1 of_IO rO_NN1 has_VHZ yet_RR to_TO be_VBI investigated_VVN ._. 
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<s>
The_AT remainder_NN1 of_IO the_AT article_NN1 is_VBZ organized_VVN as_CSA follows_VVZ ._. 
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<s>
A_AT1 rule_NN1 may_VM contain_VVI further_JJR sets_NN2 of_IO conditions_NN2 known_VVN as_II '_NULL special_JJ conditions_NN2 '_NULL that_CST are_VBR used_VVN to_TO define_VVI particular_JJ subgroups_NN2 of_IO the_AT main_JJ set_NN1 of_IO records_NN2 ._. 
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<s>
However_RR ,_, one_MC1 user_NN1 may_VM be_VBI concentrative_JJ on_II more_DAR than_CSN one_MC1 category_NN1 and_CC one_MC1 item_NN1 may_VM belong_VVI to_II multiple_JJ genres_NN2 in_II actual_JJ situation_NN1 ._. 
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<s>
In_II this_DD1 case_NN1 ,_, the_AT formulas_NN2 in_II &lsqb;_( 22_MC &rsqb;_) can_VM be_VBI partially_RR simplified_VVN ,_, but_CCB they_PPHS2 still_RR involve_VV0 several_DA2 integrations_NN2 and_CC it_PPH1 does_VDZ not_XX seem_VVI trivial_JJ to_TO reduce_VVI them_PPHO2 to_II (_( 2.3_MC )_) ._. 
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<s>
The_AT OFI_NN1 has_VHZ proved_VVN useful_JJ in_II many_DA2 areas_NN2 of_IO statistical_JJ research_NN1 including_II the_AT algorithm_NN1 (_( Louis_NP1 ,_, 1982_MC )_) ,_, generalized_JJ linear_JJ models_NN2 (_( Firth_NN1 ,_, 1993_MC )_) ,_, semiparametric_JJ models_NN2 (_( Murphy_NP1 and_CC van_NP1 der_NP1 Vaart_NP1 ,_, 1999_MC )_) ,_, hidden_VVN Markov_NP1 models_NN2 (_( Lystig_NP1 and_CC Hughes_NP1 ,_, 2002_MC )_) and_CC likelihood_NN1 theory_NN1 (_( Reid_NP1 ,_, 2003_MC )_) to_TO name_VVI a_AT1 few_DA2 ._. 
</s>
<s>
This_DD1 increases_VVZ the_AT reliability_NN1 of_IO these_DD2 tools_NN2 and_CC improves_VVZ recall_NN1 rate_NN1 as_CSA sequencing_NN1 depth_NN1 is_VBZ reduced_VVN ._. 
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<s>
An_AT1 open_JJ challenge_NN1 is_VBZ how_RRQ to_TO compare_VVI quantitatively_RR ,_, reliably_RR and_CC systematically_RR two_MC given_JJ mutational_JJ signatures_NN2 ._. 
</s>
<s>
In_II "_" Web_NN1 Appendix_NN1 C_ZZ1 "_" ,_, Figures_NN2 S6_FO and_CC S7_FO present_JJ similar_JJ colored_JJ surfaces_NN2 but_II21 for_II22 and_CC ;_; the_AT results_NN2 are_VBR essentially_RR the_AT same_DA ._. 
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<s>
The_AT red_JJ segments_NN2 ,_, which_DDQ highlight_VV0 the_AT satisfied_JJ bonds_NN2 ,_, are_VBR useful_JJ to_TO keep_VVI track_NN1 of_IO the_AT energy_NN1 contribution_NN1 of_IO the_AT structures_NN2 ._. 
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<s>
Suppose_VV0 our_APPGE data_NN undergoes_VVZ a_AT1 change_NN1 from_II pre?_FO (_( 00_MC ,_, )_) Xpre?N_NP1 (_( 00_VV0 ,_, )_) to_II post?_FO (_( 00_MC ,_, )_) Xpost?_FO (_( 00_MC ,_, )_) this_DD1 will_VM cause_VVI the_AT data_NN points_VVZ to_TO spread_VVI out_RP in_II the_AT directions_NN2 of_IO the_AT principal_JJ components_NN2 ._. 
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<s>
A_AT1 common_JJ critical_JJ issue_NN1 holding_VVG by_II methods_NN2 above_RL is_VBZ that_CST they_PPHS2 find_VV0 out_RP only_RR one_MC1 feature_NN1 subset_NN1 in_II31 terms_II32 of_II33 SNP–QT_NP1 associations_NN2 for_IF all_DB diagnostic_JJ groups_NN2 ._. 
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<s>
As_CSA in_II the_AT dataset_NN1 studied_VVN in_II Sect._NP1 7_MC ,_, we_PPIS2 consider_VV0 right-censored_JJ response_NN1 variables_NN2 with_IW uk_NN1 equal_JJ to_II 50_MC ,_, for_IF any_DD =1_FO ,_, ,_, k=1_FO ,_, ,_, p_ZZ1 ._. 
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<s>
Furthermore_RR ,_, our_APPGE findings_NN2 show_VV0 that_CST the_AT effect_NN1 of_IO news_NN1 on_II expectations_NN2 is_VBZ ,_, on_II impact_NN1 ,_, larger_JJR than_CSN the_AT effect_NN1 on_II current_JJ assessment_NN1 ._. 
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<s>
Especially_RR when_CS multiple_JJ hypotheses_NN2 are_VBR tested_VVN ,_, permutation_NN1 methods_NN2 are_VBR often_RR powerful_JJ since_CS they_PPHS2 can_VM take_VVI into_II account_NN1 the_AT dependence_NN1 structure_NN1 in_II the_AT data_NN (_( Westfall_NP1 and_CC Young_NP1 ,_, 1993_MC ;_; Hemerik_NP1 and_CC Goeman_NP1 ,_, 2018b_FO ;_; Hemerik_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ._. 
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<s>
In_II the_AT following_JJ theorem_NN1 ,_, we_PPIS2 establish_VV0 that_CST the_AT estimator_NN1 <equation>_FO is_VBZ inadmissible_JJ ._. 
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<s>
Multiplying_VVG equation_NN1 by_II the_AT characteristic_JJ times_NNT2 τ_NULL a_AT1 ,_, we_PPIS2 reach_VV0 the_AT final_JJ result_NN1 ,_, This_DD1 result_NN1 is_VBZ called_VVN the_AT fundamental_JJ theorem_NN1 of_IO asset_NN1 pricing_NN1 (_( FTAP_NP1 )_) ._. 
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<s>
For_REX21 instance_REX22 ,_, the_AT volatility-adjusted_JJ hybrid_JJ scheme_NN1 '_NULL s_ZZ1 welfare_NN1 gain_NN1 is_VBZ 3.9%_FO compared_VVN to_II the_AT OI_UH plan_NN1 if_CS =3_FO ._. 
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<s>
The_AT point_NN1 estimates_VVZ for_IF the_AT ad_NN1 libitum_NN1 group_NN1 are_VBR plotted_VVN by_II solid_JJ lines_NN2 and_CC the_AT interval_NN1 estimates_VVZ with_IW dark_JJ gray_JJ bands_NN2 ._. 
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<s>
The_AT parameters_NN2 m_ZZ1 ,_, K_ZZ1 and_CC maxsmax_NN1 are_VBR thus_RR increased_VVN together_RL as_CSA (_( ,_, ,_, max_NN1 )_) =_FO (_( 502,1052,1062_MC )_) (_( mn_NNU ,_, Kn_NP1 ,_, snmax_NN1 )_) =_FO (_( 502n,1052n,1062n_FO )_) for_IF ∈0_FO ,_, ,_, 5n∈0_FO ,_, ,_, 5_MC ._. 
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<s>
In_II fact_NN1 ,_, "_" in_II many_DA2 clustering_NN1 problems_NN2 one_PN1 is_VBZ particularly_RR interested_JJ in_II a_AT1 characterization_NN1 of_IO the_AT clusters_NN2 by_II31 means_II32 of_II33 typical_JJ or_CC representative_JJ objects_NN2 &lsqb;_( time_VV0 series_NN &rsqb;_) ._. 
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<s>
It_PPH1 is_VBZ also_RR related_VVN to_II Allen_NP1 and_CC Gale_NP1 '_NULL s_ZZ1 (_( 1997_MC )_) study_NN1 as_CSA we_PPIS2 compare_VV0 preference_NN1 measures_NN2 conditionally_RR to_II the_AT plan_NN1 '_NULL s_ZZ1 experience_NN1 (_( i.e._REX ,_, ex_II post_NN1 )_) ;_; the_AT authors_NN2 show_VV0 that_CST ,_, without_IW mandatory_JJ participation_NN1 ,_, the_AT system_NN1 will_VM break_VVI down_RP and_CC go_VVI back_RP to_II the_AT market_NN1 solution_NN1 with_IW a_AT1 probability_NN1 of_IO one_PN1 ._. 
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<s>
Importantly_RR ,_, this_DD1 gap_NN1 vanishes_VVZ as_CSA k_ZZ1 goes_VVZ to_II infinity_NN1 and_CC becomes_VVZ larger_JJR for_IF smaller_JJR k_ZZ1 ._. 
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The_AT empirical_JJ critical_JJ value_NN1 of_IO this_DD1 network_NN1 is_VBZ r=0.018_FO ._. 
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<s>
To_TO guarantee_VVI that_CST the_AT model_NN1 is_VBZ a_AT1 random_JJ utility_NN1 model_NN1 (_( RUM_NN1 )_) ,_, it_PPH1 is_VBZ worth_II noting_VVG that_CST the_AT condition_NN1 of_IO the_AT inclusive_JJ value_NN1 <equation>_FO takes_VVZ values_NN2 between_II zero_MC and_CC 1_MC1 which_DDQ is_VBZ satisfied_JJ ._. 
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<s>
Determining_VVG a_AT1 minimal_JJ number_NN1 of_IO epochs_NN2 is_VBZ a_AT1 difficult_JJ general_JJ problem_NN1 ,_, but_CCB our_APPGE results_NN2 suggest_VV0 a_AT1 rule_NN1 of_IO thumb_NN1 of_IO '_NULL 1_MC1 million_NNO divided_VVN by_II the_AT number_NN1 of_IO cells_NN2 in_II the_AT dataset_NN1 '_NULL epochs_NN2 for_IF first_MD pass_NN1 analysis_NN1 ._. 
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<s>
This_DD1 mechanism_NN1 demonstrates_VVZ that_CST two_MC exceptional_JJ phenomena_NN2 beyond_II the_AT standard_JJ Landau_NP1 '_NULL s_ZZ1 paradigm_NN1 ,_, i.e._REX the_AT non-Landau_NP1 quantum_NN1 phase_NN1 transitions_NN2 and_CC the_AT non-fermi_NN2 liquid_NN1 may_VM be_VBI connected_VVN :_: a_AT1 non-Landau_NP1 quantum_NN1 phase_NN1 transition_NN1 can_VM have_VHI a_AT1 large_JJ anomalous_JJ dimension_NN1 1_MC1 ,_, which_DDQ physically_RR justifies_VVZ and_CC facilitates_VVZ a_AT1 perturbative_JJ calculation_NN1 of_IO the_AT boson–fermion_NN1 coupling_NN1 fixed_JJ point_NN1 ._. 
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<s>
An_AT1 interesting_JJ open_JJ problem_NN1 would_VM be_VBI to_TO obtain_VVI the_AT analogue_NN1 of_IO formula_NN1 (_( 7.8_MC )_) when_RRQ the_AT symbol_NN1 has_VHZ FH_NP1 singularities_NN2 ._. 
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<s>
Propose_VV0 a_AT1 candidate_NN1 model_NN1 index_NN1 <equation>_FO from_II <equation>_FO using_VVG (_( 15_MC )_) ._. 
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<s>
We_PPIS2 assess_VV0 the_AT relative_JJ importance_NN1 of_IO these_DD2 two_MC explanations_NN2 by_II studying_VVG how_RRQ the_AT outcomes_NN2 of_IO children_NN2 who_PNQS move_VV0 across_II areas_NN2 vary_VV0 with_IW the_AT age_NN1 at_II which_DDQ they_PPHS2 move_VV0 ._. 
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<s>
But_CCB in_II the_AT experimental_JJ part_NN1 ,_, we_PPIS2 does_VDZ not_XX make_VVI such_DA assumption_NN1 ._. 
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<s>
In_II Fig._NN1 1_MC1 ,_, we_PPIS2 show_VV0 some_DD typical_JJ barycenters_VVZ obtained_VVN by_II our_APPGE algorithm_NN1 in_II this_DD1 setting_NN1 ._. 
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<s>
So_RR using_VVG Eq_NN1 ._. 
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<s>
(_( 38_MC )_) ,_, the_AT effective_JJ temperature_NN1 can_VM be_VBI computed_VVN 0<<1_FO ,_, Teff_NP1 has_VHZ a_AT1 similar_JJ scaling_NN1 form_NN1 as_II the_AT one_PN1 obtained_VVN in_II Ref_NN1 ._. 
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<s>
However_RR ,_, the_AT theoretical_JJ properties_NN2 of_IO standard_JJ survival_NN1 analysis_NN1 methods_NN2 under_II covariateadaptive_JJ randomization_NN1 remain_VV0 largely_RR unknown_JJ ,_, although_CS covariateadaptive_JJ randomization_NN1 has_VHZ been_VBN used_VVN in_II survival_NN1 analysis_NN1 for_IF a_AT1 long_JJ time_NNT1 ._. 
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<s>
This_DD1 results_VVZ in_II a_AT1 PM_NP1 sampling_NN1 scheme_NN1 with_IW a_AT1 slightly_RR perturbed_JJ posterior_NN1 ._. 
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<s>
Of_RR21 course_RR22 ,_, this_DD1 value_NN1 is_VBZ finite_JJ ,_, but_CCB it_PPH1 is_VBZ practically_RR difficult_JJ to_TO estimate_VVI this_DD1 value_NN1 using_VVG classical_JJ estimators_NN2 of_IO the_AT variance_NN1 ._. 
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<s>
The_AT existence_NN1 of_IO such_DA a_AT1 transition_NN1 has_VHZ been_VBN proven_VVN (_( in_II a_AT1 slightly_RR weaker_JJR sense_NN1 )_) ,_, as_II31 well_II32 as_II33 lower_JJR and_CC upperbounds_VVZ on_II the_AT threshold_NN1 sat_VVD ,_, that_CST become_VV0 tighter_JJR and_CC tighter_JJR as_CSA k_ZZ1 grows_VVZ ._. 
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<s>
The_AT data_NN contain_VV0 three_MC fluorescent-labeled_JJ markers_NN2 ,_, namely_REX CD3_FO ,_, CD5_FO ,_, and_CC CD19_FO ,_, on_II a_AT1 sample_NN1 of_IO 8183_MC cells_NN2 derived_VVN from_II the_AT lymph_NN1 nodes_NN2 of_IO one_MC1 patient_NN1 diagnosed_VVN with_IW DLBCL_NP1 ._. 
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<s>
In_BCL21 order_BCL22 to_TO choose_VVI the_AT pA_NN1 unsuitable_JJ sites_NN2 we_PPIS2 use_VV0 fractal_JJ landscapes_NN2 which_DDQ are_VBR constructed_VVN by_II using_VVG the_AT fractional_JJ Brownian_JJ motion_NN1 &lsqb;_( 13_MC &rsqb;_) ,_, which_DDQ is_VBZ a_AT1 generalization_NN1 of_IO a_AT1 random_JJ process_NN1 X(t)_NP1 with_IW Gaussian_JJ increments_NN2 with_IW mean_JJ zero_NN1 and(1)var_NN1 (_( X_ZZ1 (_( t2_FO )_) X(t1)_FO )_) |_NULL t2t1_FO |_NULL 2H,0<H<1.The_FO Hurst_NP1 exponent_NN1 ,_, H_ZZ1 ,_, determines_VVZ the_AT roughness_NN1 of_IO the_AT landscape_NN1 ._. 
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<s>
Optimizing_VVG equation_NN1 (_( 2.2_MC )_) by_II block_NN1 gradient_NN1 descent_NN1 ,_, while_CS possible_JJ ,_, is_VBZ highly_RR inefficient_JJ due_II21 to_II22 having_VHG to_TO deal_VVI with_IW the_AT discontinuities_NN2 in_II the_AT objective_JJ function_NN1 space_NN1 ._. 
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<s>
It_PPH1 makes_VVZ sense_NN1 to_TO think_VVI that_CST costs_VVZ arising_VVG from_II depreciation_NN1 due_JJ to_TO balance_VVI sheets_NN2 and_CC cost_NN1 of_IO production_NN1 effects_NN2 may_VM be_VBI alleviated_VVN through_II competitiveness_NN1 channel_NN1 for_IF these_DD2 firms_NN2 ._. 
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<s>
Further_JJR evidence_NN1 that_CST most_DAT of_IO the_AT rise_NN1 in_II market_NN1 power_NN1 occurs_VVZ within_II industry_NN1 comes_VVZ from_II comparison_NN1 of_IO our_APPGE results_NN2 with_IW those_DD2 based_VVN on_II aggregate_JJ data_NN (_( industry-level_NN1 or_CC economy-wide_JJ )_) ._. 
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<s>
Then_RT the_AT biologically_RR feasible_JJ region_NN1 of_IO solution_NN1 for_IF our_APPGE mathematical_JJ model_NN1 of_IO C._NP1 Auris_NP1 infections_NN2 (_( 1_MC1 )_) is<equation>and_FO the_AT following_JJ Lemma_NN1 holds_VVZ ._. 
</s>
<s>
Hence_RR ,_, we_PPIS2 fit_VV0 a_AT1 least_DAT squares_NN2 regression_NN1 line_NN1 to_II the_AT past_JJ values_NN2 of_IO <equation>_FO and_CC terminate_VV0 Algorithm_NN1 1_MC1 once_RR the_AT gradient_NN1 of_IO the_AT regression_NN1 line_NN1 becomes_VVZ negative_JJ (_( see_VV0 Tan_NN1 2018_MC )_) ._. 
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<s>
Boulatov_NP1 and_CC Dieckmann_NP1 (_( 2013_MC )_) expressed_VVD positive_JJ opinions_NN2 about_II the_AT involvement_NN1 of_IO disaster_NN1 insurance_NN1 funds_NN2 and_CC noted_VVD that_CST well-designed_JJ policies_NN2 can_VM promote_VVI demand_NN1 in_II the_AT private_JJ market_NN1 ._. 
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<s>
Ancillary_JJ results_NN2 and_CC the_AT proofs_NN2 of_IO the_AT main_JJ results_NN2 follow_VV0 in_II a_AT1 separate_JJ subsection_NN1 ._. 
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<s>
This_DD1 bound_NN1 is_VBZ expressed_VVN through_II pH=aHDG/D_FU ,_, where_CS aH?U(0,1)_FO is_VBZ the_AT unknown_JJ probability_NN1 that_CST a_AT1 prevalent_JJ diagnosed_VVD MSM_NP1 who_PNQS has_VHZ attended_VVN a_AT1 GUM_NN1 clinic_NN1 in_II 2012_MC was_VBDZ newly_RR diagnosed_VVN that_DD1 year_NNT1 ._. 
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<s>
Whenever_RRQV the_AT numéraire_NN1 <equation>_FO is_VBZ tradable_JJ ,_, an_AT1 ELMM_NP1 corresponds_VVZ to_II a_AT1 risk-neutral_JJ measure_NN1 (_( see_VV0 Sect._NP1 3_MC )_) ,_, which_DDQ has_VHZ been_VBN precisely_RR characterised_VVN in_II the_AT previous_JJ sections_NN2 of_IO the_AT paper_NN1 ._. 
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<s>
The_AT overall_JJ performance_NN1 was_VBDZ measured_VVN by_II average_JJ precision_NN1 (_( MAP_NN1 )_) (_( approximates_VVZ the_AT area_NN1 under_II the_AT curve_NN1 )_) of_IO PR_NP1 curve_NN1 (_( Manning_NP1 et_RA21 al._RA22 ,_, 2008_MC )_) ._. 
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<s>
Thus_RR Lemma_NN1 3.5_MC (_( a_ZZ1 )_) is_VBZ true_JJ ._. 
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<s>
This_DD1 asymmetry_NN1 translates_VVZ into_II significant_JJ countercyclical_JJ volatility_NN1 in_II our_APPGE model_NN1 with_IW financial_JJ shocks_NN2 ._. 
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<s>
In_II section_NN1 3_MC ,_, we_PPIS2 introduce_VV0 the_AT variational_JJ method_NN1 and_CC its_APPGE numerical_JJ implementation_NN1 ,_, and_CC in_II section_NN1 4_MC ,_, we_PPIS2 investigate_VV0 the_AT unstable_JJ periodic_JJ orbits_NN2 in_II the_AT GLTS_NP1 ._. 
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<s>
Our_APPGE choice_NN1 of_IO the_AT crucial_JJ ingredients_NN2 (_( summary_NN1 statistics_NN and_CC distances_NN2 based_VVN on_II the_AT underlying_JJ invariant_JJ distribution_NN1 and_CC a_AT1 measure-preserving_JJ numerical_JJ method_NN1 )_) yields_VVZ excellent_JJ results_NN2 even_CS21 when_CS22 applied_VVN to_II ABC_NP1 in_II its_APPGE basic_JJ form_NN1 ._. 
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<s>
For_IF an_AT1 observed_JJ sequence_NN1 of_IO random_JJ variables_NN2 x1:n_FO ,_, PELT_NP1 finds_VVZ ,_, which_DDQ minimise_VV0 the_AT Bayesian_JJ information_NN1 criterion_NN1 (_( Schwarz_NP1 1978_MC )_) ,_, The_AT proofs_NN2 of_IO the_AT theorems_NN2 are_VBR given_VVN in_II Appendix_NN1 ._. 
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<s>
The_AT Laplace_NP1 approximation_NN1 methods_NN2 tend_VV0 to_TO have_VHI larger_JJR time-normalized_JJ ESS_NN1 than_CSN the_AT exact_JJ methods_NN2 (_( all_DB data_NN sets_VVZ apart_II21 from_II22 Leukemia_NP1 )_) ._. 
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<s>
The_AT question_NN1 may_VM arise_VVI :_: "_" What_DDQ is_VBZ the_AT operational_JJ status_NN1 of_IO a_AT1 particular_JJ component_NN1 when_CS a_AT1 system_NN1 fails_VVZ ?_? "_" 
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<s>
The_AT biggest_JJT difference_NN1 between_II the_AT two_MC models_NN2 is_VBZ that_CST in_II Model_NN1 III_MC the_AT society_NN1 as_II a_AT1 whole_NN1 ends_VVZ up_RP closer_RRR to_II the_AT truth_NN1 when_CS confidence_NN1 is_VBZ low_JJ than_CSN it_PPH1 does_VDZ in_II Model_NN1 IV_MC ._. 
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<s>
Finally_RR ,_, in_II both_DB2 fields_NN2 ,_, contextual_JJ information_NN1 beyond_II the_AT raw_JJ sample-by-feature_JJ matrix_NN1 is_VBZ typically_RR available_JJ ._. 
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<s>
Given_VVN the_AT intricacy_NN1 of_IO the_AT covariance_NN1 in_II Formula_NN1 (_( 21_MC )_) ,_, we_PPIS2 do_VD0 not_XX present_VVI a_AT1 thorough_JJ analytical_JJ study_NN1 of_IO the_AT correlation_NN1 structure_NN1 ,_, although_CS we_PPIS2 illustrate_VV0 how_RGQ even_RR high_JJ positive_JJ dependence_NN1 can_VM be_VBI reached_VVN and_CC relate_VV0 this_DD1 possibility_NN1 to_II the_AT richer_JJR cluster_NN1 mean_JJ patterns_NN2 of_IO the_AT EFD_NN1 over_II the_AT FD_NP1 ._. 
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<s>
Now_RT ,_, using_VVG the_AT results_NN2 of_IO section_NN1 3_MC ,_, it_PPH1 is_VBZ easy_JJ to_TO see_VVI that_CST ,_, <equation>_FO at_II any_DD time_NNT1 t_ZZ1 ._. 
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<s>
In_II the_AT present_JJ case_NN1 ,_, however_RR ,_, this_DD1 is_VBZ not_XX immediate_JJ ,_, as_II VA_FW is_VBZ random_JJ ;_; moreover_RR ,_, we_PPIS2 want_VV0 to_TO prove_VVI convergence_NN1 of_IO the_AT conditional_JJ distributions_NN2 ._. 
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<s>
Canada_NP1 ,_, China_NP1 ,_, Mexico_NP1 ,_, Russia_NP1 ,_, Turkey_NP1 ,_, and_CC the_AT EU_NP1 enacted_VVD retaliatory_JJ tariffs_NN2 against_II the_AT United_NP1 States_NP1 ,_, and_CC collectively_RR these_DD2 retaliations_NN2 covered_VVD $127_NNU billion_NNO (_( 8.2%_FO )_) of_IO annual_JJ U.S._NP1 exports_VVZ across_II 7,763_MC products_NN2 ._. 
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<s>
The_AT rest_NN1 of_IO the_AT procedure_NN1 stands_VVZ :_: each_DD1 cohort_NN1 of_IO patients_NN2 is_VBZ assigned_VVN to_II the_AT arm_NN1 by_II using_VVG the_AT obtained_VVN values_NN2 of_IO information_NN1 gain_NN1 δ_NULL ,_, =1_FO ,_, ,_, δ_NULL nj*_FO ,_, j=1_FO ,_, ,_, m_ZZ1 ,_, that_CST are_VBR updated_VVN once_RR the_AT outcomes_NN2 have_VH0 been_VBN observed_VVN ._. 
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<s>
The_AT cycle_NN1 is_VBZ completed_VVN by_II driving_VVG back_RP the_AT system_NN1 to_II the_AT equilibrium_NN1 state_VV0 A._NNU In_II the_AT setting_NN1 of_IO reference_NN1 ,_, the_AT measurement_NN1 is_VBZ taken_VVN on_RP the_AT equilibrium_NN1 state_NN1 A_ZZ1 (_( light_JJ blue_JJ arrow_NN1 )_) and_CC work_NN1 is_VBZ extracted_VVN (_( light_JJ orange_JJ arrow_NN1 )_) from_II the_AT resulting_JJ state_NN1 ._. 
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<s>
We_PPIS2 then_RT developed_VVD several_DA2 skeleton_NN1 builders_NN2 to_TO visualize_VVI vasculature_NN1 morphologies_NN2 in_II various_JJ styles_NN2 ,_, making_VVG it_PPH1 possible_JJ to_TO visually_RR analyze_VVI their_APPGE structure_NN1 (_( e.g._REX how_RRQ each_DD1 section_NN1 is_VBZ sampled_VVN and_CC whether_CSW there_EX is_VBZ an_AT1 overlapping_JJ between_II or_CC within_II the_AT sections_NN2 or_CC not_XX )_) and_CC the_AT connectivity_NN1 between_II its_APPGE different_JJ components_NN2 (_( segments_NN2 or_CC sectionsrefer_VV0 to_II Fig._NN1 1_MC1 )_) ._. 
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<s>
Many_DA2 physical_JJ systems_NN2 such_II21 as_II22 magnetic_JJ traps_NN2 &lsqb;_( 13_MC &rsqb;_) ,_, electron_NN1 magnetotransport_NN1 in_II classical_JJ and_CC quantum_NN1 wells_NN2 &lsqb;_( 14_MC &rsqb;_) ,_, and_CC particle_NN1 accelerators_NN2 &lsqb;_( 15_MC &rsqb;_) can_VM be_VBI modeled_VVN by_II using_VVG the_AT standard_JJ map_NN1 as_II a_AT1 first_MD approximation_NN1 ._. 
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<s>
To_II this_DD1 end_NN1 ,_, we_PPIS2 compare_VV0 both_RR the_AT primal_JJ and_CC the_AT dual_JJ problem_NN1 with_IW their_APPGE randomised_JJ counterpart_NN1 in_II the_AT frictionless_JJ market_NN1 induced_VVN by_II <equation>_FO and_CC constructed_VVN in_II Sect._NP1 3_MC ._. 
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<s>
The_AT authors_NN2 identified_VVN a_AT1 temperature_NN1 Tonset_NN1 ,_, higher_JJR than_CSN the_AT usual_JJ dynamical_JJ temperature_NN1 Td_NN1 ,_, below_II which_DDQ the_AT system_NN1 memorises_VVZ the_AT initial_JJ condition_NN1 when_CS instantaneously_RR quenched_VVD to_II a_AT1 sufficiently_RR low_JJ temperature_NN1 ._. 
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<s>
The_AT CPU_NN1 times_NNT2 required_VVN by_II the_AT algorithm_NN1 for_IF computing_VVG approximate_JJ designs_NN2 are_VBR noticeably_RR short_JJ ._. 
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<s>
Interpreting_VVG the_AT clustering_NN1 result_NN1 is_VBZ equally_RR important_JJ (_( Kiselev_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ._. 
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<s>
This_DD1 average_JJ value_NN1 represents_VVZ the_AT amount_NN1 of_IO contacts_NN2 spread_VVN over_II the_AT regions_NN2 involved_VVD ._. 
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<s>
Kombi_NN2 provided_VVD us_PPIO2 with_IW a_AT1 longitudinal_JJ data_NN set_VVN with_IW information_NN1 about_II all_DB draws_NN2 conducted_VVN between_II 1998_MC and_CC 2011_MC ._. 
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<s>
As_II the_AT only_JJ difference_NN1 between_II Bayesian_JJ and_CC Bayesian_JJ MLE_NN1 is_VBZ whether_CSW peak_NN1 positions_NN2 are_VBR determined_VVN for_IF z-score_JJ calculation_NN1 ,_, we_PPIS2 conclude_VV0 that_CST the_AT probabilistic_JJ z-score_JJ inference_NN1 have_VH0 a_AT1 great_JJ impact_NN1 on_II the_AT performance_NN1 ._. 
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<s>
In_RR21 particular_RR22 ,_, these_DD2 include_VV0 the_AT dynamic_JJ Nelson–Siegel_NN1 model_NN1 of_IO Diebold_NP1 and_CC Li_NP1 (_( 2006_MC )_) which_DDQ we_PPIS2 adapted_VVD to_II the_AT multiple_JJ curve_NN1 setting_NN1 as_CSA described_VVN in_II Appendix_NN1 B._NP1 Recently_RR ,_, also_RR various_JJ machine_NN1 learning_NN1 approaches_NN2 have_VH0 been_VBN utilised_VVN to_TO forecast_VVI financial_JJ time_NNT1 series_NN ._. 
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<s>
The_AT transition_NN1 took_VVD place_NN1 in_II the_AT period_NN1 about_RG 2010_MC in_II club_NN1 2_MC and_CC club_NN1 3_MC ,_, and_CC narrowing_NN1 of_IO their_APPGE curves_NN2 is_VBZ more_RGR significant_JJ during_II 2010–2014._MCMC 2010_MC is_VBZ the_AT last_MD year_NNT1 of_IO the_AT Eleventh_MD Five-Year_JJ Plan_NN1 in_II China_NP1 ._. 
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<s>
This_DD1 also_RR implies_VVZ that_CST <equation>_FO holds_VVZ -a.e_NNU ._. 
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<s>
As_II a_AT1 consequence_NN1 ,_, the_AT MST_RA ,_, MSN_NP1 and_CC MT_NP1 distributions_NN2 all_DB contain_VV0 the_AT MN_FO distribution_NN1 as_II a_AT1 limiting/special_JJ case_NN1 ._. 
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<s>
Sections_NN2 S4_FO and_CC S5_FO of_IO the_AT supplement_NN1 give_VV0 the_AT more_RGR complex_JJ target_NN1 density_NN1 and_CC sampling_VVG schemes_NN2 required_VVN for_IF estimating_VVG the_AT posterior_JJ distribution_NN1 of_IO the_AT factor_NN1 SV_NP1 model_NN1 ._. 
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<s>
Of_RR21 course_RR22 ,_, for_IF states_NN2 in_II different_JJ modules_NN2 we_PPIS2 can_VM have_VHI an_AT1 eS_FW suppression_NN1 ,_, coming_VVG from_II the_AT overall_JJ OPE_NN1 coefficient_NN1 ._. 
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By_II the_AT fact_NN1 that_CST <equation>_FO for_IF every_AT1 <equation>_FO ,_, the_AT assertion_NN1 follows_VVZ ._. 
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<s>
In_RR21 general_RR22 ,_, the_AT random_JJ sample_NN1 size_NN1 <equation>_FO is_VBZ conditionally_RR binomially_RR distributed_VVN <equation>_FO given_VVN the_AT population_NN1 size_NN1 <equation>_FO and_CC selection_NN1 probability_NN1 p_ZZ1 ._. 
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<s>
Furthermore_RR ,_, there_EX are_VBR numerous_JJ human_JJ proteins_NN2 ,_, where_CS specific_JJ binding_JJ sites_NN2 for_IF chloride_NN1 were_VBDR revealed_VVN and/or_CC which_DDQ are_VBR shown_VVN to_TO be_VBI affected_VVN upon_II interaction_NN1 with_IW chloride_NN1 ._. 
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<s>
The_AT BART_NN1 model_NN1 is_VBZ an_AT1 additive_JJ ensemble_NN1 of_IO many_DA2 single_JJ regression_NN1 trees_NN2 with_IW each_DD1 tree_NN1 explaining_VVG a_AT1 small_JJ portion_NN1 of_IO the_AT outcome_NN1 ,_, and_CC it_PPH1 can_VM accommodate_VVI nonlinear_JJ main_JJ effects_NN2 as_II31 well_II32 as_II33 complex_JJ interaction_NN1 effects_NN2 without_IW the_AT need_NN1 to_TO specify_VVI their_APPGE functional_JJ forms_NN2 ._. 
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<s>
This_DD1 table_NN1 presents_NN2 univariate_VV0 correlations_NN2 of_IO college_NN1 characteristics_NN2 with_IW mobility_NN1 statistics_NN ,_, with_IW standard_JJ errors_NN2 in_II parentheses_NN2 ._. 
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<s>
However_RR ,_, the_AT fractional_JJ differential_JJ equation_NN1 approach_NN1 bridges_NN2 a_AT1 solid_JJ connection_NN1 between_II the_AT classical_JJ risk_NN1 model_NN1 and_CC a_AT1 class_NN1 of_IO renewal_NN1 models_NN2 which_DDQ might_VM be_VBI applied_VVN in_II a_AT1 more_RGR sophisticated_JJ model_NN1 ._. 
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<s>
Considering_CS mainly_RR this_DD1 approach_NN1 ,_, several_DA2 authors_NN2 have_VH0 established_VVN constraints_NN2 on_II the_AT coefficients_NN2 of_IO different_JJ non-linear_JJ models_NN2 under_II which_DDQ a_AT1 stationary_JJ solution_NN1 is_VBZ reached_VVN ._. 
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<s>
Xia_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2002_MC )_) proposed_VVD the_AT minimum_JJ average_JJ variance_NN1 estimation_NN1 (_( MAVE_NP1 )_) method_NN1 ,_, while_CS later_RRR ,_, Xia_NP1 (_( 2007_MC )_) proposed_VVD a_AT1 procedure_NN1 similar_JJ to_TO MAVE_VVI ,_, called_VVN the_AT dMAVE_NN1 ._. 
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<s>
This_DD1 result_NN1 can_VM be_VBI surprising_JJ ,_, because_CS for_IF e2=+e1_FO the_AT difference_NN1 between_II two_MC groups_NN2 is_VBZ the_AT same_DA as_CSA for_IF e2=+e1_FO in_II simulation_NN1 A_ZZ1 ,_, except_CS one_MC1 single_JJ cell_NN1 ._. 
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<s>
The_AT latter_DA could_VM make_VVI attempts_NN2 to_TO shorten_VVI the_AT distance_NN1 to_II one_MC1 of_IO its_APPGE neighbors_NN2 ._. 
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<s>
We_PPIS2 address_VV0 these_DD2 limitations_NN2 of_IO previous_JJ studies_NN2 by_II using_VVG the_AT recently_RR developed_JJ vine_NN1 copula4_FO and_CC suggest_VV0 an_AT1 approach_NN1 to_II measuring_VVG the_AT solvency_NN1 of_IO a_AT1 non-life_JJ insurer_NN1 on_II both_RR asset_NN1 and_CC liability_NN1 by_II building_VVG a_AT1 two-step_JJ aggregation_NN1 model_NN1 :_: base_NN1 level_NN1 and_CC top_JJ level_NN1 ._. 
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<s>
The_AT DOS_NN1 was_VBDZ obtained_VVN through_II the_AT following_JJ equation<equation>_FO ,_, (_( 5_MC )_) m_ZZ1 ,_, kB_NNU ,_, T_ZZ1 ,_, and_CC are_VBR the_AT mass_NN1 ,_, Boltzmann_NP1 constant_JJ ,_, the_AT temperature_NN1 ,_, and_CC the_AT angular_JJ frequency_NN1 ,_, respectively_RR ._. 
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<s>
The_AT second_MD argument_NN1 highlights_VVZ the_AT fact_NN1 that_CST the_AT presence_NN1 of_IO unions_NN2 is_VBZ endogenous_JJ ,_, i.e._REX unions_NN2 are_VBR more_RGR likely_JJ to_TO be_VBI created_VVN once_RR their_APPGE workers_NN2 perceive_VV0 that_CST rents_NN2 are_VBR being_VBG extracted_VVN from_II the_AT consumer_NN1 ._. 
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The_AT challenge_NN1 for_IF high_JJ dimensional_JJ change_NN1 point_NN1 detection_NN1 is_VBZ how_RRQ to_TO aggregate_VVI efficiently_RR ._. 
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<s>
In_II Assumption_NN1 2_MC ,_, we_PPIS2 replace_VV0 (_( n_ZZ1 )_) (_( θ_NULL )_) by_II L(n)_NP1 (_( θ_NULL )_) ,_, so_CS21 that_CS22 θ_NULL n_ZZ1 is_VBZ now_RT an_AT1 MLE_NN1 ,_, <equation>_FO ._. 
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<s>
In_II this_DD1 study_NN1 ,_, marrow_NN1 or_CC thymus_NN1 cells_NN2 from_II two_MC biological_JJ replicates_VVZ of_IO each_DD1 of_IO three_MC different_JJ murine_JJ lines_NN2 were_VBDR extracted_VVN and_CC genome-wide_JJ methylation_NN1 levels_NN2 measured_VVN with_IW WGBS_NP1 ._. 
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<s>
In_II this_DD1 sense_NN1 ,_, the_AT situation_NN1 is_VBZ simple_JJ ,_, and_CC an_AT1 obvious_JJ approximate_JJ treatment_NN1 consists_VVZ in_II keeping_VVG only_RR the_AT large_JJ elements_NN2 ._. 
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<s>
However_RR ,_, when_CS it_PPH1 deviates_VVZ from_II half-filling_NN1 ,_, there_EX are_VBR no_AT rigorous_JJ analytical_JJ results_NN2 anymore_RR ._. 
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<s>
Similarly_RR ,_, it_PPH1 can_VM be_VBI shown_VVN that_CST 1&lsqb;_FO |_NULL |_NULL &rsqb;_) En1&lsqb;_FO |_NULL xn_FO |_NULL k_ZZ1 &rsqb;_) can_VM be_VBI expressed_VVN as_II a_AT1 function_NN1 of_IO |_NULL 1_MC1 |_NULL |_NULL xn1_FO |_NULL kfor_NN1 >2k>2_FO ,_, cf._VV0 Compared_VVN with_IW the_AT short-term_JJ equilibrium_NN1 risk_NN1 premium_NN1 in_II Eq_NN1 ._. 
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<s>
(_( 8_MC )_) ,_, the_AT long-run_JJ equilibrium_NN1 risk_NN1 premium_NN1 is_VBZ the_AT upper-bound_JJ ._. 
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Deeper_JJR understanding_NN1 requires_VVZ more_RGR quantitative_JJ studies_NN2 ._. 
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Thus_RR the_AT short-selling_JJ constraints_NN2 enlarge_VV0 the_AT portion_NN1 of_IO time_NNT1 on_II which_DDQ the_AT equilibrium_NN1 strategy_NN1 is_VBZ more_RGR favorable_JJ than_CSN the_AT riskless_JJ one_PN1 ,_, which_DDQ suggests_VVZ that_CST short-selling_JJ constraints_NN2 are_VBR more_RGR useful_JJ for_IF a_AT1 time-consistent_JJ investor_NN1 when_CS he_PPHS1 becomes_VVZ less_RGR risk-averse_JJ ._. 
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The_AT set_NN1 Sd_NP1 is_VBZ the_AT unit_NN1 sphere_NN1 in_II Rd_NN1 ,_, i.e._REX the_AT unit_NN1 circle_NN1 S2_FO in_II two_MC dimensions_NN2 ._. 
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<s>
Events_NN2 that_CST occur_VV0 have_VH0 the_AT same_DA forecasted_JJ variance_NN1 as_CSA events_NN2 that_CST do_VD0 not_XX occur_VVI ,_, suggesting_VVG that_DD1 AECO_NN1 is_VBZ not_XX adjusting_VVG the_AT variance_NN1 of_IO its_APPGE forecasts_NN2 in_II anticipation_NN1 of_IO occurrences_NN2 and_CC non-occurrences_NN2 ._. 
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<s>
We_PPIS2 define_VV0 a_AT1 tract_NN1 for_IF a_AT1 pair_NN of_IO haplotypes_NN2 as_II a_AT1 shared_JJ substring_NN1 that_CST starts_VVZ and_CC ends_VVZ at_II the_AT same_DA positions_NN2 in_II both_DB2 haplotypes_NN2 ._. 
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<s>
Ranked_JJ set_NN1 sampling_NN1 (_( RSS_NP1 )_) was_VBDZ introduced_VVN by_II McIntyre_NP1 (_( 1952_MC )_) for_IF estimating_VVG the_AT pasture_NN1 yields_NN2 ._. 
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<s>
When_CS the_AT medium_NN1 is_VBZ at_II equilibrium_NN1 ,_, and_CC the_AT only_JJ nonequilibrium_NN1 component_NN1 is_VBZ the_AT external_JJ driving_JJ ,_, the_AT correct_JJ dissipation_NN1 is_VBZ obtained_VVN from_II the_AT effective_JJ description_NN1 of_IO the_AT particle_NN1 ._. 
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<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 provide_VV0 additional_JJ properties_NN2 for_IF the_AT systemic_JJ risk_NN1 measure_NN1 <equation>_FO from_II (_( 1.5_MC )_) and_CC for_IF the_AT systemic_JJ risk_NN1 allocations_NN2 <equation>_FO ,_, <equation>_FO ,_, from_II (_( 1.8_MC )_) ._. 
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<s>
The_AT empirical_JJ literature_NN1 at_II the_AT country_NN1 level_NN1 has_VHZ focused_VVN mainly_RR in_II OECD_NP1 countries_NN2 ,_, since_CS traditionally_RR they_PPHS2 have_VH0 represented_VVN a_AT1 prominent_JJ share_NN1 of_IO world_NN1 '_NULL s_ZZ1 FDI_NP1 flows_NN2 (_( et_RA21 al_RA22 ._. 
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2007_MC ;_; Talamo_NP1 2007_MC )_) ._. 
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<s>
Employers_NN2 have_VH0 an_AT1 incentive_NN1 to_TO fill_VVI managerial_JJ positions_NN2 with_IW the_AT most_RGT able_JJ candidates_NN2 ,_, and_CC they_PPHS2 face_VV0 a_AT1 central_JJ choice_NN1 of_IO promoting_VVG from_II inside_RL or_CC outside_II the_AT firm_NN1 ._. 
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<s>
Furthermore_RR ,_, the_AT choice_NN1 of_IO such_DA thresholds_NN2 is_VBZ often_RR driven_VVN by_II the_AT type_NN1 of_IO analysis_NN1 required_VVN or_CC computational_JJ simplifications_NN2 ._. 
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<s>
Implicitly_RR speaking_VVG ,_, our_APPGE resultant_JJ variable_NN1 selection_NN1 rule_NN1 is_VBZ justified_VVN by_II the_AT asymptotic_JJ error_NN1 rates_NN2 that_CST they_PPHS2 induce_VV0 ._. 
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<s>
Regulators_NN2 and_CC policy_NN1 makers_NN2 took_VVD advantage_NN1 of_IO two_MC main_JJ regulatory_JJ changes_NN2 (_( Reg_NP1 NMS_NP1 in_II the_AT US_NP1 and_CC MiFID_NN1 in_II Europe_NP1 )_) which_DDQ were_VBDR followed_VVN by_II the_AT creation_NN1 of_IO worldwide_JJ trade_NN1 repositories_NN2 ._. 
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<s>
Heman_NP1 Shakeri_NP1 :_: Conceptualization_NN1 ,_, Methodology_NN1 ,_, Software_NN1 ,_, Formal_JJ analysis_NN1 ,_, Writing_VVG ._. 
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<s>
Note_VV0 that_CST ,_, although_CS it_PPH1 was_VBDZ found_VVN that_CST δ_NULL δ_NULL nj_NNU tends_VVZ to_II a_AT1 nonpositive_JJ value_NN1 ,_, its_APPGE exact_JJ value_NN1 for_IF moderate_JJ sample_NN1 sizes_NN2 can_VM be_VBI above_II 0_MC as_CSA demonstrated_VVN in_II Fig._NN1 1_MC1 ._. 
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<s>
Schultz_NP1 (_( 2001_MC )_) ,_, Bessembinder_NP1 et_RA21 al_RA22 ._. 
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(_( 2006_MC )_) ,_, Goldstein_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2007_MC )_) ,_, and_CC Bessembinder_NP1 and_CC Maxwell_NP1 (_( 2008_MC )_) focus_VV0 on_II trading_NN1 costs_VVZ in_II the_AT corporate_JJ bond_NN1 market_NN1 as_CSA trade_NN1 reporting_NN1 became_VVD timelier_JJR and_CC more_RGR transparent_JJ through_II the_AT Trade_NN1 Reporting_NN1 and_CC Compliance_NN1 Engine_NN1 (_( TRACE_NN1 )_) system_NN1 ._. 
</s>
<s>
These_DD2 daily_JJ predictions_NN2 were_VBDR carried_VVN out_RP on_II 30,000_MC hexagons_NN2 (_( approximately_RR 150_MC km_NNU resolution_NN1 )_) from_II an_AT1 ISEA_NN1 hexagonal_JJ grid_NN1 (_( described_VVN in_II Section_NN1 3.4_MC )_) covering_VVG the_AT region_NN1 of_IO interest_NN1 (_( which_DDQ recall_VV0 I_PPIS1 have_VH0 called_VVN a_AT1 sub-geoid_NN1 )_) and_CC can_VM be_VBI viewed_VVN on_II YouTube_NP1 at_II :_: https_NNU :_: //www.youtube.com/watch_VV0 ?_? v=KXIddBuHoU_FO ;_; it_PPH1 is_VBZ also_RR available_JJ in_II the_AT supplemental_JJ material_NN1 ._. 
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<s>
Our_APPGE theoretical_JJ results_NN2 are_VBR verified_VVN using_VVG numerical_JJ simulations_NN2 under_II finite_JJ size_NN1 system_NN1 ._. 
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<s>
Interestingly_RR ,_, when_CS the_AT optimal_JJ alignment_NN1 score_NN1 is_VBZ below_RG –40_JJ ,_, approximately_RR 50%_NNU of_IO the_AT reads_NN2 are_VBR incorrect-by-score_JJ ,_, meaning_VVG no_AT alignment_NN1 was_VBDZ reported_VVN or_CC the_AT heuristics_NN2 have_VH0 lead_VVN to_II an_AT1 erroneous_JJ suboptimal_JJ alignment_NN1 for_IF the_AT majority_NN1 of_IO these_DD2 reads_NN2 ._. 
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<s>
In_II &lsqb;_( 10_MC &rsqb;_) ,_, all_DB models_NN2 were_VBDR specified_VVN with_II31 respect_II32 to_II33 the_AT real-world_JJ probability_NN1 measure_NN1 including_II the_AT unspecified_JJ process_NN1 of_IO cost-of-capital_NN1 rates_NN2 defining_VVG the_AT capital_NN1 provider_NN1 '_NULL s_ZZ1 acceptability_NN1 criterion_NN1 ._. 
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<s>
The_AT present_JJ paper_NN1 is_VBZ organized_VVN as_CSA follows_VVZ ._. 
</s>
<s>
The_AT number_NN1 of_IO frequencies_NN2 and_CC their_APPGE values_NN2 are_VBR kept_VVN fixed_JJ ,_, and_CC ,_, conditional_NN1 on_II the_AT relocation_NN1 ,_, the_AT linear_JJ coefficients_NN2 for_IF the_AT segments_NN2 affected_VVN by_II the_AT relocation_NN1 are_VBR sampled_VVN ._. 
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<s>
Moreover_RR ,_, each_DD1 mean_JJ rEFD_NN1 lies_VVZ on_II the_AT segment_NN1 joining_VVG the_AT barycenter_JJR and_CC the_AT rth_NNU simplex_NN1 vertex_NN1 ._. 
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<s>
The_AT graph_NN1 properties_NN2 ,_, number_NN1 of_IO vertices_NN2 ,_, edges_NN2 ,_, average_JJ degree_NN1 ,_, diameter_NN1 and_CC clustering_NN1 coefficient_NN1 of_IO the_AT largest_JJT connected_JJ component_NN1 of_IO DREAM1-3_MC and_CC BioGRID_JJ networks_NN2 are_VBR shown_VVN in_II Table_NN1 1_MC1 ._. 
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<s>
Because_CS there_EX is_VBZ only_RR one_MC1 way_NN1 to_TO impose_VVI censoring_VVG when_RRQ no_AT nomination_NN1 data_NN is_VBZ observed_VVN ,_, Figure_NN1 3_MC presents_VVZ a_AT1 point_NN1 estimate_NN1 rather_II21 than_II22 a_AT1 distribution_NN1 of_IO estimates_NN2 when_RRQ <equation>_FO ._. 
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<s>
The_AT resulting_JJ structure_NN1 is_VBZ a_AT1 directed_JJ acyclic_JJ graph_NN1 with_IW N_ZZ1 sources_NN2 nodes_NN2 ._. 
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<s>
For_IF each_DD1 time_NNT1 step_NN1 ,_, a_AT1 counter_NN1 ti_NN2 defines_VVZ the_AT time_NNT1 of_IO infection_NN1 of_IO node_NN1 i_ZZ1 ._. 
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<s>
However_RR ,_, it_PPH1 is_VBZ unclear_JJ why_RRQ sheet_NN1 propensity_NN1 has_VHZ little_DA1 contribution_NN1 to_II solubility_NN1 as_CSA β_NULL -sheets_NN2 have_VH0 been_VBN shown_VVN to_TO link_VVI closely_RR with_IW protein_NN1 aggregation_NN1 (_( Idicula-Thomas_NP1 and_CC Balaji_NP1 ,_, 2005_MC )_) ._. 
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<s>
The_AT molecular_JJ changes_NN2 induced_VVN by_II perturbations_NN2 such_II21 as_II22 drugs_NN2 and_CC ligands_NN2 are_VBR highly_RR informative_JJ of_IO the_AT intracellular_JJ wiring_NN1 ._. 
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<s>
Our_APPGE main_JJ result_NN1 is_VBZ that_CST we_PPIS2 find_VV0 two_MC kinds_NN2 of_IO quasiparticle_NN1 excitations_NN2 ,_, which_DDQ we_PPIS2 dub_VV0 intrachain_NN1 and_CC interchain_VV0 mesons_NN2 ,_, that_CST correspond_VV0 to_TO bound_VVI states_NN2 of_IO kinks_NN2 within_II the_AT same_DA chain_NN1 or_CC between_II different_JJ ones_NN2 ,_, respectively_RR ._. 
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<s>
In_II fact_NN1 ,_, the_AT gap_NN1 among_II different_JJ regions_NN2 has_VHZ been_VBN increasing_VVG over_II the_AT past_JJ few_DA2 decades_NNT2 ._. 
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<s>
We_PPIS2 refer_VV0 to_II Esary_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 1967_MC )_) for_IF a_AT1 detailed_JJ discussion_NN1 of_IO the_AT notion_NN1 of_IO association_NN1 ,_, as_RG well_RR as_CSA to_II Furman_NP1 and_CC Zitikis_NP1 ,_, 2010_MC ,_, Furman_NP1 and_CC Zitikis_NP1 ,_, 2009_MC for_IF applications_NN2 to_II insurance_NN1 pricing_NN1 ._. 
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<s>
To_TO study_VVI associations_NN2 between_II the_AT level_NN1 of_IO expression_NN1 of_IO the_AT extracted_JJ genes_NN2 and_CC the_AT responses_NN2 predicted_VVN by_II ATIL_NN1 for_IF each_DD1 drug_NN1 in_II each_DD1 TCGA_NN1 cohort_NN1 ,_, we_PPIS2 fit_VV0 multivariate_JJ linear_JJ regression_NN1 models_NN2 to_II the_AT gene_NN1 expression_NN1 of_IO those_DD2 genes_NN2 and_CC the_AT responses_NN2 to_II that_DD1 drug_NN1 predicted_VVN by_II AITL_NP1 ._. 
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<s>
Further_RRR ,_, the_AT MSE_NN1 of_IO MOAD_NP1 was_VBDZ ,_, nearly_RR ,_, uniformly_RR less_DAR than_CSN that_DD1 of_IO the_AT FLOD_NN1 ._. 
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<s>
Under_II independence_NN1 ,_, the_AT distribution_NN1 of_IO the_AT change-point_JJ statistics_NN does_VDZ not_XX dependent_JJ on_II the_AT beginning_NN1 of_IO the_AT changed_JJ segment_NN1 ,_, only_RR on_II the_AT length_NN1 ._. 
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<s>
We_PPIS2 apply_VV0 a_AT1 algorithm_NN1 with_IW an_AT1 independence_NN1 sampler_NN1 ,_, considering_VVG a_AT1 gamma_NN1 (_( 2_VV0 ,_, )_) gamma_NN1 (_( 2_VV0 ,_, ukl_NN1 )_) proposal_NN1 distribution_NN1 ._. 
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<s>
It_PPH1 may_VM be_VBI desirable_JJ to_TO borrow_VVI information_NN1 from_II multiple_JJ historical_JJ trials_NN2 through_II a_AT1 fixed_JJ prior_RR specified_VVN a_JJ21 priori_JJ22 ._. 
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<s>
Note_VV0 that_CST it_PPH1 is_VBZ more_RGR difficult_JJ to_TO validate_VVI these_DD2 convergence_NN1 rates_NN2 for_IF =4q=4_FO ,_, for_IF all_DB three_MC test_NN1 problems_NN2 and_CC small_JJ >0h>0_FO ,_, since_CS numerical_JJ instability_NN1 can_VM contaminate_VVI the_AT analytical_JJ rates_NN2 ._. 
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<s>
Hurst_NP1 surfaces_NN2 of_IO the_AT futures_NN2 system_NN1 ,_, spot_NN1 system_NN1 and_CC their_APPGE interaction_NN1 system_NN1 ._. 
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<s>
We_PPIS2 varied_VVD the_AT training_NN1 size_NN1 from_II 300_MC to_II 8000_MC ,_, and_CC the_AT cut-off_NN1 factor_NN1 from_II 3.0_MC to_II +3.0_MC in_II 0.5_MC increments_NN2 to_TO generate_VVI silver_NN1 standard_NN1 using_VVG the_AT unlabeled_JJ data_NN ._. 
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<s>
Secondly_RR ,_, we_PPIS2 investigate_VV0 possible_JJ heterogeneity_NN1 in_II price_NN1 elasticities_NN2 and_CC other_JJ factors_NN2 between_II different_JJ groups_NN2 of_IO consumers_NN2 ._. 
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<s>
In_II the_AT limit_NN1 l_ZZ1 →_NULL 0_MC ,_, β_NULL →_NULL ∞_FO ,_, the_AT extreme_JJ condition_NN1 yields_VVZ the_AT same_DA form_NN1 of_IO the_AT equations_NN2 that_CST appear_VV0 in_II the_AT fixed_JJ point_NN1 condition_NN1 of_IO the_AT SE_ND1 equations_NN2 –_- ._. 
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<s>
Outlier_JJR cluster_NN1 1_MC1 (_( 10_MC points_NN2 )_) :_: Uniform&lsqb;2_FO ,_, 5_MC &rsqb;_) ._. 
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<s>
The_AT contrasting_JJ results_NN2 of_IO simulated_JJ datasets_NN2 indicate_VV0 that_CST MetaRib_NP1 is_VBZ able_JK to_TO capture_VVI most_DAT information_NN1 in_II relatively_RR well-characterized_JJ environments_NN2 while_CS it_PPH1 is_VBZ more_RGR likely_JJ to_TO generate_VVI false_JJ positives_NN2 and_CC partial_JJ sequences_NN2 for_IF poorly_RR characterized_VVN environments_NN2 ._. 
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To_II that_DD1 end_NN1 ,_, we_PPIS2 repeat_VV0 the_AT exercise_NN1 for_IF the_AT censuses_NN2 in_II different_JJ industries_NN2 ._. 
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<s>
The_AT last_MD equation_NN1 is_VBZ called_VVN measurement_NN1 equation_NN1 with_IW errors_NN2 <equation>_FO which_DDQ updates_VVZ the_AT realized_JJ volatility_NN1 <equation>_FO from_II <equation>_FO ._. 
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<s>
The_AT software_NN1 can_VM also_RR generate_VVI reports_NN2 for_IF use_NN1 in_II auditing_NN1 and_CC compliance_NN1 with_IW Sarbanes-Oxley_NN1 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, Lemma_NN1 5.2_MC shows_VVZ that_CST the_AT mapping_NN1 <equation>_FO is_VBZ decreasing_VVG as_RR21 well_RR22 ._. 
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<s>
The_AT generalization_NN1 of_IO the_AT SIS_NN1 model_NN1 to_II arbitrary_JJ number_NN1 of_IO multiple_JJ contagions_NN2 ,_, however_RR ,_, has_VHZ not_XX yet_RR been_VBN developed_VVN ._. 
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<s>
That_REX21 is_REX22 ,_, the_AT probability_NN1 pi_NN1 of_IO an_AT1 observation_NN1 (_( ai_NNU )_) is_VBZ given_VVN by_II the_AT solution_NN1 of_IO the_AT entropy_NN1 maximization_NN1 problem_NN1 ._. 
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This_DD1 must_VM include_VVI rejected_JJ particles_NN2 to_TO avoid_VVI a_AT1 bias_NN1 ._. 
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<s>
This_DD1 superposition_NN1 of_IO time-correlated_JJ oscillation_NN1 was_VBDZ contemporaneous_JJ with_IW non-oscillatory_JJ patterns_NN2 of_IO gene_NN1 expression_NN1 involved_JJ with_IW cell_NN1 differentiation_NN1 :_: the_AT observed_JJ patterns_NN2 of_IO gene_NN1 activation_NN1 simultaneously_RR and_CC collectively_RR encoded_VVD multiple_JJ oscillatory_JJ mechanisms_NN2 ,_, in_II an_AT1 almost_RR '_NULL holographic_JJ '_NULL sense_NN1 ,_, based_VVN on_II gene_NN1 activations_NN2 at_II individual_JJ cellsand_NN1 yet_RR each_DD1 gene_NN1 simultaneously_RR and_CC separately_RR also_RR served_VVD its_APPGE own_DA unique_JJ role_NN1 in_II development_NN1 ,_, unrelated_JJ per_RR21 se_RR22 to_II the_AT oscillation_NN1 to_II which_DDQ it_PPH1 contributed_VVD ._. 
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<s>
When_CS short-read_JJ contigs_NN2 were_VBDR supplied_VVN ,_, SALSA2_FO generated_VVN only_RR fragmented_JJ scaffolds_NN2 ;_; thus_RR ,_, accuracy_NN1 statistics_NN could_VM not_XX be_VBI computed_VVN for_IF chromosome-length_JJ scaffolds_NN2 ,_, and_CC the_AT HiC-Hiker_NP1 algorithm_NN1 could_VM not_XX be_VBI applied_VVN under_II these_DD2 conditions_NN2 ._. 
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<s>
We_PPIS2 base_VV0 our_APPGE criteria_NN2 for_IF model_NN1 selection_NN1 on_II Akaike_NP1 Information_NN1 Criterion_NN1 (_( AIC_NP1 )_) and_CC coverage_NN1 ,_, i.e._REX how_RGQ often_RR the_AT data_NN is_VBZ covered_VVN by_II the_AT 95%_NNU point_NN1 wise_JJ in-sample_JJ prediction_NN1 interval_NN1 evaluated_VVN at_II the_AT best_JJT choice_NN1 of_IO parameters_NN2 ._. 
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<s>
In_II this_DD1 case_NN1 ,_, the_AT family_NN1 of_IO solutions_NN2 is_VBZ increasing_VVG in_II <equation>_FO ._. 
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<s>
In_RR21 general_RR22 ,_, the_AT map_NN1 <equation>_FO is_VBZ not_XX monotonic_JJ ._. 
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<s>
The_AT curly_JJ brackets_NN2 in_II equation_NN1 (_( 1_MC1 )_) denote_VV0 the_AT anti-commutator_NN1 ,_, and_CC we_PPIS2 set_VV0 =_FO 1_MC1 ._. 
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<s>
Then_RT ,_, the_AT solution_NN1 of_IO (_( 13_MC )_) is_VBZ given_VVN by_II <equation>_FO ,_, where_CS <equation>_FO and_CC <equation>_FO ._. 
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<s>
The_AT length_NN1 of_IO b_ZZ1 should_VM be_VBI larger_JJR than_CSN the_AT bandwidth_NN1 of_IO the_AT prior_JJ covariance_NN1 ._. 
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<s>
We_PPIS2 provide_VV0 a_AT1 formal_JJ justification_NN1 of_IO this_DD1 intuitive_JJ algorithm_NN1 by_II showing_VVG that_CST it_PPH1 optimizes_VVZ a_AT1 variational_JJ approximation_NN1 to_II the_AT posterior_JJ distribution_NN1 under_II SuSiE_NP1 ._. 
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<s>
Further_RRR ,_, this_DD1 approximate_JJ posterior_JJ distribution_NN1 naturally_RR yields_VVZ convenient_JJ novel_JJ summaries_NN2 of_IO uncertainty_NN1 in_II variable_JJ selection_NN1 ,_, providing_VVG a_AT1 credible_JJ set_NN1 of_IO variables_NN2 for_IF each_DD1 selection_NN1 ._. 
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<s>
Ohlson_NN1 and_CC Von_NP1 Rosen_NP1 (_( 2010_MC )_) suggested_VVD general_JJ estimation_NN1 principle_NN1 for_IF a_AT1 class_NN1 of_IO variance_NN1 matrix_NN1 structures_NN2 which_DDQ can_VM be_VBI applied_VVN to_II the_AT uniform_JJ correlation_NN1 structure_NN1 ._. 
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<s>
Doublets_NN2 rate_NN1 depends_VVZ on_II the_AT concentration_NN1 of_IO the_AT input_NN1 cells_NN2 ,_, which_DDQ is_VBZ estimated_VVN from_II the_AT dilution_NN1 Poisson_NP1 statistics_NN (_( Macaulay_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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<s>
NMF_NP1 based_VVN on_II negative_JJ binomial_JJ distribution_NN1 has_VHZ already_RR been_VBN applied_VVN in_II recommendation_NN1 systems_NN2 (_( Gouvert_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) and_CC cell-type_JJ detection_NN1 in_II single-cell_JJ RNAseq_JJ data_NN (_( Sun_NN1 et_RA21 al._RA22 ,_, 2019_MC )_) ,_, but_CCB not_XX yet_RR to_II mutation_NN1 count_NN1 data_NN for_IF mutational_JJ signature_NN1 extraction_NN1 ._. 
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<s>
We_PPIS2 select_VV0 a_AT1 fraction_NN1 7/10_MF of_IO the_AT total_JJ entries_NN2 uniformly_RR chosen_VVN at_RR21 random_RR22 as_CSA the_AT observation_NN1 set_VVN so_CS21 that_CS22 |_NULL |_NULL =72/10_FU |_NULL |_NULL =7p2/10_FU ._. 
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<s>
The_AT opinion_NN1 of_IO the_AT ith_MD independent_JJ agent_NN1 at_II time-step_NN1 t_ZZ1 is_VBZ denoted_VVN by_II Iti_NP1 ._. 
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<s>
In_II this_DD1 attack_NN1 mode_NN1 ,_, the_AT effect_NN1 of_IO changing_VVG the_AT largest_JJT cluster_NN1 size_NN1 and_CC network_NN1 efficiency_NN1 is_VBZ explored_VVN ._. 
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<s>
For_IF our_APPGE comparisons_NN2 ,_, we_PPIS2 also_RR apply_VV0 the_AT MMD-MA_JJ algorithm_NN1 ,_, which_DDQ adopts_VVZ a_AT1 MMD_MC term_NN1 to_TO reduce_VVI distribution_NN1 discrepancy_NN1 in_II feature_NN1 spaces_NN2 and_CC to_TO align_VVI the_AT simulated_JJ datasets_NN2 using_VVG its_APPGE defaulting_JJ parameters_NN2 ._. 
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<s>
The_AT image_NN1 plots_NN2 of_IO Fig._NN1 10_MC ,_, Fig._NN1 11_MC suggest_VV0 that_CST our_APPGE density_NN1 forecasts_NN2 give_VV0 a_AT1 reasonable_JJ approximation_NN1 to_II the_AT true_JJ densities_NN2 on_II the_AT unit_NN1 square_NN1 in_II Models_NN2 4–6_MCMC ,_, even_CS21 though_CS22 the_AT forecasts_NN2 are_VBR somewhat_RR less_RGR precise_JJ than_CSN those_DD2 of_IO the_AT benchmark_NN1 method_NN1 ._. 
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<s>
However_RR ,_, the_AT method_NN1 is_VBZ applicable_JJ only_RR in_II situations_NN2 ,_, where_RRQ multiple_JJ exchangeable_JJ samples_NN2 are_VBR available_JJ ,_, and_CC hence_RR not_XX generally_RR applicable_JJ ._. 
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<s>
Species_NN trees_NN2 are_VBR important_JJ models_NN2 that_CST can_VM be_VBI used_VVN to_TO address_VVI many_DA2 biological_JJ questions_NN2 ,_, for_REX21 example_REX22 how_RRQ is_VBZ biodiversity_NN1 created/maintained_VVN and_CC how_RRQ do_VD0 species_NN adapt_VV0 to_II their_APPGE environments_NN2 (_( Cracraft_NP1 et_RA21 al._RA22 ,_, 2004_MC )_) ._. 
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<s>
In_RR21 addition_RR22 ,_, more_RRR and_CC more_DAR scholars_NN2 believe_VV0 that_CST the_AT occurrence_NN1 of_IO financial_JJ contagion_NN1 is_VBZ more_RGR likely_JJ due_II21 to_II22 the_AT overlapping_JJ portfolios_NN2 among_II banks_NN2 ,_, and_CC its_APPGE impact_NN1 on_II financial_JJ contagion_NN1 may_VM be_VBI much_RR greater_JJR than_CSN the_AT direct_JJ relationship_NN1 based_VVN on_II interbank_JJ lending_NN1 market_NN1 &lsqb;_( 22_MC &rsqb;_) ._. 
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<s>
For_IF KNN_NP1 ,_, we_PPIS2 used_VVD the_AT R_NP1 implementation_NN1 in_II the_AT class_NN1 package_NN1 with_IW k=5_FO and_CC for_IF LDA_NP1 the_AT implementation_NN1 in_II MASS_NN1 ._. 
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As_II a_AT1 result_NN1 ,_, measuring_VVG WTP_NP1 is_VBZ straightforward_JJ ._. 
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<s>
When_CS using_VVG =1000Q=1000_FO ,_, as_CSA suggested_VVN in_II Wang_NP1 and_CC Samworth_NP1 (_( 2018_MC )_) ,_, a_AT1 Wild_JJ Binary_JJ Segmentation_NN1 (_( Fryzlewicz_NP1 2014_MC )_) approach_NN1 is_VBZ implemented_VVN to_TO detect_VVI multiple_JJ changes_NN2 ._. 
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<s>
One_PN1 can_VM take_VVI an_AT1 array_NN1 of_IO genes/transcripts_NN2 ,_, and_CC collect_VV0 an_AT1 abundance_NN1 signature_NN1 across_II thousands_NNO2 of_IO datasets_NN2 ,_, and_CC then_RT perform_VV0 unsupervised_JJ clustering_NN1 to_TO look_VVI for_IF patterns_NN2 ._. 
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<s>
Hence_RR ,_, the_AT result_NN1 in_II equation_NN1 (_( 40_MC )_) predicts_VVZ a_AT1 linear_JJ increase_NN1 of_IO the_AT hopping_NN1 with_IW a_AT1 slope_NN1 2I_NN2 (_( k_ZZ1 '_NULL )_) ,_, multiplied_VVN by_II a_AT1 factor_NN1 of_IO 1_MC1 or_CC k_ZZ1 for_IF the_AT strong_JJ (_( even_RR )_) and_CC weak_JJ (_( odd_JJ )_) bonds_NN2 ._. 
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<s>
Discussion_NN1 of_IO the_AT case_NN1 <equation>_FO is_VBZ postponed_VVN until_CS Sect._NP1 3.3.5_MC below_RL ._. 
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<s>
Revuz_VV0 and_CC Yor_NP1 &lsqb;_( 36_MC ,_, Theorem_NN1 VII.2.7_FO &rsqb;_) requires_VVZ an_AT1 extension_NN1 of_IO the_AT probability_NN1 space_NN1 when_CS the_AT coefficients_NN2 <equation>_FO and_CC <equation>_FO vanish_VV0 ._. 
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<s>
All_DB k-dimensional_JJ coordinates_NN2 in_II embeddings_NN2 space_NN1 are_VBR concatenated_VVN and_CC serve_VV0 as_CSA input_VVN for_IF a_AT1 multi-layer_JJ perceptron_NN1 (_( MLP_NP1 )_) ._. 
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<s>
If_CS a_AT1 borrower_NN1 has_VHZ multiple_NN1 lead_VVN lenders_NN2 ,_, then_RT the_AT lead_NN1 bank_NN1 arranging_VVG the_AT most_DAT amount_NN1 of_IO credit_NN1 in_II dollar_NNU1 terms_NN2 is_VBZ selected_VVN ._. 
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<s>
For_IF ,_, the_AT probability_NN1 ,_, and_CC (_( 2.1_MC )_) holds_VVZ ._. 
</s>
<s>
In_RR21 addition_RR22 ,_, we_PPIS2 also_RR pre-computed_JJ the_AT mean_JJ signal_NN1 using_VVG WiggleTools_NP1 (_( Zerbino_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) and_CC store_VV0 these_DD2 files_NN2 ._. 
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<s>
To_TO model_VVI a_AT1 variable_NN1 based_VVN on_II N_ZZ1 data-points_NN2 (_( or_CC groups_NN2 )_) arranged_VVD in_II descending_JJ order_NN1 of_IO importance_NN1 with_IW ith_MD item_NN1 having_VHG rank_NN1 ri_NN2 and_CC size_NN1 ni_NN2 ,_, the_AT most_RGT commonly_RR used_JJ RO_NN1 distribution_NN1 is_VBZ the_AT hyperbolic_JJ Pareto_NP1 (_( Zipf_NP1 '_NULL s_ZZ1 )_) law_NN1 ._. 
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<s>
A_AT1 fourth_MD file_NN1 contains_VVZ data_NN on_II exact_JJ attendance_NN1 dates_VVZ for_IF the_AT university_NN1 '_NULL s_ZZ1 gym_NN1 and_CC recreational_JJ facilities_NN2 ._. 
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<s>
Two_MC interesting_JJ findings_NN2 are_VBR that_CST the_AT choice_NN1 of_IO K_ZZ1 does_VDZ not_XX seem_VVI to_TO be_VBI too_RG sensitive_JJ as_CS31 soon_CS32 as_CS33 K_ZZ1 is_VBZ large_JJ enough_RR ,_, and_CC there_EX seems_VVZ to_TO be_VBI some_DD correlation_NN1 between_II and_CC while_CS β_NULL is_VBZ rather_RG independent_JJ of_IO the_AT latest_JJT ._. 
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<s>
As_CSA skewness_NN1 is_VBZ a_AT1 key_JJ difference_NN1 between_II stable_JJ and_CC Gaussian_JJ kernel_NN1 distributions_NN2 ,_, it_PPH1 is_VBZ important_JJ to_TO understand_VVI what_DDQ is_VBZ gained_VVN from_II it_PPH1 within_II the_AT IDE_NN1 modelling_NN1 framework_NN1 ._. 
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<s>
BUS_NN1 is_VBZ evaluated_VVN by_II simulation_NN1 studies_NN2 and_CC a_AT1 real_JJ breast_NN1 cancer_NN1 dataset_NN1 combined_VVN from_II three_MC batches_NN2 measured_VVN on_II two_MC platforms_NN2 ._. 
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<s>
For_IF relation_NN1 prediction_NN1 ,_, we_PPIS2 compare_VV0 models_NN2 by_II plotting_VVG their_APPGE precision–recall_NN1 (_( PR_NP1 )_) curves_NN2 ._. 
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<s>
Both_DB2 these_DD2 scenarios_NN2 include_VV0 discontinuous_JJ changes_NN2 in_II social_JJ distancing_NN1 and_CC possess_VV0 the_AT same_DA first_MD transition_NN1 ._. 
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<s>
COMUNET_NP1 returned_VVD a_AT1 list_NN1 of_IO interacting_JJ partners_NN2 sorted_VVN by_II increasing_JJ dissimilarity_NN1 with_IW the_AT specified_JJ pattern_NN1 (_( bottom_JJ left_JJ )_) ._. 
</s>
<s>
In_BCL21 order_BCL22 to_TO bolster_VVI our_APPGE results_NN2 with_IW analytical_JJ arguments_NN2 ,_, we_PPIS2 then_RT considered_VVD an_AT1 even_RR simpler_JJR model_NN1 ,_, where_CS the_AT existence_NN1 of_IO a_AT1 phase_NN1 transition_NN1 can_VM be_VBI verified_VVN mathematically_RR ._. 
</s>
<s>
One_MC1 set_NN1 of_IO notable_JJ omissions_NN2 are_VBR the_AT state-level_JJ welfare_NN1 reforms_NN2 made_VVN by_II states_NN2 that_CST sought_VVD to_TO increase_VVI family_NN1 self-sufficiency_NN1 ._. 
</s>
<s>
LinearFold_RR uses_VVZ k-best_RRT parsing_VVG (_( Huang_NP1 and_CC Chiang_NP1 ,_, 2005_MC )_) to_TO reduce_VVI runtime_NNT1 from_II O(nb2)_FO to_II O(nblogb)_NP1 without_IW losing_VVG accuracy_NN1 ._. 
</s>
<s>
By_II construction_NN1 it_PPH1 is_VBZ not_XX affected_VVN by_II strictly_RR monotonic_JJ transformations_NN2 ,_, and_CC hence_RR it_PPH1 is_VBZ perfectly_RR designed_VVN for_IF ordinal_JJ data_NN where_CS only_RR the_AT ranking_NN1 of_IO the_AT values_NN2 matters_NN2 while_CS the_AT distance_NN1 between_II possible_JJ values_NN2 has_VHZ no_AT meaning_NN1 ,_, see_VV0 Proposition_NN1 3_MC ._. 
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<s>
We_PPIS2 geocode_VV0 the_AT location_NN1 of_IO the_AT 952,376_MC firms_NN2 that_CST appeared_VVD in_II the_AT sample_NN1 and_CC then_RT compute_VV0 the_AT distance_NN1 between_II each_DD1 firm_NN1 and_CC its_APPGE closest_JJT water_NN1 quality_NN1 monitoring_VVG station.15_FO Nearly_RR 5%_NNU of_IO the_AT firms_NN2 in_II the_AT ASIF_NN1 database_NN1 belong_VV0 to_II a_AT1 parent_NN1 multiunit_NN1 firm_NN1 ;_; we_PPIS2 exclude_VV0 them_PPHO2 from_II subsequent_JJ analyses_NN2 because_CS the_AT parent_NN1 firm_NN1 might_VM avoid_VVI regulation_NN1 by_II reallocating_VVG production_NN1 activities_NN2 across_II its_APPGE subordinate_JJ firms_NN2 ._. 
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<s>
It_PPH1 is_VBZ only_RR fair_JJ to_TO note_VVI that_CST the_AT authors_NN2 are_VBR aware_JJ of_IO this_DD1 shortcoming_NN1 (_( see_VV0 Reifschneider_JJR and_CC Tulip_NP1 2007_MC ,_, pp_NN1 ._. 
</s>
<s>
Chromosome_NN1 3_MC p-arm_JJ loss_NN1 and_CC q-arm_JJ gain_NN1 have_VH0 been_VBN shown_VVN to_TO be_VBI a_AT1 dominant_JJ feature_NN1 of_IO squamous_JJ cell_NN1 carcinomas_NN2 (_( Taylor_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
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<s>
Due_II21 to_II22 the_AT ultra-low_JJ coverage_NN1 ,_, copy_VV0 number_NN1 calls_VVZ in_II individual_JJ cells_NN2 are_VBR prone_JJ to_II errors_NN2 ._. 
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<s>
We_PPIS2 find_VV0 no_AT significant_JJ effect_NN1 on_II the_AT Gini_JJ net_NN1 ,_, suggesting_VVG that_CST after_CS taxes_NN2 and_CC transfers_NN2 ,_, the_AT positive_JJ impact_NN1 of_IO the_AT liberalization_NN1 of_IO securities_NN2 markets_NN2 on_II equality_NN1 is_VBZ cushioned_VVN ._. 
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<s>
The_AT first_MD common_JJ factor_NN1 that_CST represents_VVZ not_XX only_RR financial_JJ market_NN1 but_CCB also_RR real_JJ activity_NN1 variables_NN2 seems_VVZ to_TO play_VVI a_AT1 dominantly_RR important_JJ role_NN1 in_II predicting_VVG the_AT vulnerability_NN1 in_II the_AT financial_JJ markets_NN2 in_II Korea_NP1 ._. 
</s>
<s>
The_AT overall_JJ findings_NN2 on_II spurious_JJ inferences_NN2 can_VM be_VBI summarized_VVN in_II the_AT following_JJ way_NN1 :_: (_( i_ZZ1 )_) the_AT Gibbs–Wilbraham_NP1 phenomenon_NN1 is_VBZ relevant_JJ for_IF the_AT and_CC Baxter–King_VVG filters_NN2 ,_, whereas_CS no_AT obvious_JJ evidence_NN1 of_IO the_AT Slutzky–Yule_NN1 phenomenon_NN1 could_VM be_VBI found_VVN ;_; (_( ii_MC )_) the_AT wrong_JJ choice_NN1 of_IO filtering_VVG bands_NN2 may_VM lead_VVI to_II spurious_JJ inferences_NN2 about_II the_AT dominant_JJ periodicity_NN1 ;_; (_( iii_MC )_) the_AT spectral_JJ pattern_NN1 of_IO the_AT original_JJ regular_JJ and_CC irregular_JJ components_NN2 was_VBDZ well_RR preserved_VVN after_II detrending_VVG ,_, but_CCB changes_NN2 in_II the_AT magnitude_NN1 of_IO the_AT spectral_JJ density_NN1 peaks_NN2 are_VBR possible_JJ ;_; (_( iv_MC )_) the_AT changes_NN2 in_II the_AT cross-correlation_JJ structure_NN1 can_VM be_VBI substantial_JJ and_CC may_VM lead_VVI to_II spurious_JJ inferences_NN2 about_II the_AT interaction_NN1 between_II the_AT detrended_JJ series_NN ._. 
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<s>
Trading_VVG volume_NN1 is_VBZ the_AT average_JJ daily_JJ total_JJ par_NN1 value_NN1 of_IO bonds_NN2 traded_VVN during_II the_AT year_NNT1 ._. 
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<s>
In_II contrast_NN1 to_II Bühlmann_NP1 (_( 1997_MC )_) ,_, who_PNQS implemented_VVD the_AT Yule–Walker_NP1 (_( YW_NP1 )_) estimator_NN1 ,_, we_PPIS2 rely_VV0 on_II the_AT standard_NN1 OLS_VVZ estimator_NN1 ._. 
</s>
<s>
This_DD1 table_NN1 shows_VVZ the_AT results_NN2 of_IO a_AT1 decomposition_NN1 of_IO the_AT change_NN1 in_II the_AT labor_NN1 share_NN1 using_VVG the_AT dynamic_JJ Melitz_NP1 and_CC Polanec_NP1 (_( 2015_MC )_) methodology_NN1 as_CSA described_VVN in_II the_AT text_NN1 and_CC notes_NN2 to_II Table_NN1 IV_MC ._. 
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<s>
Both_RR Du_FW et_RA21 al_RA22 ._. 
</s>
<s>
and_CC Choy_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
chose_VVD to_TO train_VVI their_APPGE models_NN2 on_II a_AT1 limited_JJ set_NN1 of_IO genes_NN2 ,_, mainly_RR protein_NN1 coding_NN1 ,_, and_CC some_DD microRNAs_NN2 (_( 24_MC 447_MC and_CC 20_MC 531_MC genes_NN2 ,_, respectively_RR )_) ._. 
</s>
<s>
It_PPH1 is_VBZ widely_RR known_VVN that_CST financial_JJ depth_NN1 ,_, education_NN1 attainment_NN1 ,_, and_CC foreign_JJ direct_JJ investment_NN1 also_RR can_VM be_VBI determined_VVN by_II economic_JJ growth_NN1 ,_, and_CC the_AT quality_NN1 of_IO institutions_NN2 can_VM be_VBI shaped_VVN in_II the_AT process_NN1 of_IO economic_JJ development_NN1 ._. 
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<s>
Let_VV0 DBR_NP1 and_CC DBV_NP1 be_VBI the_AT matrices_NN2 between_II sets_NN2 of_IO structural_JJ breaks_NN2 for_IF the_AT log_NN1 return_NN1 and_CC Parkinson_NP1 variance_NN1 time_NNT1 series_NN ,_, respectively_RR ._. 
</s>
<s>
The_AT numbers_NN2 in_II the_AT brackets_NN2 give_VV0 the_AT difference_NN1 between_II the_AT EGOE_NN1 values_NN2 and_CC those_DD2 from_II the_AT bivariate_JJ q-normal_JJ ._. 
</s>
<s>
Zeros_NN2 can_VM also_RR be_VBI missing_JJ observations_NN2 that_CST are_VBR wrongly_RR recorded_VVN as_CSA zero_MC ._. 
</s>
<s>
It_PPH1 states_VVZ that_CST the_AT degrees_NN2 of_IO freedom_NN1 of_IO a_AT1 mechanical_JJ system_NN1 act_NN1 as_II a_AT1 thermometer_NN1 :_: temperature_NN1 is_VBZ equal_JJ to_II the_AT mean_JJ variance_NN1 of_IO their_APPGE oscillations_NN2 divided_VVN by_II their_APPGE stiffness_NN1 ._. 
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<s>
Originally_RR ,_, BERT_NP1 was_VBDZ trained_VVN on_II a_AT1 large_JJ collection_NN1 of_IO books_NN2 and_CC English_JJ Wikipedia_NP1 ,_, but_CCB recently_RR two_MC BERT_NP1 models_NN2 trained_VVN on_II biomedical_JJ abstracts_NN2 and_CC full_JJ texts_NN2 have_VH0 been_VBN released_VVN ,_, BioBERT_NP1 (_( Lee_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) and_CC SciBERT_NP1 (_( Beltagy_NP1 et_RA21 al._RA22 ,_, 2019b_FO )_) ._. 
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<s>
Given_VVN a_AT1 source_NN1 CNP_NP1 S_ZZ1 ,_, a_AT1 target_NN1 CNP_NP1 T_ZZ1 and_CC a_AT1 weight_NN1 function_NN1 w_ZZ1 ,_, find_VV0 a_AT1 shortest_JJT phase-bounded_NN1 semi-ordered_VVD CNT_NP1 E_NP1 having_VHG a_AT1 minimum_JJ weight_NN1 ,_, minE_PPGE :_: |_NULL E_ZZ1 |_NULL =d_NN1 (_( S_ZZ1 ,_, T_ZZ1 )_) W(E)_PPIS2 ._. 
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<s>
In_II Section_NN1 3_MC we_PPIS2 will_VM present_VVI our_APPGE modelling_NN1 approach_NN1 in_II a_AT1 discrete-time_JJ framework_NN1 while_CS Section_NN1 4_MC is_VBZ embedded_VVN in_II a_AT1 continuous-time_JJ setting_NN1 ._. 
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<s>
However_RR ,_, once_CS >1_FO ,_, the_AT process_NN1 Xt_NP1 has_VHZ the_AT LRD_NP1 feature_NN1 ._. 
</s>
<s>
Remember_VV0 that_CST D_ZZ1 measures_VVZ the_AT distance_NN1 (_( in_II probability_NN1 space_NN1 )_) from_II the_AT vdW_NNU distribution_NN1 to_II the_AT uniform_JJ one_PN1 ._. 
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<s>
To_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, most_DAT studies_NN2 on_II stock_NN1 network_NN1 construction_NN1 only_RR consider_VV0 one_MC1 kind_NN1 of_IO relationship_NN1 among_II stocks_NN2 ,_, such_II21 as_II22 Pearson_NP1 correlation_NN1 ,_, Granger_NP1 causality_NN1 and_RR31 so_RR32 on_RR33 ._. 
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<s>
Raghunathan_NN1 and_CC Grizzle_NP1 (_( 1995_MC )_) proposed_VVD a_AT1 so-called_JJ split_JJ questionnaire_NN1 survey_NN1 design_NN1 (_( SQS_NNU2 )_) which_DDQ is_VBZ a_AT1 planned_JJ missing-by-design_JJ pattern_NN1 that_CST aims_VVZ to_TO avoid_VVI the_AT identification_NN1 problem_NN1 by_II ensuring_VVG that_CST everything_PN1 that_CST is_VBZ to_TO be_VBI jointly_RR analyzed_VVN remains_NN2 observed_VVD in_RP at_RR21 least_RR22 one_MC1 subsample_NN1 ._. 
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<s>
First_MD ,_, we_PPIS2 attempt_VV0 to_TO establish_VVI the_AT direction_NN1 of_IO causality_NN1 ,_, from_II agriculture_NN1 toward_II other_JJ sectors_NN2 ._. 
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<s>
The_AT area_NN1 below_II each_DD1 curve_NN1 is_VBZ the_AT unstable_JJ region_NN1 in_II which_DDQ the_AT density_NN1 waves_NN2 appear_VV0 ._. 
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<s>
Table_NN1 4_MC shows_VVZ that_CST the_AT number_NN1 of_IO firms_NN2 that_CST invest_VV0 in_II the_AT same_DA function_NN1 is_VBZ two_MC times_NNT2 higher_RRR in_II manufacturing_NN1 than_CSN in_II service_NN1 sectors_NN2 ._. 
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<s>
Thus_RR ,_, it_PPH1 is_VBZ a_AT1 plausible_JJ strategy_NN1 to_TO break_VVI down_RP the_AT problem_NN1 of_IO investigating_VVG the_AT bias_NN1 of_IO rO_NN1 into_II investigating_VVG the_AT bias_NN1 of_IO rI_NN2 and_CC rRI_NN2 separately_RR ,_, which_DDQ is_VBZ much_RR easier_JJR ._. 
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<s>
The_AT procedure_NN1 of_IO creating_VVG simulated_JJ doublets_NN2 was_VBDZ repeated_VVN 100_MC times_NNT2 ._. 
</s>
<s>
This_DD1 greatly_RR speeds_VVZ up_RP computations_NN2 using_VVG the_AT formulae_NN2 of_IO Dunnett_NP1 and_CC Sobel_NP1 (_( 1954_MC )_) and_CC ensure_VV0 all_DB parameters_NN2 can_VM be_VBI correctly_RR estimated_VVN ._. 
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<s>
The_AT link_NN1 between_II currency_NN1 availability_NN1 and_CC cash_NN1 withdrawals_NN2 validates_VVZ the_AT usefulness_NN1 of_IO our_APPGE geographic_JJ shock_NN1 measure_NN1 and_CC provides_VVZ prima_JJ21 facie_JJ22 evidence_NN1 of_IO a_AT1 cash_NN1 shortfall_NN1 ._. 
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<s>
Since_CS there_EX are_VBR concave_JJ and_CC convex_JJ parts_NN2 to_II the_AT utility_NN1 ,_, we_PPIS2 could_VM reasonably_RR expect_VVI that_CST either_DD1 might_VM be_VBI dominant_JJ ,_, depending_II21 on_II22 parameters_NN2 ._. 
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<s>
There_EX are_VBR exceptions_NN2 ,_, however_RR ;_; see_VV0 Sections_NN2 5_MC and_CC 5_MC ._. 
</s>
<s>
Then_RT in_II (_( 3_MC )_) the_AT b_ZZ1 content_NN1 of_IO the_AT upper_JJ (_( dark_JJ yellow_JJ )_) site_NN1 is_VBZ increased_VVN ._. 
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<s>
The_AT algorithm_NN1 is_VBZ outlined_VVN here_RL ,_, with_IW pseudocode_NN1 presented_VVN in_II Algorithm_NN1 3.2_MC ._. 
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<s>
It_PPH1 is_VBZ easy_JJ to_TO understand_VVI that_CST the_AT effect_NN1 of_IO increasing_VVG r_ZZ1 and_CC imp_NN1 is_VBZ to_TO reduce_VVI the_AT usable_JJ space_NN1 and_CC increase_VVI the_AT probability_NN1 of_IO deceleration_NN1 ._. 
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<s>
Represents_VVZ a_AT1 significant_JJ value_NN1 at_II the_AT level_NN1 of_IO 1%_NNU ._. 
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<s>
We_PPIS2 made_VVD the_AT assumption_NN1 that_CST the_AT variables_NN2 are_VBR pairwise_RR independent_JJ ._. 
</s>
<s>
For_IF <equation>_FO ,_, the_AT disjoint_JJ decomposition_NN1 of_IO <equation>_FO ,_, the_AT vector_NN1 <equation>_FO ,_, with_IW elements_NN2 arranged_VVN in_II the_AT proper_JJ order_NN1 ,_, represents_VVZ the_AT situation_NN1 where_RRQ all_DB the_AT components_NN2 in_II the_AT subsystem_NN1 <equation>_FO are_VBR in_II the_AT working(failed)_JJ state_NN1 and_CC the_AT states_NN2 of_IO the_AT components_NN2 in_II <equation>_FO are_VBR as_CSA specified_VVN by_II the_AT binary_JJ vector_NN1 <equation>_FO ._. 
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<s>
It_PPH1 is_VBZ not_XX difficult_JJ to_TO find_VVI that_CST under_II the_AT maximum_JJ degree_NN1 attack_NN1 mode_NN1 ,_, the_AT two_MC metrics_NN2 have_VH0 similar_JJ trends_NN2 at_II the_AT beginning_NN1 ,_, and_CC the_AT network_NN1 gradually_RR collapses_VVZ as_II the_AT P_NP1 value_NN1 increases_NN2 ._. 
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The_AT parameter_NN1 <equation>_FO is_VBZ not_XX directly_RR observable_JJ and_CC varies_VVZ over_II time_NNT1 and_CC across_II countries_NN2 ._. 
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<s>
We_PPIS2 follow_VV0 the_AT suggestion_NN1 by_II Kashyap_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 1993_MC )_) to_TO identify_VVI the_AT pass-through_JJ of_IO the_AT interest_NN1 rates_NN2 to_II the_AT credit_NN1 supply_NN1 ._. 
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<s>
Here_RL we_PPIS2 took_VVD advantage_NN1 of_IO the_AT stationarity_NN1 of_IO the_AT stochastic_JJ force_NN1 ,_, <equation>_FO ._. 
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<s>
Based_VVN on_II historical_JJ data_NN ,_, Pencavel_NP1 (_( 2015_MC )_) presents_VVZ evidence_NN1 that_CST productivity_NN1 decreases_VVZ with_IW increasing_JJ working_NN1 hours_NNT2 ._. 
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<s>
In_II relative_JJ terms_NN2 ,_, this_DD1 decline_NN1 is_VBZ slightly_RR more_RGR significant_JJ for_IF shorter-term_JJ contracts_NN2 than_CSN for_IF longer_JJR arrangements_NN2 ._. 
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<s>
This_DD1 function_NN1 adds_VVZ (_( i.e._REX ,_, moves_VVZ to_II X_ZZ1 )_) any_DD ∈zi∈_FO for_IF which_DDQ it_PPH1 finds_VVZ a_AT1 way_NN1 to_TO do_VDI so_RR that_DD1 decreases_VVZ cost()cost(Ci)_NN2 ._. 
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<s>
Several_DA2 authors_NN2 ,_, including_II Walls_NP1 (_( 1997_MC )_) ,_, Hand_NN1 (_( 2001_MC )_) ,_, McKenzie_NP1 (_( 2008_MC )_) and_CC others_NN2 fit_VV0 models_NN2 with_IW Paretian_JJ tails_NN2 to_II theatrical_JJ film_NN1 returns_VVZ data_NN ;_; Maddison_NP1 (_( 2004_MC )_) performs_VVZ a_AT1 similar_JJ exercise_NN1 for_IF Broadway_NP1 shows_VVZ ._. 
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<s>
It_PPH1 is_VBZ not_XX immediately_RR clear_JJ whether_CSW the_AT sequence_NN1 (_( )_) (_( Xk_FO )_) will_VM remain_VVI bounded_VVN since_CS several_DA2 spectral_JJ penalty_NN1 functions_NN2 (_( like_II the_AT MC+_FO penalty_NN1 )_) are_VBR bounded_VVN ._. 
</s>
<s>
Such_DA efforts_NN2 will_VM encounter_VVI theoretical_JJ difficulties_NN2 ,_, such_II21 as_II22 problems_NN2 of_IO collapsibility_NN1 of_IO the_AT causal_JJ effect_NN1 parameters_NN2 ._. 
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<s>
Instead_II21 of_II22 working_VVG with_IW an_AT1 abstract_JJ filtered_JJ probability_NN1 space_NN1 satisfying_VVG the_AT usual_JJ conditions_NN2 ,_, we_PPIS2 recall_VV0 an_AT1 explicit_JJ construction_NN1 ._. 
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<s>
However_RR ,_, the_AT essential_JJ results_NN2 were_VBDR preserved_VVN in_II31 comparison_II32 with_II33 the_AT initially_RR estimated_VVN models_NN2 ._. 
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<s>
The_AT sample_NN1 period_NN1 ranges_VVZ from_II February_NPM1 1984_MC to_II December_NPM1 2018_MC ._. 
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<s>
The_AT shape_NN1 of_IO curve_NN1 of_IO the_AT velocity_NN1 difference_NN1 between_II the_AT front_NN1 and_CC target_NN1 vehicles_NN2 in_II Fig._NN1 14(c)_FO and_CC (_( d_ZZ1 )_) is_VBZ broadly_RR the_AT same_DA as_CSA the_AT velocity_NN1 standard_NN1 deviation_NN1 in_II Fig._NN1 14(a)_FO and_CC (_( b_ZZ1 )_) ,_, but_CCB the_AT second_MD peak_NN1 is_VBZ less_RGR obvious_JJ (_( pure_JJ car_NN1 traffic_NN1 does_VDZ not_XX have_VHI the_AT second_MD peak_NN1 )_) ._. 
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<s>
As_II a_AT1 result_NN1 ,_, we_PPIS2 obtain_VV0 five_MC OWA_NP1 ._. 
</s>
<s>
We_PPIS2 explore_VV0 the_AT role_NN1 of_IO large_JJ eigenvalues_NN2 by_II dissecting_VVG data_NN matrices_NN2 with_IW singular_JJ value_NN1 decomposition_NN1 in_II section_NN1 ._. 
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<s>
Government_NN1 expenditure_NN1 is_VBZ further_RRR classified_VVN by_II economic_JJ or_CC functional_JJ classification_NN1 ._. 
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<s>
Equating_VVG this_DD1 number_NN1 to_II one_PN1 recovers_VVZ the_AT rule_NN1 ._. 
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<s>
Felbermayr_VV0 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2011_MC )_) also_RR use_VV0 both_RR cross-sectional_JJ (_( 85_MC countries_NN2 )_) and_CC panel_NN1 (_( 20_MC OECD_NP1 countries_NN2 )_) analysis_NN1 and_CC find_VV0 that_CST greater_JJR trade_NN1 openness_NN1 is_VBZ usually_RR associated_VVN with_IW a_AT1 lower_JJR rate_NN1 of_IO structural_JJ unemploymentnever_NN1 a_AT1 higher_JJR ratein_NN1 the_AT long_JJ run_NN1 ._. 
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<s>
Three_MC descriptive_JJ facts_NN2 can_VM be_VBI derived_VVN from_II the_AT data_NN ._. 
</s>
<s>
Results_NN2 concerning_II the_AT convergence_NN1 of_IO this_DD1 approach_NN1 to_II an_AT1 approximate_JJ solution_NN1 of_IO the_AT inverse_JJ problem_NN1 are_VBR provided_VVN ._. 
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<s>
Figure_NN1 8_MC visualizes_VVZ the_AT modeling_NN1 outcome_NN1 ._. 
</s>
<s>
Reluctance_NN1 to_TO contemplate_VVI large_JJ unpleasant_JJ risks_NN2 has_VHZ been_VBN raised_VVN in_II the_AT literature_NN1 ,_, particularly_RR in_II other_JJ developing_JJ country_NN1 settings_NN2 where_RRQ people_NN are_VBR severely_RR limited_VVN in_II the_AT steps_NN2 they_PPHS2 can_VM take_VVI to_TO address_VVI these_DD2 risks_NN2 (_( Case_NN1 et_RA21 al_RA22 ._. 
</s>
<s>
2013_MC )_) ._. 
</s>
<s>
Using_VVG macro-data_NN from_II 23_MC OECD_NP1 countries_NN2 and_CC applying_VVG a_AT1 vector_NN1 autoregressive_JJ model_NN1 ,_, Thurik_NP1 et_RA21 al_RA22 ._. '_NULL s_ZZ1 (_( 2008_MC )_) results_NN2 indicate_VV0 that_DD1 unemployment_NN1 and_CC self-employment_NN1 simultaneously_RR affect_VV0 each_PPX221 other_PPX222 ._. 
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<s>
Other_JJ rate_NN1 constants_NN2 are_VBR the_AT same_DA as_CSA in_II figure_NN1 1(b)_FO ._. 
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<s>
Columns_NN2 5_MC through_II 8_MC identify_VV0 treated_JJ industries_NN2 as_CSA those_DD2 with_IW implied_JJ changes_NN2 above_II the_AT 95th_MD percentile_NN1 ._. 
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<s>
In_II this_DD1 regime_NN1 ,_, it_PPH1 was_VBDZ shown_VVN that_CST the_AT behavior_NN1 changes_NN2 in_II a_AT1 drastic_JJ manner_NN1 from_II the_AT leading_JJ order_NN1 in_II τ_NULL result_NN1 at_II small_JJ τ_NULL ._. 
</s>
<s>
The_AT matrix_NN1 elements_NN2 considered_VVN here_RL are_VBR also_RR relevant_JJ for_IF calculating_VVG the_AT spectrum_NN1 of_IO the_AT Hamiltonian_JJ deformed_JJ by_II a_AT1 primary_JJ operator_NN1 ._. 
</s>
<s>
As_II such_DA ,_, we_PPIS2 adopt_VV0 the_AT phase-by-phase_JJ approach_NN1 instead_II21 of_II22 using_VVG the_AT path-by-path_JJ approach_NN1 ._. 
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<s>
The_AT backbone_NN1 tree_NN1 topologies_NN2 are_VBR set_VVN to_II those_DD2 of_IO previously_RR published_VVN phylogenies_NN2 for_IF yeast_NN1 (_( Shen_FW et_RA21 al._RA22 ,_, 2016_MC ;_; Sulo_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ,_, Drosophila_NP1 (_( Miller_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) and_CC Columbicola_NP1 (_( Boyd_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
</s>
<s>
If<equation>_FO ,_, for_IF all<equation>_FO ,_, then_RT with<equation>_FO ,_, After_CS ,_, to_TO calculate_VVI the_AT heat_NN1 flux_NN1 ,_, at_RR21 first_RR22 ,_, it_PPH1 is_VBZ necessary_JJ to_TO obtain_VVI the_AT accumulative_JJ energy_NN1 extracted_VVN from_II the_AT hot_JJ or_CC inserted_VVN to_II the_AT cold_JJ baths_NN2 ._. 
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<s>
SNBNMF_NP1 can_VM be_VBI adapted_VVN to_TO use_VVI the_AT prediction_NN1 of_IO APOBEC_NP1 expression_NN1 (_( sum_NN1 of_IO APOBEC3a_FO and_CC APOBEC3b_FO )_) in_II a_AT1 supervised_JJ learning_NN1 task_NN1 ._. 
</s>
<s>
The_AT gene_NN1 expression_NN1 profiles_NN2 comprised_VVD scores_NN2 that_CST were_VBDR calculated_VVN using_VVG the_AT characteristic_JJ direction_NN1 method_NN1 (_( Clark_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) ,_, which_DDQ compares_VVZ gene_NN1 expression_NN1 levels_NN2 in_II diseased_JJ tissues_NN2 with_IW those_DD2 in_II control_NN1 tissues_NN2 ._. 
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<s>
Taking_VVG the_AT cost_NN1 of_IO new_JJ high-speed_JJ railway_NN1 stations_NN2 built_VVN in_II China_NP1 in_II the_AT past_JJ decade_NNT1 as_II a_AT1 reference_NN1 ,_, the_AT cost_NN1 of_IO medium_NN1 and_CC large_JJ high-speed_JJ railway_NN1 stations_NN2 is_VBZ about_RG 15_MC billion_NNO (_( such_II21 as_II22 Guangzhou_NP1 south_ND1 railway_NN1 station_NN1 and_CC Wuhan_NP1 railway_NN1 station_NN1 )_) ._. 
</s>
<s>
Columns_NN2 show_VV0 the_AT effect_NN1 of_IO misspecification_NN1 on_II each_DD1 of_IO three_MC types_NN2 of_IO parameters_NN2 ._. 
</s>
<s>
The_AT dependent_JJ variable_NN1 of_IO interest_NN1 is_VBZ the_AT weekly_JJ average_JJ levels_NN2 of_IO ozone_NN1 (_( <equation>_FO )_) with_IW relatively_RR small_JJ autocorrelation_NN1 coefficients_NN2 ,_, and_CC the_AT other_JJ five_MC variables_NN2 are_VBR :_: nitrogen_NN1 dioxide_NN1 ,_, <equation>_FO ,_, (_( N_ZZ1 )_) sulphur_NN1 dioxide_NN1 ,_, <equation>_FO ,_, (_( S_ZZ1 )_) ,_, respirable_JJ particulates_NN2 (_( P_ZZ1 )_) ,_, temperature_NN1 (_( T_ZZ1 )_) ,_, and_CC humidity_NN1 (_( H_ZZ1 )_) ._. 
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This_DD1 article_NN1 starts_VVZ by_II documenting_VVG the_AT main_JJ patterns_NN2 of_IO markups_NN2 in_II the_AT U.S._NP1 economy_NN1 over_II the_AT past_JJ six_MC decades_NNT2 ,_, and_CC in_II doing_VDG so_RR we_PPIS2 provide_VV0 new_JJ stylized_JJ facts_NN2 on_II the_AT cross-section_NN1 and_CC time-series_NN of_IO markups_NN2 ._. 
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The_AT rewiring_JJ score_NN1 between_II these_DD2 time_NNT1 points_NN2 showed_VVD a_AT1 transition_NN1 of_IO the_AT topic_NN1 weights_NN2 across_II time_NNT1 points_NN2 ._. 
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The_AT N_ZZ1 (_( 0_MC ,_, 2_MC )_) effect_NN1 θ_NULL s_ZZ1 was_VBDZ included_VVN to_TO afford_VVI extra_JJ spatial_JJ residual_JJ variability_NN1 ._. 
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We_PPIS2 concluded_VVD from_II their_APPGE feedback_NN1 that_CST our_APPGE tool_NN1 will_VM be_VBI an_AT1 essential_JJ component_NN1 in_II vascular_JJ modeling_NN1 and_CC simulation_NN1 in_II the_AT future_NN1 ._. 
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The_AT estimated_JJ WTP_NP1 of_IO $1,070_NNU combined_VVN with_IW the_AT net_JJ cost_NN1 of_IO $1,074_NNU implies_VVZ an_AT1 MVPF_NP1 of_IO 0.996_MC (_( which_DDQ rounds_VVZ to_II 1_MC1 in_II Table_NN1 II_MC )_) ._. 
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Below_RL we_PPIS2 review_VV0 the_AT methods_NN2 discussed_VVN and_CC evaluated_VVN in_II the_AT remainder_NN1 of_IO this_DD1 paper_NN1 ._. 
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Most_DAT species_NN (_( 48%48%_FO )_) have_VH0 estimated_VVN proportions_NN2 of_IO variances_NN2 due_II21 to_II22 common_JJ factors_NN2 less_DAR than_CSN 0.25_MC ._. 
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We_PPIS2 also_RR repeat_VV0 our_APPGE tests_NN2 on_II the_AT subsample_NN1 of_IO industries_NN2 for_IF which_DDQ there_EX have_VH0 not_XX been_VBN substantive_JJ changes_NN2 to_II industry_NN1 classification_NN1 codes_NN2 over_II long_JJ periods_NN2 of_IO time_NNT1 ._. 
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Hence_RR the_AT contribution_NN1 of_IO the_AT first_MD term_NN1 to_II the_AT search_NN1 time_NNT1 in_II equation_NN1 is_VBZ negligible_JJ ._. 
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Nevertheless_RR ,_, to_II further_JJR address_NN1 this_DD1 concern_NN1 ,_, we_PPIS2 use_VV0 a_AT1 randomization_NN1 inference_NN1 (_( RI_NP1 )_) approach_VV0 that_CST conducts_VVZ exact_JJ finite_JJ sample_NN1 inference_NN1 and_CC remains_VVZ valid_JJ even_CS21 when_CS22 the_AT number_NN1 of_IO observations_NN2 is_VBZ small_JJ (_( cf._VV0 ,_, Rosenbaum_NP1 ,_, 2002_MC )_) ._. 
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The_AT relationship_NN1 between_II the_AT two_MC incremental_JJ spreading_JJ prevalence_NN1 δ_NULL Pappro_NN1 and_CC δ_NULL PQMF_NP1 for_IF β_NULL =0.1_FO and_CC β_NULL =0.3_FO ._. 
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It_PPH1 contains_VVZ 162_MC binding_JJ domains_NN2 from_II the_AT RNA_NN1 Recognition_NN1 Motif_NN1 (_( RRM_NP1 )_) family_NN1 ._. 
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Fig._NN1 9_MC shows_VVZ histograms_NN2 of_IO the_AT forecasting_VVG errors_NN2 (_( residuals_NN2 )_) for_IF the_AT discount_NN1 ,_, 3_MC month_NNT1 and_CC 6_MC month_NNT1 yields_VVZ with_IW maturities_NN2 in_II 1_MC1 year_NNT1 and_CC 3_MC years_NNT2 (_( results_NN2 for_IF yields_NN2 of_IO other_JJ maturities_NN2 are_VBR comparable_JJ )_) ._. 
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It_PPH1 is_VBZ clearly_RR observed_VVN that_CST the_AT coarse_JJ graining_NN1 has_VHZ a_AT1 role_NN1 in_II smoothing_VVG out_RP intense_JJ fluctuations_NN2 ._. 
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The_AT difference_NN1 between_II TM_NP1 in_II equation_NN1 6_MC )_) and_CC TS_ZZ2 in_II equation_NN1 7_MC )_) is_VBZ the_AT variance_NN1 estimator_NN1 in_II the_AT denominator_NN1 ._. 
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However_RR ,_, adversarial_JJ adaptation_NN1 that_CST addresses_VVZ the_AT discrepancies_NN2 in_II both_DB2 the_AT input_NN1 and_CC output_NN1 spaces_NN2 have_VH0 not_XX yet_RR been_VBN explored_VVN neither_RR for_IF pharmacogenomics_NN2 nor_CC for_IF other_JJ applications_NN2 ._. 
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Results_NN2 obtained_VVN by_II the_AT most_RGT straightforward_JJ aggregation_NN1 approach_NN1 (_( sum_NN1 aggregation_NN1 ,_, solid_JJ lines_NN2 )_) demonstrated_VVD that_CST Proline_NP1 retrieves_VVZ a_AT1 high_JJ proportion_NN1 of_IO true_JJ positive_JJ (_( TP_NP1 )_) UPS1_FO proteins_NN2 while_CS maintaining_VVG a_AT1 low_JJ rate_NN1 of_IO false_JJ positive_JJ (_( FP_NP1 )_) yeast_VV0 proteins_NN2 ._. 
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As_CSA argued_VVN above_RL ,_, we_PPIS2 apply_VV0 difference_NN1 GMM_NP1 to_TO estimate_VVI a_AT1 dynamic_JJ panel_NN1 model_NN1 with_IW fixed_JJ effects_NN2 where_RRQ the_AT lagged_JJ unemployment_NN1 rate_NN1 is_VBZ treated_VVN as_CSA endogenous_JJ variables_NN2 ._. 
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This_DD1 choice_NN1 is_VBZ motivated_VVN by_II the_AT Nyquist–Shannon_NP1 criterion_NN1 ,_, which_DDQ is_VBZ also_RR used_VVN for_IF basis_NN1 function_NN1 placement_NN1 by_II Zammit-Mangion_NP1 et_RA21 al_RA22 ._. 
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(_( 2012_MC )_) ._. 
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In_II31 accordance_II32 with_II33 recent_JJ works_NN &lsqb;_( 9_MC ,_, 10_MC &rsqb;_) ,_, the_AT limit_NN1 probability_NN1 distribution_NN1 of_IO equation_NN1 (_( 1_MC1 )_) ,_, given_VVN in_II figure_NN1 3_MC ,_, is_VBZ obtained_VVN as_II a_AT1 linear_JJ combination_NN1 of_IO a_AT1 Gaussian_JJ arises_VVZ from_II the_AT initial_JJ conditions_NN2 located_VVN in_II the_AT chaotic_JJ sea_NN1 and_CC a_AT1 q-Gaussian_JJ with_IW q_ZZ1 =_FO 1.935_MC ±_FO 0.005_MC arises_VVZ from_II the_AT initial_JJ conditions_NN2 located_VVN in_II the_AT stability_NN1 islands_NN2 ._. 
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The_AT authors_NN2 are_VBR grateful_JJ to_II the_AT Editor_NN1 ,_, the_AT Associate_JJ Editor_NN1 ,_, two_MC referees_NN2 ,_, Michel_NP1 Baes_NP2 ,_, Fabio_NP1 Bellini_NP1 ,_, Paul_NP1 Embrechts_NP1 ,_, Fabio_NP1 Maccheroni_NP1 ,_, Tiantian_JJ Mao_NP1 ,_, Alfred_NP1 Müller_NP1 ,_, Marcel_NP1 Nutz_NP1 ,_, Jan_NP1 Oboj_NP1 ,_, Sidney_NP1 Resnick_NP1 ,_, Ludger_NP1 Rüschendorf_NP1 ,_, Alexander_NP1 Schied_JJ and_CC Xiaolu_NP1 Tan_NN1 for_IF various_JJ helpful_JJ suggestions_NN2 and_CC discussions_NN2 on_II an_AT1 earlier_JJR version_NN1 of_IO the_AT paper_NN1 ._. 
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For_IF settings_NN2 where_CS either_RR the_AT false_JJ discovery_NN1 standard_NN1 deviation_NN1 normalized_VVD by_II expected_JJ value_NN1 or_CC the_AT power_NN1 standard_NN1 deviation_NN1 normalized_VVD by_II expected_JJ value_NN1 is_VBZ greater_JJR than_CSN 0.01_MC ,_, we_PPIS2 plot_VV0 the_AT expected_JJ value_NN1 with_IW a_AT1 cross_NN1 and_CC the_AT 1_MC1 around_II the_AT mean_JJ with_IW a_AT1 rectangle_NN1 ._. 
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Additional_JJ simulation_NN1 results_NN2 for_IF different_JJ parameter_NN1 values_NN2 are_VBR given_VVN in_II the_AT online_JJ supplementary_JJ material_NN1 ._. 
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The_AT country_NN1 of_IO the_AT first_MD author_NN1 also_RR plays_VVZ a_AT1 role_NN1 in_II the_AT number_NN1 of_IO citations_NN2 :_: the_AT United_NP1 Kingdom_NP1 ,_, the_AT USA_NP1 ,_, Switzerland_NP1 ,_, and_CC Austria_NP1 are_VBR the_AT four_MC countries_NN2 that_RG best_RRT predict_VV0 academic_JJ success_NN1 in_II31 terms_II32 of_II33 the_AT average_JJ number_NN1 of_IO citations_NN2 per_II year_NNT1 ._. 
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The_AT difference_NN1 between_II the_AT extremes_NN2 has_VHZ a_AT1 t-value_NN1 of_IO 1.56_MC ._. 
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It_PPH1 is_VBZ seen_VVN that_CST the_AT NuPF_NN1 outperforms_VVZ the_AT BPF_NP1 for_IF the_AT whole_JJ range_NN1 of_IO values_NN2 of_IO N_ZZ1 in_II the_AT experiment_NN1 ,_, in_II31 terms_II32 of_II33 both_DB2 the_AT mean_JJ and_CC the_AT standard_JJ deviation_NN1 of_IO the_AT errors_NN2 ,_, although_CS the_AT NMSE_NN1 values_NN2 become_VV0 closer_JJR for_IF larger_JJR N._NNU The_AT plot_NN1 on_II the_AT right_NN1 displays_VVZ the_AT values_NN2 of_IO x2_FO ,_, t_ZZ1 and_CC its_APPGE estimates_NN2 for_IF a_AT1 typical_JJ simulation_NN1 ._. 
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Obsolescence_NN1 lowers_VVZ the_AT return_NN1 to_TO experience_VVI ,_, flattening_VVG the_AT age-earnings_NN2 profile_VV0 in_II faster-changing_JJR careers_NN2 ._. 
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We_PPIS2 next_MD report_NN1 the_AT corresponding_JJ results_NN2 subject_II21 to_II22 precision_NN1 in_II Fig._NN1 3_MC ._. 
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We_PPIS2 further_RRR examined_VVD whether_CSW the_AT module_NN1 knowledge_NN1 from_II DAVID_NP1 generates_VVZ a_AT1 reasonable_JJ module_NN1 size_NN1 and_CC facilitates_VVZ robust_JJ RAD_NN1 deconvolution_NN1 ._. 
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Thus_RR the_AT density_NN1 of_IO XX_NP1 equals_VVZ f(xx)=c_NNU (_( F1_FO (_( x1_FO )_) ,_, ,_, Fd(xd)_NP1 )_) i∈_FO &lsqb;_( d_ZZ1 &rsqb;_) fi(xi)_NN2 ,_, where_CS fi_NN2 and_CC f_ZZ1 are_VBR the_AT densities_NN2 of_IO Xi_NN1 and_CC XX_NP1 respectively_RR ._. 
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The_AT estimation_NN1 accuracy_NN1 is_VBZ adversely_RR affected_VVN when_CS the_AT size_NN1 of_IO the_AT training_NN1 sample_NN1 decreases_VVZ quickly_RR ._. 
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We_PPIS2 highlight_VV0 the_AT predictors_NN2 selected_VVN in_II each_DD1 application_NN1 with_IW and_CC without_IW using_VVG the_AT two-step_JJ algorithm_NN1 in_II Fig._NN1 5_MC ._. 
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An_AT1 essential_JJ function_NN1 of_IO Pentecostal_JJ churches_NN2 in_II Ghana_NP1 ,_, in_RR21 particular_RR22 in_II urban_JJ areas_NN2 ,_, is_VBZ to_TO offer_VVI a_AT1 place_NN1 for_IF social_JJ gathering_NN1 ._. 
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Due_II21 to_II22 the_AT absence_NN1 of_IO a_AT1 definite_JJ starting_NN1 date_NN1 of_IO the_AT COVID-19_MC outbreak_NN1 ,_, the_AT stabilization_NN1 period_NN1 was_VBDZ defined_VVN as_II the_AT period_NN1 from_II Aug_NPM1 1_MC1 ,_, 2019_MC ,_, to_II Dec_NPM1 31_MC ,_, 2019_MC ,_, while_CS the_AT fluctuation_NN1 period_NN1 was_VBDZ defined_VVN as_II the_AT period_NN1 from_II Jan_NPM1 1_MC1 ,_, 2020_MC ,_, to_II Mar_NPM1 1_MC1 ,_, 2020_MC (_( the_AT end_NN1 date_NN1 of_IO data_NN collection_NN1 for_IF this_DD1 study_NN1 )_) ._. 
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To_TO understand_VVI the_AT source_NN1 of_IO each_DD1 latent_JJ factor_NN1 more_RGR closely_RR ,_, we_PPIS2 estimate_VV0 the_AT factor_NN1 loading_NN1 coefficients_NN2 (_( <equation>_FO )_) ._. 
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It_PPH1 is_VBZ assumed_VVN in_II secondstage_NN1 assumption_NN1 4_MC that_CST the_AT sizes_NN2 Ni_NP1 of_IO the_AT PSUs_NN1 are_VBR comparable_JJ ,_, and_CC that_CST the_AT numbers_NN2 ni_NN2 of_IO SSUs_NN1 selected_VVN inside_II the_AT PSUs_NN1 are_VBR also_RR comparable_JJ ._. 
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<s>
In_II31 addition_II32 to_II33 demonstrating_VVG H-MIN_NNU for_IF few_DA2 well_RR known_VVN bipartite_JJ states_NN2 ,_, its_APPGE direct_JJ connection_NN1 to_II other_JJ MINs_NNT2 are_VBR also_RR shown_VVN ._. 
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However_RR ,_, we_PPIS2 point_VV0 out_RP that_CST such_DA an_AT1 expected_JJ result_NN1 is_VBZ no_RR21 longer_RR22 easy_JJ to_TO prove_VVI in_RR21 general_RR22 (_( for_REX21 example_REX22 when_CS the_AT premia_NN1 do_VD0 not_XX coincide_VVI )_) ._. 
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<s>
Mean_JJ reversion_NN1 in_II different_JJ variables_NN2 '_NULL dynamics_NN is_VBZ spotlighted_VVN in_II researches_NN2 such_II21 as_II22 Poterba_NP1 and_CC Summers_NP1 (_( 1988_MC )_) ,_, Wong_NP1 and_CC Lo_FW (_( 2009_MC )_) and_CC Liang_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) ._. 
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Using_VVG a_AT1 2_MC per_II d.f_NNU ._. 
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for_IF model_NN1 selection_NN1 allows_VVZ both_RR the_AT model-order_NN1 and_CC possible_JJ scaling_NN1 to_TO be_VBI determined_VVN together_RL ,_, as_CSA the_AT plateau_NN1 to_II the_AT right_NN1 of_IO the_AT model_NN1 selection_NN1 curve_NN1 can_VM be_VBI used_VVN as_II a_AT1 scaling_NN1 factor_NN1 ._. 
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This_DD1 holds_VVZ for_IF changes_NN2 in_II employment_NN1 and_CC establishment_NN1 closures_NN2 as_RG well_RR as_CSA for_IF both_DB2 lender_NN1 experience_NN1 measures_NN2 ._. 
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The_AT SL_NP1 methods_NN2 additionally_RR required_VVN a_AT1 set_NN1 of_IO negative_JJ genes_NN2 for_IF each_DD1 given_JJ geneset_NN1 for_IF training_NN1 ,_, and_CC both_RR SL_NP1 and_CC LP_NN1 methods_NN2 require_VV0 a_AT1 set_NN1 of_IO negative_JJ genes_NN2 for_IF each_DD1 geneset_NN1 for_IF testing_NN1 ._. 
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For_IF solving_VVG this_DD1 problem_NN1 ,_, the_AT PLoM_NN1 method_NN1 published_VVN in_II Soize_NP1 and_CC Ghanem_NP1 (_( 2016_MC )_) requires_VVZ key_JJ modifications_NN2 ._. 
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The_AT number_NN1 l_ZZ1 can_VM be_VBI chosen_VVN to_II one_PN1 unless_CS there_EX is_VBZ an_AT1 issue_NN1 of_IO numerical_JJ instability_NN1 of_IO leapfrog_NN1 trajectories_NN2 ._. 
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CBT_NP1 seems_VVZ to_TO have_VHI a_AT1 dampening_JJ effect_NN1 on_II unemployment_NN1 ._. 
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Firms_NN2 are_VBR invited_VVN to_TO answer_VVI most_DAT of_IO the_AT questions_NN2 on_II a_AT1 three-category_JJ scale_NN1 :_: '_NULL good/better_NN1 '_NULL ,_, '_NULL satisfactorily/same_FU '_NULL or_CC '_NULL bad/worse_NN1 '_NULL ._. 
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Notably_RR ,_, it_PPH1 is_VBZ not_XX possible_JJ to_TO apply_VVI directly_RR the_AT results_NN2 of_IO Bouchard_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 11_MC &rsqb;_) (_( or_CC a_AT1 straightforward_JJ adaptation_NN1 of_IO them_PPHO2 )_) to_II <equation>_FO ._. 
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GSE19830_FO contains_VVZ RMA-normalized_JJ Affymetrix_NN1 expressions_NN2 of_IO cells_NN2 from_II rat_NN1 brain_NN1 ,_, liver_NN1 and_CC lung_NN1 biospecimens_NN2 (_( Shen-Orr_NP1 et_RA21 al._RA22 ,_, 2010_MC )_) ._. 
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If_CS they_PPHS2 do_VD0 ,_, the_AT project_NN1 occurs_VVZ and_CC both_DB2 parties_NN2 receive_VV0 the_AT same_DA payoff_NN1 they_PPHS2 get_VV0 from_II a_AT1 settlement_NN1 but_CCB with_IW an_AT1 additional_JJ proxy_NN1 fight_NN1 cost_NN1 ._. 
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SparkINFERNO_NN1 implements_VVZ scalable_JJ genomic_JJ querying_NN1 (_( Supplementary_JJ Figs_NN2 S2_FO and_CC S3_FO )_) using_VVG Spark_NN1 parallel_NN1 transformations_NN2 and_CC Giggle-based_JJ genomic_JJ indexing_NN1 (_( Layer_NN1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
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The_AT background_NN1 filtration_NN1 <equation>_FO is_VBZ now_RT the_AT natural_JJ filtration_NN1 of_IO the_AT process_NN1 <equation>_FO ._. 
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Percolation_NN1 serves_VVZ as_II a_AT1 typical_JJ paradigm_NN1 in_II statistical_JJ physics_NN1 and_CC probability_NN1 theory_NN1 ,_, due_II21 to_II22 its_APPGE wide_JJ applications_NN2 in_II a_AT1 large_JJ variety_NN1 of_IO natural_JJ and_CC technological_JJ and_CC social_JJ systems_NN2 ._. 
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In_II this_DD1 section_NN1 we_PPIS2 introduce_VV0 the_AT statistics_NN that_CST are_VBR used_VVN to_TO detect_VVI the_AT evolution_NN1 of_IO the_AT interbank_JJ network_NN1 structure_NN1 ._. 
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One_MC1 iteration_NN1 of_IO the_AT algorithm_NN1 goes_VVZ as_CSA follows_VVZ ._. 
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The_AT correction_NN1 affects_VVZ very_RG little_DA1 on_II the_AT values_NN2 of_IO the_AT percolation_NN1 threshold_NN1 :_: it_PPH1 makes_VVZ the_AT percolation_NN1 threshold_NN1 systematically_RR smaller_JJR by_II about_II 0.005%_FO on_II average_NN1 ._. 
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Fig._NN1 11_MC shows_VVZ the_AT distribution_NN1 of_IO the_AT number_NN1 of_IO surviving_JJ banks_NN2 in_II the_AT banking_NN1 network_NN1 system_NN1 under_II different_JJ deposit_NN1 reserve_NN1 ratio_NN1 ._. 
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This_DD1 method_NN1 is_VBZ applicable_JJ to_TO implicitly_RR defined_VVN models_NN2 having_VHG analytically_RR intractable_JJ transition_NN1 densities_NN2 ._. 
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First_MD ,_, our_APPGE results_NN2 remain_VV0 when_CS using_VVG various_JJ subsamples_NN2 and_CC different_JJ performance_NN1 measures_NN2 ._. 
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Column_NN1 (_( 5_MC )_) reports_VVZ the_AT IV_MC regression_NN1 that_CST estimates_VVZ the_AT U.S._NP1 export_NN1 supply_NN1 curve_NN1 at_II the_AT variety_NN1 level_NN1 ._. 
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In_RR21 addition_RR22 ,_, the_AT frequency_NN1 location_NN1 of_IO these_DD2 sharp_JJ peaks_NN2 changed_VVN over_II time_NNT1 ._. 
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Among_II such_DA settings_NN2 ,_, sales_NN is_VBZ particularly_RR attractive_JJ from_II a_AT1 research_NN1 perspective_NN1 ._. 
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To_TO exclude_VVI any_DD effect_NN1 from_II a_AT1 particular_JJ machine_NN1 ,_, the_AT runs_NN2 were_VBDR repeated_VVN on_II two_MC other_JJ machines_NN2 ._. 
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HiChIP-Peaks_NN2 is_VBZ freely_RR available_JJ at_II https_NNU :_: ._. 
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Lastly_RR ,_, there_EX is_VBZ the_AT related_JJ reduced-form_JJ literature_NN1 on_II intensity-based_JJ models_NN2 for_IF large_JJ portfolio_NN1 credit_NN1 risk_NN1 (_( see_VV0 e.g._REX Of_IO note_NN1 ,_, since_CS separate_JJ random_JJ walks_NN2 can_VM be_VBI performed_VVN in_II parallel_NN1 ,_, RNBRW_NP1 weights_NN2 can_VM be_VBI estimated_VVN very_RG quickly_RR ,_, even_RR for_IF large_JJ graphs_NN2 ._. 
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Alternatively_RR ,_, one_PN1 can_VM simply_RR test_VVI for_IF pairwise_RR independence_NN1 between_II clusterings_NN2 ,_, instead_II21 of_II22 testing_VVG for_IF mutual_JJ independence_NN1 between_II clusterings_NN2 on_II all_DB views_NN2 ,_, as_CSA we_PPIS2 did_VDD in_II Section_NN1 6_MC ._. 
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As_CS31 far_CS32 as_CS33 we_PPIS2 are_VBR aware_JJ ,_, these_DD2 estimates_NN2 are_VBR not_XX available_JJ from_II results_NN2 elsewhere_RL in_II the_AT literature_NN1 ,_, and_CC we_PPIS2 believe_VV0 they_PPHS2 are_VBR of_IO independent_JJ interest_NN1 ._. 
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Once_RR all_DB monotigs_NN2 are_VBR computed_VVN ,_, they_PPHS2 are_VBR given_VVN as_CSA input_VVN to_II BLight_NN1 ._. 
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Ostwald_VV0 ripening_VVG involves_VVZ decay_NN1 of_IO short_JJ islands_NN2 and_CC growth_NN1 of_IO long_JJ islands_NN2 ._. 
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However_RR ,_, even_CS21 if_CS22 the_AT assumptions_NN2 are_VBR true_JJ ,_, the_AT IV_MC estimates_NN2 in_RR21 general_RR22 only_RR yield_VV0 a_AT1 local_JJ average_JJ treatment_NN1 effect_NN1 for_IF the_AT part_NN1 of_IO the_AT population_NN1 that_CST changes_VVZ treatment_NN1 status_NN1 due_II21 to_II22 the_AT instrument_NN1 ,_, called_VVN compliers_NN2 (_( see_VV0 Imbens_NN2 and_CC Angrist_NN1 1994_MC )_) ._. 
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The_AT K1_FO group_NN1 ,_, i.e._REX ,_, the_AT group_NN1 of_IO oscillators_NN2 with_IW the_AT coupling_NN1 constant_NN1 K1_FO <_FO 0_MC ,_, generally_RR shows_VVZ a_AT1 broader_JJR angular_JJ distribution_NN1 than_CSN the_AT K2_NP1 group_NN1 ,_, because_CS each_DD1 K1_FO oscillator_NN1 repels_VVZ all_DB the_AT other_JJ oscillators_NN2 ,_, whereas_CS each_DD1 K2_NP1 oscillator_NN1 attracts_VVZ all_DB the_AT other_JJ oscillators_NN2 ._. 
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Because_II21 of_II22 the_AT data_NN structure_NN1 ,_, each_DD1 node_NN1 from_II A_ZZ1 can_VM maximally_RR have_VHI one_MC1 possible_JJ edge_NN1 that_CST connects_VVZ it_PPH1 to_II a_AT1 node_NN1 in_II B_ZZ1 and_CC vice_RR21 versa_RR22 ._. 
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The_AT monomials_NN2 with_IW sign_NN1 indicate_VV0 a_AT1 microhomology_NN1 feature_NN1 ,_, which_DDQ are_VBR identical_JJ patterns_NN2 repeating_VVG around_II the_AT cut_NN1 site_NN1 and_CC enrich_VV0 for_IF a_AT1 deletion_NN1 outcome_NN1 ._. 
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For_REX21 example_REX22 ,_, in_II Fig._NN1 10_MC ,_, <equation>_FO spans_VVZ a_AT1 range_NN1 of_IO approximately_RR 420_MC ,_, whereas_CS the_AT other_JJ ALE_NN1 main_JJ effect_NN1 functions_NN2 have_VH0 ranges_NN2 less_DAR than_CSN 100_MC ._. 
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Betas_NN2 are_VBR estimated_VVN using_VVG daily_JJ night_NNT1 returns_VVZ over_RP a_AT1 one-year_JJ rolling_JJ window_NN1 ._. 
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Another_DD1 possible_JJ case_NN1 is_VBZ that_CST the_AT scaling_NN1 of_IO rank–size_JJ distribution_NN1 will_VM break_VVI into_II two_MC parts_NN2 ,_, and_CC thus_RR two_MC scaling_NN1 ranges_NN2 will_VM appear_VVI on_II a_AT1 log–log_NN1 plot_NN1 for_IF rank–size_JJ distribution_NN1 ._. 
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<s>
This_DD1 can_VM be_VBI understood_VVN with_IW the_AT work_NN1 of_IO Borgas_NP2 ,_, which_DDQ connects_VVZ Lagrangian_JJ and_CC Eulerian_JJ self-similarity_NN1 ._. 
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<s>
We_PPIS2 show_VV0 that_CST the_AT sum_NN1 of_IO the_AT optimal_JJ investment_NN1 amounts_NN2 is_VBZ given_VVN by_II the_AT optimal_JJ amount_NN1 in_II the_AT associated_JJ univariate_NN1 case_NN1 ;_; further_RRR ,_, if_CS the_AT non-hedgeable_JJ claim_NN1 sizes_NN2 are_VBR multi-variate_JJ Gaussian_JJ ,_, the_AT allocation_NN1 of_IO the_AT total_JJ optimal_JJ investment_NN1 amount_NN1 into_II the_AT single_JJ asset_NN1 dimensions_NN2 follows_VVZ the_AT covariance_NN1 principle_NN1 (_( refer_VV0 to_II Theorem_NN1 12_MC ,_, Theorem_NN1 13_MC )_) ._. 
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<s>
Thus_RR ,_, the_AT direct_JJ effect_NN1 for_IF a_AT1 population_NN1 intervention_NN1 corresponds_VVZ to_II contrasts_NN2 between_II treatment_NN1 regimes_NN2 of_IO a_AT1 randomized_JJ experiment_NN1 via_II interventions_NN2 on_II A_ZZ1 and_CC Z_ZZ1 ,_, unlike_II the_AT natural_JJ direct_JJ effect_NN1 for_IF the_AT average_JJ treatment_NN1 effect_NN1 (_( Robins_NN2 and_CC Richardson_NP1 ,_, 2010_MC )_) ._. 
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<s>
Hence_RR we_PPIS2 conclude_VV0 that_CST there_EX exists_VVZ a_AT1 solution_NN1 to_II (_( 2.23_MC )_) ._. 
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<s>
It_PPH1 should_VM be_VBI noted_VVN that_CST the_AT model_NN1 here_RL in_II fact_NN1 is_VBZ homogeneous_JJ so_CS it_PPH1 may_VM be_VBI argued_VVN that_CST we_PPIS2 should_VM instead_RR use_VVI the_AT homogeneous_JJ estimator_NN1 where_CS we_PPIS2 set_VV0 ?_NULL /_FO (_( )_) =1_FO ?_NULL /_FO (_( x_ZZ1 )_) =1_FO in_II (_( 30_MC )_) –_- (_( 32_MC )_) ._. 
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<s>
This_DD1 reduced_VVD functional_JJ coherence_NN1 is_VBZ more_RGR visible_JJ when_CS using_VVG spectral_JJ clustering_NN1 ,_, which_DDQ is_VBZ more_RGR sensitive_JJ to_II network_NN1 rewiring_VVG because_CS it_PPH1 groups_VVZ together_RL nodes_NN2 that_CST are_VBR densely_RR connected_VVN as_CSA its_APPGE sole_JJ criterion_NN1 ._. 
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<s>
The_AT ALE_NN1 plots_NN2 that_CST we_PPIS2 have_VH0 proposed_VVN in_II this_DD1 paper_NN1 are_VBR an_AT1 alternative_JJ that_CST has_VHZ two_MC important_JJ advantages_NN2 over_II PD_NP1 plots_NN2 ._. 
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<s>
U∈U0_FO ,_, H∈Hwhere_FO U0_FO is_VBZ the_AT set_NN1 of_IO all_DB the_AT orthonormal_JJ bases_NN2 for_IF R_ZZ1 (_( U_ZZ1 &lsqb;_( k_ZZ1 &rsqb;_) )_) ,_, and_CC H_ZZ1 is_VBZ the_AT set_NN1 of_IO all_DB normalized_JJ indicator_NN1 matrices_NN2 for_IF K-rays_NN2 data_NN ,_, i.e.<equation>_FO ._. 
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<s>
If_CS protecting_VVG their_APPGE strategies_NN2 from_II reverse_JJ engineering_NN1 is_VBZ an_AT1 underlying_JJ factor_NN1 in_II investors_NN2 '_NULL behavior_NN1 ,_, we_PPIS2 would_VM expect_VVI them_PPHO2 to_TO generally_RR avoid_VVI disclosure_NN1 ,_, be_VBI it_PPH1 on_II the_AT long_JJ side_NN1 or_CC the_AT short_JJ side_NN1 ._. 
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<s>
We_PPIS2 now_RT combine_VV0 the_AT previously_RR estimated_VVN parameters_NN2 with_IW a_AT1 supply_NN1 side_NN1 of_IO the_AT U.S._NP1 economy_NN1 ._. 
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<s>
In_II other_JJ words_NN2 ,_, to_TO prevent_VVI the_AT traffic_NN1 efficiency_NN1 decreasing_VVG ,_, it_PPH1 is_VBZ better_JJR to_TO avoid_VVI the_AT narrow_JJ door_NN1 ._. 
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<s>
In_II this_DD1 section_NN1 we_PPIS2 discuss_VV0 the_AT performance_NN1 of_IO the_AT proposed_JJ MSM_NP1 of_IO Gaussian_JJ densities_NN2 through_II the_AT analysis_NN1 of_IO different_JJ synthetic_JJ and_CC real_JJ datasets_NN2 ._. 
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<s>
In_II contrast_NN1 ,_, the_AT weak_JJ correlation_NN1 (_( small_JJ PCC_NP1 )_) only_RR plays_VVZ the_AT role_NN1 of_IO maintaining_VVG network_NN1 connectivity_NN1 &lsqb;_( 23_MC &rsqb;_) ._. 
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<s>
Because_CS <equation>_FO ,_, <equation>_FO is_VBZ increasing_JJ and_CC <equation>_FO a.s_NNU ._. 
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<s>
for_IF all_DB <equation>_FO and_CC <equation>_FO ,_, it_PPH1 is_VBZ not_XX hard_JJ to_TO see_VVI that_CST <equation>_FO for_IF any_DD <equation>_FO ._. 
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<s>
Given_VVN its_APPGE power_NN1 of_IO precisely_RR modeling_VVG the_AT mixed_JJ effects_NN2 from_II multiple_JJ sources_NN2 of_IO random_JJ variations_NN2 ,_, the_AT method_NN1 has_VHZ been_VBN widely_RR used_VVN in_II biomedical_JJ computation_NN1 ,_, for_REX21 instance_REX22 in_II the_AT genome-wide_JJ association_NN1 studies_NN2 (_( GWASs_NP1 )_) that_CST aim_VV0 to_TO detect_VVI genetic_JJ variance_NN1 significantly_RR associated_VVN with_IW phenotypes_NN2 such_II21 as_II22 human_JJ diseases_NN2 ._. 
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<s>
Again_RT ,_, we_PPIS2 see_VV0 that_CST the_AT use_NN1 of_IO the_AT L2_FO loss_NN1 ,_, using_VVG either_RR FPOP_VV0 or_CC WBS_NP1 ,_, performs_VVZ poorly_RR when_CS the_AT degrees_NN2 of_IO freedom_NN1 are_VBR small_JJ ._. 
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We_PPIS2 present_VV0 a_AT1 control_NN1 to_TO reduce_VVI the_AT infection_NN1 thanks_NN2 to_II the_AT exact_JJ solution_NN1 ._. 
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<s>
Advanced_JJ economies_NN2 differ_VV0 widely_RR in_II the_AT policies_NN2 and_CC institutions_NN2 that_CST support_VV0 school-to-work_JJ transitions_NN2 for_IF young_JJ people_NN (_( Ryan_NP1 2001_MC )_) ._. 
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<s>
To_TO prove_VVI (_( 4.21_MC )_) ,_, we_PPIS2 can_VM use_VVI the_AT same_DA arguments_NN2 together_RL with_IW Fatou_NP1 '_NULL s_ZZ1 lemma_NN1 ._. 
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<s>
K-means_NN ,_, hierarchical_JJ ,_, self-organizing_JJ map_NN1 (_( SOM_NNU1 )_) ,_, and_CC fuzzy_JJ C-means_NN are_VBR some_DD of_IO the_AT popular_JJ clustering_NN1 methods_NN2 which_DDQ are_VBR commonly_RR used_VVN in_II different_JJ academic_JJ works_NN (_( Nanda_NP1 et_RA21 al_RA22 ._. 
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<s>
2010_MC )_) ._. 
</s>
<s>
The_AT first_MD shows_VVZ that_CST for_IF the_AT Ornstein–Uhlenbeck_NN1 model_NN1 (_( <equation>_FO for_IF all_DB <equation>_FO )_) ,_, we_PPIS2 always_RR have_VH0 the_AT positive_JJ recurrence_NN1 property_NN1 ._. 
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<s>
Note_VV0 that_CST the_AT distinction_NN1 between_II red_JJ and_CC black_JJ ,_, as_II31 well_II32 as_II33 the_AT distinction_NN1 between_II green_JJ and_CC light_JJ green_NN1 ,_, are_VBR only_RR used_VVN for_IF visualization_NN1 ,_, in_II order_NN1 to_TO better_RRR illustrate_VVI the_AT features_NN2 of_IO the_AT pattern_NN1 generator_NN1 ;_; they_PPHS2 do_VD0 not_XX affect_VVI the_AT analysis_NN1 ._. 
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<s>
In_II fact_NN1 ,_, this_DD1 extension_NN1 is_VBZ crucial_JJ for_IF the_AT study_NN1 of_IO electronic_JJ systems_NN2 where_RRQ the_AT charge_NN1 distribution_NN1 is_VBZ a_AT1 continuous_JJ function_NN1 of_IO the_AT position_NN1 ._. 
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<s>
We_PPIS2 thus_RR have_VH0 to_TO resort_NN1 to_II a_AT1 different_JJ approach_NN1 ,_, that_CST we_PPIS2 now_RT describe_VV0 ,_, and_CC that_CST also_RR allows_VVZ us_PPIO2 to_TO determine_VVI some_DD aspects_NN2 of_IO the_AT behavior_NN1 of_IO the_AT SCGF_NP1 that_CST go_VV0 beyond_II the_AT exponential_NN1 behavior_NN1 of_IO equation_NN1 ._. 
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<s>
This_DD1 is_VBZ no_AT surprise_NN1 since_CS the_AT Pi_NN1 model_NN1 is_VBZ a_AT1 state-of-the-art_NN1 semi-supervised_VVN model_NN1 that_CST makes_VVZ use_NN1 of_IO both_DB2 labelled_VVN data_NN from_II the_AT gold_NN1 standard_NN1 set_NN1 and_CC unlabelled_JJ data_NN from_II METASPACE_NP1 ._. 
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<s>
Intuitively_RR ,_, the_AT IV_MC averages_NN2 out_RP two_MC types_NN2 of_IO performance_NN1 comparisons_NN2 :_: first_MD ,_, the_AT performance_NN1 difference_NN1 between_II high-potential_JJ participants_NN2 and_CC similar_JJ potential_JJ type_NN1 one_MC1 applicants_VVZ who_PNQS were_VBDR mistakenly_RR rejected_VVN ,_, and_CC second_NNT1 ,_, the_AT performance_NN1 difference_NN1 between_II low-potential_JJ rejected_JJ applicants_NN2 and_CC similar_JJ potential_JJ type_NN1 two_MC participants_NN2 who_PNQS were_VBDR mistakenly_RR accepted_VVN ._. 
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<s>
Just_RR before_II cell_NN1 division_NN1 ,_, two_MC precursor_NN1 pools_NN2 ,_, which_DDQ will_VM be_VBI inherited_VVN by_II the_AT two_MC daughter_NN1 cells_NN2 and_CC are_VBR represented_VVN schematically_RR by_II D1_FO and_CC D2_FO in_II Fig._NN1 3_MC ,_, begin_VV0 to_TO form_VVI by_II gradual_JJ transfer_NN1 of_IO precursors_NN2 from_II the_AT mother_NN1 pool_NN1 with_IW the_AT rates_NN2 kcy1_FO and_CC kcy2_FO ,_, respectively_RR ._. 
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<s>
Even_CS21 if_CS22 this_DD1 statement_NN1 were_VBDR challenged_VVN ,_, we_PPIS2 point_VV0 out_RP that_CST the_AT consequence_NN1 of_IO this_DD1 study_NN1 is_VBZ to_TO show_VVI that_DD1 membership_NN1 of_IO these_DD2 two_MC classes_NN2 can_VM be_VBI predicted_VVN with_IW a_AT1 non-trivial_JJ accuracy_NN1 on_II unseen_JJ test_NN1 data_NN ,_, and_CC hence_RR these_DD2 two_MC classes_NN2 must_VM have_VHI different_JJ enrichments_NN2 and_CC characteristics_NN2 ._. 
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No_AT structural_JJ break_NN1 is_VBZ detected_VVN in_II the_AT daily_JJ return_NN1 series_NN ,_, the_AT numbers_NN2 of_IO structural_JJ breaks_NN2 shown_VVN in_II the_AT last_MD column_NN1 of_IO Table_NN1 3_MC are_VBR different_JJ for_IF the_AT daily_JJ volatilities_NN2 ,_, and_CC all_DB the_AT daily_JJ return_NN1 and_CC volatility_NN1 series_NN experience_VV0 the_AT properties_NN2 of_IO fat_NN1 tailed_VVD and_CC stationary_JJ ._. 
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A_ZZ1 Nash_NP1 bargaining_NN1 model_NN1 is_VBZ applied_VVN to_TO identify_VVI the_AT "_" best_JJT "_" weights_NN2 allocated_VVN to_II the_AT two_MC parties_NN2 ._. 
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<s>
The_AT sensitivity_NN1 analysis_NN1 results_NN2 are_VBR consistent_JJ with_IW the_AT actual_JJ situation_NN1 ,_, which_DDQ reflects_VVZ the_AT effectiveness_NN1 of_IO the_AT model_NN1 and_CC algorithm_NN1 ._. 
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<s>
The_AT reason_NN1 is_VBZ that_CST the_AT fluctuation_NN1 path_NN1 which_DDQ reaches_VVZ a_AT1 point_NN1 x_II that_DD1 is_VBZ not_XX a_AT1 saddle_NN1 (_( i.e._REX x_MC xs_MC2 )_) displays_VVZ a_AT1 boundary_NN1 layer_NN1 of_IO size_NN1 τ_NULL close_RR to_II t_ZZ1 =_FO 0_MC ._. 
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<s>
The_AT gene_NN1 module_NN1 compression_NN1 in_II our_APPGE work_NN1 is_VBZ knowledge-driven_JJ ,_, which_DDQ is_VBZ reliable_JJ even_CS21 when_CS22 only_RR limited_JJ tumor_NN1 samples_NN2 are_VBR available_JJ ,_, in_II contrast_NN1 to_II prior_JJ work_NN1 using_VVG data-driven_JJ clustering_NN1 of_IO coexpressed_JJ genes_NN2 (_( Zaitsev_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ,_, which_DDQ is_VBZ more_RGR dependent_JJ on_II large_JJ sample_NN1 sizes_NN2 ._. 
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<s>
When_CS <equation>_FO is_VBZ a_AT1 constant_JJ (_( and_CC more_RGR generally_RR ,_, when_CS <equation>_FO is_VBZ boundedly_RR replicable_JJ )_) ,_, it_PPH1 is_VBZ known_VVN that_CST the_AT product_NN1 of_IO the_AT primal_JJ and_CC dual_JJ optimisers_NN2 is_VBZ a_AT1 martingale_NN1 (_( see_VV0 e.g._REX We_PPIS2 show_VV0 that_CST for_IF any_DD r1_FO r2_FO the_AT current_NN1 grows_VVZ linearly_RR with_IW time_NNT1 ,_, with_IW a_AT1 coefficient_NN1 proportional_JJ to_II (_( r1_FO r2_FO )_) ._. 
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The_AT last_MD set_NN1 are_VBR all_DB relatively_RR neutral_JJ ._. 
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<s>
We_PPIS2 use_VV0 generalized_JJ latent_JJ variable_NN1 models_NN2 (_( Skrondal_NP1 and_CC Rabe-Hesketh_NP1 2004_MC )_) to_TO formulate_VVI a_AT1 measurement_NN1 model_NN1 for_IF MTMM_NP1 data_NN from_II an_AT1 administrative_JJ register_NN1 and_CC a_AT1 survey_NN1 that_CST can_VM account_VVI for_IF nonclassical_JJ error_NN1 processes_NN2 ,_, nonnormal_JJ distributions_NN2 ,_, and_CC categorical_JJ data_NN ._. 
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<s>
To_TO evaluate_VVI our_APPGE method_NN1 ,_, we_PPIS2 apply_VV0 it_PPH1 to_II a_AT1 bacterial_JJ artificial_JJ chromosome_NN1 (_( BAC_NP1 )_) array_NN1 datasetFootnote_NN1 1_MC1 with_IW experimentally_RR tested_VVN DNA_NN1 copy_NN1 number_NN1 alterations_NN2 ._. 
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Rather_RR ,_, it_PPH1 is_VBZ possible_JJ that_CST monetary_JJ policies_NN2 respond_VV0 to_II booming_JJ credit_NN1 conditions_NN2 ._. 
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<s>
The_AT choice_NN1 of_IO B*2_FO can_VM also_RR be_VBI informed_VVN by_II the_AT extent_NN1 to_II which_DDQ the_AT meta-analyzed_JJ studies_NN2 differ_VV0 with_II31 respect_II32 to_II33 existing_JJ confounding_JJ control_NN1 ._. 
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<s>
For_IF all_DB data_NN generating_JJ mechanisms_NN2 ,_, we_PPIS2 set_VV0 <equation>_FO ,_, <equation>_FO ,_, <equation>_FO ,_, and_CC <equation>_FO ._. 
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We_PPIS2 show_VV0 the_AT data_NN for_IF several_DA2 values_NN2 of_IO ?_MC up_RG21 to_RG22 1000_MC ._. 
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For_IF each_DD1 individual_JJ year_NNT1 of_IO study_NN1 ,_, the_AT selected_JJ spatial_JJ filters_NN2 provided_VVD a_AT1 tool_NN1 which_DDQ was_VBDZ able_JK to_TO capture_VVI the_AT spatial_JJ dependency_NN1 of_IO the_AT mortality_NN1 data_NN ,_, accounting_VVG for_IF the_AT spatial_JJ variability_NN1 driving_VVG the_AT calculated_JJ MC_NN1 values_NN2 ._. 
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<s>
Centroid-based_JJ clustering_NN1 ,_, e.g._REX k-means_JJ clustering_NN1 ,_, is_VBZ a_AT1 method_NN1 often_RR used_VMK to_TO classify_VVI objects_NN2 into_II their_APPGE nearest_JJT centroids_NN2 ,_, where_CS the_AT number_NN1 of_IO centroids_NN2 k_ZZ1 is_VBZ preset_VVN and_CC the_AT initial_NN1 k_ZZ1 centroids_NN2 are_VBR selected_VVN randomly_RR ._. 
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<s>
The_AT authors_NN2 declare_VV0 that_CST they_PPHS2 have_VH0 no_AT known_JJ competing_JJ financial_JJ interests_NN2 or_CC personal_JJ relationships_NN2 that_CST could_VM have_VHI appeared_VVN to_TO influence_VVI the_AT work_NN1 reported_VVN in_II this_DD1 paper_NN1 ._. 
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<s>
Vehtari_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2019c_FO )_) propose_VV0 a_AT1 finite_JJ sample_NN1 diagnostic_JJ based_VVN on_II fitting_VVG a_AT1 generalized_JJ Pareto_NP1 distribution_NN1 to_II the_AT upper_JJ tail_NN1 of_IO the_AT distribution_NN1 of_IO the_AT importance_NN1 weights_NN2 ._. 
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<s>
Since_CS intensity_NN1 captures_VVZ the_AT number_NN1 of_IO trades_NN2 ,_, Out-intensity_NN1 is_VBZ measured_VVN by_II the_AT number_NN1 of_IO times_NNT2 that_DD1 bank_NN1 j_ZZ1 has_VHZ lent_VVN to_II k_ZZ1 ,_, with_IW k=1_FO ,_, ,_, n_ZZ1 ._. 
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<s>
Previous_JJ studies_NN2 in_II DR_NNB were_VBDR primarily_RR focused_VVN on_II drug_NN1 and_CC disease_NN1 activities_NN2 to_TO uncover_VVI statistical_JJ associations_NN2 between_II them_PPHO2 (_( Dakshanamurthy_NP1 et_RA21 al._RA22 ,_, 2012_MC ;_; Sanseau_NP1 et_RA21 al._RA22 ,_, 2012_MC ;_; Ye_PPY et_RA21 al._RA22 ,_, 2014_MC )_) ._. 
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Controlling_VVG for_IF these_DD2 differences_NN2 would_VM require_VVI additional_JJ measurements_NN2 of_IO the_AT respective_JJ samples_NN2 ._. 
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<s>
Non-sample_JJ people_NN who_PNQS move_VV0 into_II a_AT1 SOEP_NN1 household_NN1 are_VBR also_RR included_VVN in_II all_DB subsequent_JJ iterations_NN2 of_IO the_AT survey_NN1 ._. 
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<s>
Therefore_RR ,_, they_PPHS2 do_VD0 not_XX have_VHI access_NN1 to_II either_RR the_AT information_NN1 contained_VVD in_RP ,_, or_CC the_AT constraints_NN2 imposed_VVD by_RP ,_, the_AT UMI-to-gene_NP1 mappings_NN2 ._. 
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The_AT model_NN1 targets_NN2 16_MC benchmarks_NN2 :_: all_DB coefficients_NN2 except_II21 for_II22 cell_NN1 fixed_JJ effects_NN2 from_II the_AT postlottery_JJ participation_NN1 and_CC consumption_NN1 EPFs_NN2 ,_, and_CC the_AT lottery_NN1 coefficients_NN2 from_II participation_NN1 and_CC consumption_NN1 regressions_NN2 by_II prelottery_JJ participation_NN1 status_NN1 ._. 
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Similar_JJ to_II the_AT procedure_NN1 used_VVN for_IF municipal_JJ bonds_NN2 ,_, we_PPIS2 sort_VV0 corporate_JJ bonds_NN2 into_II six_MC groups_NN2 based_VVN on_II the_AT average_JJ monthly_JJ trading_NN1 volume_NN1 in_II 2003_MC :_: the_AT no-trade_JJ group_NN1 (_( Group_NN1 0_MC )_) and_CC the_AT quintile_JJ groups_NN2 conditional_NN1 on_II positive_JJ trading_NN1 volume_NN1 (_( Groups_NN2 1–5_MCMC )_) ._. 
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File_VV0 B_ZZ1 contained_VVD the_AT data_NN from_II m_ZZ1 =_FO 696023_MC second_NNT1 deliveries_NN2 from_II 1999_MC until_II 2010_MC ._. 
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By_II contrast_NN1 ,_, the_AT project_NN1 fixed_JJ effects_NN2 can_VM be_VBI understood_VVN as_II the_AT quality_NN1 of_IO the_AT project_NN1 that_CST all_DB judges_NN2 agree_VV0 on_RP ;_; they_PPHS2 represent_VV0 "_" adjusted_JJ scores_NN2 "_" after_II controlling_VVG for_IF potential_JJ systematic_JJ differences_NN2 in_II scoring_VVG generosity_NN1 across_II judges_NN2 ._. 
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First_MD ,_, human_JJ capital_NN1 ,_, which_DDQ is_VBZ generally_RR considered_VVN to_TO be_VBI significant_JJ (_( Bartkowska_NP1 and_CC Riedla_NP1 2012_MC )_) ,_, is_VBZ not_XX irreplaceable_JJ in_II this_DD1 paper_NN1 ._. 
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Also_RR ,_, we_PPIS2 discuss_VV0 an_AT1 alternative_JJ approach_NN1 to_II Binary_JJ Segmentation_NN1 that_CST can_VM be_VBI applied_VVN to_II the_AT univariate_NN1 mapped_VVN series_NN ._. 
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<s>
As_CSA x_ZZ1 increases_VVZ ,_, xrb_NNU increases_NN2 and_CC 2lx_FO decreases_VVZ ;_; therefore_RR ,_, the_AT numerator_NN1 and_CC denominator_NN1 in_II Eq_NN1 ._. 
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(_( 53_MC )_) decrease_VV0 ._. 
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Yet_RR ,_, such_DA a_AT1 description_NN1 of_IO identifiability_NN1 is_VBZ necessary_JJ to_TO select_VVI perturbations_NN2 that_CST maximize_VV0 the_AT number_NN1 of_IO inferable_JJ parameters_NN2 ._. 
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The_AT top-scoring_JJ compounds_NN2 are_VBR then_RT recommended_VVN for_IF experimental_JJ testing_NN1 ._. 
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An_AT1 important_JJ ,_, yet_RR often_RR neglected_VVN ,_, feature_NN1 of_IO crude_JJ oil_NN1 price_NN1 when_CS examining_VVG its_APPGE effect_NN1 on_II economic_JJ activity_NN1 is_VBZ that_DD1 crude_JJ oil_NN1 price_NN1 has_VHZ undergone_VVN dramatic_JJ changes_NN2 in_II its_APPGE behaviour_NN1 in_II the_AT last_MD five_MC decades_NNT2 ._. 
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We_PPIS2 conclude_VV0 based_VVN on_II the_AT preceding_JJ analysis_NN1 that_CST the_AT black-white_JJ intergenerational_JJ gap_NN1 in_II individual_JJ income_NN1 is_VBZ substantial_JJ for_IF men_NN2 ,_, but_CCB quite_RG small_JJ for_IF women_NN2 ._. 
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<s>
The_AT curve_NN1 LC1_FO is_VBZ determined_VVN by_II a_AT1 set_NN1 of_IO points_NN2 in_II a_AT1 two-dimensional_JJ continuous_JJ differentiable_JJ mapping_NN1 T_ZZ1 that<equation>_FO ,_, where_CS Jacobian_JJ matrix_NN1 is_VBZ ,_, ,_, the_AT critical_JJ curves_NN2 LC1_FO can_VM be_VBI calculated_VVN as(25)<equation>_FO ,_, where_CS <equation>_FO ._. 
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Here_RL ,_, we_PPIS2 choose_VV0 the_AT discrete_JJ Markov_NP1 chain_NN1 (_( DMC_NP1 )_) method_NN1 since_CS it_PPH1 requires_VVZ less_DAR time_NNT1 and_CC still_RR predicts_VVZ the_AT Monte_NP1 Carlo_NP1 simulation_NN1 well_RR ._. 
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Spreading_JJ dynamics_NN of_IO complex_JJ networks_NN2 has_VHZ attracted_VVN more_RRR and_CC more_DAR attention_NN1 and_CC is_VBZ currently_RR an_AT1 area_NN1 of_IO intense_JJ interest_NN1 ._. 
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Engle_NP1 (_( 2002_MC )_) presented_VVD dynamic_JJ conditional_JJ correlation_NN1 models_NN2 to_TO estimate_VVI time-varying_JJ correlations_NN2 ._. 
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Another_DD1 issue_NN1 that_CST deserves_VVZ an_AT1 in-depth_JJ investigation_NN1 is_VBZ to_TO investigate_VVI how_RRQ the_AT accuracy_NN1 of_IO China_NP1 '_NULL s_ZZ1 preliminary_JJ data_NN is_VBZ optimally_RR improved_VVN based_VVN only_RR on_II econometric_JJ models_NN2 ._. 
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Set_VV0 values_NN2 of_IO all_DB nodes_NN2 to_II 0_MC ._. 
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For_IF each_DD1 read_VVD ,_, we_PPIS2 sampled_VVD 15-mer_JJ matches_NN2 from_II the_AT read_NN1 and_CC found_VVD their_APPGE positions_NN2 in_II the_AT human_JJ genome_NN1 variation_NN1 graph_NN1 using_VVG a_AT1 k-mer_JJ lookup_NN1 table_NN1 ._. 
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However_RR ,_, for_IF the_AT case_NN1 of_IO a_AT1 memory-less_DAR dissipation_NN1 ,_, the_AT subdiffusive_JJ regime_NN1 does_VDZ not_XX exist_VVI &lsqb;_( 25_MC &rsqb;_) ,_, and_CC thermal_JJ fluctuations_NN2 are_VBR treated_VVN as_II the_AT delta-correlated_JJ Gaussian_JJ noise_NN1 ._. 
</s>
<s>
We_PPIS2 demonstrate_VV0 that_CST our_APPGE guided_JJ intermediate_JJ resampling_JJ filter_NN1 (_( GIRF_NP1 ,_, Algorithm_NN1 3_MC )_) can_VM be_VBI used_VVN to_TO enable_VVI likelihood-based_JJ inference_NN1 in_II this_DD1 class_NN1 of_IO models_NN2 ._. 
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See_VV0 Fig._NN1 11_MC for_IF a_AT1 graphical_JJ summary_NN1 of_IO our_APPGE approach_NN1 ._. 
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Serpentine_NP1 binning_NN1 can_VM be_VBI applied_VVN on_II a_AT1 single_JJ matrix_NN1 ._. 
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<s>
Therefore_RR ,_, we_PPIS2 recommend_VV0 using_VVG only_JJ PCs_NN2 that_CST show_VV0 structure_NN1 (_( e.g._REX PC1–PC16_NP1 in_II Supplementary_JJ Fig_NN1 ._. 
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<s>
S9_FO )_) and_CC excluding_VVG PCs_NN2 that_CST do_VD0 not_XX seem_VVI to_TO capture_VVI any_DD population_NN1 structure_NN1 (_( e.g._REX PC17–PC20_NP1 in_II Supplementary_JJ Fig_NN1 ._. 
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<s>
S9_FO )_) ._. 
</s>
<s>
The_AT null_JJ hypothesis_NN1 of_IO no_AT treatment_NN1 effect_NN1 is<equation>_FO for_IF all_DB possible_JJ t_ZZ1 and_CC v_ZZ1 ,_, versus_II the_AT alternative_NN1 that_CST H0_FO does_VDZ not_XX hold_VVI ,_, where_RRQ (_( t_ZZ1 ,_, v_ZZ1 ,_, 1_MC1 )_) and_CC (_( t_ZZ1 ,_, v_ZZ1 ,_, 0_MC )_) are_VBR the_AT true_JJ underlying_JJ hazard_NN1 functions_NN2 of_IO 1X1*_FO and_CC 0X0*_FO respectively_RR ,_, for_IF an_AT1 individual_JJ with_IW covariate_NN1 V=v_FO ._. 
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<s>
Since_CS particle_NN1 filters_NN2 provide_VV0 approximations_NN2 of_IO the_AT marginal_JJ likelihood_NN1 in_II HMMs_NP1 ,_, the_AT iAPF_NN1 can_VM also_RR be_VBI used_VVN in_II alternative_JJ parameter_NN1 estimation_NN1 procedures_NN2 ,_, such_II21 as_II22 simulated_JJ maximum_JJ likelihood_NN1 (_( Lerman_NP1 and_CC Manski_NP1 1981_MC ;_; Diggle_NP1 and_CC Gratton_NP1 1984_MC )_) ._. 
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<s>
Inadmissibility_NN1 of_IO the_AT best_JJT affine_JJ equivariant_JJ estimator_NN1 (_( BAEE_NP1 )_) of_IO <equation>_FO is_VBZ established_VVN by_II deriving_VVG a_AT1 Stein-type_JJ estimator_NN1 ._. 
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<s>
Dietrich_NP1 Stauffer_NP1 was_VBDZ very_RG keen_JJ in_II propagating_VVG basic_JJ statistical_JJ mechanics_NN2 ideas_NN2 and_CC models_NN2 toward_II other_JJ branches_NN2 of_IO sciences_NN2 &lsqb;_( 1_MC1 &rsqb;_) ,_, &lsqb;_( 2_MC &rsqb;_) ,_, &lsqb;_( 3_MC &rsqb;_) ,_, &lsqb;_( 4_MC &rsqb;_) ._. 
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<s>
In_II Fig._NN1 3_MC we_PPIS2 show_VV0 the_AT residuals_NN2 Zon_NP1 the_AT globe_NN1 together_RL with_IW the_AT 8×88×8_FO box_NN1 (_( left_JJ panel_NN1 )_) and_CC a_AT1 zoomed-in_JJ view_NN1 of_IO these_DD2 residuals_NN2 around_II Papua_NP1 New_NP1 Guinea_NP1 (_( right_JJ panel_NN1 )_) ._. 
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An_AT1 example_NN1 of_IO this_DD1 is_VBZ given_VVN in_II Figure_NN1 1_MC1 ,_, for_IF a_AT1 dataset_NN1 of_IO significant_JJ wave_NN1 heights_NN2 ,_, to_TO be_VBI analyzed_VVN in_II Section_NN1 4.1_MC ._. 
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<s>
Zhou_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2019_MC )_) fixed_JJ 0=10=1_FO and_CC considered_VVD a_AT1 tMVN_NNU prior_JJ (_( 0_MC ,_, 2_MC )_) N_ZZ1 (_( 0_MC ,_, τ_NULL 2_MC )_) on_II (_( ,_, )_) (_( ,_, )_) restricted_VVN to_II the_AT region_NN1 given_VVN by_II the_AT inequality_NN1 constraints_NN2 in_II (_( 11_MC )_) ._. 
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<s>
In_II our_APPGE meta-analysis_NN1 ,_, we_PPIS2 attempted_VVD to_TO identify_VVI any_DD time_NNT1 correlation_NN1 present_NN1 in_II gene_NN1 activity_NN1 in_II the_AT EPIC_JJ dataset_NN1 ._. 
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We_PPIS2 sincerely_RR thank_VV0 the_AT anonymous_JJ reviewers_NN2 and_CC Editor_NN1 for_IF helpful_JJ remarks_NN2 ._. 
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Farhad_NP1 Khoeini_NP1 :_: Contributed_VVN in_II analyzing_VVG the_AT results_NN2 and_CC preparing_VVG the_AT manuscript_NN1 ._. 
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<s>
Considering_CS the_AT barycenters_VVZ in_II Fig._NN1 8_MC ,_, it_PPH1 seems_VVZ that_CST there_EX are_VBR no_RR very_RG clear_JJ effects_NN2 of_IO the_AT season_NNT1 on_II the_AT assaults_NN2 ._. 
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<s>
We_PPIS2 consider_VV0 a_AT1 singlesite_NN1 Gibbs_NP1 sampler_NN1 ,_, called_VVN a_AT1 heat_NN1 bath_NN1 algorithm_NN1 in_II this_DD1 context_NN1 ,_, to_TO approximate_VVI the_AT distribution_NN1 θ_NULL given_VVN a_AT1 value_NN1 of_IO θ_NULL ._. 
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<s>
With_IW the_AT parameters_NN2 and_CC the_AT factor-process_JJ values_NN2 ,_, we_PPIS2 can_VM in_II turn_VVI compute_VV0 the_AT difference_NN1 between_II the_AT model_NN1 and_CC market_VV0 CDS_NN2 spreads_VVZ ._. 
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<s>
Mishra_NN1 and_CC Smyth_NP1 (_( 2016_MC )_) find_VV0 that_CST futures_NN2 prices_NN2 provide_VV0 some_DD information_NN1 relevant_JJ for_IF predicting_VVG the_AT direction_NN1 of_IO change_NN1 in_II the_AT Henry_NP1 Hub_NN1 spot_NN1 prices_NN2 ;_; however_RR ,_, it_PPH1 is_VBZ not_XX enough_RR to_TO predict_VVI the_AT magnitude_NN1 of_IO price_NN1 changes_NN2 ._. 
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The_AT d-dimensional_JJ analog_NN1 of_IO generalizes_VVZ expression_NN1 (_( 10_MC )_) ,_, and_CC is_VBZ discussed_VVN in_II Remark_NN1 3_MC ._. 
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Exemplar_JJ areas_NN2 of_IO application_NN1 include_VV0 bioinformatics_NN2 (_( Olshen_NP1 et_RA21 al_RA22 ._. 
</s>
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2004_MC ;_; Futschik_NP1 et_RA21 al_RA22 ._. 
</s>
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2014_MC )_) ,_, ion_NN1 channels_NN2 (_( Hotz_NP1 et_RA21 al_RA22 ._. 
</s>
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2013_MC )_) ,_, climate_NN1 records_NN2 (_( Reeves_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
2007_MC )_) ,_, oceonagraphic_JJ data_NN (_( Killick_NP1 et_RA21 al_RA22 ._. 
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<s>
2010_MC ;_; Killick_NP1 ,_, Fearnhead_NP1 ,_, and_CC Eckley_NP1 2012_MC )_) ,_, and_CC finance_NN1 (_( Kim_NP1 ,_, Morley_NP1 ,_, and_CC Nelson_NP1 2005_MC )_) ._. 
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<s>
In_II Appendix_NN1 B_ZZ1 ,_, we_PPIS2 obtain_VV0 the_AT resolvent_NN1 measure_NN1 killed_VVN at_II <equation>_FO and_CC the_AT following_JJ result_NN1 as_II a_AT1 corollary_NN1 ._. 
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<s>
The_AT plots_NN2 of_IO locations_NN2 of_IO each_DD1 species_NN are_VBR shown_VVN in_II Fig._NN1 1_MC1 in_II the_AT supplementary_JJ material_NN1 ._. 
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<s>
The_AT denominator_NN1 for_IF import_NN1 (_( export_NN1 )_) share_NN1 is_VBZ the_AT total_NN1 2017_MC annual_JJ US$_FO value_NN1 of_IO all_DB U.S._NP1 imports_NN2 (_( exports_VVZ )_) ._. 
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<s>
These_DD2 indices_NN2 consist_VV0 of_IO stocks_NN2 ,_, bonds_NN2 ,_, real_JJ estate_NN1 and_CC money_NN1 market_NN1 ,_, usually_RR accounting_VVG for_IF most_DAT investments_NN2 by_II non-life_JJ insurers_NN2 (_( Eling_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ._. 
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<s>
Let_VV0 nbin_NN1 be_VBI the_AT total_JJ number_NN1 of_IO nodes_NN2 present_VV0 in_II the_AT predicted_JJ bin_NN1 and_CC define_VV0 ref_NN1 as_II the_AT reference_NN1 replicon_NN1 sequence_NN1 with_IW a_AT1 highest_JJT number_NN1 of_IO nodes_NN2 in_II each_DD1 bin_NN1 ._. 
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<s>
It_PPH1 shows_VVZ that_CST daily_JJ rainfall_NN1 is_VBZ a_AT1 binary_JJ event_NN1 with_IW plenty_PN of_IO data_NN (_( more_RRR than_CSN 66%_NNU of_IO the_AT whole_JJ sample_NN1 for_IF NYC_NP1 and_CC 90%_NNU for_IF LA_NP1 )_) taking_VVG the_AT value_NN1 of_IO zero_NN1 ._. 
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This_DD1 is_VBZ substantially_RR improved_VVN when_CS using_VVG the_AT optimized_JJ parameter_NN1 settings_NN2 with_IW penalty_NN1 15_MC ._. 
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When_CS macroscopic_JJ detailed_JJ balance_NN1 does_VDZ not_XX hold_VVI ,_, one_PN1 has_VHZ to_TO come_VVI back_RP to_II the_AT complete_JJ Hamilton–Jacobi_JJ equation_NN1 (_( 21_MC )_) whose_DDQGE steady-state_JJ solution_NN1 is_VBZ ._. 
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First_MD ,_, we_PPIS2 study_VV0 the_AT local_JJ effects_NN2 of_IO agricultural_JJ productivity_NN1 growth_NN1 ._. 
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The_AT greater_JJR the_AT value_NN1 of_IO the_AT degree_NN1 is_VBZ ,_, the_AT higher_JJR the_AT FDI_NP1 relationships_NN2 are_VBR ._. 
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<s>
Therefore_RR we_PPIS2 considered_VVD as_CSA diagnosed_VVN only_RR the_AT severe_JJ and_CC critical_JJ cases_NN2 ,_, which_DDQ are_VBR pronounced_JJ subjects_NN2 for_IF testing_NN1 ,_, and_CC 20%_NNU of_IO the_AT mild_JJ cases_NN2 ._. 
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Such_DA a_AT1 generalization_NN1 is_VBZ only_RR possible_JJ from_II Potts_NP1 models_NN2 with_IW an_AT1 external_JJ field_NN1 parameter_NN1 ._. 
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<s>
Simultaneously_RR ,_, the_AT three_MC initial_JJ values_NN2 are_VBR non-negative_JJ ,_, and_CC the_AT sum_NN1 of_IO N(t)_NN1 is_VBZ an_AT1 invariant_JJ ._. 
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<s>
This_DD1 property_NN1 is_VBZ analogous_JJ to_II what_DDQ occurs_VVZ in_II standard_JJ group_NN1 sequential_JJ designs_NN2 ,_, e.g._REX using_VVG efficacy_NN1 stopping_VVG boundaries_NN2 of_IO O_ZZ1 '_NULL Brien_NP1 and_CC Fleming_NP1 (_( 1979_MC )_) ,_, which_DDQ decrease_VV0 (_( on_II the_AT zstatistic_JJ scale_NN1 )_) at_II each_DD1 stage_NN1 because_CS more_DAR information_NN1 is_VBZ available_JJ ._. 
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<s>
This_DD1 corresponds_VVZ to_II the_AT transaction_NN1 cost_NN1 function_NN1 <equation>_FO ,_, where_CS <equation>_FO is_VBZ the_AT bid–ask_NN1 spread_VVN at_II time_NNT1 <equation>_FO ._. 
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<s>
We_PPIS2 demonstrate_VV0 how_RRQ our_APPGE approach_NN1 tends_VVZ to_TO outperform_VVI the_AT saddlepoint_NN1 approach_NN1 in_II31 terms_II32 of_II33 accuracy_NN1 ,_, at_RR21 least_RR22 in_II our_APPGE test_NN1 examples_NN2 we_PPIS2 consider_VV0 ,_, with_IW less_DAR tuning_NN1 ._. 
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<s>
The_AT first_MD step_NN1 of_IO iThrive_VV0 included_VVN a_AT1 biometric_JJ health_NN1 screening_NN1 and_CC an_AT1 online_JJ HRA_NN1 ._. 
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To_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, this_DD1 is_VBZ the_AT first_MD attempt_NN1 to_TO introduce_VVI Poisson_NP1 observations_NN2 in_II the_AT problem_NN1 of_IO capital_NN1 structures_NN2 ._. 
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<s>
The_AT parameter_NN1 ranges_NN2 of_IO the_AT SEAIR_NN1 model_NN1 and_CC the_AT SIR_NN1 model_NN1 are_VBR shown_VVN in_II Table_NN1 1_MC1 ._. 
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<s>
First_MD ,_, the_AT impact_NN1 of_IO behavioral_JJ responses_NN2 on_II the_AT government_NN1 budget_NN1 is_VBZ counted_VVN in_II the_AT denominator_NN1 ,_, not_XX the_AT numerator_NN1 ._. 
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<s>
The_AT empirical_JJ analyses_NN2 in_II the_AT previous_JJ sections_NN2 show_VV0 that_CST because_II21 of_II22 the_AT political_JJ stakes_NN2 associated_VVN with_IW water_NN1 quality_NN1 readings_NN2 ,_, local_JJ government_NN1 officials_NN2 impose_VV0 tighter_JJR environmental_JJ regulations_NN2 on_II polluting_VVG firms_NN2 located_VVN in_II the_AT near_JJ upstream_JJ of_IO national_JJ monitoring_NN1 stations_NN2 ,_, as_CSA compared_VVN with_IW their_APPGE near_JJ downstream_JJ counterparts_NN2 ._. 
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Moreover_RR ,_, entry_NN1 and_CC exit_VV0 in_II the_AT sample_NN1 of_IO publicly_RR traded_VVN firms_NN2 is_VBZ nonrandom_NN1 ._. 
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Finally_RR ,_, Chen_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 8_MC &rsqb;_) derived_VVD linear_JJ ordinary_JJ differential_JJ equations_NN2 for_IF ruin_NN1 probabilities_NN2 in_II Poisson_NP1 jump-diffusion_JJ processes_NN2 with_IW phase-type_JJ jumps_NN2 and_CC obtained_VVD explicit_JJ results_NN2 in_II a_AT1 few_DA2 instances_NN2 ._. 
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For_IF many_DA2 nodes_NN2 ,_, memory_NN1 increases_VVZ the_AT opportunity_NN1 to_TO develop_VVI into_II a_AT1 hub_NN1 ,_, as_II31 opposed_II32 to_II33 the_AT BA_NN1 model_NN1 where_CS only_RR early_JJ members_NN2 have_VH0 a_AT1 chance_NN1 of_IO becoming_VVG a_AT1 hub_NN1 ._. 
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If_CS we_PPIS2 were_VBDR to_TO select_VVI a_AT1 vector_NN1 of_IO probability_NN1 measures_NN2 <equation>_FO different_JJ from_II <equation>_FO to_TO compute_VVI the_AT risk_NN1 allocation_NN1 with_IW the_AT formula_NN1 <equation>_FO ,_, the_AT property_NN1 (_( 6.8_MC )_) would_VM be_VBI lost_VVN in_RR21 general_RR22 ._. 
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We_PPIS2 measure_VV0 δ_NULL j_ZZ1 empirically_RR using_VVG SkillChangeo_NP1 from_II equation_NN1 (_( 1_MC1 )_) ._. 
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This_DD1 approach_NN1 is_VBZ substantial_JJ to_TO classify_VVI and_CC reveal_VVI vessel_NN1 abnormalities_NN2 more_RGR faithfully_RR using_VVG multi-dimensional_JJ transfer_NN1 functions_NN2 ,_, allowing_VVG diagnosis_NN1 of_IO vascular_JJ diseases_NN2 ,_, such_II21 as_II22 atherosclerosis_NN1 or_CC stenosis_NN1 ._. 
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We_PPIS2 use_VV0 this_DD1 variation_NN1 to_TO assess_VVI whether_CSW destination_NN1 municipalities_NN2 more_RGR financially_RR connected_VVN to_II origin_NN1 municipalities_NN2 experiencing_VVG agricultural_JJ productivity_NN1 growth_NN1 received_VVD larger_JJR capital_NN1 inflows_NN2 ._. 
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<s>
First_MD ,_, we_PPIS2 document_VV0 that_CST our_APPGE measure_NN1 of_IO bank_NN1 exposure_NN1 predicts_VVZ aggregate_JJ deposit_NN1 growth_NN1 at_II the_AT bank_NN1 level_NN1 ._. 
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<s>
Second_MD ,_, much_DA1 of_IO the_AT theory_NN1 in_II adaptive_JJ designs_NN2 assumes_VVZ that_CST (_( T1_FO |_NULL 1_MC1 ,_, ,_, T_ZZ1 |_NULL )_) T_ZZ1 (_( y1T_VV0 |_NULL 1_MC1 ,_, ,_, ydT_NN1 |_NULL d_ZZ1 )_) T_ZZ1 is_VBZ a_AT1 vector_NN1 of_IO independent_JJ responses_NN2 ._. 
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<s>
The_AT response_NN1 variable_NN1 is_VBZ whether_CSW the_AT tumour_NN1 exhibited_VVD microsatellite_NN1 instability_NN1 ,_, among_II which_DDQ we_PPIS2 have_VH0 78_MC microsatellite_NN1 instable_JJ (_( MSI_NP1 )_) tumours_NN2 and_CC 77_MC microsatellite_NN1 stable_NN1 (_( MSS_NP1 )_) tumours_NN2 ._. 
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Statistics_NN in_II this_DD1 table_NN1 are_VBR constructed_VVN based_VVN on_II online_JJ data_NN Table_NN1 2_MC ._. 
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<s>
Section_NN1 2_MC provides_VVZ the_AT mathematical_JJ background_NN1 required_VVN in_II the_AT subsequent_JJ sections_NN2 and_CC presents_VVZ the_AT original_JJ and_CC extended_VVD Gneiting_VVG classes_NN2 of_IO covariances_NN2 ._. 
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<s>
In_II the_AT supplementary_JJ appendix_NN1 ,_, we_PPIS2 provide_VV0 a_AT1 more_RGR complete_JJ treatment_NN1 of_IO this_DD1 model_NN1 for_IF the_AT general_JJ case_NN1 of_IO t_ZZ1 and_CC 2t_FO being_NN1 two_MC time-varying_JJ parameters_NN2 ._. 
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Our_APPGE numerical_JJ results_NN2 with_IW <equation>_FO are_VBR almost_RR identical_JJ to_II those_DD2 for_IF <equation>_FO ._. 
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<s>
One_PN1 could_VM somewhat_RR validate_VVI such_DA a_AT1 claim_NN1 showing_VVG clustering_NN1 for_IF at_RR21 least_RR22 certain_JJ names_NN2 ,_, i.e._REX the_AT most_RGT popular_JJ ones_NN2 ._. 
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<s>
If_CS the_AT network_NN1 topology_NN1 and_CC perturbation_NN1 targets_NN2 are_VBR correctly_RR stated_VVN and_CC take_VV0 these_DD2 effects_NN2 into_II consideration_NN1 ,_, there_EX will_VM be_VBI no_AT zero-parameters_NN2 and_CC therefore_RR the_AT non-cancellation_JJ assumption_NN1 holds_VVZ ._. 
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<s>
In_II contrast_NN1 ,_, total_JJ net_JJ flows_NN2 ,_, which_DDQ are_VBR typically_RR employed_VVN in_II mutual-fund_JJ studies_NN2 ,_, are_VBR driven_VVN mainly_RR by_II investors_NN2 '_NULL long-term_JJ saving_NN1 decisions_NN2 and_CC reflect_VV0 trends_NN2 in_II amounts_NN2 injected_VVN into_II retirement_NN1 accounts_NN2 and_CC asset_NN1 management_NN1 more_RGR generally_RR ._. 
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<s>
We_PPIS2 allowed_VVD a_AT1 single_JJ trait_NN1 to_TO have_VHI a_AT1 non-zero_JJ <equation>_FO ,_, where_CS the_AT <equation>_FO was_VBDZ the_AT effect_NN1 size_NN1 per_II allele_NN1 and_CC chosen_VVN such_CS21 that_CS22 the_AT marginal_JJ power_NN1 for_IF a_AT1 single_JJ trait_NN1 was_VBDZ 0.80_MC for_IF a_AT1 nominal_JJ Type-I_NN1 error_NN1 rate_NN1 of_IO 0.05_MC ._. 
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<s>
First_MD ,_, we_PPIS2 consider_VV0 that_CST query_VV0 results_NN2 include_VV0 three_MC family_NN1 members_NN2 in_II set_NN1 F_ZZ1 (_( father_NN1 ,_, mother_NN1 and_CC sister_NN1 )_) ._. 
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<s>
The_AT value_NN1 of_IO k=10_FO is_VBZ suggestive_JJ from_II our_APPGE empirical_JJ evaluation_NN1 for_IF high_JJ accuracy_NN1 and_CC scalability_NN1 ._. 
</s>
<s>
Obviously_RR ,_, GFPLM_NP1 has_VHZ much_DA1 more_DAR flexibility_NN1 than_CSN functional_JJ linear_JJ regression_NN1 model_NN1 ._. 
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Average_JJ same-month_NNT1 and_CC other-month_JJ returns_NN2 in_II Fama-MacBeth_NP1 regressions_NN2 ._. 
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TreeSAPP_NN1 is_VBZ a_AT1 functional_JJ and_CC taxonomic_JJ annotation_NN1 software_NN1 that_CST uses_VVZ phylogenetic_JJ placement_NN1 for_IF accurate_JJ classifications_NN2 ._. 
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<s>
For_IF values_NN2 above/below_II those_DD2 thresholds_NN2 of_IO the_AT acceleration_NN1 propensity_NN1 score_NN1 ,_, we_PPIS2 can_VM not_XX estimate_VVI marginal_JJ effects_NN2 ,_, as_CSA there_EX are_VBR no_AT selection_NN1 mistakes_NN2 to_TO use_VVI in_II the_AT estimation_NN1 (_( i.e._REX ,_, no_AT applicants_NN2 with_IW an_AT1 acceleration_NN1 propensity_NN1 below_RL (_( above_RL )_) 0.35_MC (_( 0.75_MC )_) were_VBDR mistakenly_RR selected_VVN (_( rejected_VVN )_) by_II the_AT program_NN1 )_) ._. 
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The_AT cash_NN1 flow_NN1 of_IO the_AT replicating_JJ portfolio_NN1 is_VBZ given_VVN by_II an_AT1 <equation>-adapted_FO stochastic_JJ process_NN1 <equation>_FO ._. 
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<s>
A_AT1 good_JJ review_NN1 of_IO many_DA2 different_JJ methods_NN2 and_CC their_APPGE classification_NN1 is_VBZ presented_VVN in_II Bugallo_NP1 et_RA21 al_RA22 ._. 
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(_( 2017_MC )_) ._. 
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<s>
The_AT source_NN1 code_NN1 for_IF this_DD1 method_NN1 is_VBZ available_JJ under_II the_AT opensource_NN1 Apache_NN 2.0_MC license_VV0 in_II the_AT latest_JJT release_NN1 of_IO the_AT LeafCutter_NN1 software_NN1 package_NN1 available_JJ online_JJ at_II http_NNU :_: ._. 
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<s>
The_AT kNN_NNU was_VBDZ trained_VVN on_II 80%_NNU of_IO the_AT data_NN and_CC tested_VVN on_II 20%_NNU ;_; this_DD1 was_VBDZ repeated_VVN 100_MC times_NNT2 for_IF each_DD1 task_NN1 ._. 
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<s>
Taken_VVN together_RL ,_, these_DD2 results_NN2 yield_VV0 the_AT following_JJ insights_NN2 ._. 
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<s>
Suppose_VV0 that_CST there_EX is_VBZ a_AT1 set_NN1 of_IO measures_NN2 <equation>_FO defined_VVN on_II an_AT1 abstract_JJ sample_NN1 space_NN1 ._. 
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<s>
The_AT Net-2020_MC is_VBZ laid_VVN out_RP and_CC embedded_VVN into_II the_AT map_NN1 in_II the_AT same_DA way_NN1 as_CSA shown_VVN in_II Fig._NN1 5_MC ._. 
</s>
<s>
Figure_NN1 6_MC displays_VVZ the_AT OOS_NP2 investment_NN1 downturns_NN2 probability_NN1 forecast_NN1 ,_, using_VVG TS_ZZ2 ,_, CS_NP2 and_CC <equation>_FO as_CSA control_NN1 variables_NN2 and_CC confirms_VVZ the_AT message_NN1 from_II the_AT table_NN1 ._. 
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<s>
We_PPIS2 are_VBR very_RG grateful_JJ to_II the_AT referees_NN2 ,_, the_AT Associate_JJ Editor_NN1 and_CC the_AT Co-Editor_NN1 for_IF calling_VVG our_APPGE attention_NN1 to_II a_AT1 serious_JJ conceptual_JJ error_NN1 in_II an_AT1 earlier_JJR version_NN1 of_IO this_DD1 paper_NN1 ,_, as_RG well_RR as_CSA for_IF their_APPGE many_DA2 and_CC constructive_JJ comments_NN2 which_DDQ helped_VVD us_PPIO2 improve_VVI drastically_RR the_AT quality_NN1 of_IO this_DD1 work_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, we_PPIS2 extend_VV0 our_APPGE results_NN2 to_II a_AT1 situation_NN1 where_RRQ the_AT insurer_NN1 '_NULL s_ZZ1 decision_NN1 making_NN1 is_VBZ dictated_VVN by_II the_AT rank-dependent_JJ expected_JJ utility_NN1 (_( RDEU_NP1 )_) theory_NN1 ._. 
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<s>
In_II this_DD1 full_JJ information_NN1 counterfactual_JJ ,_, the_AT <equation>_FO equilibrium_NN1 prevails_VVZ for_IF all_DB of_IO cautious_JJ A_ZZ1 '_NULL s_ZZ1 opportunities_NN2 ,_, and_CC the_AT prevails_VVZ for_IF all_DB of_IO aggressive_JJ A_ZZ1 '_NULL s_ZZ1 opportunities_NN2 ,_, neither_DD1 of_IO which_DDQ have_VH0 reputation_NN1 building_NN1 ._. 
</s>
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In_II contrast_NN1 ,_, self-exciting_JJ intensity_NN1 models_NN2 have_VH0 demonstrated_VVN encouraging_JJ model_NN1 fit_VV0 ,_, with_IW the_AT best_JJT performance_NN1 achieved_VVN with_IW a_AT1 novel_JJ nonparametric_JJ model_NN1 which_DDQ should_VM asymptotically_RR converge_VVI to_II any_DD true_JJ underlying_JJ excitation_NN1 function_NN1 ._. 
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Else_RR ,_, set_VV0 k=k+1_FO and_CC B=_FO &lsqb;_( Bk_NP1 &rsqb;_) nk_NNU ,_, and_CC return_VV0 to_TO step_VVI 2_MC ._. 
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Again_RT ,_, the_AT choice_NN1 of_IO N_NP1 was_VBDZ made_VVN as_CSA in_II Section_NN1 7.4_MC as_CSA it_PPH1 provided_VVD the_AT required_JJ stability_NN1 ._. 
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Here_RL ,_, we_PPIS2 focus_VV0 on_II one_MC1 scenario_NN1 :_: m=1000_FO cells_NN2 ,_, n=100_FO genes_NN2 ,_, 2=10_FO ._. 
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Centers_NN2 are_VBR drawn_VVN from_II a_AT1 Normal_JJ (_( =_FO 0_MC ,_, 2=1_FO )_) distribution_NN1 ._. 
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A_AT1 stationary_JJ point_NN1 <equation>_FO with_IW data_NN <equation>_FO is_VBZ stable_JJ if_CS for_IF every_AT1 sequence_NN1 <equation>_FO such_CS21 that_CS22 <equation>_FO in_II norm_NN1 ,_, the_AT sequence_NN1 <equation>_FO of_IO solutions_NN2 obtained_VVN with_IW the_AT algorithm_NN1 of_IO (_( 4.6_MC )_) considering_II the_AT data_NN <equation>_FO for_IF each_DD1 <equation>_FO has_VHZ a_AT1 subsequence_NN1 ._. 
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Firms_NN2 whose_DDQGE preexisting_JJ lenders_NN2 had_VHD a_AT1 larger_JJR exposure_NN1 to_II the_AT soy-driven_JJ deposit_NN1 increase_NN1 experienced_VVD a_AT1 larger_JJR growth_NN1 in_II employment_NN1 and_CC their_APPGE wage_NN1 bill.48_FO Next_MD we_PPIS2 estimate_VV0 the_AT same_DA equation_NN1 by_II sector_NN1 of_IO operation_NN1 of_IO each_DD1 firm_NN1 ._. 
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Finally_RR ,_, let_VV0 us_PPIO2 note_VVI that_CST during_II the_AT second_MD half_NN1 of_IO the_AT 2000s_MC2 ,_, Brazil_NP1 experienced_VVD a_AT1 fast_JJ increase_NN1 in_II nonagricultural_JJ bank_NN1 lending_NN1 ,_, documented_VVN in_II Online_JJ Appendix_NN1 Figure_NN1 C8_FO ._. 
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First_MD ,_, they_PPHS2 exclude_VV0 funded_JJ pension_NN1 wealth_NN1 before_II 2012_MC ,_, because_CS such_DA assets_NN2 were_VBDR not_XX subject_II21 to_II22 wealth_NN1 taxation_NN1 ._. 
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A_ZZ1 =_FO 1_MC1 (_( magnitude_NN1 of_IO the_AT jump_NN1 of_IO the_AT velocity_NN1 )_) ,_, γ_NULL =_FO 1_MC1 and_CC δ_NULL t_ZZ1 =_FO 103_MC are_VBR used_VVN to_TO calculate_VVI equation_NN1 ._. 
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The_AT value_NN1 of_IO the_AT corresponding_JJ bound_NN1 <equation>_FO given_VVN by_II (_( 21_MC )_) is_VBZ just_RR of_IO <equation>_FO ,_, and_CC (_( 22_MC )_) follows_VVZ from_II (_( 9_MC )_) ._. 
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Further_RRR ,_, notice_VV0 that_CST most_DAT of_IO the_AT data_NN sets_NN2 (_( 5_MC out_II21 of_II22 6_MC )_) that_CST do_VD0 not_XX reject_VVI the_AT lognormal_JJ in_II31 favor_II32 of_II33 the_AT PlN_NP1 fall_NN1 under_II the_AT truncated_JJ category_NN1 ._. 
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If_CS we_PPIS2 weight_VV0 each_DD1 estimate_NN1 by_II its_APPGE inverse_JJ variance_NN1 ,_, our_APPGE average_NN1 estimated_VVD economic_JJ effect_NN1 is_VBZ 0.0040_MC standard_JJ deviations_NN2 for_IF a_AT1 one_MC1 standard_JJ deviation_NN1 increase_NN1 in_II common_JJ ownership_NN1 ._. 
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In_II these_DD2 conditions_NN2 ,_, a_AT1 huge_JJ temperature_NN1 difference_NN1 can_VM be_VBI reached_VVN with_IW just_RR a_AT1 few_DA2 mW_NNU of_IO laser_NN1 power_NN1 :_: at_II roughly_RR 9_MC mW_NNU the_AT temperature_NN1 at_II the_AT tip_NN1 Tmax_NN1 is_VBZ around_RG 700_MC K_ZZ1 higher_RRR than_CSN the_AT temperature_NN1 at_II the_AT base_NN1 (_( see_VV0 figure_NN1 )_) ._. 
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The_AT results_NN2 suggest_VV0 that_CST the_AT transmission_NN1 of_IO conventional_JJ monetary_JJ policy_NN1 to_II the_AT real_JJ economy_NN1 was_VBDZ weakened_VVN after_II the_AT financial_JJ crisis_NN1 of_IO 2008_MC in_II the_AT euro_NN1 area_NN1 ._. 
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We_PPIS2 employ_VV0 these_DD2 finite-time_JJ adiabatic_JJ processes_NN2 to_TO build_VVI the_AT corresponding_JJ adiabatic_JJ branches_NN2 of_IO the_AT irreversible_JJ Carnot_NN1 engine_NN1 ._. 
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Given_VVN multiple_JJ traded_JJ assets_NN2 ,_, the_AT prices_NN2 of_IO which_DDQ depend_VV0 on_II multiple_JJ observable_JJ stochastic_JJ factors_NN2 ,_, we_PPIS2 construct_VV0 a_AT1 large_JJ class_NN1 of_IO forward_JJ performance_NN1 processes_NN2 ,_, as_II31 well_II32 as_II33 the_AT corresponding_JJ optimal_JJ portfolios_NN2 ,_, with_IW power-utility_JJ initial_JJ data_NN and_CC for_IF stock–factor_NN1 correlation_NN1 matrices_NN2 with_IW eigenvalue_NN1 equality_NN1 (_( EVE_NP1 )_) structure_NN1 ,_, which_DDQ we_PPIS2 introduce_VV0 here_RL ._. 
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This_DD1 assumption_NN1 guarantees_VVZ that_CST the_AT inequality_NN1 of_IO lemma_NN1 2_MC holds_NN2 ;_; however_RR ,_, in_II practice_NN1 the_AT result_NN1 of_IO lemma_NN1 2_MC ,_, usually_RR ,_, holds_VVZ even_RR in_II cases_NN2 when_CS this_DD1 condition_NN1 does_VDZ not_XX ._. 
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First_MD ,_, our_APPGE computational_JJ complexity_NN1 comparison_NN1 between_II leaveoneout_NN1 crossvalidation_NN1 and_CC approximate_JJ leaveoneout_NN1 crossvalidation_NN1 ,_, confirmed_VVN by_II extensive_JJ numerical_JJ experiments_NN2 ,_, show_VV0 that_CST approximate_JJ leaveoneout_NN1 crossvalidation_NN1 offers_VVZ a_AT1 major_JJ reduction_NN1 in_II the_AT computational_JJ complexity_NN1 of_IO estimating_VVG the_AT outofsample_NN1 risk_NN1 ._. 
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The_AT smoothing_JJ parameter_NN1 controls_VVZ the_AT trade-off_NN1 between_II fidelity_NN1 to_II the_AT data_NN and_CC complexity_NN1 of_IO the_AT link_NN1 function_NN1 f_ZZ1 τ_NULL ._. 
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This_DD1 paper_NN1 is_VBZ concerned_JJ with_IW fuzzy_JJ hypothesis_NN1 testing_VVG in_II the_AT framework_NN1 of_IO the_AT randomized_JJ and_CC non-randomized_JJ hypergeometric_JJ test_NN1 for_IF a_AT1 proportion_NN1 ._. 
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We_PPIS2 formalize_VV0 these_DD2 ideas_NN2 in_II the_AT following_JJ problem_NN1 ._. 
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Policy_NN1 changes_NN2 surrounding_VVG the_AT H-1B_FO temporary_JJ visa_NN1 program_NN1 have_VH0 been_VBN debated_VVN heatedly_RR since_CS the_AT program_NN1 was_VBDZ first_MD implemented_VVN in_II the_AT 1990s_MC2 ._. 
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The_AT diagnosis_NN1 of_IO all_DB the_AT tissues_NN2 was_VBDZ confirmed_VVN with_IW histopathology_NN1 ,_, and_CC the_AT TNM_NP1 Classification_NN1 of_IO Malignant_NP1 Tumors_NP1 (_( TNM_NP1 )_) clinical_JJ stages_NN2 were_VBDR determined_VVN based_VVN on_II the_AT American_JJ Joint_JJ Committee_NN1 on_II Cancer_NN1 and_CC the_AT Union_NN1 for_IF International_JJ Cancer_NN1 Control_NN1 in_II 2002_MC ._. 
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Strain-specific_JJ TF_NN1 binding_VVG sites_NN2 were_VBDR identified_VVN for_IF each_DD1 factor_NN1 and_CC analyzed_VVN with_IW MAGGIE_NP1 ._. 
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This_DD1 simulation_NN1 demonstrates_VVZ that_CST a_AT1 simple_JJ optimization_NN1 principle_NN1 ,_, such_II21 as_II22 minimal_JJ metabolic_JJ adjustments_NN2 in_II MOMA_NP1 ,_, can_VM not_XX ensure_VVI that_CST the_AT resulting_JJ production_NN1 strain_NN1 yields_VVZ improved_JJ biochemical_JJ production_NN1 ._. 
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Typically_RR ,_, the_AT representation_NN1 of_IO the_AT mapping_NN1 points_NN2 comes_VVZ in_II many_DA2 forms_NN2 ,_, which_DDQ means_VVZ that_CST it_PPH1 is_VBZ not_XX unique_JJ &lsqb;_( 23_MC &rsqb;_) ,_, moving_VVG or_CC rotation_NN1 does_VDZ not_XX change_VVI their_APPGE distances_NN2 ._. 
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AUPRC_NP1 is_VBZ the_AT area_NN1 under_II the_AT precision_NN1 recall_VV0 curve_NN1 ,_, the_AT method_NN1 with_IW the_AT highest_JJT AUPRC_NN1 is_VBZ printed_VVN in_II bold_JJ ._. 
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These_DD2 correlations_NN2 also_RR emerge_VV0 from_II the_AT simple_JJ regression_NN1 results_NN2 reported_VVN in_II Table_NN1 1_MC1 ._. 
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The_AT R-optimal_JJ designs_NN2 for_IF the_AT matrices_NN2 defined_VVN in_II (_( 11_MC )_) and_CC (_( 12_MC )_) are_VBR ,_, respectively_RR ,_, to_TO estimate_VVI the_AT pairs_NN2 of_IO the_AT parameters_NN2 <equation>_FO and_CC <equation>_FO precisely_RR ._. 
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Clearly_RR ,_, there_EX is_VBZ a_AT1 lot_NN1 of_IO variation_NN1 in_II the_AT perception_NN1 of_IO wage_NN1 inequality_NN1 across_II individuals_NN2 ,_, as_CSA indicated_VVN by_II the_AT corresponding_JJ standard_JJ deviation_NN1 of_IO about_RG 0.161_MC (_( see_VV0 also_RR "_" Online_JJ Appendix_NN1 B.4_FO "_" for_IF further_JJR evidence_NN1 on_II (_( residual_JJ )_) variation_NN1 in_II inequality_NN1 perceptions_NN2 )_) ._. 
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However_RR ,_, the_AT grouping_NN1 also_RR brings_VVZ a_AT1 risk_NN1 chain_NN1 and_CC produces_VVZ a_AT1 "_" domino_NN1 "_" effect_NN1 ._. 
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As_CSA before_RT ,_, both_RR symbolic_JJ composite_JJ MLEs_NN2 converge_VV0 as_II the_AT number_NN1 of_IO bins_NN2 increases_VVZ ._. 
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The_AT second_MD column_NN1 of_IO Figs_NN2 3_MC and_CC 4_MC plot_VV0 <equation>_FO respectively_RR ,_, for_IF LOAD_NN1 (_( the_AT full_JJ curve_NN1 )_) and_CC MOAD_NP1 (_( the_AT broken_JJ curve_NN1 )_) ._. 
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We_PPIS2 now_RT prove_VV0 that_CST the_AT latter_DA statement_NN1 implies_VVZ that_CST for_IF all_DB <equation>_FO ,_, there_EX exists_VVZ <equation>_FO such_CS21 that_CS22 (_( 2.26_MC )_) holds_VVZ ._. 
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<s>
SAT_VVD scores_NN2 for_IF 47.6%_FO of_IO college-goers_NN2 are_VBR obtained_VVN directly_RR from_II the_AT College_NN1 Board_NN1 ;_; composite_JJ test_NN1 scores_NN2 for_IF another_DD1 26.2%_FO of_IO college-goers_NN2 are_VBR obtained_VVN from_II ACT_NN1 and_CC converted_VVN to_II an_AT1 SAT_VVN score_NN1 ._. 
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The_AT BS_NP1 recommends_VVZ the_AT dose_NN1 with_IW the_AT same_DA efficacy_NN1 ,_, but_CCB noticeably_RR greater_JJR toxicity_NN1 in_II 17%_NNU of_IO trials_NN2 ._. 
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In_II the_AT example_NN1 shown_VVN in_II Figure_NN1 2c_FO ,_, there_EX are_VBR two_MC mutations_NN2 :_: insertion_NN1 '_NULL G_ZZ1 >_FO GTT_NP1 '_NULL and_CC SNV_NP1 '_NULL G>T_FO '_NULL ._. 
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We_PPIS2 also_RR confirm_VV0 that_DD1 algorithm_NN1 2_MC maximizes_VVZ the_AT probability_NN1 of_IO X=Y_FO ._. 
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If_CS <equation>_FO ,_, then_RT <equation>_FO is_VBZ concave_JJ and_CC there_EX is_VBZ no_AT correspondingly_RR simple_JJ expression_NN1 for_IF <equation>_FO ,_, although_CS we_PPIS2 have_VH0 the_AT simple_JJ bound_NN1 <equation>_FO ._. 
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<s>
It_PPH1 is_VBZ these_DD2 final_JJ quasi-2D_NNU systems_NN2 which_DDQ are_VBR the_AT focus_NN1 of_IO this_DD1 work_NN1 ._. 
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We_PPIS2 quantify_VV0 other_JJ aspects_NN2 of_IO clinical_JJ drug_NN1 development_NN1 including_II CRs_NP1 ,_, duration_NN1 ,_, and_CC POS_NN2 for_IF non-industry-sponsored_JJ trials_NN2 ,_, which_DDQ we_PPIS2 summarize_VV0 here_RL (_( see_VV0 Sections_NN2 A9_FO through_II A14_FO in_II the_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR for_IF details_NN2 )_) ._. 
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We_PPIS2 have_VH0 not_XX seen_VVN this_DD1 mentioned_VVD before_RT in_II the_AT literature_NN1 on_II improving_JJ data_NN fusion_NN1 using_VVG auxiliary_JJ information_NN1 ,_, but_CCB we_PPIS2 consider_VV0 it_PPH1 a_AT1 relevant_JJ caveat_NN1 finding_NN1 of_IO our_APPGE study_NN1 ._. 
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Since_CS particles_NN2 do_VD0 not_XX jump_VVI between_II different_JJ levels_NN2 ,_, no_AT heat_NN1 is_VBZ released_VVN in_II this_DD1 transformation_NN1 ,_, so_CS the_AT work_NN1 equals_VVZ the_AT change_NN1 in_II internal_JJ energy_NN1 ,_, where_RRQ ._. 
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Further_JJR work_NN1 will_VM involve_VVI the_AT mathematical_JJ and_CC empirical_JJ study_NN1 of_IO more_RGR complex_JJ models_NN2 ._. 
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To_TO obtain_VVI posterior_JJ samples_NN2 from_II both_DB2 models_NN2 ,_, we_PPIS2 run_VV0 OpenBUGS_NP1 &lsqb;_( an_AT1 open-source_JJ variant_NN1 of_IO WinBUGS_NP1 (_( Lunn_NP1 et_RA21 al_RA22 ._. 
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2000_MC )_) &rsqb;_) from_II the_AT statistical_JJ software_NN1 R_ZZ1 using_VVG the_AT package_NN1 "_" R2OpenBUGS_FO "_" (_( Sturtz_NP1 et_RA21 al_RA22 ._. 
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2010_MC )_) ._. 
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In_II the_AT above_JJ representation_NN1 formula_NN1 ,_, the_AT convex_JJ dual_JJ <equation>_FO yields_VVZ the_AT "_" penalty_NN1 "_" process_NN1 <equation>_FO ,_, <equation>_FO ,_, which_DDQ is_VBZ added_VVN to_II the_AT original_JJ risk_NN1 position_NN1 ._. 
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In_II Table_NN1 2_MC ,_, the_AT symbol_NN1 t_ZZ1 stands_VVZ for_IF the_AT age_NN1 group_NN1 ._. 
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The_AT reasoning_NN1 behind_II this_DD1 choice_NN1 is_VBZ that_CST we_PPIS2 are_VBR interested_JJ in_II a_AT1 relative_JJ measure_NN1 assessing_VVG the_AT trade-off_NN1 between_II goodness-of-fit_JJ and_CC complexity_NN1 of_IO the_AT models_NN2 on_II the_AT one_MC1 hand_NN1 ,_, and_CC in_II an_AT1 absolute_JJ measure_NN1 of_IO how_RGQ well_RR the_AT models_NN2 actually_RR deal_VV0 with_IW variability_NN1 in_II the_AT data_NN on_II the_AT other_JJ hand_NN1 ._. 
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The_AT DFA_NN1 scaling_NN1 exponent_NN1 is_VBZ obtained_VVN as_II the_AT slope_NN1 of_IO the_AT linear_JJ regression_NN1 of_IO logF(n)_NN1 versus_II logn_NN1 ._. 
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However_RR ,_, as_CSA already_RR described_VVN in_II Section_NN1 2_MC ,_, several_DA2 other_JJ possibilities_NN2 are_VBR possible_JJ and_CC usually_RR if_CS you_PPY do_VD0 not_XX know_VVI what_DDQ to_TO do_VDI ,_, do_VD0 nothing_PN1 rule_VVI was_VBDZ used_VVN in_II papers_NN2 on_II the_AT SM_NP1 ._. 
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The_AT estimation_NN1 of_IO the_AT expectation_NN1 at_II the_AT proposed_JJ point_NN1 by_II SUR_NP1 is_VBZ carried_VVN out_RP with_IW one_MC1 of_IO the_AT methods_NN2 detailed_VVN in_II Sect._NP1 2_MC (_( FPCA_NP1 ,_, crude_JJ MC_NN1 ,_, maximin-GFQ_NN1 ,_, 2L2-GFQ_NN1 )_) ._. 
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This_DD1 means_VVZ that_CST the_AT ratio_NN1 between_II the_AT two_MC probabilities_NN2 that_CST the_AT right_JJ nearest_JJT neighbor_NN1 of_IO a_AT1 given_JJ reference_NN1 particle_NN1 is_VBZ located_VVN at_II a_AT1 certain_JJ distance_NN1 r_ZZ1 and_CC belongs_VVZ to_II species_NN j_ZZ1 and_CC k_ZZ1 ,_, respectively_RR ,_, becomes_VVZ asymptotically_RR insensitive_JJ to_II the_AT nature_NN1 of_IO the_AT reference_NN1 particle_NN1 in_II the_AT limit_NN1 of_IO large_JJ separations_NN2 ._. 
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Note_VV0 also_RR that_CST letting_VVG →_NULL ∞_FO brings_VVZ ,_, for_IF any_DD fixed_JJ n_ZZ1 ,_, this_DD1 smoothed_JJ empirical_JJ quantile_JJ function_NN1 arbitrarily_RR close_RR to_II the_AT non-smooth_JJ piecewise_JJ constant_JJ one_MC1 Qn_NP1 (_( in_II the_AT sense_NN1 that_CST lim_VV0 →_NULL ∞Qn_FO ,_, (_( u_ZZ1 )_) =Qn(u)_FO for_IF every_AT1 u∈ni=1Ci_FO ,_, hence_RR for_IF almost_RR every_AT1 u_ZZ1 )_) while_CS ,_, as_CSA →_NULL 0_MC (_( fixed_JJ n_ZZ1 )_) ,_, Qn_NP1 ,_, approaches_VVZ the_AT improper_JJ (_( constant_JJ )_) quantile_JJ function_NN1 mapping_NN1 uto_NN1 X_ZZ1 ?_NULL ?_NULL ?_NULL ?_NULL n1nni=1Xi_FO ,_, the_AT ultimate_JJ smooth_JJ version_NN1 of_IO Qn_NP1 ,_, ._. 
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It_PPH1 is_VBZ evident_JJ that_CST rOncs_NN2 for_IF =3n=3_FO is_VBZ the_AT best_JJT estimate_NN1 out_II21 of_II22 its_APPGE counterparts_NN2 ,_, with_IW an_AT1 apparent_JJ outperformance_NN1 observed_VVN over_II the_AT naive_JJ and_CC splitting_VVG approaches_NN2 ._. 
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Extensive_JJ experiments_NN2 showed_VVD that_CST our_APPGE approach_NN1 achieved_VVN improved_JJ performance_NN1 than_CSN multiple_JJ baselines_NN2 for_IF DR_NNB analysis_NN1 ._. 
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When_CS considering_VVG realistic_JJ metagenomic_JJ dataset_NN1 analyses_VVZ on_II a_AT1 few_DA2 dozens_NNO2 of_IO domains_NN2 ,_, S3A_FO can_VM ,_, in_II the_AT same_DA running_JJ time_NNT1 and_CC final_JJ accuracy_NN1 as_CSA a_AT1 metagenomic_JJ assembler_NN1 ,_, annotate_VV0 six_MC to_II eight_MC times_NNT2 more_RRR samples_NN2 ._. 
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The_AT training_NN1 data_NN contain_VV0 232_MC unique_JJ observations_NN2 of_IO &lsqb;_( mRNA_NN1 &rsqb;_) train_VV0 ._. 
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Each_DD1 of_IO these_DD2 observations_NN2 is_VBZ associated_VVN with_IW the_AT DNA_NN1 sequence_NN1 that_CST drives_VVZ the_AT expression_NN1 together_RL with_IW the_AT concentration_NN1 level_NN1 of_IO TFs_NN2 that_CST is_VBZ characteristic_JJ of_IO the_AT position_NN1 of_IO the_AT observed_JJ nucleus_NN1 in_II the_AT embryo_NN1 ._. 
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We_PPIS2 also_RR applied_VVD COCA_NP1 to_II this_DD1 dataset_NN1 ,_, with_IW the_AT initial_JJ clusters_NN2 for_IF each_DD1 dataset_NN1 obtained_VVN with_IW the_AT same_DA clustering_NN1 algorithms_NN2 as_CSA those_DD2 used_VVN for_IF the_AT consensus_NN1 matrices_NN2 ._. 
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We_PPIS2 aim_VV0 to_TO provide_VVI a_AT1 functional-analytic_JJ framework_NN1 that_CST unifies_VVZ and_CC elaborates_VVZ these_DD2 existing_JJ results_NN2 and_CC allows_VVZ extending_VVG the_AT analysis_NN1 beyond_II the_AT convergence_NN1 of_IO sequences_NN2 ._. 
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This_DD1 stage_NN1 also_RR removes_VVZ PETs_NN2 which_DDQ include_VV0 non-standard_JJ residues_NN2 (_( e.g._REX ,_, the_AT letter_NN1 N_ZZ1 )_) ._. 
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The_AT source_NN1 of_IO data_NN is_VBZ shown_VVN in_II Supplementary_JJ Table_NN1 S3_FO ._. 
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The_AT family_NN1 of_IO functions_NN2 <equation>_FO forms_VVZ a_AT1 semigroup_NN1 with_II31 respect_II32 to_II33 function_NN1 composition_NN1 ._. 
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<s>
Let_VV0 ?_ZZ1 (_( ,_, β_NULL ,_, γ_NULL )_) be_VBI the_AT log-likelihood_JJ function_NN1 for_IF a_AT1 random_JJ sample_NN1 ,_, where_CS A_ZZ1 is_VBZ the_AT parameter_NN1 space_NN1 of_IO ._. 
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The_AT CA_NP1 model_VVI of_IO cars_NN2 and_CC trucks_NN2 in_II the_AT heterogeneous_JJ traffic_NN1 based_VVN on_II car–truck_NN1 combination_NN1 effect_NN1 is_VBZ constructed_VVN in_II this_DD1 section_NN1 ._. 
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Finally_RR ,_, the_AT expected_JJ satisfaction_NN1 level_NN1 is_VBZ larger_JJR for_IF the_AT constant_JJ benefit_NN1 level_NN1 scheme_NN1 over_II shorter_JJR time_NNT1 horizons_NN2 and_CC the_AT behaviour_NN1 reverts_VVZ over_II the_AT long_JJ run_NN1 ._. 
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In_BCL21 order_BCL22 to_TO illustrate_VVI the_AT applicability_NN1 of_IO this_DD1 method_NN1 ,_, we_PPIS2 calculated_VVD the_AT periodic_JJ orbits_NN2 with_IW topological_JJ length_NN1 less_DAR than_CSN five_MC ._. 
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For_IF each_DD1 moment_NN1 and_CC subsample_NN1 ,_, we_PPIS2 present_VV0 average_JJ observed_JJ values_NN2 in_II the_AT data_NN ,_, standard_JJ errors_NN2 (_( SE_NP1 )_) for_IF data_NN averages_NN2 clustered_VVD by_II activist_NN1 ,_, average_JJ predicted_JJ values_NN2 in_II our_APPGE baseline_NN1 model_NN1 ,_, no-reputation_NN1 ,_, and_CC full-information_JJ models_NN2 ,_, and_CC local_JJ elasticities_NN2 of_IO our_APPGE baseline_NN1 model_NN1 '_NULL s_ZZ1 prediction_NN1 for_IF each_DD1 moment_NN1 to_II changes_NN2 in_II each_DD1 parameter_NN1 ._. 
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In_II each_DD1 scenario_NN1 a_AT1 weak_JJ association_NN1 ,_, =0.25_FO ,_, between_II the_AT toxicity_NN1 and_CC efficacy_NN1 biomarker_NN1 was_VBDZ assumed_VVN ._. 
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This_DD1 exercise_NN1 confirms_VVZ the_AT that_RG main_JJ factor_NN1 discriminating_VVG between_II asymptotic_JJ behaviours_NN2 is_VBZ indeed_RR the_AT number_NN1 of_IO degrees_NN2 of_IO freedom_NN1 and_CC consequently_RR our_APPGE criterion_NN1 ._. 
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Now_RT each_DD1 worker_NN1 needs_VVZ to_TO have_VHI access_NN1 only_RR to_II the_AT subsampled_JJ dataset_NN1 ,_, as_II31 well_II32 as_II33 <equation>_FO ._. 
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Finding_VVG the_AT optimal_JJ value_NN1 in_II (_( 6_MC )_) and_CC the_AT corresponding_JJ k_ZZ1 which_DDQ satisfies_VVZ =1=i=1mki=K_FO is_VBZ straightforward_JJ if_CS no_AT pseudo-count_NN1 is_VBZ used_VVN when_CS computing_VVG p-value_JJ estimates_NN2 (_( =0c=0_FO in_II (_( 4_MC )_) )_) and_CC more_RGR challenging_JJ with_IW a_AT1 pseudo-count_NN1 (_( =1c=1_FO in_II (_( 4_MC )_) )_) ._. 
</s>
<s>
For_IF practical_JJ computations_NN2 ,_, it_PPH1 suffices_VVZ to_TO transform_VVI the_AT empirical_JJ support_NN1 to_II <equation>_FO ._. 
</s>
<s>
However_RR ,_, it_PPH1 can_VM still_RR be_VBI deduced_VVN that_CST the_AT gain_NN1 in_II efficiency_NN1 of_IO the_AT threefold_JJ cross-splitting_JJ approach_NN1 over_II other_JJ approaches_NN2 is_VBZ recognizable_JJ and_CC is_VBZ not_XX entirely_RR due_II21 to_II22 evaluating_VVG the_AT estimator_NN1 at_II a_AT1 larger_JJR 2N2_FO ._. 
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<s>
Revised_JJ actuals_NN2 for_IF all_DB macroeconomic_JJ series_NN are_VBR obtained_VVN from_II the_AT Real-Time_JJ OECD_NP1 Database_NN1 (_( visit_VV0 https_NNU :_: //stats.oecd.org_FU )_) ._. 
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<s>
The_AT choice_NN1 of_IO the_AT geographical_JJ variable_NN1 is_VBZ motivated_VVN by_II the_AT fact_NN1 that_CST ,_, by_II swapping_NN1 or_CC changing_VVG it_PPH1 ,_, it_PPH1 is_VBZ usually_RR less_RGR likely_JJ to_TO generate_VVI unreasonable_JJ combinations_NN2 of_IO categorical_JJ variables_NN2 ,_, like_II for_REX21 instance_REX22 a_AT1 pregnant_JJ man_NN1 or_CC a_AT1 10_MC year_NNT1 old_JJ lawyer_NN1 ._. 
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<s>
We_PPIS2 obtain_VV0 a_AT1 point_NN1 prediction_NN1 of_IO yi(t)_NN1 ,_, denoted_VVD yi(t)_NN1 ,_, via_II the_AT median_NN1 of_IO the_AT posterior_JJ distribution_NN1 of_IO fi(t)_JJ ,_, the_AT "_" underlying_JJ "_" function_NN1 value_NN1 ._. 
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<s>
Thus_RR ,_, with_IW these_DD2 restrictions_NN2 on_II the_AT parameters_NN2 ,_, the_AT model_NN1 (_( 4_MC )_) will_VM be_VBI identifiable_JJ ._. 
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<s>
For_IF the_AT mixed_JJ demand_NN1 system_NN1 ,_, McLaren_NP1 and_CC Wong_NP1 (_( 2009_MC )_) endogenize_VV0 consumption_NN1 expenditure_NN1 for_IF unconstrained_JJ goods_NN2 by_II making_VVG it_PPH1 a_AT1 function_NN1 of_IO total_JJ expenditure_NN1 which_DDQ is_VBZ the_AT sum_NN1 of_IO expenditures_NN2 on_II unconstrained_JJ and_CC constrained_VVD commodities_NN2 ._. 
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<s>
However_RR ,_, most_RGT empirical_JJ studies_NN2 in_II this_DD1 literature_NN1 face_VV0 a_AT1 challenge_NN1 in_II surmounting_VVG endogeneity_NN1 problems_NN2 ,_, and_CC it_PPH1 is_VBZ generally_RR hard_JJ to_TO rule_VVI out_RP the_AT possibility_NN1 that_CST confounding_VVG factors_NN2 explain_VV0 both_RR the_AT religiosity_NN1 of_IO a_AT1 population_NN1 and_CC the_AT growth_NN1 of_IO its_APPGE economy_NN1 ._. 
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<s>
The_AT results_NN2 can_VM be_VBI found_VVN in_II Table_NN1 3_MC ._. 
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<s>
Thus_RR ,_, subspace_VV0 stability_NN1 selection_NN1 is_VBZ far_RG less_RGR sensitive_JJ to_II the_AT particular_JJ choice_NN1 of_IO ,_, which_DDQ removes_VVZ the_AT need_NN1 for_IF fine_JJ tuning_NN1 ._. 
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<s>
We_PPIS2 distinguish_VV0 between_II prediction_NN1 ,_, variable_JJ selection_NN1 and_CC ranking_NN1 and_CC use_VV0 the_AT following_JJ metrics_NN2 ._. 
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<s>
We_PPIS2 will_VM say_VVI such_DA cryptocurrencies_NN2 are_VBR inconsistent_JJ with_II31 respect_II32 to_II33 time_NNT1 ._. 
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<s>
NTBs_NP1 reduce_VV0 the_AT opportunity_NN1 to_II the_AT utilisation_NN1 of_IO fewer_DAR opportunities_NN2 in_II31 relation_II32 to_II33 those_DD2 available_JJ ._. 
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<s>
It_PPH1 is_VBZ determined_VVN only_RR by_II the_AT structure_NN1 of_IO the_AT R-matrix_NN1 entering_VVG the_AT commutation_NN1 relation_NN1 of_IO monodromy_JJ matrices_NN2 ._. 
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<s>
Finally_RR ,_, F(1)_FO ,_, F(2)_FO ,_, and_CC F(3)_FO are_VBR functions_NN2 of_IO st_NNU and_CC sth_NNU ,_, (_( see_VV0 Appendix_NN1 B_ZZ1 )_) ._. 
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<s>
In_II other_JJ words_NN2 ,_, the_AT generalized_JJ entropy_NN1 of_IO the_AT whole_NN1 is_VBZ greater_JJR than_CSN the_AT sum_NN1 of_IO the_AT entropies_NN2 of_IO the_AT parts_NN2 if_CS q<1_FO (_( superextensivity_NN1 )_) ,_, whereas_CS the_AT generalized_JJ entropy_NN1 of_IO the_AT system_NN1 is_VBZ smaller_JJR than_CSN the_AT sum_NN1 of_IO the_AT entropies_NN2 of_IO the_AT parts_NN2 if_CS q>1_FO (_( subextensivity_NN1 )_) ._. 
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<s>
We_PPIS2 now_RT consider_VV0 data_NN for_IF the_AT following_JJ 12_MC Asian_JJ countries_NN2 over_II the_AT period_NN1 1970–2014_MCMC :_: China_NP1 ,_, Hong_NP1 Kong_NP1 ,_, Indonesia_NP1 ,_, India_NP1 ,_, Japan_NP1 ,_, Korea_NP1 ,_, Malaysia_NP1 ,_, Philippines_NP ,_, Singapore_NP1 ,_, Sri_NP1 Lanka_NP1 ,_, Thailand_NP1 ,_, and_CC Taiwan_NP1 ._. 
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<s>
This_DD1 paper_NN1 is_VBZ to_TO be_VBI interpreted_VVN in_II the_AT context_NN1 of_IO hedging_VVG in_II incomplete_JJ markets_NN2 ._. 
</s>
<s>
If_CS that_DD1 worker_NN1 is_VBZ not_XX promoted_VVN in_II that_DD1 periodor_NN1 if_CS he_PPHS1 or_CC she_PPHS1 is_VBZ never_RR promotedthe_VV0 left_JJ side_NN1 takes_VVZ a_AT1 value_NN1 of_IO 0_MC ._. 
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For_IF each_DD1 transaction_NN1 executed_VVN ,_, the_AT system_NN1 produces_VVZ a_AT1 string_NN1 of_IO data_NN ._. 
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<s>
In_II contrast_NN1 ,_, estimator_NN1 (_( 3.1_MC )_) with_IW the_AT choice_NN1 *_FU is_VBZ used_VVN in_II31 conjunction_II32 with_II33 =0.7_FO to_TO produce_VVI a_AT1 subspace_NN1 stability_NN1 selection_NN1 tangent_NN1 space_NN1 via_II algorithm_NN1 1_MC1 ._. 
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<s>
In_II fact_NN1 ,_, WEDetthen_NP1 has_VHZ comparable_JJ power_NN1 with_IW that_DD1 of_IO FR_NP1 ,_, while_CS treating_VVG almost_RR 40_MC more_DAR patients_NN2 on_II the_AT superior_JJ treatment_NN1 ._. 
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A_AT1 sufficient_JJ condition_NN1 for_IF =0_FO is_VBZ that_DD1 working_JJ model_NN1 (_( 5_MC )_) is_VBZ correct_JJ ._. 
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<s>
We_PPIS2 release_VV0 the_AT condition_NN1 of_IO very_RG large_JJ anisotropy_NN1 exploiting_VVG semiclassical_JJ quantization_NN1 ._. 
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<s>
The_AT Gross–Witten_JJ picture_NN1 is_VBZ recovered_VVN in_II the_AT limit_NN1 →_NULL ∞_FO ,_, with_IW β_NULL GW_NP1 ≡_NULL β_NULL e_ZZ1 fixed_JJ ._. 
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<s>
Another_DD1 unusual_JJ cell_NN1 community_NN1 is_VBZ C2_FO ,_, which_DDQ is_VBZ specifically_RR enriched_VVN in_II neurotransmitter_NN1 and_CC calcium_NN1 homeostasis_NN1 functions_NN2 (_( Calcium_NN1 and_CC cAMP_NN1 ;_; Hofer_NP1 and_CC Lefkimmiatis_NP1 ,_, 2007_MC )_) ._. 
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<s>
Remaining_JJ parameter_NN1 estimates_NN2 are_VBR in_II31 line_II32 with_II33 expectations_NN2 ._. 
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<s>
One_MC1 observation_NN1 that_CST leads_VVZ to_II a_AT1 lower_JJR bound_NN1 is_VBZ as_CSA follows_VVZ ._. 
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<s>
Table_NN1 16_MC presents_VVZ the_AT estimation_NN1 results_NN2 of_IO production_NN1 technologies_NN2 across_II regimes_NN2 ._. 
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<s>
In_II what_DDQ follows_VVZ ,_, we_PPIS2 replace_VV0 the_AT integral_JJ part_NN1 of_IO the_AT PIDE_NP1 (_( 2.7_MC )_) by_II the_AT right-hand_JJ side_NN1 of_IO (_( 2.12_MC )_) ._. 
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<s>
A_AT1 brief_JJ introduction_NN1 is_VBZ given_VVN in_II this_DD1 section_NN1 ._. 
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<s>
We_PPIS2 find_VV0 that_CST UnionCom_NP1 aligns_VVZ the_AT cells_NN2 between_II the_AT two_MC datasets_NN2 quite_RG well_RR in_II 2D_NNU space_NN1 by_II aligning_VVG the_AT cells_NN2 between_II the_AT datasets_NN2 along_II a_AT1 linear_JJ trajectory_NN1 and_CC by_II merging_VVG the_AT two_MC datasets_NN2 on_II a_AT1 common_JJ region_NN1 with_IW similar_JJ distributions_NN2 (_( Fig._NN1 5c_FO ,_, upper_JJ right_JJ panel_NN1 )_) ;_; when_CS looking_VVG at_II the_AT cell_NN1 labels_NN2 of_IO time_NNT1 stages_NN2 ,_, we_PPIS2 find_VV0 that_CST UnionCom_NP1 preserves_VVZ the_AT global_JJ structures_NN2 of_IO time_NNT1 stage_NN1 orders_NN2 (_( Fig._NN1 5c_FO ,_, lower_JJR right_JJ panel_NN1 )_) ._. 
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<s>
When_CS the_AT parental_JJ flagellum_NN1 shrinks_VVZ to_II length_NN1 fNFLM(In)=4m_FO (_( fNF=0.67_FO ,_, LM(In)=6m_FO )_) ,_, two_MC new_JJ flagella_NN1 emerge_VV0 from_II the_AT adjacent_JJ daughter_NN1 pools_NN2 ._. 
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<s>
Before_II presenting_VVG the_AT results_NN2 ,_, let_VV0 us_PPIO2 introduce_VVI the_AT following_JJ definitions_NN2 :_: suppose_VV0 ,_, the_AT total_JJ number_NN1 of_IO realizations_NN2 generated_VVN by_II the_AT MC_NN1 sampling_NN1 is_VBZ n_ZZ1 ._. 
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<s>
Let_VV0 Li(t)_NN1 and_CC Li(t)_RR denote_VVI the_AT length_NN1 of_IO flagellum_NN1 and_CC at_II time_NNT1 t_ZZ1 in_II ith_MD realization_NN1 ._. 
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<s>
A_AT1 similar_JJ sampler_NN1 is_VBZ used_VVN by_II Wyse_NP1 and_CC Friel_NP1 (_( 2012_MC )_) to_TO estimate_VVI the_AT number_NN1 of_IO clusters_NN2 in_II stochastic_JJ blockmodels_NN2 ._. 
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<s>
Establishment_NN1 controls_NN2 include_VV0 age_NN1 ,_, the_AT number_NN1 of_IO establishments_NN2 ,_, and_CC the_AT number_NN1 of_IO establishments_NN2 per_II segment_NN1 ._. 
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<s>
In_II Figure_NN1 7_MC ,_, we_PPIS2 show_VV0 the_AT 2D_NNU UMAP_NN1 embeddings_NN2 of_IO the_AT clustered_JJ data_NN ,_, colored_VVN by_II cell-type_JJ annotations_NN2 generated_VVD using_VVG marker_NN1 genes_NN2 ,_, as_CSA detailed_VVN in_II the_AT Seurat_NN1 pipeline_NN1 (_( Stuart_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ._. 
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<s>
For_REX21 example_REX22 if_CS in_II a_AT1 given_JJ dataset_NN1 j_ZZ1 all_RR the_AT counts_NN2 of_IO k-mers_NN2 present_VV0 in_II S_ZZ1 are_VBR identical_JJ (_( |_NULL Count&lsqb;i&rsqb;_NP1 &lsqb;_( j_ZZ1 &rsqb;_) ,_, is.t.Count&lsqb;i&rsqb;_NNU &lsqb;_( j_ZZ1 &rsqb;_) >0_FO |_NULL =1_FO )_) ,_, then_RT we_PPIS2 report_VV0 a_AT1 single_JJ count_NN1 value_NN1 for_IF this_DD1 dataset_NN1 ._. 
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<s>
The_AT above_JJ theorem_NN1 demonstrates_VVZ the_AT ability_NN1 of_IO the_AT variable_JJ selection_NN1 rule_NN1 to_TO avoid_VVI type_NN1 I_MC1 error_NN1 inflation_NN1 due_II21 to_II22 the_AT increase_NN1 of_IO pn_NNU ,_, a_AT1 tendency_NN1 to_TO select_VVI all_DB true_JJ signal_NN1 variables_NN2 ,_, and_CC omit_VV0 all_DB noise_NN1 variables_NN2 ._. 
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<s>
In_II that_DD1 limit_NN1 ,_, not_XX only_RR do_VD0 the_AT adiabatic_JJ processes_NN2 become_VV0 quasi-static_JJ but_CCB also_RR the_AT isothermal_JJ ones_NN2 ,_, recovering_VVG the_AT quasi-static_JJ Carnot_NN1 engine_NN1 introduced_VVN in_II section_NN1 ,_, with_IW optimal_JJ efficiency_NN1 ._. 
</s>
<s>
The_AT comparison_NN1 results_NN2 between_II the_AT rewritten_VVN SSE_ND1 50_MC (_( 180_MC )_) Index_NN1 and_CC the_AT real_JJ SSE_ND1 50_MC (_( 180_MC )_) Index_NN1 are_VBR shown_VVN in_II Fig._NN1 2_MC ._. 
</s>
<s>
To_TO illustrate_VVI the_AT concepts_NN2 of_IO centered_JJ and_CC invariant_JJ quantiles_NN2 introduced_VVN in_II this_DD1 section_NN1 ,_, we_PPIS2 look_VV0 at_II a_AT1 numerical_JJ example_NN1 next_MD ._. 
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<s>
In_II the_AT following_JJ ,_, we_PPIS2 denote_VV0 by_II <equation>_FO the_AT <equation>th_FO unit_NN1 vector_NN1 of_IO <equation>_FO ._. 
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<s>
The_AT values_NN2 of_IO the_AT hyperparameters_NN2 for_IF the_AT respective_JJ prior_JJ distributions_NN2 are_VBR listed_VVN in_II Table_NN1 3_MC ._. 
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<s>
MIAMI_NP1 provides_VVZ an_AT1 interactive_JJ ,_, dynamic_JJ force_NN1 directed_VVD network_NN1 visualization_NN1 with_IW an_AT1 extensive_JJ set_NN1 of_IO visualization_NN1 options_NN2 ._. 
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<s>
For_IF the_AT implementation_NN1 of_IO the_AT E-Divisive_JJ method_NN1 ,_, we_PPIS2 use_VV0 the_AT ecp_NN1 package_NN1 (_( James_NP1 and_CC Matteson_NP1 2014_MC )_) with_IW =1=1_FO ;_; minimum_JJ segment_NN1 size_NN1 of_IO 30_MC ;_; a_AT1 significance_NN1 level_NN1 of_IO 0.05_MC ;_; and_CC =499R=499as_FO suggested_VVN by_II Matteson_NP1 and_CC James_NP1 (_( 2014_MC )_) ._. 
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<s>
Species_NN richness_NN1 ,_, for_IF many_DA2 taxa_NN2 ,_, is_VBZ positively_RR correlated_VVN with_IW the_AT habitat_NN1 size_NN1 ._. 
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<s>
The_AT last_MD column_NN1 in_II Table_NN1 1_MC1 corresponds_VVZ to_II <equation>_FO ,_, whereas_CS this_DD1 table_NN1 reports_VVZ results_NN2 for_IF lower_JJR values_NN2 of_IO ,_, as_CSA identified_VVN by_II the_AT column_NN1 headings_NN2 ._. 
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<s>
We_PPIS2 believe_VV0 that_CST the_AT forecasting_VVG approach_NN1 of_IO Kuang_NP1 et_RA21 al._RA22 ,_, 2008a_FO ,_, Kuang_NP1 et_RA21 al._RA22 ,_, 2008b_FO ,_, Kuang_NP1 et_RA21 al._RA22 ,_, 2011_MC and_CC its_APPGE further_JJR developments_NN2 in_II Nielsen_NP1 and_CC Nielsen_NP1 (_( 2014_MC )_) ,_, Nielsen_NP1 ,_, 2015_MC ,_, Nielsen_NP1 ,_, 2018_MC ,_, Harnau_NP1 ,_, 2018a_FO ,_, Harnau_NP1 ,_, 2018b_FO ,_, Fannon_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2018_MC )_) and_CC Harnau_NP1 and_CC Nielsen_NP1 (_( 2018_MC )_) could_VM benefit_VVI from_II the_AT new_JJ insight_NN1 of_IO this_DD1 paper_NN1 and_CC the_AT provided_VVN supplementary_JJ material_NN1 ._. 
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<s>
These_DD2 interactions_NN2 provide_VV0 information_NN1 on_II the_AT three-dimensional_JJ genome_NN1 structure_NN1 (_( Fullwood_NP1 and_CC others_NN2 ,_, 2009_MC )_) ._. 
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<s>
In_RR21 particular_RR22 ,_, the_AT proofs_NN2 boil_VV0 down_RP to_II establishing_VVG convergence_NN1 for_IF image_NN1 measures_NN2 with_II31 respect_II32 to_II33 <equation>_FO and_CC give_VV0 no_AT new_JJ insight_NN1 on_II adapted_JJ Wasserstein_NN1 distances_NN2 ,_, so_CS we_PPIS2 skip_VV0 them_PPHO2 ._. 
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<s>
The_AT weight_NN1 parameters_NN2 vary_VV0 depending_II21 on_II22 the_AT specific_JJ form_NN1 of_IO the_AT weights_NN2 and_CC will_VM be_VBI fully_RR specified_VVN in_II each_DD1 case_NN1 ._. 
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<s>
We_PPIS2 note_VV0 that_CST in_II a_AT1 right_JJ neighbourhood_NN1 of_IO zero_NN1 ,_, <equation>_FO has_VHZ the_AT same_DA sign_NN1 as_CSA <equation>_FO ._. 
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<s>
Epidemics_NN2 can_VM be_VBI considered_VVN to_TO be_VBI a_AT1 problem_NN1 of_IO physics_NN1 concerning_II reaction_NN1 and_CC relaxation_NN1 processes_NN2 and_CC the_AT simplest_JJT understanding_NN1 of_IO its_APPGE outbreak_NN1 can_VM be_VBI provided_VVN by_II a_AT1 mean_JJ field_NN1 analysis_NN1 ._. 
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<s>
The_AT next_MD result_NN1 identifies_VVZ the_AT image_NN1 <equation>_FO of_IO the_AT map_NN1 <equation>_FO ,_, and_CC further_RRR shows_VVZ that_CST <equation>_FO is_VBZ a_AT1 bijection_NN1 ._. 
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<s>
Results_NN2 for_IF all_DB taxonomic_JJ levels_NN2 are_VBR in_II the_AT Supplementary_JJ Figure_NN1 S9_FO and_CC Supplementary_JJ Material_NN1 S2_FO ._. 
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<s>
Recall_VV0 that_CST ClonArch_NP1 takes_VVZ as_CSA input_VVN a_AT1 set_NN1 T_ZZ1 of_IO phylogenetic_JJ trees_NN2 and_CC a_AT1 frequency_NN1 matrix_NN1 F._NP1 For_IF each_DD1 tree_NN1 T∈T_FO ,_, matrix_NN1 U_ZZ1 describes_VVZ the_AT clonal_JJ prevalence_NN1 of_IO each_DD1 biopsy_NN1 on_II a_AT1 regular_JJ grid_NN1 ._. 
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<s>
Second_MD ,_, the_AT majority_NN1 of_IO the_AT existing_JJ literature_NN1 assumes_VVZ continuous_JJ observation_NN1 using_VVG a_AT1 continuous_JJ asset_NN1 value_NN1 process_NN1 ;_; in_II this_DD1 case_NN1 ,_, the_AT asset_NN1 value_NN1 at_II bankruptcy_NN1 is_VBZ in_II any_DD event_NN1 precisely_RR <equation>_FO ._. 
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<s>
C5_FO is_VBZ the_AT most_RGT abnormal_JJ community_NN1 ,_, having_VHG lost_VVN half_DB of_IO the_AT pathways_NN2 completely_RR (_( almost_RR zero_MC expression_NN1 )_) ,_, including_II PI3K-Akt_NP1 ,_, ECM-receptor_JJ and_CC Calcium_NN1 ._. 
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<s>
In_II the_AT basic_JJ setting_NN1 ,_, the_AT explanatory_JJ variables_NN2 are_VBR CBT_NP1 ,_, CBI_NP1 ,_, GDP_NN1 growth_NN1 and_CC GDP_NN1 per_RR21 capita_RR22 ._. 
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<s>
The_AT paper_NN1 concludes_VVZ with_IW Sect._NP1 5_MC which_DDQ provides_VVZ a_AT1 discussion_NN1 of_IO key_JJ findings_NN2 and_CC suggestions_NN2 for_IF future_JJ research_NN1 ._. 
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<s>
In_II these_DD2 ,_, a_AT1 kernel_NN1 function_NN1 (_( which_DDQ defines_VVZ similarities_NN2 between_II different_JJ units_NN2 of_IO observation_NN1 )_) is_VBZ associated_VVN with_IW each_DD1 dataset_NN1 ._. 
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For_IF an_AT1 equiprobable_JJ distribution_NN1 〈_NULL (_( x_ZZ1 ,_, u=0_FO )_) 〉_NULL is_VBZ constant_JJ and_CC <equation>_FO ._. 
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SCAD_NP1 transition_NN1 in_II performance_NN1 SCAD_NN1 has_VHZ a_AT1 similar_JJ transition_NN1 property_NN1 for_IF prediction_NN1 as_II21 for_II22 ranking_NN1 (_( see_VV0 above_RL )_) ,_, but_CCB with_IW the_AT difference_NN1 that_CST SCAD_NP1 does_VDZ not_XX become_VVI the_AT worst_JJT performing_NN1 method_NN1 as_CSA scenario_NN1 difficulty_NN1 increases_NN2 ;_; Ridge_NN1 or_CC AdaLasso_NP1 still_RR performs_VVZ worse_JJR (_( black_JJ line_NN1 in_II Fig._NN1 5c_FO )_) ._. 
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<s>
In_II column_NN1 (_( 2_MC )_) ,_, estimates_VVZ from_II the_AT conditional_JJ logit_NN1 model_NN1 imply_VV0 a_AT1 similar_JJ WTP_NP1 of_IO 17_MC percentile_NN1 ranks_NN2 ._. 
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<s>
Indeed_RR ,_, by_II virtue_NN1 of_IO its_APPGE cluster_NN1 flexibility_NN1 ,_, the_AT EFD_NN1 can_VM locate_VVI two_MC of_IO its_APPGE components_NN2 (_( clusters_NN2 )_) along_II a_AT1 line_NN1 in_II close_JJ agreement_NN1 with_IW the_AT data_NN ._. 
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<s>
From_II Table_NN1 6_MC ,_, we_PPIS2 notice_VV0 that_CST except_II21 for_II22 LorSLIM-based_NN1 CF_VV0 method_NN1 ,_, the_AT proposed_JJ approach_NN1 behaves_VVZ well_RR when_CS compared_VVN with_IW other_JJ models_NN2 ._. 
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Suppose_VV0 Assumptions_NN2 2_MC and_CC 6_MC hold_NN1 ._. 
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<s>
Our_APPGE associated_JJ Webina_NN1 web_NN1 app_NN1 ,_, which_DDQ leverages_NN2 the_AT Webina_NP1 library_NN1 ,_, also_RR provides_VVZ user-friendly_JJ tools_NN2 for_IF setting_VVG up_RP docking_VVG calculations_NN2 (_( e.g._REX identifying_VVG an_AT1 appropriate_JJ docking_NN1 box_NN1 )_) and_CC analyzing_VVG docking_NN1 output_NN1 (_( e.g._REX examining_VVG predicted_JJ binding_NN1 poses_VVZ )_) ._. 
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<s>
The_AT cross-section_NN1 of_IO the_AT staircase_NN1 has_VHZ a_AT1 260_MC mm_NNU tread_VV0 ,_, 150_MC mm_NNU riser_NN1 and_CC 1240_MC mm_NNU width_NN1 ,_, as_CSA in_II figure_NN1 ._. 
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Formulas_NN2 in_II the_AT multi-layer_JJ case_NN1 are_VBR also_RR given_VVN in_II &lsqb;_( 42_MC ,_, Eq_NN1 ._. 
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(_( 92_MC )_) &rsqb;_) ,_, where_CS the_AT price_NN1 is_VBZ expressed_VVN as_II the_AT Laplace_NP1 transform_VV0 of_IO an_AT1 exactly_RR computable_JJ quantity_NN1 ._. 
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<s>
The_AT limited_JJ range_NN1 of_IO the_AT momentum_NN1 reflects_VVZ the_AT doubling_NN1 of_IO the_AT unit_NN1 cell_NN1 due_II21 to_II22 the_AT staggered_JJ background_NN1 field_NN1 ._. 
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<s>
As_CSA shown_VVN in_II Figure_NN1 1B_FO ,_, we_PPIS2 generate_VV0 a_AT1 total_NN1 of_IO 23_MC features_NN2 for_IF describing_VVG each_DD1 residue_NN1 of_IO a_AT1 model_NN1 that_CST includes_VVZ distance-based_JJ weighted_JJ histogram_NN1 alignment_NN1 ,_, sequence_NN1 versus_II structure_NN1 consistency_NN1 and_CC ROSETTA_NP1 centroid_NN1 energy_NN1 terms_NN2 ._. 
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<s>
These_DD2 reference_NN1 sequences_NN2 were_VBDR used_VVN to_TO simulate_VVI 5_MC million_NNO Illumina_NP1 pair-end_JJ sequencing_NN1 reads_VVZ following_VVG a_AT1 log-normal_JJ abundance_NN1 distribution_NN1 ,_, using_VVG ART_NN1 (_( Huang_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ._. 
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<s>
These_DD2 facts_NN2 are_VBR formalized_VVN in_II Section_NN1 2.3_MC ._. 
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<s>
Sparser_JJR representation_NN1 of_IO glycerolipids_NN2 in_II the_AT negative_JJ polarity_NN1 data_NN (_( Fig._NN1 3c_FO )_) illustrates_VVZ the_AT common_JJ knowledge_NN1 of_IO the_AT positive_JJ mode_NN1 being_VBG the_AT preferred_JJ way_NN1 of_IO ionization_NN1 for_IF this_DD1 class_NN1 of_IO lipids_NN2 ._. 
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<s>
We_PPIS2 introduce_VV0 the_AT useful_JJ notion_NN1 of_IO a_AT1 kernel_NN1 ._. 
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<s>
Note_VV0 that_CST the_AT observed_JJ and_CC expected_JJ elemental_JJ information_NN1 depend_VV0 on_II the_AT design_NN1 point_NN1 x_ZZ1 through_II the_AT parameter_NN1 =_FO θ_NULL (_( x_ZZ1 )_) ._. 
</s>
<s>
The_AT γ_NULL curves_NN2 in_II figures_NN2 (_( a_ZZ1 )_) and_CC (_( d_ZZ1 )_) already_RR hint_VV0 at_II two_MC other_JJ significant_JJ transitions_NN2 ;_; one_PN1 in_II the_AT upper-critical_JJ and_CC the_AT other_JJ in_II the_AT subcritical_JJ regime_NN1 ._. 
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<s>
We_PPIS2 assumed_VVD a_AT1 proportional_JJ hazards_NN2 model_VV0 for_IF the_AT time_NNT1 to_II second_MD delivery_NN1 ._. 
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<s>
Core_NN1 (_( peripheral_JJ )_) establishments_NN2 are_VBR establishments_NN2 operating_VVG in_II three-digit_NN1 SIC_RR industries_NN2 that_CST account_VV0 for_IF more_DAR than_CSN (_( less_RRR than_CSN )_) 25%_NNU of_IO the_AT firm_NN1 '_NULL s_ZZ1 total_JJ employment_NN1 expenditures_NN2 ._. 
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<s>
The_AT simulated_JJ dataset_NN1 is_VBZ illustrated_VVN in_II Fig._NN1 1_MC1 ._. 
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<s>
However_RR ,_, the_AT walkers_NN2 on_II the_AT topmost_JJ tier_NN1 are_VBR unconstrained_JJ and_CC therefore_RR free_JJ to_TO meet_VVI ,_, so_CS the_AT entire_JJ structure_NN1 relaxes_VVZ '_NULL top–down_NN1 '_NULL ._. 
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<s>
However_RR ,_, it_PPH1 turns_VVZ out_RP to_TO be_VBI simpler_JJR to_TO directly_RR study_VVI market_NN1 models_NN2 as_CSA follows_VVZ ._. 
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<s>
Footnote_VV0 8_MC Quantifying_JJ dependence_NN1 among_II financial_JJ variables_NN2 is_VBZ one_MC1 of_IO the_AT key_JJ objectives_NN2 of_IO financial_JJ econometrics_NN2 ._. 
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<s>
Whose_DDQGE dynamics_NN could_VM in_II turn_VVI be_VBI driven_VVN by_II the_AT convergence_NN1 in_II the_AT cost_NN1 of_IO capital_NN1 across_II advanced_JJ economies_NN2 ,_, see_VV0 Mazet-Sonilhac_JJ and_CC Mésonnier_NP1 (_( 2016_MC )_) ._. 
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<s>
It_PPH1 is_VBZ important_JJ to_TO note_VVI that_CST this_DD1 does_VDZ not_XX penalize_VVI or_CC prevent_VVI signatures_NN2 being_VBG shared_VVN across_II cancer_NN1 types_NN2 ._. 
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<s>
Past_JJ studies_NN2 have_VH0 reported_VVN increases_NN2 in_II oil_NN1 price_NN1 volatility_NN1 in_II the_AT mid-1980s_NN2 ._. 
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<s>
In_II Fig._NN1 13(d)_FO ,_, higher_JJR imp_NN1 results_NN2 in_II lower_JJR lane-changing_JJ rate_NN1 of_IO trucks_NN2 when_RRQ 15_MC <_FO <_FO 75_MC veh/km/ln_NN1 ._. 
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<s>
Let_VV0 <equation>_FO and_CC let_VVI <equation>_FO denote_VV0 the_AT smallest_JJT right-continuous_JJ filtration_NN1 that_CST makes_VVZ <equation>_FO adapted_VVN and_CC contains_VVZ all_DB the_AT information_NN1 of_IO <equation>_FO already_RR at_II time_NNT1 0_MC ._. 
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<s>
For_IF this_DD1 ,_, we_PPIS2 first_MD denote_VV0 the_AT nine_MC scale_NN1 rectangles_NN2 as_CSA A11_FO ,_, ..._... ,_, 
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<s>
A33_FO in_II figure_NN1 9_MC ,_, corresponding_VVG to_II the_AT vertical_JJ and_CC horizontal_JJ scale_NN1 intervals_NN2 presented_VVN in_II figures_NN2 3_MC and_CC 4_MC ._. 
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<s>
The_AT pooled_JJ lottery_NN1 sample_NN1 has_VHZ slightly_RR less_DAR wealth_NN1 than_CSN the_AT matched_JJ population_NN1 sample_NN1 ,_, has_VHZ slightly_RR more_DAR debt_NN1 ,_, and_CC is_VBZ slightly_RR more_RGR likely_JJ to_TO own_VVI real_JJ estate_NN1 ._. 
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<s>
On_II BioNLP_NP1 2013_MC (_( E3_FO )_) ,_, PEDL_NP1 achieves_VVZ an_AT1 AP_NP1 score_VV0 that_DD1 is_VBZ 6.07_MC pp_NNU2 higher_RRR than_CSN that_DD1 of_IO comb-dist_NN1 ,_, while_CS on_II PID_NP1 (_( E1_FO ,_, mixing_VVG predictions_NN2 for_IF all_DB PPA_NN1 types_NN2 )_) it_PPH1 is_VBZ 1.24_MC pp_NNU2 higher_RRR ._. 
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<s>
Figure_NN1 5_MC compares_VVZ the_AT results_NN2 of_IO GLMM_NP1 and_CC cGLMM_NNU on_II the_AT real_JJ human_JJ genomic_JJ dataset_NN1 containing_VVG 150_MC SNPs_NP2 (_( including_II 10_MC significant_JJ SNPs_NP2 between_II the_AT two_MC groups_NN2 )_) over_II the_AT 2000_MC genomes_NN2 in_II two_MC groups_NN2 ._. 
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<s>
The_AT probability_NN1 density_NN1 function_NN1 of_IO the_AT asymptotically_RR equivalent_JJ linear_JJ rule_NN1 hregi_NN2 ,_, n(Sn)_NNU is_VBZ also_RR represented_VVN there_RL ._. 
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<s>
The_AT SRA_NP1 alignment_NN1 and_CC proposed_JJ consensus_NN1 structure_NN1 used_VVN in_II Novikova_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2012_MC )_) were_VBDR unavailable_JJ to_II us_PPIO2 ._. 
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<s>
For_IF illustration_NN1 ,_, we_PPIS2 treat_VV0 the_AT sample_NN1 SI_FW as_CS21 if_CS22 it_PPH1 was_VBDZ selected_VVN by_II31 means_II32 of_II33 stratified_JJ rejective_JJ sampling_NN1 ._. 
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<s>
This_DD1 gap_NN1 slightly_RR increases_VVZ when_RRQ we_PPIS2 include_VV0 student-level_JJ controls_NN2 (_( column_NN1 (_( 3_MC )_) )_) .58_MC Consistently_RR with_IW the_AT result_NN1 in_II Table_NN1 VII_MC ,_, math_NN1 teacher_NN1 stereotypes_NN2 have_VH0 a_AT1 strong_JJ positive_JJ and_CC statistically_RR significant_JJ impact_NN1 on_II the_AT choice_NN1 of_IO vocational_JJ track_NN1 for_IF girls_NN2 ,_, with_II31 respect_II32 to_II33 boys_NN2 in_II the_AT same_DA class_NN1 ._. 
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<s>
Weighted_JJ fusion_NN1 shows_VVZ a_AT1 similar_JJ performance_NN1 to_II unweighted_JJ fusion_NN1 (_( not_XX shown_VVN )_) ._. 
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<s>
Note_VV0 that_CST while_CS the_AT number_NN1 of_IO subgroups_NN2 is_VBZ 10_MC and_CC 20_MC ,_, the_AT results_NN2 are_VBR calculated_VVN based_VVN on_II Top-10_MC recommendation_NN1 ._. 
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<s>
No_AT extension_NN1 of_IO the_AT peaks_NN2 was_VBDZ done_VDN ._. 
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<s>
This_DD1 driving_JJ time_NNT1 also_RR equals_VVZ the_AT driving_JJ distance_NN1 multiplied_VVN by_II the_AT ratio_NN1 of_IO the_AT walking_NN1 speed_NN1 to_II the_AT driving_JJ speed_NN1 in_II the_AT lot_NN1 ;_; we_PPIS2 denote_VV0 this_DD1 ratio_NN1 by_II ._. 
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<s>
The_AT pseudocode_NN1 is_VBZ presented_VVN in_II Algorithm_NN1 1_MC1 which_DDQ is_VBZ guaranteed_VVN to_TO converge_VVI to_II a_AT1 local_JJ optimum_JJ ._. 
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<s>
Accordingly_RR ,_, there_EX is_VBZ growing_JJ interest_NN1 in_II using_VVG text_NN1 that_CST spans_VVZ multiple_JJ sentences_NN2 for_IF distantly_RR supervised_VVN biomedical_JJ relation_NN1 extraction_NN1 ._. 
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<s>
Atmospheric_JJ inversion_NN1 of_IO CO2_FO transport_NN1 to_TO obtain_VVI surface_NN1 fluxes_NN2 ,_, or_CC the_AT slightly_RR mis-named_VVN but_CCB shorter_JJR ,_, "_" CO2_FO flux_NN1 inversion_NN1 ,_, "_" is_VBZ the_AT recovery_NN1 of_IO the_AT surface_NN1 flux_NN1 field_NN1 of_IO CO2_FO (_( i.e._REX ,_, sources_NN2 and_CC sinks_NN2 )_) from_II data_NN that_CST represent_VV0 an_AT1 indirect_JJ measure_NN1 of_IO it_PPH1 (_( e.g._REX ,_, atmospheric_JJ CO2_FO data_NN in_II ppm_NNU )_) ._. 
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<s>
Sophisticated_JJ traders_NN2 tend_VV0 to_TO reduce_VVI its_APPGE turnover_NN1 when_CS optimizing_VVG performance_NN1 in_II practice_NN1 ._. 
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<s>
We_PPIS2 introduce_VV0 the_AT invariant_JJ measure-based_JJ summary_NN1 statistics_NN and_CC propose_VV0 a_AT1 proper_JJ distance_NN1 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, when_CS we_PPIS2 take_VV0 →_NULL ∞_FO the_AT fluctuations_NN2 go_VV0 to_II 0_MC ,_, which_DDQ is_VBZ the_AT case_NN1 for_IF Boltzmann–Gibbs_NP1 statistics_NN ._. 
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<s>
In_II Sect._NP1 2_MC ,_, we_PPIS2 describe_VV0 the_AT data_NN and_CC preliminaries_NN2 ._. 
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<s>
Members_NN2 of_IO the_AT Lok_NP1 Sabha_NP1 are_VBR elected_VVN by_II adult_JJ universal_JJ suffrage_NN1 and_CC a_AT1 first-past-the-post_JJ system_NN1 to_TO represent_VVI their_APPGE respective_JJ constituencies_NN2 ;_; more_RRR lucidly_RR ,_, they_PPHS2 are_VBR elected_VVN by_II being_VBG voted_VVN upon_II by_II all_DB adult_JJ citizens_NN2 of_IO India_NP1 ,_, from_II a_AT1 set_NN1 of_IO candidates_NN2 who_PNQS stand_VV0 in_II their_APPGE respective_JJ constituencies_NN2 ._. 
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<s>
The_AT package_NN1 can_VM be_VBI found_VVN at_II https_NNU :_: ._. 
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<s>
Every_AT1 computation_NN1 neural_NN1 node_NN1 follows_VVZ the_AT same_DA pattern_NN1 as_CSA in_II Fig._NN1 4.1_MC ._. 
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<s>
The_AT results_NN2 we_PPIS2 have_VH0 described_VVN open_RR many_DA2 questions_NN2 ._. 
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<s>
For_IF the_AT AD_NN1 map_NN1 ,_, we_PPIS2 further_RRR include_VV0 copy-number_JJ variations_NN2 '_NULL information_NN1 from_II Malacards_NP2 ,_, which_DDQ was_VBDZ missing_VVG in_II the_AT case_NN1 of_IO IPF_NP1 ._. 
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<s>
We_PPIS2 investigated_VVD why_RRQ our_APPGE VAECox_NN1 model_NN1 did_VDD not_XX outperform_VVI Cox-nnet_NN1 in_II LUAD_NP1 and_CC LUSC_NP1 survival_NN1 predictions_NN2 ._. 
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<s>
We_PPIS2 relax_VV0 the_AT parametric_JJ frailty_NN1 assumption_NN1 in_II this_DD1 class_NN1 of_IO models_NN2 by_II using_VVG a_AT1 non-parametric_JJ discrete_JJ distribution_NN1 ._. 
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<s>
When_CS the_AT trajectory_NN1 is_VBZ viewed_VVN in_II the_AT reverse_JJ order_NN1 ,_, an_AT1 analogous_JJ situation_NN1 is_VBZ that_CST the_AT final_JJ state_NN1 (_( ,_, )_) (_( xbj_NNU ,_, vbj_NNU )_) and_CC the_AT intermediate_JJ states_NN2 (_( ,_, )_) ;_; 1≤<_FO (_( xbjbj_NNU ,_, vbjbj_NNU )_) ;_; 1≤j<j_FO satisfy_VV0 (_( 22_MC )_) ._. 
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<s>
The_AT separation_NN1 is_VBZ maximal_JJ with_IW Mann–Whitney_NP1 U_JJ test_NN1 yields_VVZ a_AT1 statistic=0_FO ,_, and_CC a_AT1 P-value_NN1 <e34_FO ._. 
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<s>
When_CS the_AT theoretical_JJ results_NN2 are_VBR applied_VVN in_II practice_NN1 ,_, the_AT cases_NN2 where_CS this_DD1 estimator_NN1 performs_VVZ better_NN1 are_VBR pointed_VVN out_RP in_II Tables_NN2 1_MC1 ,_, 2_MC ,_, 3_MC ,_, 4_MC ,_, 5_MC ,_, 6_MC ,_, and_CC 7_MC depending_II21 on_II22 whether_CSW the_AT conditions_NN2 of_IO the_AT theorems_NN2 are_VBR satisfied_JJ ._. 
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<s>
This_DD1 process_NN1 was_VBDZ repeated_VVN 100_MC times_NNT2 and_CC averages_NN2 are_VBR reported_VVN ._. 
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<s>
In_II model_NN1 (_( i_ZZ1 )_) ,_, the_AT mean_JJ effect_NN1 is_VBZ 3.74_MC with_IW a_AT1 standard_JJ deviation_NN1 of_IO 0.42_MC ._. 
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<s>
In_II this_DD1 fashion_NN1 ,_, the_AT statistic_NN1 of_IO interest_NN1 is_VBZ never_RR degenerate_JJ ._. 
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<s>
It_PPH1 is_VBZ worth_II mentioning_VVG that_CST the_AT superior_JJ result_NN1 among_II four_MC presented_JJ models_NN2 are_VBR represented_VVN in_II a_AT1 bold_JJ color_NN1 for_IF all_DB different_JJ experiments_NN2 ._. 
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<s>
Notice_VV0 that_CST the_AT <equation>_FO notation_NN1 for_IF a_AT1 set_NN1 <equation>_FO refers_VVZ to_II being_VBG a_AT1 subset_NN1 of_IO the_AT enlarged_JJ space_NN1 <equation>_FO and_CC should_VM not_XX be_VBI mixed_VVN up_RP with_IW the_AT closure_NN1 <equation>_FO of_IO a_AT1 set_NN1 <equation>_FO ._. 
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<s>
Interestingly_RR ,_, most_DAT of_IO the_AT evaluated_VVN tools_NN2 succeeded_VVN in_II this_DD1 respect_NN1 ,_, which_DDQ makes_VVZ them_PPHO2 suitable_JJ to_TO use_VVI for_IF prokaryotic_JJ datasets_NN2 that_CST vary_VV0 in_II sequencing_NN1 depths_NN2 and_CC resolutions_NN2 ._. 
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<s>
Letting_VVG fB_NNU be_VBI the_AT density_NN1 of_IO the_AT individual_JJ birth_NN1 data_NN (_( Xi_NN1 ,_, Yi_NP1 )_) ,_, the_AT birth_NN1 counts_NN2 Bst_RA can_VM be_VBI regarded_VVN as_II histogram_NN1 values_NN2 which_DDQ estimate_VV0 the_AT quantities_NN2 ss1tt1fB_NNU (_( x_ZZ1 ,_, y_ZZ1 )_) dxdy_NN1 ._. 
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<s>
The_AT fact_NN1 that_CST the_AT coefficients_NN2 on_II the_AT cost_NN1 share_NN1 here_RL are_VBR larger_JJR than_CSN 1_MC1 indicates_VVZ that_DD1 capital_NN1 does_VDZ not_XX adjust_VVI frictionlessly_RR ._. 
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<s>
Finally_RR ,_, we_PPIS2 preclude_VV0 possibilities_NN2 that_CST market_VV0 reactions_NN2 on_II the_AT event_NN1 day_NNT1 are_VBR induced_VVN by_II the_AT secondary_JJ dissemination_NN1 of_IO analyst_NN1 recommendations_NN2 ,_, firm-specific_JJ news_NN1 releases_NN2 ,_, media_NN coverage_NN1 ,_, and_CC previous_JJ positive_JJ significant_JJ abnormal_JJ returns_NN2 ._. 
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<s>
Over_II the_AT last_MD decades_NNT2 ,_, stochastic_JJ differential_JJ equations_NN2 (_( SDEs_NP2 )_) have_VH0 become_VVN an_AT1 established_JJ and_CC powerful_JJ tool_NN1 for_IF modelling_VVG time-dependent_JJ ,_, real-world_JJ phenomena_NN2 with_IW underlying_JJ random_JJ effects_NN2 ._. 
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<s>
Specifically_RR ,_, the_AT effect_NN1 of_IO RM_NP1 seems_VVZ to_TO increase_VVI from_II lower_JJR to_II upper_JJ quantile_JJ levels_NN2 ,_, while_CS the_AT effect_NN1 of_IO log(TAX)_NN1 seems_VVZ to_TO decrease_VVI from_II lower_JJR to_II upper_JJ quantile_JJ levels_NN2 (_( comparing_VVG the_AT absolute_JJ values_NN2 of_IO the_AT coefficients_NN2 )_) ._. 
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<s>
The_AT cumulative_JJ number_NN1 of_IO calls_NN2 to_II f_ZZ1 has_VHZ been_VBN decreased_VVN by_II a_AT1 factor_NN1 greater_JJR than_CSN 3_MC in_II31 comparison_II32 with_II33 the_AT two_MC other_JJ methods_NN2 ._. 
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<s>
The_AT insurance_NN1 benefits_NN2 were_VBDR not_XX adjusted_VVN to_II inflation_NN1 by_II the_AT insurance_NN1 company_NN1 ,_, and_CC thus_RR our_APPGE treatment_NN1 is_VBZ 40%_NNU lower_JJR in_II wave_NN1 2_MC ,_, compared_VVN with_IW wave_NN1 1_MC1 ._. 
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<s>
In_RR21 particular_RR22 ,_, solving_VVG problem_NN1 (_( 3.8_MC )_) in_II the_AT case_NN1 of_IO variable_JJ selection_NN1 is_VBZ easy_JJ because_CS the_AT operators_NN2 PT_NN1 and_CC avgPavgare_VV0 both_RR diagonal_JJ (_( and_CC hence_RR trivially_RR simultaneously_RR diagonalizable_JJ )_) in_II that_DD1 case_NN1 ;_; as_II a_AT1 result_NN1 ,_, we_PPIS2 can_VM decompose_VVI problem_NN1 (_( 3.8_MC )_) into_II a_AT1 set_NN1 of_IO onevariable_JJ problems_NN2 ._. 
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<s>
These_DD2 methods_NN2 usually_RR begin_VV0 by_II an_AT1 exploration_NN1 phase_NN1 ,_, during_II which_DDQ the_AT output_NN1 of_IO the_AT code_NN1 is_VBZ computed_VVN on_II an_AT1 experimental_JJ design_NN1 of_IO size_NN1 n_ZZ1 ._. 
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<s>
Owing_II21 to_II22 interdependencies_NN2 ,_, a_AT1 failure_NN1 in_II one_MC1 layer_NN1 can_VM produce_VVI iterative_JJ cascade_NN1 of_IO failures_NN2 in_II other_JJ layers_NN2 ,_, which_DDQ may_VM eventually_RR lead_VVI to_II the_AT catastrophic_JJ collapse_NN1 of_IO the_AT whole_JJ interdependent_JJ network_NN1 system_NN1 ._. 
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<s>
LPM_NP1 fits_VVZ a_AT1 linear_JJ combination_NN1 of_IO arbitrary_JJ PMFs_NP1 to_II a_AT1 cohort_NN1 of_IO histograms_NN2 using_VVG (_( EM_FU )_) (_( Tar_VV0 et_RA21 al._RA22 ,_, 2018_MC )_) ,_, similarly_RR to_II how_RRQ pLSA_NN1 uses_VVZ EM_FU ._. 
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<s>
Here_RL ,_, we_PPIS2 show_VV0 the_AT results_NN2 of_IO the_AT attribute_NN1 inference_NN1 attack_NN1 for_IF the_AT MAF_NN1 and_CC chi-square_JJ queries_NN2 ._. 
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<s>
From_II the_AT first_MD three_MC columns_NN2 in_II both_DB2 panel_NN1 A_ZZ1 and_CC B_ZZ1 ,_, we_PPIS2 can_VM see_VVI that_CST coefficients_NN2 derived_VVN for_IF different_JJ sources_NN2 are_VBR quite_RG close_JJ ._. 
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<s>
For_IF this_DD1 reason_NN1 ,_, we_PPIS2 may_VM now_RT assume_VVI that_CST <equation>_FO is_VBZ itself_PPX1 a_AT1 martingale_NN1 ._. 
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<s>
In_II section_NN1 ,_, we_PPIS2 present_VV0 the_AT phase_NN1 transition_NN1 boundary_NN1 for_IF the_AT separability_NN1 of_IO two_MC classes_NN2 under_II several_DA2 settings_NN2 ._. 
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<s>
Based_VVN on_II the_AT phase_NN1 transition_NN1 results_NN2 in_II Section_NN1 3_MC ,_, we_PPIS2 propose_VV0 four_MC experiments_NN2 to_TO assess_VVI the_AT reliability_NN1 of_IO spectral_JJ clustering_NN1 in_II31 terms_II32 of_II33 r3_FO ,_, r_ZZ1 and_CC three_MC parameters_NN2 above_RL ._. 
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<s>
Let_VV0 <equation>_FO be_VBI a_AT1 log-concave_JJ density_NN1 supported_VVN on_II the_AT closed_JJ interval_NN1 <equation>_FO ,_, where_CS <equation>_FO ._. 
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<s>
When_CS estimating_VVG our_APPGE model_NN1 ,_, we_PPIS2 find_VV0 that_CST r_ZZ1 >_FO 0_MC fits_VVZ the_AT data_NN significantly_RR better_RRR than_CSN <equation>_FO meaning_VVG these_DD2 type_NN1 of_IO resets_VVZ seem_VV0 to_TO occur_VVI in_II the_AT data.9_FO See_VV0 Appendix_NN1 A_ZZ1 for_IF the_AT relevant_JJ formulas_NN2 ._. 
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<s>
Assumption_NN1 5_MC ._. 
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<s>
The_AT rows_NN2 of_IO are_VBR independent_JJ zeromean_JJ Gaussian_JJ vectors_NN2 with_IW covariance_NN1 ._. 
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<s>
Let_VV0 max_NN1 denote_VVI the_AT largest_JJT eigenvalue_NN1 of_IO ._. 
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<s>
This_DD1 is_VBZ the_AT main_JJ result_NN1 of_IO this_DD1 paper_NN1 ;_; it_PPH1 connects_VVZ information_NN1 thermodynamics_NN1 with_IW the_AT MDL_MC principle_NN1 ._. 
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<s>
According_II21 to_II22 Theorem_NN1 3.3_MC ,_, we_PPIS2 have_VH0 <equation>_FO for_IF any_DD <equation>_FO and_CC <equation>_FO on_II <equation>_FO ._. 
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<s>
Coefficients_NN2 and_CC 95%_NNU confidence_NN1 intervals_NN2 are_VBR obtained_VVN by_II estimating_VVG Eq_NN1 ._. 
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<s>
(_( 1_MC1 )_) in_II the_AT post-1999_JJ sample_NN1 of_IO &lsqb;_( Math_NN1 Processing_NN1 Error_NN1 &rsqb;_) equity_NN1 market_NN1 nonparticipants_NN2 ._. 
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<s>
While_CS this_DD1 new_JJ method_NN1 has_VHZ at_RR21 most_RR22 <equation>_FO time_NNT1 complexity_NN1 ._. 
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<s>
The_AT most_RGT prominent_JJ to_II date_NN1 are_VBR three_MC mutations_NN2 in_II the_AT TERT_NN1 promoter_NN1 region_NN1 (_( Horn_NN1 et_RA21 al._RA22 ,_, 2013_MC ;_; Huang_NP1 et_RA21 al._RA22 ,_, 2013_MC ;_; Weinhold_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) ._. 
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Panel_NN1 B_ZZ1 plots_VVZ the_AT relationship_NN1 for_IF manager_NN1 value_NN1 added_VVN and_CC collaboration_NN1 experience_NN1 ._. 
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<s>
Furthermore_RR ,_, it_PPH1 is_VBZ found_VVN that_CST nontrivial_JJ behaviors_NN2 of_IO the_AT coupling_NN1 scheme_NN1 in_II the_AT small-size_JJ oscillatory_JJ power_NN1 network_NN1 potentially_RR vary_VV0 with_IW the_AT synchronous_JJ patterns_NN2 ._. 
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<s>
With_IW that_DD1 notion_NN1 ,_, we_PPIS2 decided_VVD also_RR to_TO include_VVI water_NN1 molecules_NN2 in_II the_AT analysis_NN1 of_IO interactions_NN2 ._. 
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<s>
Country_NN1 fixed_JJ effects_NN2 ,_, used_VVN in_II the_AT two_MC regressions_NN2 in_II the_AT table_NN1 '_NULL s_ZZ1 left_JJ half_NN1 ,_, are_VBR replaced_VVN by_II geographic_JJ and_CC economic_JJ region_NN1 fixed_JJ effects_NN2 in_II the_AT table_NN1 '_NULL s_ZZ1 right_JJ half_NN1 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, the_AT computation_NN1 of_IO correlation_NN1 functions_NN2 turned_VVD out_RP to_TO be_VBI much_RR more_RGR challenging_JJ ,_, as_CSA it_PPH1 is_VBZ notoriously_RR the_AT case_NN1 for_IF Bethe-Ansatz_NP1 solvable_JJ models_NN2 ._. 
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<s>
The_AT <equation>_FO model_NN1 faces_VVZ difficulties_NN2 in_II reproducing_VVG long-term_JJ spreads_NN2 ;_; for_REX21 example_REX22 ,_, its_APPGE RMSE_NN1 is_VBZ twice_RR as_RG large_JJ as_II the_AT one_PN1 of_IO the_AT unconstrained_JJ <equation>_FO for_IF the_AT 10-year_JJ maturity_NN1 spread_NN1 for_IF both_DB2 firms_NN2 ._. 
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<s>
The_AT third_MD subgroup_NN1 of_IO patients_NN2 also_RR had_VHN onset_NN1 after_II the_AT start_NN1 of_IO the_AT trial_NN1 but_CCB positive_JJ ALSFRS_NN2 slope_NN1 ._. 
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<s>
Simulated_JJ method_NN1 of_IO moments_NN2 (_( SMM_NP1 )_) is_VBZ the_AT most_RGT common_JJ ,_, employed_VVD recently_RR in_II Nikolov_NP1 and_CC Whited_JJ (_( 2014_MC )_) ,_, Dimopoulos_NP2 and_CC Sacchetto_NP1 (_( 2014_MC )_) ,_, Schroth_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2014_MC )_) ,_, Warusawitharana_NP1 (_( 2015_MC )_) ,_, and_CC Glover_NP1 (_( 2016_MC )_) ,_, among_II others_NN2 ._. 
</s>
<s>
The_AT sign_NN1 of_IO δ_NULL can_VM be_VBI reversed_VVN with_IW a_AT1 spin_NN1 flip_NN1 applied_VVN to_II one_MC1 of_IO the_AT two_MC chains_NN2 ,_, without_IW altering_VVG the_AT spectrum_NN1 ._. 
</s>
<s>
Since_CS the_AT reference_NN1 system_NN1 is_VBZ a_AT1 Gaussian_JJ form_NN1 ,_, Wick_NP1 '_NULL s_ZZ1 theorem_NN1 applies_VVZ ,_, but_CCB only_RR to_II the_AT deviation_NN1 δ_NULL u_ZZ1 ._. 
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Similarly_RR ,_, the_AT point-wise_JJ interval_NN1 estimates_VVZ for_IF f_ZZ1 and_CC F_ZZ1 yield_VV0 approximately_RR the_AT supposed_JJ coverage_NN1 rate_NN1 of_IO 90%_NNU in_II all_DB considered_VVN setups_NN2 ._. 
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<s>
Namely_REX ,_, if_CS we_PPIS2 consider_VV0 an_AT1 observable_JJ such_II21 as_II22 the_AT total_JJ energy_NN1 within_II some_DD region_NN1 ,_, it_PPH1 can_VM be_VBI written_VVN as_II the_AT sum_NN1 of_IO a_AT1 large_JJ number_NN1 of_IO weakly_RR correlated_VVN contributions_NN2 ,_, and_CC hence_RR is_VBZ sharply_RR peaked_VVN over_II the_AT ensemble_NN1 of_IO states_NN2 ._. 
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<s>
Extensive_JJ simulation_NN1 studies_NN2 show_VV0 that_CST the_AT dataadaptive_JJ techniques_NN2 proposed_VVN outperform_VV0 the_AT existing_JJ methods_NN2 under_II various_JJ model_NN1 settings_NN2 and_CC alternative_JJ structures_NN2 ._. 
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This_DD1 implies_VVZ that_CST in_BCL21 order_BCL22 to_TO cross_VVI the_AT barrier_NN1 ,_, the_AT particle_NN1 has_VHZ to_TO reach_VVI xcr_NNU by_II moving_VVG along_II the_AT stable_JJ manifold_NN1 ,_, and_CC then_RT ,_, once_RR xcr_NNU is_VBZ reached_VVN ,_, it_PPH1 can_VM '_NULL fly_VVI over_II '_NULL the_AT barrier_NN1 using_VVG the_AT deterministic_JJ dynamics_NN ._. 
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<s>
TandemQUAST_NN1 uses_VVZ the_AT read_NN1 alignments_NN2 (_( truncated_VVN with_II31 respect_II32 to_II33 their_APPGE longest_JJT chains_NN2 )_) to_TO construct_VVI the_AT coverage_NN1 plot_NN1 and_CC reveal_VVI regions_NN2 with_IW abnormal_JJ coverage_NN1 that_CST may_VM point_VVI to_II assembly_NN1 errors_NN2 (_( Fig._NN1 3_MC )_) ._. 
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Moreover_RR ,_, the_AT generality_NN1 of_IO our_APPGE forward_JJ rate_NN1 formulation_NN1 with_IW stochastic_JJ discontinuities_NN2 enables_VVZ us_PPIO2 to_TO directly_RR embed_VVI market_NN1 models_NN2 ._. 
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The_AT empirical_JJ framework_NN1 follows_VVZ the_AT approach_NN1 of_IO Elder_NN1 and_CC Serletis_NP1 (_( 2009_MC ,_, 2010_MC ,_, 2011_MC )_) and_CC Bredin_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) ,_, who_PNQS measure_VV0 the_AT impact_NN1 of_IO oil_NN1 price_NN1 uncertainty_NN1 in_II a_AT1 vector_NN1 autoregressive_JJ (_( VAR_NP1 )_) model_NN1 ._. 
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The_AT estimated_JJ observed_JJ efficiency_NN1 ,_, effeff_VV0 θ_NULL n_ZZ1 ,_, and_CC the_AT efficiency_NN1 of_IO a_AT1 design_NN1 with_II31 respect_II32 to_II33 estimated_JJ OFI_NN2 ,_, OFIEff()OFIEff_NP1 (_( θ_NULL n_ZZ1 )_) ,_, are_VBR also_RR important_JJ benchmarks_NN2 for_IF the_AT performance_NN1 of_IO a_AT1 design_NN1 ._. 
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So_RR it_PPH1 is_VBZ feasible_JJ to_TO neglect_VVI the_AT influence_NN1 of_IO the_AT magnetic_JJ field_NN1 ._. 
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<s>
More_RGR recently_RR it_PPH1 has_VHZ been_VBN developed_VVN further_RRR for_IF the_AT specific_JJ needs_NN2 of_IO functional_JJ data_NN by_II Zhang_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) and_CC Zhang_NP1 and_CC Shao_NP1 (_( 2015_MC )_) (_( see_VV0 also_RR Shao_NP1 (_( 2015_MC )_) for_IF a_AT1 recent_JJ review_NN1 )_) ._. 
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Table_NN1 7_MC presents_VVZ summary_NN1 statistics_NN for_IF each_DD1 trading_NN1 volume_NN1 group_NN1 ._. 
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This_DD1 paper_NN1 solves_VVZ the_AT hierarchical_JJ hub_NN1 location_NN1 problem_NN1 of_IO large-scale_JJ agricultural_JJ products_NN2 transportation_NN1 network_NN1 ._. 
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If_CS we_PPIS2 resample_VV0 ,_, we_PPIS2 assign_VV0 each_DD1 of_IO the_AT new_JJ particles_NN2 a_AT1 weight_NN1 1/N_FU ._. 
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<s>
More_RGR precisely_RR ,_, we_PPIS2 find_VV0 that_CST the_AT comovement_NN1 and_CC causality_NN1 in_II the_AT two_MC combinations_NN2 ,_, (_( ER_NP1 ,_, ID+_FO )_) and_CC (_( ER_NP1 ,_, ID_NN1 )_) ,_, are_VBR relatively_RR intensified_VVN ,_, whereas_CS in_II the_AT other_JJ two_MC combinations_NN2 ,_, (_( ER+_FO ,_, ID_NN1 )_) and_CC (_( ER+_FO ,_, ID+_FO )_) are_VBR rather_RG scarce_JJ ._. 
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Indeed_RR ,_, intensity_NN1 statistics_NN allow_VV0 us_PPIO2 to_TO investigate_VVI competing_JJ mechanisms_NN2 of_IO tie_NN1 formation_NN1 and_CC therefore_RR illuminate_VV0 the_AT merits_NN2 of_IO the_AT REM_NN1 approach_NN1 ._. 
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It_PPH1 consisted_VVD of_IO comparing_VVG several_DA2 realizations_NN2 of_IO the_AT system_NN1 which_DDQ differed_VVD from_II each_PPX221 other_PPX222 only_RR by_II the_AT initial_JJ damage_NN1 ._. 
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I_PPIS1 follow_VV0 Duffee_NP1 (_( 2005_MC )_) to_TO use_VVI monthly_JJ data_NN indexed_VVN with_IW t_ZZ1 ._. 
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Monthly_JJ real_JJ consumption_NN1 is_VBZ defined_VVN as_II the_AT sum_NN1 of_IO seasonally_RR adjusted_VVN real_JJ aggregate_JJ expenditures_NN2 on_II nondurable_JJ goods_NN2 and_CC services_NN2 (_( source_NN1 :_: U.S._NP1 Bureau_NN1 of_IO Economic_JJ Analysis_NN1 ,_, BEA_NP1 )_) ._. 
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From_II a_AT1 regulatory_JJ perspective_NN1 ,_, this_DD1 means_VVZ that_CST insurers_NN2 should_VM be_VBI put_VVN under_II stricter_JJR supervision_NN1 compared_VVN to_II banks_NN2 and_CC other_JJ services_NN2 ._. 
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A_AT1 key_JJ contribution_NN1 of_IO HLN_NP1 is_VBZ to_TO show_VVI that_CST this_DD1 exhaustive_JJ protocol_NN1 for_IF testing_VVG and_CC comparing_VVG models_NN2 controls_VVZ the_AT size_NN1 of_IO the_AT resulting_JJ stepwise_JJ approach_NN1 ._. 
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This_DD1 rate_NN1 of<equation>_FO is_VBZ much_RR slower_RRR than_CSN our_APPGE <equation>_FO ,_, the_AT latter_DA being_NN1 the_AT same_DA rate_NN1 as_CSA obtained_VVN by_II Marron_NP1 (_( 1987_MC )_) for_IF independent_JJ and_CC identically_RR distributed_VVN (_( IID_NP1 )_) data_NN ._. 
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However_RR ,_, in_II that_DD1 article_NN1 they_PPHS2 employ_VV0 smooths_VVZ of_IO one_MC1 covariate_NN1 and_CC only_RR require_VV0 terms_NN2 of_IO the_AT form_NN1 XTjWXj_NP1 ,_, but_CCB not_XX XTjWXk_NP1 ._. 
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Outbreaks_NN2 can_VM start_VVI in_II big_JJ cities_NN2 and_CC propagate_VVI to_II the_AT countryside_NN1 or_CC there_EX might_VM be_VBI multiple_JJ foci_NN2 of_IO infection_NN1 ._. 
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We_PPIS2 appreciate_VV0 the_AT help_NN1 of_IO the_AT Director_NN1 of_IO the_AT newspaper_NN1 "_" El_NP1 Sur_NP1 de_NP1 Acapulco_NP1 "_" and_CC especially_RR to_II Lic_NN1 ._. 
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<s>
Suppose_VV0 that_CST S_ZZ1 is_VBZ a_AT1 k-step_JJ farthest_JJT traversal_NN1 of_IO X._NP1 Then_RT ,_, QQ-plots_NN2 of_IO empirical_JJ and_CC simulated_JJ rainfall_NN1 for_IF LA_NP1 in_II the_AT case_NN1 β_NULL =2_FO ._. 
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It_PPH1 is_VBZ evident_JJ from_II the_AT illustration_NN1 (_( b_ZZ1 )_) that_CST the_AT particles_NN2 tend_VV0 to_TO move_VVI to_II the_AT right_NN1 ,_, that_REX21 is_REX22 ,_, to_TO escape_VVI to_II the_AT higher_JJR price_NN1 region_NN1 ._. 
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U-estimator_NN1 ,_, O-estimator_JJ and_CC MU-estimator_NN1 were_VBDR compared_VVN by_II differences_NN2 between_II mean_JJ values_NN2 of_IO different_JJ estimators_NN2 ,_, too_RR ._. 
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Since_CS we_PPIS2 extracted_VVD common_JJ traits_NN2 of_IO pan-cancers_NN2 and_CC transfer_VV0 the_AT knowledge_NN1 to_II each_DD1 cancer_NN1 model_NN1 ,_, we_PPIS2 selected_VVD 20_MC 502_MC genes_NN2 commonly_RR included_VVN in_II cancer_NN1 gene_NN1 expression_NN1 datasets_NN2 ._. 
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Respiratory_JJ disease_NN1 is_VBZ the_AT second_MD most_RGT common_JJ cause_NN1 of_IO death_NN1 in_II Scotland_NP1 behind_II cancer_NN1 (_( http_NNU :_: )_) ,_, and_CC in_II this_DD1 study_NN1 ,_, we_PPIS2 focus_VV0 on_II the_AT Greater_NP1 Glasgow_NP1 and_CC Clyde_NP1 health_NN1 board_NN1 because_CS Glasgow_NP1 is_VBZ one_MC1 of_IO the_AT unhealthiest_JJT cities_NN2 in_II Europe_NP1 (_( Gray_NP1 and_CC others_NN2 ,_, 2012_MC )_) ._. 
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The_AT two_MC players_NN2 '_NULL profits_NN2 under_II the_AT LDM_NP1 quantum_NN1 scheme_NN1 will_VM increase_VVI with_IW the_AT degree_NN1 of_IO quantum_NN1 entanglement_NN1 increasing_VVG from_II 0_MC to_II +∞_FO as_II the_AT relative_JJ marginal_JJ cost_NN1 is_VBZ between_II 1/2_MF and_CC 2_MC ._. 
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We_PPIS2 set_VV0 regression_NN1 coefficients_NN2 to_TO be_VBI identical_JJ in_II a_AT1 subset_NN1 V0V_FO of_IO the_AT subgroups_NN2 ,_, such_CS21 that_CS22 the_AT size_NN1 K0=_FO |_NULL V0_FO |_NULL of_IO the_AT subset_NN1 governs_VVZ the_AT extent_NN1 to_II which_DDQ information_NN1 sharing_VVG via_II the_AT joint_JJ lasso_NN1 could_VM be_VBI useful_JJ ._. 
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Compared_VVN with_IW two_MC state-of-the-art_JJ methods_NN2 (_( Fang_NN1 et_RA21 al._RA22 ,_, 2016_MC ;_; Yan_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ,_, the_AT experimental_JJ results_NN2 show_VV0 that_CST MT–SCCALR_NP1 performs_VVZ better_JJR than_CSN or_CC similarly_RR to_II benchmarks_NN2 in_II31 terms_II32 of_II33 correlation_NN1 coefficients_NN2 and_CC classification_NN1 accuracies_NN2 ._. 
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Most_RGT importantly_RR ,_, the_AT gap_NN1 can_VM be_VBI closed_VVN by_II the_AT use_NN1 of_IO language_NN1 model_NN1 pre-training_NN1 ._. 
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However_RR ,_, an_AT1 alternative_JJ approach_NN1 is_VBZ required_VVN when_CS it_PPH1 is_VBZ long_JJ ._. 
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Specifically_RR ,_, the_AT smaller_JJR the_AT value_NN1 is_VBZ ,_, the_AT greater_JJR the_AT impact_NN1 of_IO the_AT risk_NN1 spread_VVN on_II the_AT stock_NN1 market_NN1 ._. 
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Since_CS a_AT1 particle_NN1 after_II the_AT resampling_JJ step_NN1 at_II stage_NN1 p_ZZ1 is_VBZ approximately_RR a_AT1 sample_NN1 from_II (_( )_) p_ZZ1 (_( θ_NULL )_) and_CC Kp_NP1 is_VBZ p-invariant_JJ ,_, no_AT burn-in_NN1 period_NN1 is_VBZ required_VVN as_CSA in_II MCMC_NP1 methods_NN2 ,_, where_CS often_RR a_AT1 very_RG large_JJ number_NN1 of_IO burn-in_NN1 iterations_NN2 are_VBR required_VVN ._. 
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The_AT work_NN1 extraction_NN1 phase_NN1 C_ZZ1 →_NULL D_ZZ1 corresponds_VVZ to_II adjusting_VVG the_AT energy_NN1 levels_NN2 →_NULL '_NULL without_IW changing_VVG the_AT population_NN1 n_ZZ1 of_IO the_AT levels_NN2 (_( see_VV0 figure_NN1 )_) ._. 
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A_AT1 risk_NN1 factor_NN1 is_VBZ here_RL a_AT1 single_JJ asset_NN1 or_CC a_AT1 single_JJ line_NN1 of_IO insurance_NN1 business_NN1 ._. 
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The_AT theoretical_JJ value_NN1 range_NN1 of_IO each_DD1 parameter_NN1 and_CC the_AT setting_NN1 in_II this_DD1 paper_NN1 are_VBR shown_VVN in_II Table_NN1 2_MC ._. 
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Under_II the_AT null_JJ hypothesis_NN1 ,_, the_AT performance_NN1 of_IO all_DB methods_NN2 is_VBZ similar_JJ and_CC the_AT type_NN1 I_MC1 error_NN1 is_VBZ controlled_VVN ._. 
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Condition_NN1 (_( 3.2_MC )_) is_VBZ generally_RR fulfilled_VVN in_II insurance_NN1 applications_NN2 ,_, preventing_VVG pure_JJ premiums_NN2 i_ZZ1 to_TO become_VVI too_RG small_JJ and_CC variances_NN2 2i_FO to_TO become_VVI too_RG large_JJ ._. 
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In_II Figs._NN2 1(d)_FO and_CC 1(h)_FO ,_, the_AT large_JJ frequency_NN1 components_NN2 are_VBR somewhat_RR obscured_VVN ._. 
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We_PPIS2 next_MD modify_VV0 Example_NN1 5.7_MC to_TO illustrate_VVI that_CST it_PPH1 is_VBZ also_RR possible_JJ that_CST the_AT local_JJ martingale_NN1 part_NN1 <equation>_FO in_II the_AT multiplicative_JJ decomposition_NN1 of_IO <equation>_FO is_VBZ continuous_JJ ._. 
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Having_VHG a_AT1 publicly_RR available_JJ specification_NN1 and_CC open-source_JJ software_NN1 libraries_NN2 for_IF working_VVG with_IW SBML_NP1 content_NN1 from_II many_DA2 operating_NN1 systems_NN2 and_CC programming_VVG languages_NN2 has_VHZ been_VBN instrumental_JJ in_II ensuring_VVG that_CST over_RG 250_MC tools_NN2 are_VBR compatible_JJ with_IW the_AT format_NN1 today_RT ._. 
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Thus_RR ,_, it_PPH1 seems_VVZ that_CST the_AT location_NN1 of_IO each_DD1 olive_JJ tree_NN1 and_CC the_AT trees_NN2 distances_NN2 can_VM be_VBI an_AT1 effective_JJ fact_NN1 in_II the_AT dissemination_NN1 of_IO this_DD1 disease_NN1 (_( Sergeeva_NP1 and_CC Spooner-Hart_NP1 2009_MC )_) ._. 
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On_II a_AT1 conceptual_JJ level_NN1 ,_, any_DD criterion_NN1 that_CST characterises_VVZ a_AT1 certain_JJ object_NN1 should_VM give_VVI rise_NN1 to_II some_DD kind_NN1 of_IO compactness_NN1 when_CS applied_VVN uniformly_RR to_II a_AT1 family_NN1 of_IO objects_NN2 ._. 
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For_IF sufficiently_RR low_JJ temperatures_NN2 ,_, this_DD1 will_VM always_RR be_VBI the_AT case_NN1 ,_, but_CCB the_AT energy_NN1 gap_NN1 and_CC the_AT density_NN1 of_IO states_NN2 determine_VV0 how_RGQ low_RR the_AT temperature_NN1 needs_VVZ to_TO be_VBI ._. 
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This_DD1 research_NN1 poses_VVZ numerous_JJ interesting_JJ directions_NN2 for_IF the_AT future_NN1 ._. 
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The_AT RPS_NP1 on_II each_DD1 system_NN1 is_VBZ an_AT1 average_JJ RPS_NP1 for_IF all_DB forecasts_NN2 in_II the_AT system_NN1 ._. 
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Then_RT ,_, for_IF a_AT1 proper_JJ choice_NN1 of_IO the_AT function_NN1 ,_, the_AT limit_NN1 is_VBZ (_( excluding_VVG a_AT1 degenerate_JJ distribution_NN1 )_) the_AT survival_NN1 function_NN1 of_IO a_AT1 so-called_JJ generalized_JJ Pareto_NP1 distribution_NN1 :_: (_( 1+_FO γ_NULL x_ZZ1 )_) 1/_FO γ_NULL for_IF some_DD real_JJ γ_NULL ∈R_FO ,_, the_AT extreme_JJ value_NN1 index_NN1 ._. 
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In_RR21 particular_RR22 ,_, the_AT estimation_NN1 of_IO undirected_JJ figureical_JJ models_NN2 has_VHZ been_VBN extensively_RR studied_VVN with_IW efficient_JJ algorithms_NN2 and_CC high-dimensional_JJ theoretical_JJ guarantees_NN2 ,_, notably_RR by_II Meinshausen_NP1 and_CC Bühlmann_NP1 (_( 2006_MC )_) ,_, Yuan_NNU and_CC Lin_NP1 (_( 2007_MC )_) ,_, Friedman_NP1 et_RA21 al_RA22 ._. 
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(_( 2008_MC )_) ,_, Rothman_NP1 et_RA21 al_RA22 ._. 
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(_( 2008_MC )_) ,_, Lam_NP1 and_CC Fan_NN1 (_( 2009_MC )_) ,_, Peng_NP1 et_RA21 al_RA22 ._. 
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(_( 2009_MC )_) ,_, Ravikumar_NP1 et_RA21 al_RA22 ._. 
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(_( 2010_MC )_) ,_, Witten_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) ,_, Cai_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) ,_, Ravikumar_NP1 et_RA21 al_RA22 ._. 
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(_( 2011_MC )_) ,_, among_II others_NN2 ._. 
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The_AT patterns_NN2 are_VBR very_RG similar_JJ when_CS we_PPIS2 use_VV0 the_AT Racial_JJ Animus_NN1 Index_NN1 to_II proxy_NN1 for_IF racial_JJ bias_NN1 ._. 
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Note_VV0 the_AT restriction_NN1 of_IO this_DD1 result_NN1 to_II a_AT1 certain_JJ class_NN1 of_IO models_NN2 f_ZZ1 ._. 
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However_RR ,_, we_PPIS2 consider_VV0 a_AT1 different_JJ set_NN1 of_IO strategies_NN2 that_CST can_VM be_VBI applied_VVN in_BCL21 order_BCL22 to_TO repay_VVI the_AT debt_NN1 to_II the_AT state_NN1 ._. 
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Secondly_RR ,_, we_PPIS2 test_VV0 the_AT methods_NN2 in_II31 terms_II32 of_II33 their_APPGE imputation_NN1 performance_NN1 ._. 
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In_II statistics_NN ,_, stochastic_JJ orders_NN2 formalize_VV0 such_DA a_AT1 concept_NN1 that_CST one_MC1 random_JJ variable_NN1 is_VBZ bigger_JJR than_CSN another_DD1 ._. 
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As_CSA directions_NN2 of_IO future_JJ research_NN1 ,_, one_PN1 could_VM also_RR extend_VVI this_DD1 work_NN1 to_II data_NN matrices_NN2 containing_VVG mixed_JJ variables_NN2 (_( quantitative_JJ and_CC categorical_JJ variables_NN2 )_) with_IW MNAR_JJ data_NN ,_, so_CS21 that_CS22 the_AT logistic_JJ regression_NN1 model_NN1 should_VM include_VVI the_AT case_NN1 of_IO categorical_JJ explanatory_JJ and_CC output_NN1 variables_NN2 ._. 
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Graph_NN1 of_IO the_AT six_MC main_JJ cities_NN2 in_II Mexico_NP1 numbered_VVD from_II 1_MC1 to_II 6_MC :_: Guadalajara_NP1 ,_, Zacatecas_NP2 ,_, Queretaro_NP1 ,_, Pachuca_NP1 ,_, Mexico_NP1 City_NN1 ,_, Puebla_NP1 ._. 
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Thus_RR ,_, hi_UH ,_, n_ZZ1 and_CC hpropi_NN2 ,_, n_ZZ1 coincide_VV0 in_II these_DD2 cases_NN2 ._. 
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However_RR ,_, other_JJ specifications_NN2 could_VM be_VBI important_JJ in_II other_JJ circumstances_NN2 ,_, and_CC this_DD1 flexible_JJ modeling_NN1 framework_NN1 can_VM handle_VVI other_JJ specifications_NN2 ._. 
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Before_CS we_PPIS2 start_VV0 with_IW the_AT detailed_JJ analysis_NN1 of_IO the_AT limit_NN1 order_NN1 book_NN1 imbalance_NN1 signal_NN1 ,_, we_PPIS2 survey_VV0 some_DD related_JJ work_NN1 on_II other_JJ processes_NN2 which_DDQ are_VBR known_VVN to_TO affect_VVI asset_NN1 prices_NN2 and_CC have_VH0 mean-reverting_JJ properties_NN2 ._. 
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LeafCutter_VV0 then_RT constructs_NN2 a_AT1 graph_NN1 whose_DDQGE nodes_NN2 are_VBR introns_NN2 connected_VVN by_II edges_NN2 representing_VVG a_AT1 shared_JJ splice_NN1 junction_NN1 between_II two_MC introns_NN2 ._. 
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Approximations_NN2 of_IO the_AT mixture_NN1 model_NN1 (_( 1_MC1 )_) can_VM be_VBI obtained_VVN fixing_VVG an_AT1 upper_JJ bound_JJ smax_NN1 for_IF the_AT depth_NN1 of_IO the_AT tree_NN1 ._. 
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We_PPIS2 will_VM artificially_RR induce_VVI <equation>_FO by_II deleting_VVG edges_NN2 of_IO individuals_NN2 with_IW more_DAR than_CSN <equation>_FO in_II two_MC different_JJ ways_NN2 ,_, first_MD by_II randomly_RR deleting_VVG edges_NN2 with_IW uniform_JJ probability_NN1 (_( as_CSA above_RL in_II the_AT simulation_NN1 study_NN1 )_) ,_, and_CC secondly_RR by_II deleting_VVG edges_NN2 with_II31 regard_II32 to_II33 the_AT order_NN1 that_CST each_DD1 individual_NN1 made_VVD their_APPGE nominations_NN2 ._. 
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The_AT overlaps_NN2 ?i_MC ,_, i+1_FO may_VM be_VBI read_VVN off_RP from_II this_DD1 representation_NN1 ._. 
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As_CSA shown_VVN by_II figure_NN1 6(c)_FO ,_, h12(r)_FO and_CC h21(r)_FO are_VBR rather_RR on_II phase_NN1 ,_, but_CCB they_PPHS2 are_VBR dephased_VVN almost_RR half_DB a_AT1 wavelength_NN1 with_II31 respect_II32 to_II33 <equation>_FO ._. 
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In_II the_AT next_MD result_NN1 ,_, we_PPIS2 recall_VV0 a_AT1 well-known_JJ explicit_JJ formula_NN1 for_IF the_AT first_MD moments_NN2 of_IO CIR_NN1 processes_NN2 and_CC squared_JJ Bessel_NN1 processes_NN2 (_( cf._VV0 Equation_NN1 (_( 57_MC )_) is_VBZ ergodic_JJ with_IW its_APPGE invariant_JJ measure_NN1 being_NN1 (_( 0_MC ,_, 1_MC1 )_) N_ZZ1 (_( 0_MC ,_, 1_MC1 )_) ._. 
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The_AT optimum_JJ strategy_NN1 depends_VVZ on_II the_AT aim_NN1 ;_; reducing_VVG the_AT epidemic_NN1 peak_NN1 or_CC accelerating_VVG the_AT stamping_VVG out_RP the_AT outbreak_NN1 ._. 
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ScaLE_NN1 was_VBDZ initialized_VVN by_II using_VVG the_AT normal_JJ approximation_NN1 that_CST is_VBZ available_JJ from_II the_AT glm_NNU fit_JJ ._. 
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Figure_NN1 4_MC compares_VVZ the_AT market_NN1 implied_VVD volatility_NN1 (_( the_AT same_DA as_CSA in_II Fig._NN1 2_MC )_) with_IW the_AT implied_JJ volatility_NN1 computed_VVN from_II the_AT nonparametric_JJ model_NN1 ._. 
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If_CS the_AT set_NN1 of_IO invalid_JJ instruments_NN2 were_VBDR known_VVN ,_, the_AT oracle_NN1 two-stage_NN1 least_DAT squares_NN2 (_( 2SLS_FO )_) estimator_NN1 would_VM be_VBI the_AT estimator_NN1 of_IO choice_NN1 in_II their_APPGE setting_NN1 ._. 
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The_AT algorithm_NN1 details_NN2 of_IO MutSpace_NP1 are_VBR discussed_VVN in_II Section_NN1 3.2_MC ._. 
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Specifically_RR we_PPIS2 assume_VV0 E(S)=1,3_FO and_CC 5_MC ._. 
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The_AT specimen_NN1 was_VBDZ subjected_VVN to_TO direct_VVI tension_NN1 under_II displacement-control_JJ mode_NN1 at_II a_AT1 rate_NN1 of_IO 0.2_MC mm/min_NNU ._. 
</s>
<s>
Finally_RR ,_, the_AT Spatial_JJ SAEM_NN1 approach_NN1 using_VVG both_DB2 clustering_VVG attributes_NN2 identifies_VVZ both_RR vortices_VVZ of_IO fibres_NN2 and_CC layers_NN2 of_IO fibres_NN2 with_IW principally_RR different_JJ main_JJ direction_NN1 ,_, cf._VV0 When_RRQ we_PPIS2 analyze_VV0 the_AT phase-space_JJ behavior_NN1 of_IO the_AT chaotic_JJ trajectories_NN2 by_II selecting_VVG the_AT initial_JJ conditions_NN2 inside_II the_AT chaotic_JJ seas_NN2 and_CC letting_VVG them_PPHO2 evolve_VVI ,_, we_PPIS2 observe_VV0 that_CST chaotic_JJ trajectories_NN2 do_VD0 not_XX spread_VVI into_II the_AT allowed_JJ energy_NN1 region_NN1 randomly_RR as_CSA expected_VVN from_II the_AT regular_JJ chaotic_JJ trajectory_NN1 like_CS we_PPIS2 see_VV0 in_II the_AT (_( K_ZZ1 =_FO 0.2_MC ,_, z_ZZ1 =_FO 40_MC )_) and_CC (_( K_ZZ1 =_FO 0.6_MC ,_, z_ZZ1 =_FO 15_MC )_) systems_NN2 ._. 
</s>
<s>
We_PPIS2 evaluate_VV0 the_AT four_MC classifiers_NN2 on_II a_AT1 grid_NN1 of_IO hyperparameters_NN2 ,_, and_CC list_VV0 the_AT best_JJT values_NN2 of_IO the_AT ones_NN2 specific_JJ to_II our_APPGE proposed_JJ approach_NN1 (_( see_VV0 Section_NN1 3.2.2_MC )_) in_II the_AT table_NN1 ._. 
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<s>
All_DB the_AT collected_JJ statistics_NN are_VBR averaged_VVN over_RG 100_MC times_NNT2 ._. 
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<s>
Similar_JJ method_NN1 is_VBZ used_VVN by_II Von_NP1 Borstel_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2016_MC )_) ._. 
</s>
<s>
Moreover_RR ,_, FZ_NP1 (_( t_ZZ1 ,_, Yt_NP1 ,_, dz_NNU )_) can_VM be_VBI interpreted_VVN as_II the_AT conditional_JJ distribution_NN1 of_IO the_AT claim_NN1 sizes_NN2 given_VVN the_AT knowledge_NN1 of_IO the_AT stochastic_JJ factor_NN1 ._. 
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<s>
We_PPIS2 merge_VV0 the_AT short_JJ position_NN1 notifications_NN2 with_IW daily_JJ stock_NN1 data_NN from_II Thomson_NP1 Reuters_NP1 Datastream_NP1 ,_, equity_NN1 lending_VVG data_NN from_II Markit_NP1 ,_, and_CC institutional_JJ investor_NN1 data_NN from_II FactSet_NP1 Ownership_NN1 and_CC Refinitiv_NP1 Eikon_NP1 ._. 
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<s>
As_CSA explained_VVN in_II Remark_NN1 6.1_MC ,_, an_AT1 "_" open_JJ market_NN1 "_" models_NN2 the_AT real_JJ world_NN1 better_RRR ._. 
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<s>
As_II an_AT1 initial_JJ sanity_NN1 test_NN1 ,_, we_PPIS2 generated_VVD a_AT1 dataset_NN1 using_VVG a_AT1 motif_NN1 model_NN1 ,_, and_CC checked_VVD that_CST MODER2_FO is_VBZ able_JK to_TO learn_VVI the_AT model_NN1 back_RP from_II the_AT generated_JJ data_NN ._. 
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<s>
So_RR there_EX is_VBZ need_NN1 to_TO select_VVI the_AT best_JJT ridge_NN1 estimator_NN1 in_II term_NN1 of_IO minimum_JJ MSE_NN1 for_IF a_AT1 certain_JJ type_NN1 of_IO regression_NN1 model_NN1 ._. 
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<s>
We_PPIS2 now_RT describe_VV0 our_APPGE three_MC main_JJ schemes_NN2 and_CC their_APPGE specific_JJ intergenerational_JJ risk-sharing_NN1 and_CC cost-sharing_JJ rules_NN2 ._. 
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<s>
B_ZZ1 ,_, B1_FO and_CC B2_FO parameters_NN2 are_VBR close_JJ to_II one_PN1 in_II almost_RR all_DB pairs_NN2 proving_VVG that_CST there_EX is_VBZ strong_JJ and_CC persistent_JJ time-varying_JJ co-movement_NN1 between_II the_AT financial_JJ institutions_NN2 and_CC the_AT financial_JJ system_NN1 ._. 
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<s>
Surprisingly_RR ,_, four_MC out_II21 of_II22 five_MC tools_NN2 demonstrating_VVG the_AT lowest_JJT consistency_NN1 between_II boundaries_NN2 (_( deDoc_NN1 ,_, GMAP_NP1 ,_, IC-Finder_NP1 and_CC TADtree_NP1 )_) had_VHD the_AT average_JJ level_NN1 of_IO concordance_NN1 for_IF the_AT domain_NN1 positions_NN2 themselves_PPX2 (_( Fig._NN1 2A_FO and_CC B_ZZ1 )_) ._. 
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<s>
In_II the_AT setting_NN1 of_IO the_AT Merton_NP1 problem_NN1 ,_, the_AT same_DA statement_NN1 is_VBZ true_JJ (_( and_CC well_RR known_VVN )_) for_IF terminal_JJ utility_NN1 functions_NN2 of_IO power_NN1 form_NN1 ._. 
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<s>
If_CS more_DAR detail_NN1 about_II the_AT strength_NN1 of_IO the_AT immune_JJ system_NN1 becomes_VVZ available_JJ we_PPIS2 can_VM anticipate_VVI models_NN2 based_VVN around_II a_AT1 universal_JJ law_NN1 covering_VVG both_DB2 the_AT infant_NN1 and_CC adult_NN1 phases_NN2 will_VM be_VBI possible_JJ ._. 
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<s>
This_DD1 information_NN1 would_VM be_VBI of_IO interest_NN1 to_II policymakers_NN2 in_II assessing_VVG the_AT economy_NN1 '_NULL s_ZZ1 near-term_JJ outlook_NN1 ,_, over_II and_CC above_II the_AT general_JJ ability_NN1 of_IO business_NN1 confidence_NN1 to_TO forecast_VVI investment_NN1 ._. 
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<s>
We_PPIS2 conjecture_VV0 that_CST this_DD1 is_VBZ due_II21 to_II22 the_AT very_RG small_JJ joint_JJ probability_NN1 of_IO opt1_NN1 (_( (_( 1_MC1 )_) )_) ≡_NULL 1opt_NN1 (_( Z_ZZ1 (_( 1_MC1 )_) )_) ≡_NULL ALL_DB and_CC opt22opt_FO being_NN1 in_II these_DD2 white_JJ areas_NN2 ;_; these_DD2 probabilities_NN2 would_VM not_XX contribute_VVI enough_RR to_II the_AT objective_JJ function_NN1 or_CC constraints_NN2 to_TO lead_VVI to_II added_JJ value_NN1 in_II rejecting_VVG null_JJ hypotheses_NN2 in_II these_DD2 areas_NN2 ,_, up_II21 to_II22 the_AT precision_NN1 that_CST is_VBZ used_VVN in_II solving_VVG the_AT sparse_JJ linear_JJ program_NN1 ._. 
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<s>
Figure_NN1 3(b)_FO corresponds_VVZ to_II the_AT corrected_JJ expression_NN1 values_NN2 by_II BUS_NN1 ,_, and_CC the_AT heatmap_NN1 illustrates_VVZ that_CST the_AT corrected_JJ values_NN2 can_VM be_VBI viewed_VVN as_CSA being_VBG measured_VVN in_II the_AT same_DA batch_NN1 ._. 
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Effectively_RR ,_, the_AT disclosure_NN1 threshold_NN1 represents_VVZ a_AT1 short-sale_JJ constraint_NN1 for_IF these_DD2 investors_NN2 ._. 
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<s>
In_BCL21 order_BCL22 to_TO obtain_VVI a_AT1 solution_NN1 to_II (_( 6.1_MC )_) ,_, choose_VV0 an_AT1 attainable_JJ allocation_NN1 <equation>_FO of_IO <equation>_FO such_CS21 that_CS22 <equation>_FO ._. 
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<s>
To_TO evaluate_VVI whether_CSW additional_JJ hours_NNT2 can_VM help_VVI women_NN2 ,_, we_PPIS2 use_VV0 our_APPGE baseline_NN1 multinomial_JJ regression_NN1 framework_NN1 and_CC estimate_VV0 additional_JJ interactions_NN2 between_II women_NN2 and_CC actual_JJ working_NN1 hours_NNT2 ._. 
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<s>
In_II the_AT current_JJ paper_NN1 ,_, we_PPIS2 propose_VV0 a_AT1 forward-simulation_JJ method_NN1 for_IF approximating_VVG the_AT guide_NN1 function_NN1 that_CST does_VDZ not_XX require_VVI transition_NN1 densities_NN2 to_TO be_VBI evaluated_VVN ._. 
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The_AT method_NN1 of_IO moments_NN2 is_VBZ examined_VVN for_IF parameters_NN2 estimation_NN1 ._. 
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<s>
The_AT singularity_NN1 spectrum_NN1 of_IO a_AT1 monofractal_JJ process_NN1 is_VBZ represented_VVN by_II a_AT1 single_JJ point_NN1 in_II the_AT f_ZZ1 plane_NN1 ,_, whereas_CS multifractal_JJ process_NN1 is_VBZ described_VVN by_II a_AT1 single_JJ humped_JJ function_NN1 ._. 
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<s>
These_DD2 statements_NN2 cover_VV0 both_RR the_AT German_JJ economy_NN1 as_II a_AT1 whole_NN1 as_II31 well_II32 as_II33 on_II specific_JJ sectors_NN2 individually_RR ._. 
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<s>
Managers_NN2 with_IW greater_JJR prepromotion_NN1 sales_NN do_VD0 indeed_RR have_VHI more_DAR manager_NN1 sales_NN credits_VVZ in_II the_AT data_NN ._. 
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<s>
In_II this_DD1 range_NN1 ,_, a_AT1 small_JJ standard_JJ deviation_NN1 can_VM be_VBI found_VVN at_II k_ZZ1 =_FO 6_MC from_II the_AT error_NN1 bars_NN2 around_II the_AT average_JJ intra-cluster_JJ distances_NN2 in_II figure_NN1 (_( a_ZZ1 )_) ._. 
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<s>
In_II this_DD1 circumstance_NN1 if_CS we_PPIS2 start_VV0 to_TO observe_VVI a_AT1 node_NN1 with_IW ki>kc_FO at_II time_NNT1 t0=104_FO ,_, the_AT time_NNT1 that_CST its_APPGE degree_NN1 share_NN1 reduces_VVZ by_II just_RR 1%_NNU is_VBZ expected_VVN to_TO be_VBI (_( 10.99_MC )_) 1000t02.3×108_FO ._. 
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<s>
Our_APPGE mvLSWimpute_NN1 technique_NN1 is_VBZ able_JK to_TO strike_VVI a_AT1 balance_NN1 between_II accurate_JJ imputation_NN1 and_CC the_AT changing_JJ dynamics_NN of_IO the_AT data_NN ._. 
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To_TO study_VVI the_AT effects_NN2 of_IO mandatory_JJ disclosure_NN1 for_IF short_JJ positions_NN2 ,_, we_PPIS2 obtain_VV0 public_JJ and_CC confidential_JJ short_JJ position_NN1 disclosures_NN2 from_II the_AT German_JJ Federal_JJ Financial_JJ Supervisory_JJ Authority_NN1 (_( BaFin_NP1 )_) for_IF November_NPM1 1_MC1 ,_, 2012_MC through_II March_NPM1 31_MC ,_, 2015_MC ._. 
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<s>
R(t)_JJ :_: number_NN1 of_IO recovered_JJ users_NN2 at_II time_NNT1 t_ZZ1 and_CC R(t)_JJ ≥_FO 0_MC ._. 
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<s>
Conspicuously_RR ,_, this_DD1 literature_NN1 assumes_VVZ that_CST the_AT location_NN1 of_IO MNE_NN1 by_II the_AT same_DA investor_NN1 is_VBZ to_TO be_VBI undertaken_VVN once_RR depending_II21 on_II22 the_AT regional_JJ characteristics_NN2 that_RG best_RRT match_VV0 the_AT goal_NN1 of_IO the_AT firm_NN1 ._. 
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<s>
Solving_NN1 (_( 2.4_MC )_) amounts_VVZ to_II minimizing_VVG a_AT1 function_NN1 which_DDQ is_VBZ jointly_RR convex_JJ in_II its_APPGE parameters_NN2 over_II a_AT1 convex_JJ constraint_NN1 set_NN1 (_( proofs_NN2 are_VBR in_II the_AT supplementary_JJ materials_NN2 ,_, along_II21 with_II22 other_JJ elementary_JJ properties_NN2 of_IO the_AT likelihood_NN1 )_) ._. 
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<s>
The_AT expressions_NN2 are(3)<equation>_FO ,_, (_( 4_MC )_) <equation>Note_FO that_CST I_PPIS1 and_CC S_ZZ1 depend_VV0 strongly_RR on_II R0_FO ._. 
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<s>
In_II fact_NN1 ,_, the_AT Fourier_NP1 transform_VV0 of_IO the_AT charged_JJ moment_NN1 Zn_NP1 (_( )_) with_II31 respect_II32 to_II33 gives_VVZ and_CC thus_RR it_PPH1 is_VBZ thus_RR directly_RR related_VVN to_II Sn_NN1 (_( q_ZZ1 )_) through_RP ._. 
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<s>
Theorem_NN1 2_MC allows_VVZ us_PPIO2 to_TO compute_VVI their_APPGE expected_JJ values_NN2 E&lsqb;fA&rsqb;=_FO θ_NULL A_ZZ1 ,_, and_CC to_TO construct_VVI test_NN1 statistics_NN from_II the_AT deviance_NN1 fA_NN1 θ_NULL A_ZZ1 under_II an_AT1 appropriate_JJ null_JJ model_NN1 ._. 
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All_DB variables_NN2 are_VBR defined_VVN in_II Appendix_NN1 A._NP1 As_CSA detailed_VVN in_II Eq_NN1 ._. 
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<s>
(_( 3_MC )_) ,_, each_DD1 regression_NN1 includes_VVZ intermediate_JJ interaction_NN1 terms_NN2 (_( point_NN1 estimates_VVZ not_XX shown_VVN )_) ._. 
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<s>
The_AT dollar_NNU1 amounts_NN2 shown_VVN in_II the_AT legend_NN1 represent_VV0 the_AT mean_JJ income_NN1 (_( in_II 2015_MC dollars_NNU2 )_) corresponding_VVG to_II the_AT relevant_JJ percentile_NN1 for_IF children_NN2 in_II the_AT analysis_NN1 sample_NN1 in_II 2014–2015_MCMC ,_, when_CS they_PPHS2 are_VBR between_II the_AT ages_NN2 of_IO 31_MC and_CC 37_MC ._. 
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A_AT1 capital_NN1 demand_NN1 effect_NN1 generates_VVZ a_AT1 reallocation_NN1 of_IO capital_NN1 toward_II agriculture_NN1 ,_, the_AT comparative_JJ advantage_NN1 sector.11_FO A_ZZ1 capital_JJ supply_NN1 effect_NN1 ,_, instead_RR ,_, generates_VVZ a_AT1 reallocation_NN1 of_IO capital_NN1 toward_II manufacturing_NN1 ,_, the_AT capital-intensive_JJ sector_NN1 ._. 
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<s>
This_DD1 reduces_VVZ the_AT growth_NN1 rate_NN1 of_IO older_JJR nodes_NN2 ,_, while_CS giving_VVG low-degree_JJ nodes_NN2 a_AT1 higher_JJR chance_NN1 to_TO receive_VVI new_JJ links_NN2 ._. 
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Results_NN2 are_VBR shown_VVN in_II Table_NN1 5_MC ._. 
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<s>
As_II an_AT1 example_NN1 ,_, Figure_NN1 D.1_FO in_II the_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR shows_VVZ the_AT simulated_JJ data_NN from_II Model_NN1 DtSt+_FO ,_, together_RL with_IW pointwise_RR 95%_NNU prediction_NN1 intervals_NN2 obtained_VVN from_II the_AT model_NN1 evaluated_VVN at_II the_AT MLE_NN1 for_IF the_AT solution_NN1 of_IO the_AT ODE_NN1 ._. 
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His_APPGE model_NN1 is_VBZ a_AT1 game_NN1 between_II a_AT1 monopoly_NN1 union_NN1 and_CC a_AT1 CB_NN1 where_CS the_AT CB_NN1 is_VBZ the_AT Stackelberg_NP1 leader_NN1 ._. 
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<s>
High-minus-low_JJ market_NN1 beta_NN1 trading_NN1 strategy_NN1 earns_VVZ negative_JJ returns_NN2 during_II open-to-close_JJ periods_NN2 (_( days_NNT2 )_) and_CC earns_VVZ positive_JJ returns_NN2 during_II close-to-open_JJ periods_NN2 (_( nights_NNT2 )_) across_RL all_RR21 but_RR22 one_MC1 size_NN1 and_CC book-to-market_JJ portfolios_NN2 ._. 
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<s>
However_RR ,_, using_VVG this_DD1 GDP_NN1 weighted_JJ index_NN1 ,_, we_PPIS2 find_VV0 that_CST the_AT degree_NN1 of_IO internal_JJ synchronization_NN1 in_II the_AT UK_NP1 ,_, DE_NP1 and_CC NL_NP1 is_VBZ much_RR lower_JJR than_CSN that_DD1 calculated_VVD with_IW the_AT original_JJ index_NN1 ._. 
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<s>
To_TO verify_VVI the_AT SEAIR_NN1 model_NN1 ,_, data_NN were_VBDR collected_VVN from_II a_AT1 Baidu_NN1 App_VV0 promotional_JJ advertisement_NN1 in_II Weibo_NP1 &lsqb;_( 39_MC &rsqb;_) ._. 
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<s>
We_PPIS2 model_VV0 CS_NP2 dataset_NN1 of_IO each_DD1 blood_NN1 cell_NN1 type_NN1 as_II a_AT1 CS_NP2 network_NN1 ,_, in_II which_DDQ nodes_NN2 represent_VV0 DNA_NN1 elements_NN2 (_( genes_NN2 and_CC non-coding_JJ RNAs_NN2 )_) and_CC in_II which_DDQ edges_NN2 connect_VV0 nodes_NN2 whose_DDQGE DNA_NN1 elements_NN2 are_VBR in_II contact_NN1 in_II the_AT CS_NP2 ._. 
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<s>
They_PPHS2 are_VBR based_VVN on_II a_AT1 large_JJ number_NN1 of_IO species_NN (_( 55_MC )_) which_DDQ is_VBZ enough_DD to_TO capture_VVI most_DAT of_IO the_AT challenges_NN2 for_IF metagenome_NN1 assembly_NN1 (_( repeated_JJ regions_NN2 ,_, chimeric_JJ nodes_NN2 )_) ._. 
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<s>
This_DD1 would_VM be_VBI consistent_JJ with_IW H0_FO (_( no_AT insurance_NN1 offered_VVN through_II the_AT church_NN1 )_) if_CS it_PPH1 were_VBDR not_XX for_IF our_APPGE results_NN2 on_II enrollment_NN1 ._. 
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<s>
This_DD1 means_VVZ that_CST if_CS we_PPIS2 wait_VV0 the_AT natural_JJ epidemic_NN1 equilibrium_NN1 ,_, the_AT number_NN1 of_IO causalities_NN2 will_VM become_VVI unacceptably_RR large_JJ ._. 
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<s>
Because_CS the_AT reverse_JJ inequality_NN1 holds_VVZ by_II definition_NN1 ,_, the_AT two_MC value_NN1 functions_NN2 <equation>_FO and_CC <equation>_FO coincide_VV0 ._. 
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<s>
This_DD1 is_VBZ very_RG typical_JJ in_II insurance_NN1 business_NN1 ,_, because_CS considering_VVG longer_JJR panels_NN2 may_VM invoke_VVI incomparability_NN1 between_II the_AT early_JJ claim_NN1 amounts_NN2 and_CC the_AT late_JJ ones_NN2 due_II21 to_II22 changing_JJ market_NN1 or_CC policies_NN2 '_NULL conditions_NN2 over_II time_NNT1 ._. 
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It_PPH1 is_VBZ straightforward_JJ obvious_JJ that_CST all_DB the_AT columns_NN2 in_II M_ZZ1 sum_VV0 up_RP to_TO zero_VVI ,_, therefore_RR <equation>_FO ,_, when_CS t_ZZ1 →_NULL ∞_FO ,_, where_CS u_ZZ1 is_VBZ the_AT eigenvector_NN1 of_IO M_ZZ1 corresponding_VVG to_II 1(M)_FO ,_, and_CC <equation>_FO ._. 
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By_II holding_VVG fewer_DAR stocks_NN2 (_( i.e._REX ,_, lower_JJR coverage_NN1 )_) ,_, a_AT1 fund_NN1 can_VM focus_VVI on_II its_APPGE best_JJT trading_NN1 ideas_NN2 ,_, leading_VVG to_II higher_JJR expected_JJ gross_JJ profits_NN2 ._. 
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<s>
Our_APPGE design_NN1 procedure_NN1 provides_VVZ a_AT1 framework_NN1 for_IF more_RGR conservatively_RR powering_VVG a_AT1 trial_NN1 by_II ensuring_VVG high_JJ weighted-average_NN1 (_( or_CC Bayesian_JJ )_) power_NN1 where_CS the_AT weights_NN2 are_VBR assigned_VVN through_II elicitation_NN1 of_IO an_AT1 alternative_JJ sampling_NN1 prior_JJ distribution_NN1 defined_VVD using_VVG the_AT historical_JJ trial_NN1 posterior_NN1 distribution_NN1 after_II conditioning_NN1 on_II the_AT alternative_JJ hypothesis_NN1 ._. 
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This_DD1 table_NN1 reports_VVZ the_AT average_JJ daily_JJ return_NN1 for_IF predictive_JJ double-sorted_JJ portfolios_NN2 ._. 
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A_AT1 simple_JJ way_NN1 to_TO construct_VVI It_PPH1 is_VBZ to_TO draw_VVI indices_NN2 i1_FO ,_, i2_FO ,_, ,_, iM_VV0 uniformly_RR from_II &lsqb;_( N_ZZ1 &rsqb;_) without_IW replacement_NN1 ,_, and_CC then_RT let_VV0 It=i1:M_FO ._. 
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We_PPIS2 refer_VV0 to_II this_DD1 scheme_NN1 as_CSA batch_NN1 nudging_VVG ,_, referring_VVG to_II selection_NN1 of_IO the_AT indices_NN2 at_RR21 once_RR22 ._. 
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In_RR21 addition_RR22 ,_, the_AT results_NN2 reveal_VV0 that_CST the_AT effect_NN1 of_IO African_JJ reciprocal_JJ RTAs_NN2 on_II export_NN1 is_VBZ significantly_RR lower_JJR than_CSN that_DD1 of_IO non-African_JJ counterparts_NN2 ,_, while_CS non-reciprocal_JJ trade_NN1 agreements_NN2 appear_VV0 to_TO perform_VVI better_RRR in_II Africa_NP1 than_CSN elsewhere_RL (_( Table_NN1 1_MC1 )_) ._. 
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<s>
The_AT authors_NN2 acknowledge_VV0 comments_NN2 from_II two_MC anonymous_JJ referees_NN2 and_CC advices_NN2 from_II the_AT coordinating_JJ editor_NN1 ,_, but_CCB the_AT usual_JJ caveats_NN2 apply_VV0 ._. 
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<s>
It_PPH1 just_RR yields_VVZ real_JJ numbers_NN2 upon_II appropriate_JJ measurements_NN2 ._. 
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This_DD1 study_NN1 extends_VVZ Duncan_NP1 and_CC Myers_NP1 '_NULL model_NN1 by_II incorporating_VVG new_JJ factors_NN2 into_II the_AT supply_NN1 and_CC demand_VV0 for_IF catastrophe_NN1 insurance_NN1 ,_, such_II21 as_II22 advanced_JJ disaster-resistant_JJ technologies_NN2 ,_, catastrophe_NN1 derivatives_NN2 ,_, or_CC public_JJ reinsurance_NN1 ._. 
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This_DD1 rich_JJ set_NN1 of_IO inter-residue_JJ geometries_NN2 allows_VVZ trRosetta_NN1 to_TO outperform_VVI leading_JJ approaches_NN2 on_II the_AT CASP13_FO dataset_NN1 ,_, even_RR with_IW a_AT1 shallower_JJR network_NN1 (_( Yang_NP1 et_RA21 al._RA22 ,_, 2020_MC )_) ._. 
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<s>
Our_APPGE method_NN1 can_VM incorporate_VVI such_DA constraints_NN2 ,_, and_CC the_AT objective_JJ function_NN1 can_VM be_VBI modified_VVN to_TO represent_VVI minimax_NN1 problems_NN2 ._. 
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<s>
To_TO compute_VVI the_AT 2_MC statistics_NN ,_, we_PPIS2 use_VV0 dataset_NN1 D2_FO ,_, in_II which_DDQ data_NN are_VBR represented_VVN as_CSA 2×3_FO and_CC 2×2_FO contingency_NN1 tables_NN2 for_IF each_DD1 SNP_NP1 ._. 
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<s>
Relating_VVG this_DD1 more_RGR specifically_RR to_II under-reporting_NN1 ,_, an_AT1 indicator_NN1 random_JJ variable_NN1 Ii_MC ,_, t_ZZ1 ,_, s_ZZ1 is_VBZ introduced_VVN ,_, to_TO index_VVI the_AT data_NN into_II fully_RR observed_VVN or_CC under-reported_JJ ._. 
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The_AT above_JJ quantities_NN2 for_IF C0=1_FO ,_, C1=1.1_FO can_VM be_VBI found_VVN in_II Table_NN1 1_MC1 ._. 
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One_MC1 reason_NN1 for_IF the_AT differences_NN2 between_II stated_JJ choice_NN1 and_CC intended_JJ choice_NN1 could_VM be_VBI that_CST respondents_NN2 tend_VV0 to_TO distort_VVI their_APPGE true_JJ evaluation_NN1 of_IO the_AT environment_NN1 ._. 
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<s>
The_AT scores_NN2 do_VD0 not_XX seem_VVI to_TO depart_VVI a_AT1 large_JJ amount_NN1 from_II normality_NN1 (_( see_VV0 Fig._NN1 6_MC in_II "_" Appendix_NN1 B.1_FO "_" )_) (_( Online_RR Resource_VV0 1_MC1 )_) ,_, and_CC thus_RR ,_, standard_JJ BSL_NN1 may_VM be_VBI suitable_JJ for_IF this_DD1 model_NN1 ._. 
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<s>
For_IF <equation>_FO ,_, we_PPIS2 denote_VV0 by_II <equation>_FO and_CC <equation>_FO ,_, respectively_RR ,_, the_AT trace_NN1 and_CC the_AT transpose_VV0 of_IO <equation>_FO and_CC set_VV0 <equation>_FO ._. 
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<s>
Vargas_NP2 is_VBZ the_AT most_RGT efficient_JJ and_CC flexible_JJ tool_NN1 for_IF establishing_VVG computational_JJ gold_NN1 standards_NN2 for_IF evaluating_VVG read_VV0 alignment_NN1 heuristics_NN2 and_CC scoring_VVG schemes_NN2 ._. 
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<s>
In_II the_AT foreground_NN1 (_( blue_JJ branches_NN2 )_) is_VBZ our_APPGE point_NN1 estimate_NN1 from_II maximum_JJ composite_JJ likelihood_NN1 ;_; in_II the_AT background_NN1 (_( gray_JJ branches_NN2 ,_, with_IW translucent_JJ pulse_NN1 arrows_NN2 )_) are_VBR 300_MC nonparametric_JJ bootstraps_NN2 ._. 
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In_II a_AT1 regulatory_JJ network_NN1 ,_, an_AT1 edge_NN1 would_VM be_VBI directed_VVN from_II the_AT '_NULL Toll-like_JJ receptor_NN1 signaling_VVG pathway_NN1 '_NULL toward_II the_AT MAPK_NN1 one_MC1 ,_, as_CSA TLR_NP1 signaling_NN1 leads_VVZ to_II the_AT activation_NN1 of_IO MAPKs_NP2 in_II mammals_NN2 through_II the_AT sequential_JJ recruitment_NN1 of_IO the_AT adapter_NN1 molecule_NN1 MyD88_FO and_CC the_AT serine-threonine_JJ kinase_NN1 IRAK_NP1 (_( Hemmi_NP1 et_RA21 al._RA22 ,_, 2002_MC )_) ._. 
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Let_VV0 us_PPIO2 define_VVI <equation>_FO as_II the_AT joint_JJ sf_NNU ,_, the_AT marginal_JJ sfs_NNU and_CC the_AT corresponding_JJ marginal_JJ pmfs_NNU ._. 
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The_AT filter_NN1 in_II the_AT first_MD layer_NN1 builds_VVZ a_AT1 particle_NN1 approximation_NN1 of_IO the_AT marginal_JJ posterior_JJ distribution_NN1 of_IO the_AT parameters_NN2 ._. 
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We_PPIS2 first_MD illustrate_VV0 this_DD1 dilemma_NN1 by_II using_VVG five_MC different_JJ survival_NN1 data_NN sets_VVZ with_IW fixed_JJ prediction_NN1 horizon_NN1 ,_, and_CC then_RT by_II varying_VVG the_AT prediction_NN1 horizon_NN1 in_II a_AT1 single_JJ data_NN set_VV0 ._. 
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The_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR provides_VVZ further_JJR results_NN2 on_II empirical_JJ performance_NN1 of_IO the_AT model_NN1 ,_, using_VVG simulated_JJ data_NN examples_NN2 ._. 
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To_TO determine_VVI whether_CSW a_AT1 record_NN1 pair_NN is_VBZ a_AT1 match_NN1 or_CC not_XX ,_, record_NN1 linkage_NN1 is_VBZ necessary_JJ (_( Fellegi_NP1 and_CC Sunter_VV0 1969_MC )_) ._. 
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As_CSA u_ZZ1 →_NULL ∞_FO ,_, V(u)_NP1 decays_VVZ to_II 0_MC but_CCB with_IW different_JJ speeds_NN2 ._. 
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Indeed_RR ,_, when_CS this_DD1 is_VBZ the_AT case_NN1 ,_, individuals_NN2 prefer_VV0 to_TO invest_VVI in_II decreasing_VVG the_AT subjective_JJ probability_NN1 of_IO loss_NN1 by_II increasing_VVG their_APPGE religious_JJ giving_VVG rather_II21 than_II22 smoothing_VVG consumption_NN1 (_( in_II other_JJ words_NN2 ,_, the_AT substitution_NN1 effect_NN1 of_IO the_AT loss_NN1 dominates_VVZ the_AT income_NN1 effect_NN1 )_) ._. 
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In_II the_AT proof_NN1 of_IO the_AT next_MD result_NN1 ,_, and_CC in_II the_AT rest_NN1 of_IO the_AT paper_NN1 ,_, we_PPIS2 use_VV0 the_AT notation_NN1 '_NULL '_NULL to_TO denote_VVI that_CST an_AT1 inequality_NN1 holds_VVZ up_II21 to_II22 a_AT1 fixed_JJ numerical_JJ constant_JJ ._. 
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In_II what_DDQ follows_VVZ we_PPIS2 specify_VV0 the_AT solution_NN1 order_NN1 by_II order_NN1 ._. 
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The_AT problem_NN1 of_IO estimating_VVG Errextra_NP1 from_II D_ZZ1 has_VHZ been_VBN studied_VVN for_IF (_( at_RR21 least_RR22 )_) the_AT past_JJ 50_MC years_NNT2 ._. 
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We_PPIS2 conduct_VV0 a_AT1 placebo_NN1 test_NN1 by_II moving_VVG the_AT original_JJ monitoring_NN1 stations_NN2 upstream_RL or_CC downstream_RL by_II 5_MC km_NNU and_CC reestimating_VVG the_AT RD_NN1 model_NN1 for_IF these_DD2 "_" placebo_NN1 "_" monitoring_NN1 stations_NN2 ._. 
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Those_DD2 who_PNQS reach_VV0 the_AT top_NN1 0.5%_FO are_VBR located_VVN at_II the_AT 99th_MD percentile_NN1 cutoff_NN1 at_II age_NN1 90_MC ,_, and_CC those_DD2 who_PNQS reach_VV0 the_AT top_NN1 0.1%_FO are_VBR located_VVN at_II the_AT 99.8th_MD percentile_NN1 cutoff_NN1 at_II age_NN1 90_MC ._. 
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TreeSAPP_VV0 '_NULL s_ZZ1 classification_NN1 workflow_NN1 requires_VVZ a_AT1 multiple_JJ sequence_NN1 alignment_NN1 (_( MSA_NP1 )_) ,_, profile_NN1 hidden_VVN Markov_NP1 model_NN1 (_( HMM_UH )_) ,_, taxonomic_JJ lineages_NN2 and_CC phylogenetic_JJ tree_NN1 for_IF all_DB reference_NN1 sequences_NN2 (_( Supplementary_JJ Fig_NN1 ._. 
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S1_FO )_) ._. 
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Figure_NN1 12(b)_FO shows_VVZ plots_NN2 of_IO Fr(t)_NP1 for_IF different_JJ values_NN2 of_IO r_ZZ1 ._. 
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Note_VV0 that_CST the_AT lasso_NN1 penalty_NN1 is_VBZ enforced_VVN on_II every_AT1 single_JJ parameter_NN1 ,_, thus_RR not_XX only_RR the_AT estimated_JJ DAG_NN1 is_VBZ sparse_JJ but_CCB also_RR the_AT covariates_NN2 corresponding_VVG to_II each_DD1 directed_JJ edge_NN1 are_VBR selected_VVN automatically_RR by_II the_AT lasso_NN1 ,_, which_DDQ then_RT improves_VVZ the_AT interpretability_NN1 of_IO the_AT model_NN1 ._. 
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In_II fact_NN1 ,_, in_II the_AT simplest_JJT case_NN1 ,_, observing_VVG wage_NN1 information_NN1 for_IF only_RR two_MC distinct_JJ groups_NN2 of_IO individuals_NN2 is_VBZ sufficient_JJ for_IF approximating_VVG the_AT underlying_JJ inequality_NN1 of_IO individual_JJ wages_NN2 ._. 
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Scirpy_NN1 is_VBZ highly_RR scalable_JJ to_II big_JJ scRNA-seq_FW data_NN and_CC ,_, thus_RR ,_, allows_VVZ the_AT joint_JJ characterization_NN1 of_IO phenotypes_NN2 and_CC immune_JJ cell_NN1 receptors_NN2 in_II hundreds_NNO2 of_IO thousands_NNO2 of_IO T_ZZ1 cells_NN2 ._. 
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Contrasting_VVG AIC_NP1 values_VVZ asymptotically_RR coincides_VVZ with_IW generalised_JJ leave-one-out_NN1 cross-validation_NN1 ._. 
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TA_UH is_VBZ the_AT temperature_NN1 averaged_VVN over_II longitude_NN1 for_IF each_DD1 latitude_NN1 and_CC vertical_JJ pressure_NN1 level_NN1 so_CS21 that_CS22 ?=2368_FO ._. 
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Our_APPGE efficient_JJ estimator_NN1 is_VBZ asymptotically_RR linear_JJ under_II a_AT1 condition_NN1 requiring_VVG n1/4consistency_NN1 of_IO certain_JJ regression_NN1 functions_NN2 ._. 
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This_DD1 result_NN1 substantiates_VVZ SL_NP1 as_II an_AT1 approach_NN1 that_CST can_VM accurately_RR predict_VVI gene_NN1 attributes_VVZ by_II taking_VVG advantage_NN1 of_IO local_JJ network_NN1 connectivity_NN1 ._. 
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One_PN1 may_VM consider_VVI thresholding_VVG a_AT1 quantity_NN1 image_NN1 as_II a_AT1 surrogate_NN1 for_IF a_AT1 statistical_JJ hypothesis_NN1 test_NN1 ._. 
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This_DD1 is_VBZ because_CS the_AT solvent_NN1 molecule_NN1 is_VBZ overall_RR neutral_JJ and_CC if_CS using_VVG the_AT zero-order_JJ approximation_NN1 ,_, the_AT solvent_NN1 molecule_NN1 can_VM be_VBI considered_VVN as_CSA neutral_JJ and_CC apolar_JJ molecule_NN1 ._. 
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But_CCB none_PN of_IO these_DD2 papers_NN2 makes_VVZ the_AT connection_NN1 to_II a_AT1 generalization_NN1 of_IO the_AT error_NN1 rate_NN1 ._. 
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Specifically_RR ,_, the_AT behaviors_NN2 of_IO predicted_JJ nodes_NN2 are_VBR different_JJ under_II different_JJ network_NN1 structure_NN1 ._. 
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Of_IO the_AT two_MC sub-tables_NN2 ,_, the_AT first_MD one_PN1 simply_RR shows_VVZ the_AT correspondence_NN1 between_II method_NN1 names_NN2 and_CC numbers_NN2 ._. 
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Additionally_RR ,_, in_II every_AT1 model_NN1 we_PPIS2 include_VV0 a_AT1 constant_JJ ,_, time_NNT1 and_CC country_NN1 fixed_JJ effects_NN2 ._. 
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The_AT other_JJ two_MC proxies_NN2 for_IF limits_NN2 to_II arbitrage_NN1 behave_VV0 similarly_RR ._. 
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Such_DA '_NULL structural_JJ '_NULL RNAs_NN2 often_RR do_VD0 not_XX show_VVI clear_JJ sequence_NN1 conservation_NN1 ,_, but_CCB have_VH0 the_AT potential_JJ to_TO fold_VVI into_II conserved_JJ homologous_JJ structures_NN2 ._. 
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The_AT optimal_JJ tuning_NN1 parameter_NN1 <equation>_FO is_VBZ determined_VVN by_II the_AT BIC_NP1 criterion_NN1 as_CSA in_II (_( 4.2_MC )_) ._. 
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Event_NN1 periods_NN2 before_II 6_MC are_VBR dropped_VVN ,_, and_CC event_NN1 periods_NN2 ≥_FO 6_MC are_VBR binned_VVN ._. 
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The_AT first-order_JJ derivative_NN1 of_IO S_ZZ1 with_II31 respect_II32 to_II33 g_ZZ1 is_VBZ shown_VVN in_II Fig._NN1 3(b)_FO ._. 
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However_RR ,_, the_AT use_NN1 of_IO flexibility_NN1 in_II solubility_NN1 prediction_NN1 has_VHZ been_VBN overlooked_VVN although_CS their_APPGE relationship_NN1 has_VHZ previously_RR been_VBN noted_VVN (_( Tsumoto_NP1 et_RA21 al._RA22 ,_, 2003_MC )_) ._. 
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We_PPIS2 can_VM find_VVI that_CST a_AT1 reasonable_JJ ds_MC2 (_( such_II21 as_II22 ds_MC2 =_FO 2_MC )_) can_VM not_XX only_RR promote_VVI cooperation_NN1 effectively_RR but_CCB also_RR control_VV0 execution_NN1 costs_NN2 ._. 
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In_RR21 particular_RR22 ,_, both_DB2 the_AT hopping_JJ amplitude_NN1 Jn_NP1 and_CC the_AT magnetic_JJ field_NN1 Bn_NNU are_VBR symmetric_JJ for_IF 1_MC1 =_FO 2_MC ._. 
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Nevertheless_RR ,_, the_AT proposed_JJ CA_VM model_VVI updates_NN2 the_AT rules_NN2 considering_II the_AT car–truck_NN1 combination_NN1 effect_NN1 ,_, which_DDQ makes_VVZ the_AT simulation_NN1 results_NN2 more_RGR accurate_JJ ._. 
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Recent_JJ developments_NN2 include_VV0 the_AT normalized_JJ power_NN1 prior_RR (_( NPP_NP1 )_) (_( Duan_NP1 and_CC others_NN2 ,_, 2006_MC )_) ,_, commensurate_JJ priors_NN2 (_( Hobbs_NP1 and_CC others_NN2 ,_, 2011_MC )_) ,_, robust_JJ meta-analytic-predictive_JJ priors_NN2 (_( MAP_NN1 )_) (_( Schmidli_NP1 and_CC others_NN2 ,_, 2014_MC )_) ,_, and_CC supervised_VVD methods_NN2 (_( Pan_NP1 and_CC others_NN2 ,_, 2016_MC )_) that_CST manually_RR adjust_VV0 the_AT informativeness_NN1 of_IO the_AT prior_RR based_VVN on_II measures_NN2 of_IO conflict_NN1 between_II the_AT prior_JJ information_NN1 and_CC the_AT new_JJ trial_NN1 data_NN ,_, assessed_VVN at_II the_AT time_NNT1 of_IO the_AT analysis_NN1 ._. 
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The_AT IAT_NN1 captures_VVZ implicit_JJ associations_NN2 between_II math-male_NN1 and_CC literature-female_NN1 (_( versus_II math-female_NN1 and_CC literature-male_NN1 )_) :_: I_PPIS1 can_VM not_XX distinguish_VVI between_II the_AT stereotype_NN1 that_CST women_NN2 are_VBR bad_JJ at_II math_NN1 and_CC men_NN2 are_VBR bad_JJ at_II reading_NN1 ._. 
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The_AT experimental_JJ results_NN2 show_VV0 that_CST our_APPGE method_NN1 achieves_VVZ better_JJR effectiveness_NN1 to_TO detect_VVI community_NN1 structure_NN1 ._. 
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Panel_NN1 A_ZZ1 is_VBZ a_AT1 correlation_NN1 test_NN1 ;_; the_AT regression_NN1 coefficients_NN2 of_IO the_AT indirect_JJ return-consumption_JJ conditional_JJ comovement_NN1 estimates_VVZ on_II the_AT direct_JJ estimates_NN2 are_VBR all_DB statistically_RR close_JJ to_II 1_MC1 at_II the_AT 5%_NNU significance_NN1 level_NN1 ._. 
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The_AT construction_NN1 of_IO this_DD1 set_NN1 of_IO non-Gaussian_JJ matrix-valued_JJ random_JJ fields_NN2 is_VBZ based_VVN on_II the_AT use_NN1 of_IO the_AT Maximum_JJ Entropy_NN1 principle_NN1 for_IF constructing_VVG a_AT1 set_NN1 of_IO positive-definite_JJ random_JJ matrices_NN2 ._. 
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We_PPIS2 also_RR discuss_VV0 some_DD statistical_JJ insights_NN2 that_CST can_VM be_VBI drawn_VVN from_II these_DD2 analysis_NN1 ._. 
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More_DAR shrinkage_NN1 towards_II the_AT Gaussian_JJ decreases_NN2 variance_NN1 but_CCB increases_VVZ bias_NN1 ._. 
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As_CSA shown_VVN in_II Theorem_NN1 2.6_MC ,_, under_II the_AT present_JJ assumptions_NN2 ,_, the_AT set_NN1 of_IO ELMDs_NP2 for_IF <equation>_FO on_II <equation>_FO is_VBZ nonempty_JJ and_CC consists_VVZ of_IO the_AT unique_JJ element_NN1 <equation>_FO ._. 
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Note_VV0 that_CST one_PN1 should_VM remove_VVI both_DB2 individuals_NN2 in_II each_DD1 pair_NN of_IO related_JJ individuals_NN2 ._. 
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The_AT important_JJ role_NN1 of_IO cytokines_NN2 as_CSA therapeutic_JJ targets_NN2 in_II IPF_NP1 has_VHZ also_RR been_VBN emphasized_VVN (_( Coker_NP1 and_CC Laurent_NP1 ,_, 1998_MC )_) ._. 
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It_PPH1 should_VM be_VBI noted_VVN that_CST the_AT relaxation_NN1 of_IO search_NN1 space_NN1 can_VM lead_VVI to_II increased_JJ runtime_NNT1 of_IO MILP_NN1 solvers_NN2 ._. 
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They_PPHS2 utilized_VVD the_AT Evolutionary_JJ Placement_NN1 Algorithm_NN1 (_( EPA_NP1 )_) to_TO identify_VVI mislabeled_JJ taxonomic_JJ annotation_NN1 ._. 
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However_RR ,_, the_AT phylogenetic_JJ trees_NN2 that_CST they_PPHS2 report_VV0 differ_VV0 significantly_RR between_II tumors_NN2 (_( even_RR those_DD2 with_IW similar_JJ characteristics_NN2 )_) ._. 
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As_CSA W(E)≤_FO for_IF any_DD phase-bounded_JJ CNT_NP1 E_ZZ1 ,_, in_BCL21 order_BCL22 to_TO minimize_VVI W(E)+_FO |_NULL E_ZZ1 |_NULL ,_, the_AT length_NN1 |_NULL E_ZZ1 |_NULL of_IO the_AT CNT_NP1 must_VM be_VBI minimized_VVN first_MD and_CC only_JJ then_RT the_AT weight_NN1 W(E)_PPIS2 of_IO the_AT CNT_NP1 should_VM be_VBI minimized_VVN ._. 
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From_II Fig._NN1 8(b)_FO ,_, the_AT Deff_NN1 as_II a_AT1 function_NN1 of_IO displays_NN2 a_AT1 maximum_JJ value_NN1 for_IF small_JJ of_IO absolute_JJ value_NN1 of_IO F_ZZ1 ,_, however_RR for_IF large_JJ of_IO absolute_JJ value_NN1 of_IO F_ZZ1 ,_, this_DD1 maximum_NN1 disappears_VVZ ,_, namely_REX ,_, the_AT Deff_NN1 increases_VVZ monotonically_RR as_CSA increases_VVZ for_IF F=0.3_FO ,_, but_II21 for_II22 F=0.3_FO it_PPH1 decreases_VVZ monotonically_RR ._. 
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Modeling_VVG copy_NN1 number_NN1 evolution_NN1 using_VVG CNPs_NP1 is_VBZ challenging_JJ because_CS ,_, unlike_JJ single-nucleotide_JJ mutations_NN2 ,_, CNAs_NN2 often_RR overlap_VV0 ,_, and_CC therefore_RR the_AT copy_NN1 numbers_NN2 of_IO different_JJ segments_NN2 are_VBR not_XX independent_JJ (_( Beerenwinkel_NP1 et_RA21 al._RA22 ,_, 2015_MC ;_; Schwartz_NP1 ,_, 2019_MC )_) ._. 
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Second_MD ,_, we_PPIS2 reexamined_VVD data_NN from_II two_MC Merkel_NP1 cell_NN1 carcinoma_NN1 (_( MCC_NP1 )_) patients_NN2 (_( Paulson_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) (_( Supplementary_JJ Material_NN1 S4_FO )_) ._. 
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If_CS public_JJ goods_NN2 are_VBR efficiently_RR provided_VVN ,_, then_RT their_APPGE prices_NN2 as_CSA implied_VVN by_II taxes_NN2 should_VM truly_RR reflect_VVI the_AT consumer_NN1 '_NULL s_ZZ1 marginal_JJ willingness_NN1 to_TO pay_VVI for_IF these_DD2 goods_NN2 ._. 
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The_AT regressions_NN2 control_VV0 for_IF sector_NN1 and_CC time_NNT1 fixed_JJ effects_NN2 ,_, and_CC cluster_VV0 standard_JJ errors_NN2 at_II the_AT sector_NN1 level_NN1 ._. 
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Another_DD1 approach_NN1 would_VM be_VBI to_TO focus_VVI on_II a_AT1 Lévy_NN1 process_NN1 with_IW two-sided_JJ phase-type_JJ distributed_JJ jumps_NN2 and_CC use_VV0 them_PPHO2 to_TO approximate_VVI a_AT1 general_JJ case_NN1 ._. 
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The_AT aim_NN1 of_IO this_DD1 section_NN1 is_VBZ to_TO identify_VVI three_MC possible_JJ limits_NN2 of_IO the_AT single-trade_JJ self-financing_JJ portfolio_NN1 equation_NN1 (_( 2.2_MC )_) ._. 
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Several_DA2 studies_NN2 report_VV0 that_DD1 fund_NN1 size_NN1 negatively_RR predicts_VVZ fund_NN1 performance_NN1 ,_, but_CCB the_AT evidence_NN1 is_VBZ somewhat_RR sensitive_JJ to_II the_AT methodology_NN1 applied_VVD ,_, as_CSA discussed_VVN earlier_RRR ._. 
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This_DD1 can_VM be_VBI straightforwardly_RR extended_VVN to_II the_AT Ridge_NN1 and_CC Elastic-net_NN1 (_( Zou_NP1 and_CC Hastie_NP1 ,_, 2005_MC )_) penalties_NN2 ._. 
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At_II the_AT top_JJ level_NN1 ,_, we_PPIS2 again_RT find_VV0 that_CST the_AT independence_NN1 assumption_NN1 needs_VVZ to_TO be_VBI taken_VVN into_II account_NN1 as_CSA evidenced_VVN by_II statistical_JJ testing_NN1 in_II panel_NN1 B_ZZ1 ,_, thus_RR we_PPIS2 can_VM conclude_VVI that_CST our_APPGE alternative_JJ model_NN1 is_VBZ robust_JJ ._. 
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Technological_JJ changes_NN2 have_VH0 also_RR brought_VVN about_RP pricing_VVG relationship_NN1 changes_NN2 in_II the_AT natural_JJ gas_NN1 sector_NN1 ._. 
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It_PPH1 follows_VVZ from_II the_AT polynomial_NN1 property_NN1 that_CST the_AT process_NN1 <equation>_FO has_VHZ a_AT1 linear_JJ drift_NN1 as_CSA in_II (_( 2.2_MC )_) and_CC (_( 2.3_MC )_) ;_; see_VV0 &lsqb;_( 24_MC ,_, Theorem_NN1 4.3_MC &rsqb;_) ._. 
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In_II this_DD1 paper_NN1 ,_, we_PPIS2 directly_RR prove_VV0 convergence_NN1 rates_NN2 without_IW first_MD fitting_VVG the_AT filter_NN1 to_II existing_JJ methods_NN2 ,_, and_CC thereby_RR lift_VV0 many_DA2 of_IO the_AT above_JJ restrictions_NN2 on_II the_AT convergence_NN1 rates_NN2 ._. 
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In_II essence_NN1 ,_, SDA_NP1 argues_VVZ that_CST many_DA2 important_JJ questions_NN2 can_VM be_VBI answered_VVN without_IW needing_VVG to_TO observe_VVI data_NN at_II the_AT micro-level_NN1 ,_, and_CC that_DD1 higher-level_NN1 ,_, group-based_JJ information_NN1 may_VM be_VBI sufficient_JJ ._. 
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At_II the_AT same_DA time_NNT1 ,_, BAPFL_NP1 is_VBZ used_VVN to_TO evaluate_VVI the_AT ability_NN1 of_IO the_AT power_NN1 grid_NN1 to_TO maintain_VVI its_APPGE original_JJ function_NN1 ._. 
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This_DD1 damping_NN1 includes_VVZ the_AT fact_NN1 that_CST the_AT degree_NN1 of_IO some_DD nodes_NN2 is_VBZ less_DAR than_CSN k/2_FU ._. 
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In_II all_DB the_AT examples_NN2 ,_, the_AT marginal_JJ cdfs_NNU are_VBR strictly_RR increasing_VVG ._. 
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Since_CS they_PPHS2 consider_VV0 all_DB claims_NN2 with_IW the_AT same_DA parameter_NN1 of_IO an_AT1 exponential_NN1 distribution_NN1 ,_, the_AT aggregated_JJ claim_NN1 (_( system_NN1 loss_NN1 )_) follows_VVZ an_AT1 Erlang_NNU distribution_NN1 ._. 
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We_PPIS2 did_VDD not_XX normalize_VVI the_AT covariates_NN2 to_TO zero_VVI mean_JJ and_CC unit_NN1 variance_NN1 as_CSA in_II Hoffman_NP1 and_CC Gelman_NP1 (_( 2014_MC )_) ,_, because_CS we_PPIS2 let_VV0 C_ZZ1 be_VBI adaptively_RR tuned_VVN ._. 
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A_AT1 location_NN1 and_CC verification_NN1 step_NN1 in_II the_AT text_NN1 is_VBZ often_RR several_DA2 times_NNT2 faster_RRR than_CSN finishing_VVG an_AT1 index-based_JJ approximate_JJ search_NN1 ._. 
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The_AT conditional_JJ methods_NN2 CSIS_NN1 and_CC CMELR-CSIS_NP1 are_VBR no_RR21 longer_RR22 effective_JJ while_CS CSIRS_NN2 and_CC CELSIRS_NN2 still_RR enjoy_VV0 good_JJ performances_NN2 ._. 
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Black_JJ boys_NN2 who_PNQS move_VV0 to_II such_DA areas_NN2 at_II younger_JJR ages_NN2 have_VH0 significantly_RR better_JJR outcomes_NN2 ,_, demonstrating_VVG that_DD1 racial_JJ disparities_NN2 can_VM be_VBI narrowed_VVN through_II changes_NN2 in_II environment_NN1 ._. 
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We_PPIS2 divide_VV0 our_APPGE empirical_JJ analysis_NN1 into_II four_MC parts_NN2 ._. 
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Continued_JJ development_NN1 of_IO time_NNT1 and_CC space-efficient_JJ algorithmic_JJ techniques_NN2 has_VHZ been_VBN pivotal_JJ for_IF dealing_VVG with_IW the_AT exponential_NN1 growth_NN1 of_IO DNA_NN1 sequencing_NN1 throughput_NN1 ._. 
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The_AT sample_NN1 includes_VVZ all_DB children_NN2 in_II our_APPGE analysis_NN1 sample_NN1 (_( 1980–82_MCMC birth_NN1 cohorts_NN2 )_) ,_, pooling_VVG non-college-goers_NN2 into_II a_AT1 single_JJ group_NN1 ._. 
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We_PPIS2 prove_VV0 that_CST the_AT optimal_JJ strategy_NN1 tends_VVZ to_TO be_VBI a_AT1 lump_NN1 sum_NN1 if_CS long-term_JJ investments_NN2 are_VBR allowed_VVN ._. 
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In_II the_AT above_JJ formulation_NN1 ,_, we_PPIS2 assume_VV0 that_DD1 yk_NN1 and_CC Xk_FO have_VH0 been_VBN standardized_VVN (_( at_II the_AT subgroup_NN1 level_NN1 )_) so_CS21 that_CS22 no_AT intercept_VV0 terms_NN2 are_VBR required_VVN ._. 
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Thus_RR ,_, any_DD predictor_NN1 plays_VVZ a_AT1 role_NN1 to_TO generate_VVI the_AT candidate_NN1 partitioning_NN1 variables_NN2 defined_VVN as_II all_DB possible_JJ partitions_NN2 of_IO the_AT predictor_NN1 '_NULL s_ZZ1 categories_NN2 into_II r_ZZ1 subgroups_VVZ such_DA to_TO induce_VVI the_AT partition_NN1 of_IO the_AT objects_NN2 ._. 
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We_PPIS2 call_VV0 the_AT expectation_NN1 of_IO the_AT <equation>_FO the_AT scaled_JJ false_JJ discovery_NN1 rate_NN1 ,_, <equation>_FO ._. 
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Table_NN1 1_MC1 summarizes_VVZ the_AT empirical_JJ results_NN2 for_IF some_DD widely_RR cited_VVN contributions_NN2 to_II the_AT crime_NN1 deterrence_NN1 literature_NN1 using_VVG aggregate_JJ data_NN ._. 
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This_DD1 estimation_NN1 process_NN1 is_VBZ called_VVN imputation_NN1 ._. 
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Finally_RR ,_, in_II section_NN1 ,_, we_PPIS2 discuss_VV0 the_AT implications_NN2 and_CC possible_JJ future_JJ extensions_NN2 of_IO our_APPGE work_NN1 ._. 
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Whilst_CS the_AT main_JJ focus_NN1 of_IO this_DD1 article_NN1 was_VBDZ on_II developing_VVG an_AT1 automated_JJ approach_NN1 to_II selecting_VVG sparse_JJ multiresponse_NN1 models_NN2 ,_, an_AT1 interesting_JJ avenue_NN1 for_IF future_JJ research_NN1 would_VM be_VBI to_TO investigate_VVI the_AT impact_NN1 of_IO modelling_VVG the_AT regression_NN1 residuals_NN2 simultaneously_RR ._. 
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<s>
The_AT different_JJ color_NN1 of_IO grid_NN1 points_NN2 indicates_VVZ whether_CSW the_AT data_NN point_NN1 was_VBDZ from_II a_AT1 biopsy_NN1 (_( black_JJ )_) ,_, or_CC interpolated_VVD (_( gray_JJ )_) ._. 
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<s>
In_RR21 general_RR22 ,_, we_PPIS2 see_VV0 that_CST there_EX is_VBZ no_AT such_DA complete_JJ convergence_NN1 to_II the_AT truth_NN1 for_IF high_JJ confidence_NN1 in_II either_RR Fig._NN1 4_MC or_CC 5_MC ._. 
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<s>
In_II fact_NN1 ,_, GDP_NN1 per_RR21 capita_RR22 is_VBZ significantly_RR and_CC positively_RR related_VVN to_II wages_NN2 in_II most_DAT estimations_NN2 ._. 
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<s>
The_AT user_NN1 should_VM be_VBI able_JK to_TO visually_RR study_VVI the_AT relationship_NN1 between_II prevalence_NN1 of_IO a_AT1 single_JJ tumor_NN1 clone_NN1 and_CC spatial_JJ location_NN1 ._. 
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<s>
Precisely_RR ,_, in_II the_AT type_NN1 II_MC censoring_JJ scheme_NN1 ,_, we_PPIS2 consider_VV0 N_ZZ1 independent_JJ lifetimes_NNT2 <equation>_FO based_VVN on_II the_AT common_JJ distribution_NN1 function_NN1 F_ZZ1 ,_, and_CC the_AT experiment_NN1 where_CS particular_JJ amount_NN1 of_IO surviving_JJ units_NN2 are_VBR removed_VVN at_II various_JJ experiment_NN1 stages_NN2 ._. 
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<s>
Miller_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2017_MC )_) find_VV0 a_AT1 causal_JJ effect_NN1 of_IO the_AT program_NN1 on_II the_AT extensive_JJ margin_NN1 labor_NN1 supply_NN1 of_IO 0.9%_FO ._. 
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<s>
The_AT convergence_NN1 of_IO the_AT sampler_NN1 to_II the_AT correct_JJ target_NN1 is_VBZ again_RT almost_RR immediate_JJ ._. 
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<s>
Thus_RR equation_NN1 (_( 3_MC )_) may_VM be_VBI written_VVN as_CSA ,_, Despite_II the_AT fact_NN1 that_CST they_PPHS2 use_VV0 firm-level_JJ data_NN ,_, their_APPGE evidence_NN1 is_VBZ based_VVN on_II AMADEUS_NN which_DDQ exhibits_VVZ a_AT1 bias_NN1 towards_II large_JJ firms_NN2 for_IF some_DD countries_NN2 ._. 
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<s>
We_PPIS2 find_VV0 also_RR that_CST the_AT accounting_NN1 price-cost_NN1 margin_NN1 seems_VVZ to_TO be_VBI a_AT1 reasonable_JJ proxy_NN1 for_IF estimated_JJ levels_NN2 but_CCB only_RR under_II the_AT assumption_NN1 of_IO competitive_JJ labour_NN1 markets_NN2 ._. 
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<s>
The_AT results_NN2 of_IO sections_NN2 and_CC are_VBR summarized_VVN in_II section_NN1 ._. 
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<s>
We_PPIS2 develop_VV0 two_MC novel_JJ methods_NN2 in_II which_DDQ the_AT trajectories_NN2 leading_VVG to_II proposals_NN2 in_II HMC_NP1 are_VBR automatically_RR tuned_VVN to_TO avoid_VVI doubling_VVG back_RP ,_, as_CSA in_II the_AT No-U-Turn_NP1 sampler_NN1 (_( NUTS_NN2 )_) ._. 
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<s>
While_CS this_DD1 work_NN1 focused_VVD only_RR on_II the_AT CDR_NP1 H3_FO loop_NN1 ,_, we_PPIS2 anticipate_VV0 that_CST applying_VVG DeepH3_FO to_II other_JJ aspects_NN2 of_IO antibody_NN1 structure_NN1 prediction_NN1 may_VM yield_VVI further_JJR advances_NN2 ._. 
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<s>
For_IF general_JJ NIDdistributions_NN2 ,_, the_AT law_NN1 of_IO (_( )_) (_( l_ZZ1 )_) has_VHZ been_VBN recently_RR obtained_VVN in_II closed_JJ form_NN1 by_II Lijoi_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2019_MC )_) when_RRQ 0=_FO (_( 0/_FO ,_, ,_, 0/_FO )_) 0=_FO (_( c0/H_FU ,_, ,_, c0/H_FU )_) ;_; the_AT extension_NN1 to_II general_JJ baseline_NN1 probabilities_NN2 00_MC is_VBZ a_AT1 straightforward_JJ modification_NN1 of_IO their_APPGE results_NN2 ._. 
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<s>
In_II each_DD1 case_NN1 ,_, the_AT positions_NN2 of_IO these_DD2 1-s_MC2 and_CC 0-s_MC2 in_II the_AT chains_NN2 are_VBR random_JJ ._. 
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<s>
Periods_NN2 of_IO extensive_JJ reservoir_NN1 and_CC electricity_NN1 production_NN1 management_NN1 are_VBR also_RR visible_JJ in_II two_MC additional_JJ periods_NN2 –_- from_II 1979_MC to_II 1981_MC ,_, and_CC from_II 1983_MC to_II 1986_MC ._. 
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<s>
In_BCL21 order_BCL22 to_TO prove_VVI our_APPGE limit_NN1 results_NN2 ,_, we_PPIS2 need_VV0 the_AT following_JJ hypotheses_NN2 ._. 
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<s>
Abundant_JJ studies_NN2 focus_VV0 on_II the_AT effect_NN1 of_IO psychological_JJ and_CC physiological_JJ behaviors_NN2 on_II pedestrian_NN1 flow_NN1 dynamics_NN ,_, such_II21 as_II22 pushing_VVG ,_, view_NN1 ,_, distraction_NN1 and_RR31 so_RR32 on_RR33 ._. 
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<s>
In_RR21 addition_RR22 ,_, a_AT1 live_JJ Jupyter-python_JJ notebook_NN1 for_IF conducting_VVG the_AT experiment_NN1 is_VBZ available_JJ as_CSA mybinder_NN1 link_NN1 ._. 
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<s>
As_II an_AT1 alternative_NN1 ,_, this_DD1 paper_NN1 provides_VVZ an_AT1 innovative_JJ partitioning_NN1 criterion_NN1 with_IW a_AT1 tree-growing_JJ algorithm_NN1 ._. 
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<s>
We_PPIS2 then_RT selected_VVD the_AT 10_MC most_RGT significant_JJ SNPs_NP2 (_( by_II using_VVG a_AT1 2_MC test_NN1 ;_; including_II five_MC positively_RR and_CC five_MC negatively_RR correlated_VVN with_IW Group_NN1 I_ZZ1 versus_II Group_NN1 II_MC )_) between_II these_DD2 two_MC groups_NN2 (_( Group_NN1 I_ZZ1 and_CC II_MC ,_, simulating_VVG the_AT case_NN1 and_CC control_NN1 groups_NN2 in_II GWAS_NN2 )_) ,_, and_CC another_DD1 randomly_RR selected_VVN 40_MC ,_, 90_MC and_CC 140_MC SNPs_NP2 to_TO form_VVI the_AT three_MC testing_JJ datasets_NN2 containing_VVG 50_MC ,_, 100_MC and_CC 150_MC SNPs_NP2 (_( used_VVN as_II the_AT fixed_JJ effect_NN1 variables_NN2 in_II GLMM_NP1 )_) ,_, with_IW the_AT total_JJ data_NN size_NN1 of_IO 28.6_MC ,_, 60.5_MC and_CC 84.0_MC KB_NNU ,_, respectively_RR ._. 
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<s>
The_AT incremental_JJ <equation>_FO from_II using_VVG third_MD month_NNT1 of_IO the_AT quarter_NN1 for_IF BCI_NP1 in_II Table_NN1 2_MC (_( our_APPGE baseline_NN1 )_) is_VBZ higher_JJR than_CSN from_II other_JJ approaches_NN2 of_IO converting_VVG monthly_JJ to_II quarterly_JJ frequency_NN1 in_II Table_NN1 10_MC ._. 
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<s>
It_PPH1 consists_VVZ of_IO detecting_VVG events_NN2 that_CST are_VBR not_XX observable_JJ ,_, but_CCB detectable_JJ on_II the_AT basis_NN1 of_IO symptoms_NN2 ,_, i.e._REX secondary_JJ phenomena_NN2 ,_, whose_DDQGE cause-effect_JJ relationship_NN1 with_IW life_NN1 time_NNT1 is_VBZ known_VVN ._. 
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In_II Sect._NP1 2.1_MC ,_, the_AT related_JJ models_NN2 and_CC the_AT switching-regime_JJ regression_NN1 are_VBR introduced_VVN ._. 
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<s>
The_AT response_NN1 nclaims_NN2 denotes_VVZ the_AT number_NN1 of_IO claims_NN2 filed_VVN to_II the_AT insurer_NN1 during_II the_AT exposure_NN1 period_NN1 ._. 
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It_PPH1 reveals_VVZ some_DD seasonal_JJ behaviour_NN1 in_II31 addition_II32 to_II33 significant_JJ serial_JJ correlations_NN2 ._. 
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<s>
We_PPIS2 generate_VV0 a_AT1 network_NN1 with_IW 100_MC nodes_NN2 and_CC 506_MC edges_NN2 in_II it_PPH1 ._. 
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<s>
Posterior_JJ samples_NN2 for_IF the_AT exponentiated_JJ Weibull_NN1 model_NN1 were_VBDR obtained_VVN using_VVG a_AT1 Metropolis-Hastings_NP1 algorithm_NN1 with_IW a_AT1 trivariate_NN1 normal_JJ proposal_NN1 distribution_NN1 on_II the_AT log-scale_JJ ._. 
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An_AT1 example_NN1 of_IO REINDEER_NN output_NN1 is_VBZ given_VVN in_II Supplementary_JJ Figure_NN1 S1_FO ._. 
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<s>
Whereas_CS ,_, out-degree_NN1 is_VBZ the_AT number_NN1 of_IO countries_NN2 from_II the_AT given_JJ country_NN1 to_II other_JJ countries_NN2 ._. 
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<s>
They_PPHS2 find_VV0 evidence_NN1 of_IO significant_JJ between_II financial_JJ markets_NN2 and_CC Brexit_NP1 uncertainty_NN1 ._. 
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The_AT authors_NN2 trained_VVN on_II the_AT network_NN1 of_IO co-authorship_NN1 links_VVZ from_II papers_NN2 written_VVN between_II 1994_MC and_CC 1996_MC ,_, and_CC then_RT tried_VVD to_TO predict_VVI new_JJ co-author_NN1 pairs_NN2 on_II papers_NN2 written_VVN between_II 1997_MC and_CC 1999_MC ._. 
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<s>
The_AT expressions_NN2 for_IF rnp_NNU and_CC rinf_VV0 in_II linear_JJ exponential_NN1 families_NN2 are_VBR easier_JJR to_TO work_VVI with_IW from_II a_AT1 practical_JJ standpoint_NN1 ,_, as_CSA most_DAT statistical_JJ software_NN1 provides_VVZ the_AT information_NN1 matrix_NN1 ,_, Wald_NP1 statistic_NN1 and_CC loglikelihood_NN1 function_NN1 ._. 
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<s>
To_TO detect_VVI the_AT changes_NN2 in_II the_AT spectral_JJ density_NN1 of_IO the_AT field_NN1 ,_, an_AT1 alternative_JJ approach_NN1 has_VHZ to_TO be_VBI designed_VVN ._. 
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<s>
Prior_JJ work_NN1 finds_VVZ controller-executive_JJ pay_NN1 premiums_NN2 in_II some_DD jurisdictions_NN2 (_( Urzua_NP1 ,_, 2009_MC ;_; Barak_NP1 et_RA21 al._RA22 ,_, 2011_MC ;_; Bozzi_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) but_CCB not_XX in_II others_NN2 (_( Elston_NP1 and_CC Goldberg_NP1 ,_, 2003_MC ;_; Croci_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ,_, and_CC does_VDZ not_XX rule_VVI out_RP the_AT possibility_NN1 that_CST controller_NN1 executives_NN2 occupy_VV0 higher_JJR positions_NN2 than_CSN they_PPHS2 would_VM if_CS they_PPHS2 were_VBDR non-controller_JJ executives_NN2 ._. 
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<s>
Some_DD of_IO these_DD2 are_VBR proved_VVN in_II Sect._NP1 6_MC on_II the_AT comparative_JJ statics_NN2 of_IO the_AT problem_NN1 ._. 
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<s>
Adjacency_NN1 matrices_NN2 of_IO the_AT graphs_NN2 returned_VVN by_II the_AT LSCGGM_NP1 and_CC LR+S_FO methods_NN2 for_IF γ_NULL =_FO 0.81_MC and_CC γ_NULL =_FO 0.68_MC ,_, respectively_RR ._. 
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<s>
This_DD1 means_VVZ that_CST events_NN2 occur_VV0 more_RGR frequently_RR in_II the_AT Zigzag_NN1 sampler_NN1 and_CC hence_RR this_DD1 lowers_VVZ its_APPGE efficiency_NN1 compared_VVN with_IW our_APPGE approach_NN1 ._. 
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<s>
Hence_RR ,_, it_PPH1 is_VBZ demonstrated_VVN that_CST the_AT complex_JJ financial_JJ networks_NN2 based_VVN on_II Granger_NP1 causality_NN1 can_VM effectively_RR clarify_VVI the_AT transmission_NN1 and_CC measurement_NN1 of_IO systemic_JJ risk_NN1 and_CC identify_VV0 the_AT financial_JJ crisis_NN1 period_NN1 ,_, providing_VVG an_AT1 effective_JJ early_JJ warning_NN1 tool_NN1 when_CS systemic_JJ risk_NN1 increases_NN2 ._. 
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<s>
In_II the_AT terminology_NN1 of_IO superhedging_VVG theory_NN1 ,_, <equation>_FO is_VBZ the_AT infimal_JJ amount_NN1 of_IO cash_NN1 that_CST needs_VVZ to_TO be_VBI invested_VVN in_II the_AT security_NN1 <equation>_FO such_CS21 that_CS22 <equation>_FO can_VM be_VBI superhedged_VVN when_CS combined_VVN with_IW a_AT1 suitable_JJ zero_NN1 cost_NN1 trade_NN1 in_II the_AT (_( security_NN1 )_) market_VV0 ._. 
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<s>
However_RR ,_, we_PPIS2 get_VV0 <equation>_FO by_II taking_VVG <equation>_FO and_CC using_VVG <equation>_FO for_IF all_DB <equation>_FO ,_, so_CS21 that_CS22 <equation>_FO and_CC <equation>_FO imply_VV0 <equation>_FO ._. 
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<s>
The_AT inverse_JJ Laplace_NP1 transform_VV0 of_IO equation_NN1 ,_, for_IF 1_MC1 <_FO <_FO 2_MC ,_, has_VHZ not_XX been_VBN analytically_RR studied_VVN due_II21 to_II22 the_AT difficulty_NN1 of_IO inverting_VVG the_AT double_JJ Laplace_NP1 transform_VV0 ._. 
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Observing_VVG the_AT dendrograms_NN2 in_II Fig._NN1 7_MC ,_, Fig._NN1 7_MC side_NN1 by_II side_NN1 ,_, slightly_RR more_DAR structure_NN1 is_VBZ observed_VVN in_II the_AT post-COVID_JJ period_NN1 ,_, with_IW a_AT1 growth_NN1 in_II the_AT total_JJ number_NN1 of_IO clusters_NN2 ._. 
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Moreover_RR ,_, foreign_JJ exchange_NN1 interventions_NN2 and_CC exchange_NN1 rate_NN1 expectations_NN2 show_VV0 stronger_JJR correlations_NN2 with_IW nominal_JJ exchange_NN1 rates_NN2 than_CSN with_IW interest_NN1 rate_NN1 differentials_NN2 ._. 
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The_AT global_JJ methodology_NN1 to_TO perform_VVI inversion_NN1 in_II the_AT presence_NN1 of_IO functional_JJ uncertainty_NN1 proposed_VVN in_II this_DD1 paper_NN1 is_VBZ summarized_VVN in_II Algorithm_NN1 4_MC ._. 
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In_II our_APPGE paper_NN1 we_PPIS2 study_VV0 the_AT optimal_JJ reinsurance_NN1 problem_NN1 under_II partial_JJ information_NN1 ._. 
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During_II the_AT first_MD half_NN1 of_IO the_AT 20th_MD century_NNT1 major_JJ pollution_NN1 episodes_NN2 occurred_VVD in_II London_NP1 ,_, notably_RR in_II 1952_MC an_AT1 episode_NN1 of_IO fog_NN1 ,_, in_II which_DDQ levels_NN2 of_IO black_JJ smoke_NN1 exceeded_VVD 4500_MC g_ZZ1 m_ZZ1 3_MC ,_, was_VBDZ associated_VVN with_IW 4000_MC excess_JJ deaths_NN2 (_( Ministry_NN1 of_IO Health_NN1 1954_MC )_) ._. 
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<s>
SSIF_NP1 achieved_VVD a_AT1 precision_NN1 of_IO 60.61%_FO according_II21 to_II22 the_AT monotonicity_NN1 rule_NN1 ,_, 60.49%_FO according_II21 to_II22 the_AT intersection_NN1 rule_NN1 and_CC 46.03%_FO according_II21 to_II22 the_AT sub-concept_JJ rule_NN1 ._. 
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<s>
This_DD1 implies_VVZ that_CST the_AT spectrum_NN1 of_IO the_AT model_NN1 depends_VVZ only_RR on_II Jn_NP1 and_CC Bn_NNU ,_, a_AT1 fact_NN1 which_DDQ obviously_RR also_RR follows_VVZ from_II the_AT observation_NN1 at_II the_AT beginning_NN1 of_IO section_NN1 ._. 
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Figure_VV0 1_MC1 presents_VVZ the_AT distribution_NN1 of_IO coefficients_NN2 of_IO the_AT euro_NN1 on_II trade_NN1 ,_, across_II samples_NN2 restricted_VVN by_II the_AT percentile_NN1 of_IO relative_JJ gap_NN1 distribution_NN1 in_II trade_NN1 data_NN ._. 
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<s>
We_PPIS2 selected_VVD highly_RR variable_JJ genes_NN2 using_VVG the_AT method_NN1 of_IO Brennecke_NP1 et_RA21 al_RA22 ._. 
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(_( 2013_MC )_) because_II21 of_II22 its_APPGE stable_JJ performance_NN1 Yip_NP1 et_RA21 al_RA22 ._. 
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(_( 2018_MC )_) ,_, and_CC embedded_VVD the_AT log-transformed_JJ data_NN using_VVG the_AT diffusion_NN1 map_NN1 implementation_NN1 destiny_NN1 Angerer_NP1 et_RA21 al_RA22 ._. 
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(_( 2016_MC )_) ._. 
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Additionally_RR ,_, clonal_JJ composition_NN1 per_II anatomical_JJ site_NN1 is_VBZ proportional_JJ to_II the_AT corresponding_JJ clone_NN1 '_NULL s_ZZ1 colored_JJ region_NN1 in_II the_AT spatial_JJ representation_NN1 (_( Fig._NN1 1d_NNU )_) ._. 
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<s>
The_AT system_NN1 uses_VVZ a_AT1 single_JJ central_JJ sorting_NN1 facility_NN1 where_CS all_DB parcels_NN2 from_II any_DD location_NN1 and_CC destined_VVN to_II any_DD other_JJ location_NN1 pass_VV0 each_DD1 night_NNT1 &lsqb;_( 2_MC &rsqb;_) ._. 
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<s>
The_AT details_NN2 of_IO the_AT statistical_JJ procedures_NN2 of_IO this_DD1 general_JJ sequential_JJ testing_NN1 procedure_NN1 are_VBR provided_VVN in_II the_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR as_II31 well_II32 as_II33 a_AT1 proof_NN1 that_CST the_AT Type-I_NN1 error_NN1 is_VBZ controlled_VVN ._. 
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<s>
The_AT practical_JJ aspect_NN1 of_IO the_AT model_NN1 is_VBZ discussed_VVN by_II using_VVG a_AT1 real-life_JJ data_NN example_NN1 ._. 
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<s>
ROC_NP1 curves_NN2 ,_, however_RR ,_, did_VDD not_XX show_VVI a_AT1 clear_JJ advantage_NN1 of_IO TargetPredict_NN1 compared_VVN to_II the_AT DSE-CSN-based_NP1 system_NN1 ._. 
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<s>
Our_APPGE results_NN2 highlight_VV0 both_RR the_AT continued_JJ relevance_NN1 of_IO the_AT EPIC_JJ technique_NN1 ,_, and_CC the_AT value_NN1 of_IO meta-analysis_NN1 of_IO previously_RR published_VVN results_NN2 ._. 
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<s>
The_AT above_JJ results_NN2 show_VV0 that_CST the_AT EFD_NN1 can_VM distinguish_VVI among_II the_AT same_DA types_NN2 of_IO simplex_NN1 independences_NN2 as_CSA the_AT FD_NP1 distribution_NN1 (_( see_VV0 Ongaro_NN1 and_CC Migliorati_NP1 2013_MC for_IF details_NN2 and_CC discussion_NN1 of_IO independence_NN1 properties_NN2 )_) ._. 
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For_IF increasing_JJ values_NN2 of_IO t_ZZ1 ,_, the_AT spectrum_NN1 will_VM become_VVI progressively_RR more_RGR smooth_JJ ,_, and_CC individual_JJ measurements_NN2 will_VM not_XX be_VBI as_CSA pronounced_VVN any_DD more_DAR ._. 
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<s>
Now_RT for_IF each_DD1 group_NN1 =_FO 1_MC1 and_CC 2_MC ,_, These_DD2 distributions_NN2 are_VBR obtained_VVN by_II truncating_VVG the_AT infinite_JJ series_NN of_IO (_( refer_VV0 to_II equation_NN1 (_( 13_MC )_) )_) and_CC retaining_VVG up_RG21 to_RG22 1000_MC terms_NN2 ._. 
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However_RR ,_, the_AT example_NN1 does_VDZ serve_VVI to_TO illustrate_VVI that_DD1 BSL_NN1 can_VM be_VBI impacted_VVN by_II non-normality_NN1 and_CC that_CST the_AT EES_NP1 may_VM not_XX provide_VVI sufficient_JJ robustness_NN1 to_II non-normality_NN1 ._. 
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As_II the_AT regression_NN1 analysis_NN1 begins_VVZ only_RR on_II Jan_NPM1 1_MC1 ,_, 1992_MC ,_, this_DD1 is_VBZ a_AT1 minor_JJ data_NN correction_NN1 ._. 
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Solving_VVG problem_NN1 (_( 3.10_MC )_) remains_VVZ very_RG challenging_JJ and_CC so_RG far_RR an_AT1 open_JJ question_NN1 ,_, to_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ._. 
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<s>
In_II its_APPGE full_JJ generality_NN1 ,_, we_PPIS2 consider_VV0 random_JJ variables_NN2 that_CST can_VM be_VBI written_VVN as_CSA finite_JJ sums_NN2 of_IO independent_JJ heterogeneous_JJ gamma_NN1 and_CC Mittag-Leffler_NP1 random_JJ variables_NN2 ._. 
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This_DD1 problematic_JJ issue_NN1 has_VHZ been_VBN partially_RR ignored_VVN in_II the_AT literature_NN1 for_IF robust_JJ (_( extended_VVN )_) GAMs_VVZ ._. 
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Alternatively_RR ,_, each_DD1 margin_NN1 has_VHZ its_APPGE grid_NN1 <equation>_FO ._. 
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<s>
The_AT edge_NN1 '_NULL s_ZZ1 weight_NN1 is_VBZ set_VVN to_II 0_MC when_RRQ its_APPGE absolute_JJ value_NN1 is_VBZ less_DAR than_CSN θ_NULL 3_MC referring_VVG to_II not-connected_NN1 ._. 
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Asymptotic_JJ linearity_NN1 and_CC efficiency_NN1 of_IO the_AT estimator_NN1 for_IF modified_JJ treatment_NN1 policies_NN2 are_VBR detailed_VVN in_II the_AT following_JJ theorem_NN1 ._. 
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<s>
We_PPIS2 demonstrate_VV0 that_CST supervised_VVD learning_VVG on_II a_AT1 gene_NN1 '_NULL s_ZZ1 full_JJ network_NN1 connectivity_NN1 outperforms_NN2 label_VV0 propagaton_NN1 and_CC achieves_VVZ high_JJ prediction_NN1 accuracy_NN1 by_II efficiently_RR capturing_VVG local_JJ network_NN1 properties_NN2 ,_, rivaling_VVG label_NN1 propagation_NN1 '_NULL s_ZZ1 appeal_VV0 for_IF naturally_RR using_VVG network_NN1 topology_NN1 ._. 
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The_AT latter_DA involves_VVZ merging_VVG two_MC existing_JJ partitions_NN2 ._. 
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There_EX are_VBR two_MC major_JJ challenges_NN2 in_II modeling_VVG copy_NN1 number_NN1 evolution_NN1 ._. 
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Of_RR21 course_RR22 ,_, thermodynamic_JJ metastability_NN1 has_VHZ dynamical_JJ implications_NN2 ;_; the_AT point_NN1 here_RL is_VBZ that_DD1 metastability_NN1 in_II trajectory_NN1 space_NN1 is_VBZ distinct_JJ from_II thermodynamic_JJ metastability_NN1 ,_, and_CC has_VHZ a_AT1 different_JJ set_NN1 of_IO implications_NN2 for_IF dynamical_JJ behaviour_NN1 ._. 
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We_PPIS2 find_VV0 in_II fact_NN1 the_AT same_DA behavior_NN1 ,_, and_CC extend_VV0 the_AT previous_JJ study_NN1 for_IF more_DAR resonances_NN2 :_: the_AT fluctuations_NN2 do_VD0 not_XX appear_VVI to_TO change_VVI sensibly_RR with_IW the_AT system_NN1 going_VVG out_II21 of_II22 equilibrium_NN1 ._. 
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However_RR ,_, they_PPHS2 are_VBR modeling_VVG growth_NN1 ,_, not_XX recovery_NN1 after_II some_DD disruptive_JJ event_NN1 ,_, and_CC assume_VV0 the_AT initial_JJ level_NN1 of_IO the_AT growth_NN1 curve_NN1 to_TO be_VBI known_VVN ,_, whereas_CS we_PPIS2 are_VBR trying_VVG to_TO predict_VVI the_AT entire_JJ post-treatment_JJ trajectory_NN1 ,_, which_DDQ includes_VVZ the_AT initial_JJ post-treatment_JJ value_NN1 ._. 
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Besides_RR ,_, interestingly_RR ,_, seen_VVN from_II Fig._NN1 1_MC1 ,_, <equation>_FO gives_VVZ shorter_JJR confidence_NN1 intervals_NN2 and_CC narrower_JJR confidence_NN1 bands_NN2 than_CSN <equation>_FO for_IF g(z)_NNU ._. 
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The_AT ultimate_JJ goal_NN1 of_IO this_DD1 computation_NN1 is_VBZ to_TO obtain_VVI the_AT summed_JJ action_NN1 of_IO activators_NN2 after_II their_APPGE contribution_NN1 has_VHZ been_VBN increased_VVN by_II coactivation_NN1 and_CC diminished_VVN by_II quenching_VVG ._. 
</s>
<s>
If_CS <equation>_FO ,_, one_MC1 of_IO R-optimal_JJ designs_NN2 is_VBZ equally_RR supported_VVN at_II the_AT points_NN2 <equation>_FO ,_, 0_MC and_CC <equation>_FO ._. 
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<s>
The_AT remainder_NN1 of_IO this_DD1 paper_NN1 proceeds_VVZ as_CSA follows_VVZ :_: The_AT following_JJ section_NN1 discusses_VVZ the_AT data_NN used_VVN in_II the_AT empirical_JJ part_NN1 of_IO the_AT paper_NN1 ._. 
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<s>
Barro_NP1 (_( 2015_MC )_) finds_VVZ conditional_NN1 in_II GDP_NN1 per_RR21 capita_RR22 since_II 1870_MC over_RG 28_MC countries_NN2 at_II a_AT1 2.6%_FO annual_JJ convergence_NN1 rate_NN1 ._. 
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<s>
Additionally_RR ,_, we_PPIS2 expand_VV0 the_AT identified_JJ proteins_NN2 with_IW all_DB homologous_JJ proteins_NN2 obtained_VVN from_II the_AT HomoloGene_NP1 database_NN1 (_( ftp_NNU :_: )_) ,_, to_TO increase_VVI the_AT number_NN1 of_IO text_NN1 spans_VVZ per_II protein_NN1 pair_NN ,_, considering_CS only_RR the_AT taxa_NN2 Homo_NN121 Sapiens_NN122 ,_, Rattus_JJ norvegicus_NN1 ,_, Mus_NN2 musculus_NN1 ,_, Oryctolagus_NP1 cuniculus_NN1 and_CC Cricetulus_NP1 longicaudatus_NN1 ._. 
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<s>
Then_RT we_PPIS2 introduce_VV0 model_NN1 uncertainty_NN1 in_II the_AT sense_NN1 of_IO Knightian_JJ uncertainty_NN1 and_CC construct_VV0 an_AT1 adapted_JJ stochastic_JJ differential_JJ game_NN1 problem_NN1 with_IW a_AT1 nonstandard_NN1 performance_NN1 functional_JJ ._. 
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For_IF just_RR under_RG 10%_NNU of_IO the_AT observations_NN2 ,_, we_PPIS2 can_VM not_XX find_VVI any_DD public_JJ filings_NN2 in_II the_AT comprehensive_JJ FactSet_NN1 ownership_NN1 database_NN1 about_II investors_NN2 '_NULL (_( long_RR )_) holdings_NN2 ._. 
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<s>
Thus_RR ,_, the_AT utility_NN1 in_II (_( 4_MC )_) indeed_RR generates_VVZ the_AT constraint_NN1 of_IO a_AT1 given_JJ fixed_JJ geometric_JJ mean_NN1 ._. 
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Panel_NN1 (_( a_ZZ1 )_) presents_VVZ the_AT case_NN1 with_IW =_FO 0.5_MC while_CS panel_NN1 (_( b_ZZ1 )_) the_AT case_NN1 with_IW =_FO 0.25_MC ._. 
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<s>
The_AT partition_NN1 function_NN1 Z_ZZ1 is_VBZ the_AT same_DA in_II the_AT two_MC expressions_NN2 and_CC ,_, and_CC in_II the_AT support_NN1 of_IO the_AT variables_NN2 wa_NN1 →_NULL i_ZZ1 are_VBR the_AT deterministic_JJ functions_NN2 of_IO defined_JJ above_RL ._. 
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The_AT number_NN1 of_IO common_JJ factors_NN2 ,_, r_ZZ1 ,_, is_VBZ constant_JJ for_IF all_DB t_ZZ1 ._. 
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<s>
Of_IO particular_JJ importance_NN1 is_VBZ the_AT condition_NN1 that_CST rmin_NN1 (_( J_ZZ1 ,_, T_ZZ1 )_) ,_, so_CS21 that_CS22 substantial_JJ dimension_NN1 reduction_NN1 can_VM be_VBI achieved_VVN ._. 
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<s>
Through_II the_AT analysis_NN1 of_IO the_AT two_MC real_JJ datasets_NN2 ,_, we_PPIS2 illustrated_VVD that_CST the_AT sCCA_NN1 methods_NN2 can_VM improve_VVI our_APPGE predictions_NN2 of_IO complex_JJ traits_NN2 in_II both_DB2 cases_NN2 :_: (_( i_ZZ1 )_) when_RRQ a_AT1 regression_NN1 model_NN1 is_VBZ built_VVN with_IW the_AT new_JJ canonical_JJ matrices_NN2 as_CSA input_NN1 matrices_NN2 and_CC (_( ii_MC )_) when_RRQ the_AT response_NN1 matrix_NN1 is_VBZ one_MC1 of_IO the_AT input_NN1 matrices_NN2 in_II the_AT data_NN integration_NN1 ._. 
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<s>
For_REX21 example_REX22 ,_, for_IF a_AT1 given_JJ province_NN1 moving_VVG from_II <equation>_FO to_II <equation>_FO ,_, the_AT province_NN1 is_VBZ treated_VVN as_II a_AT1 different_JJ unit_NN1 <equation>_FO at_II different_JJ periods_NN2 and_CC can_VM switch_VVI regimes_NN2 ._. 
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<s>
However_RR ,_, their_APPGE outcomes_NN2 on_II the_AT connection_NN1 between_II FDI_NP1 and_CC its_APPGE determinants_NN2 are_VBR not_XX consistent_JJ ._. 
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<s>
The_AT parameters_NN2 q_ZZ1 and_CC are_VBR calculated_VVN using_VVG equations_NN2 and_CC respectively_RR ;_; see_VV0 table_NN1 for_IF numerical_JJ values_NN2 ._. 
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<s>
Yet_RR ,_, looking_VVG for_IF cities_NN2 fully_RR devoted_JJ to_II a_AT1 saint_NN1 or_CC sainte_FW ,_, I_PPIS1 felt_VVD the_AT necessity_NN1 of_IO including_VVG those_DD2 referring_VVG to_II "_" Our_APPGE Lady_NN1 "_" (_( Notre-Dame_NP1 )_) ._. 
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<s>
Of_IO note_NN1 ,_, this_DD1 simulation_NN1 assumes_VVZ a_AT1 Dirichlet-Multinomial_JJ distribution_NN1 ,_, which_DDQ is_VBZ consistent_JJ with_IW both_DB2 LeafCutterMD_NP1 and_CC the_AT standard_JJ LeafCutter_NN1 ,_, and_CC thus_RR represents_VVZ a_AT1 fair_JJ comparison_NN1 of_IO the_AT methods_NN2 ._. 
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<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 review_VV0 importance_NN1 and_CC adaptive_JJ importance_NN1 samplers_NN2 ._. 
</s>
<s>
The_AT calculation_NN1 of_IO the_AT integrated_JJ likelihood_NN1 in_II (_( 9_MC )_) is_VBZ done_VDN in_II the_AT same_DA way_NN1 as_CSA for_IF the_AT marginal_JJ likelihood_NN1 ,_, and_CC the_AT integration_NN1 with_II31 respect_II32 to_II33 <equation>_FO in_II (_( 10_MC )_) is_VBZ carried_VVN out_RP in_II an_AT1 outer_JJ importance_NN1 sampling_NN1 loop_NN1 ._. 
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<s>
In_II many_DA2 situations_NN2 ,_, however_RR ,_, partially_RR identifying_VVG variables_NN2 may_VM have_VHI been_VBN registered_VVN in_II all_DB files_NN2 ._. 
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This_DD1 layer_NN1 is_VBZ illustrated_VVN on_II Fig._NN1 2(d)_FO ._. 
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<s>
Apart_II21 from_II22 the_AT huge_JJ prospects_NN2 in_II31 terms_II32 of_II33 quantitative_JJ prediction_NN1 performance_NN1 ,_, the_AT recent_JJ advances_NN2 in_II the_AT field_NN1 of_IO explainable_JJ ML_NNU research_NN1 open_VV0 exciting_JJ new_JJ avenues_NN2 for_IF deeper_JJR insights_NN2 into_II the_AT inner_JJ structure_NN1 of_IO proteins_NN2 themselves_PPX2 ._. 
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<s>
Hence_RR ,_, the_AT 1-SE_NP1 rule_NN1 attempts_NN2 to_TO select_VVI the_AT most_RGT simple_JJ model_NN1 whose_DDQGE CV_NN1 score_NN1 is_VBZ within_II one_MC1 standard_JJ error_NN1 of_IO the_AT minimal_JJ CV_NN1 score_NN1 ._. 
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<s>
This_DD1 provides_VVZ hints_NN2 for_IF possible_JJ experimental_JJ protocols_NN2 towards_II more_RGR efficient_JJ information_NN1 engines_NN2 ._. 
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Highlighting_VVG their_APPGE distinct_JJ empirical_JJ size_NN1 and_CC power_NN1 properties_NN2 in_II various_JJ small_JJ sample_NN1 settings_NN2 ,_, our_APPGE analysis_NN1 supports_VVZ an_AT1 analyst_NN1 in_II deciding_VVG for_IF a_AT1 most_RGT adequate_JJ test_NN1 conditional_NN1 on_II underlying_VVG distributional_JJ settings_NN2 or_CC data_NN characteristics_NN2 ._. 
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<s>
We_PPIS2 find_VV0 a_AT1 clear_JJ and_CC persistent_JJ pattern_NN1 that_CST direct_JJ investments_NN2 in_II children_NN2 have_VH0 yielded_VVN the_AT largest_JJT MVPFs_NP1 ._. 
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The_AT claim_NN1 now_RT follows_VVZ from_II the_AT first_MD and_CC second_MD estimates_NN2 in_II Lemma_NN1 3.9_MC ._. 
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<s>
We_PPIS2 construct_VV0 upper_JJ and_CC lower_JJR contractions_NN2 ;_; these_DD2 are_VBR fictitious_JJ complete_JJ markets_NN2 in_II which_DDQ state_VV0 variables_NN2 are_VBR fully_RR hedgeable_JJ ,_, but_CCB their_APPGE dynamics_NN is_VBZ distorted_VVN ._. 
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<s>
We_PPIS2 construct_VV0 a_AT1 kacc-nn_JJ classifier_NN1 trained_VVN by_II cells_NN2 with_IW their_APPGE labels_NN2 using_VVG Dataset_NN1 2_MC ,_, and_CC Label_VV0 Transfer_NN1 Accuracy_NN1 is_VBZ the_AT prediction_NN1 accuracy_NN1 of_IO the_AT cell_NN1 labels_NN2 on_II the_AT testing_NN1 set_NN1 ,_, i.e._REX ,_, Dataset_VV0 1_MC1 ._. 
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<s>
The_AT effect_NN1 of_IO the_AT randomness_NN1 that_CST is_VBZ induced_VVN by_II such_DA a_AT1 split_NN1 can_VM be_VBI mitigated_VVN by_II using_VVG methods_NN2 designed_VVN to_TO aggregate_VVI over_RP multiple_JJ sample_NN1 splits_NN2 ,_, as_CSA studied_VVN for_REX21 instance_REX22 in_II Meinshausen_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2009_MC )_) ._. 
</s>
<s>
Each_DD1 component_NN1 of_IO I1_FO is_VBZ associated_VVN with_IW X1_FO ,_, conditional_NN1 on_II the_AT remaining_JJ instruments_NN2 ,_, and_CC each_DD1 component_NN1 of_IO I2_FO is_VBZ associated_VVN with_IW X2_FO ,_, conditional_NN1 on_II X1_FO and_CC the_AT remaining_JJ instruments_NN2 ._. 
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The_AT first_MD three_MC IMFs_NP2 for_IF the_AT 400th_MD image_NN1 of_IO the_AT DOWN_RP region_NN1 are_VBR IMF1_FO (_( A_ZZ1 )_) ,_, IMF2_FO (_( B_ZZ1 )_) ,_, and_CC IMF3_FO (_( C_ZZ1 )_) with_IW the_AT residual_JJ image_NN1 shown_VVN in_II panel_NN1 D._NP1 Examples_NN2 of_IO original_JJ images_NN2 are_VBR in_II Fig._NN1 2D_NNU and_CC E._NP1 Below_RG critical_JJ temperature_NN1 (_( panels_NN2 A–D_NP1 )_) ,_, the_AT finest_JJT spatial_JJ scale_NN1 IMF1_FO (_( A_ZZ1 )_) shows_VVZ relatively_RR small_JJ size_NN1 fluctuations_NN2 ,_, which_DDQ correspond_VV0 to_II the_AT finest_JJT spatial_JJ scale_NN1 of_IO the_AT fluctuations_NN2 ._. 
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<s>
Fig._NN1 10b_FO shows_VVZ that_CST following_VVG a_AT1 steep_JJ initial_JJ rise_NN1 due_II21 to_II22 the_AT rupture_NN1 of_IO films_NN2 in_II the_AT one-stopper_JJ tubes_NN2 ,_, (_( t_ZZ1 )_) decays_VVZ again_RT in_II the_AT time_NNT1 interval_NN1 from_II 2_MC to_II 5_MC min_NNU ,_, as_CSA this_DD1 short-living_JJ film_NN1 population_NN1 gradually_RR vanishes_VVZ ._. 
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<s>
Thus_RR ,_, once_RR21 again_RR22 ,_, the_AT conditional_JJ SML_NP1 has_VHZ a_AT1 much_RR higher_JJR slope_NN1 than_CSN the_AT value_NN1 of_IO -4.20_MC bps_NNU obtained_VVN by_II adding_VVG the_AT day_NNT1 and_CC night_NNT1 slopes_NN2 from_II the_AT Fama-MacBeth_NP1 regressions_NN2 ._. 
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<s>
In_II this_DD1 case_NN1 it_PPH1 also_RR represents_VVZ ,_, using_VVG the_AT deviation_NN1 component_NN1 ,_, how_RRQ the_AT ADM_NP1 learned_VVD from_II data_NN differs_VVZ from_II the_AT '_NULL product_NN1 '_NULL of_IO monomer_NN1 ADMs_NN2 which_DDQ would_VM be_VBI the_AT expected_JJ dimer_NN1 model_NN1 were_VBDR there_RL no_AT interactions_NN2 ._. 
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<s>
If_CS we_PPIS2 instead_RR approximate_VV0 <equation>_FO from_II below_RL by_II stochastic_JJ subsolutions_NN2 of_IO the_AT QVIs_NN1 ,_, it_PPH1 is_VBZ by_RR31 no_RR32 means_RR33 clear_JJ if_CS the_AT pointwise_JJ supremum_NN1 of_IO the_AT stochastic_JJ subsolutions_NN2 satisfies_VVZ this_DD1 monotonicity_NN1 property_NN1 ._. 
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The_AT remainder_NN1 of_IO this_DD1 article_NN1 is_VBZ structured_VVN as_CSA follows_VVZ ._. 
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<s>
All_DB the_AT participants_NN2 were_VBDR briefed_VVN and_CC clarified_VVN on_II the_AT aims_NN2 and_CC procedures_NN2 of_IO the_AT experiment_NN1 ._. 
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<s>
Centrifuge_NN1 achieves_VVZ the_AT lowest_JJT index_NN1 size_NN1 with_IW the_AT cost_NN1 of_IO having_VHG the_AT highest_JJT memory_NN1 consumption_NN1 ._. 
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<s>
The_AT rest_NN1 of_IO the_AT paper_NN1 is_VBZ structured_VVN as_CSA follows_VVZ ._. 
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<s>
This_DD1 table_NN1 presents_VVZ summary_NN1 statistics_NN for_IF quarterly_JJ industry-level_JJ common_JJ ownership_NN1 ,_, profitability_NN1 ,_, and_CC other_JJ variables_NN2 used_VVN in_II our_APPGE analysis_NN1 ._. 
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<s>
Of_RR21 course_RR22 ,_, our_APPGE proposed_JJ model_NN1 is_VBZ intended_VVN to_II measure_NN1 the_AT market_NN1 underlying_JJ structure_NN1 of_IO the_AT crashes_NN2 or_CC bubbles_NN2 ._. 
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<s>
Using_VVG geographic_JJ variation_NN1 in_II the_AT severity_NN1 of_IO demonetization_NN1 ,_, we_PPIS2 have_VH0 shown_VVN that_CST a_AT1 sharp_JJ ,_, temporary_JJ decline_NN1 in_II currency_NN1 caused_VVN declines_VVZ in_II ATM_NN1 withdrawals_NN2 ,_, reduced_VVD economic_JJ activity_NN1 ,_, faster_JJR adoption_NN1 of_IO alternative_JJ payment_NN1 technologies_NN2 ,_, and_CC higher_JJR deposit_NN1 and_CC lower_JJR bank_NN1 credit_NN1 growth_NN1 in_II Indian_JJ districts_NN2 ._. 
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We_PPIS2 present_VV0 results_NN2 for_IF the_AT root_NN1 mean_VV0 square_JJ deviation_NN1 (_( RMSD_NP1 )_) of_IO the_AT final_JJ opinions_NN2 of_IO the_AT normal_JJ and_CC truth_NN1 seeking_VVG agents_NN2 from_II the_AT truth_NN1 ._. 
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On_II the_AT contrary_NN1 ,_, the_AT two_MC stage_NN1 TPRE_NN1 is_VBZ the_AT best_JJT with_IW <equation>_FO ._. 
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<s>
Next_MD we_PPIS2 prove_VV0 that_CST the_AT decision_NN1 rule_NN1 (_( 2.8_MC )_) indeed_RR provides_VVZ an_AT1 asymptotic_JJ level_JJ test_NN1 ._. 
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<s>
The_AT econometric_JJ analysis_NN1 reveals_VVZ that_CST factors_NN2 such_II21 as_II22 economic_JJ potential_NN1 ,_, labour_NN1 conditions_NN2 and_CC competitiveness_NN1 are_VBR important_JJ for_IF attracting_VVG FDI_NP1 both_RR at_II aggregate_NN1 and_CC sectoral_JJ levels_NN2 ._. 
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<s>
For_IF any_DD given_JJ percentile_NN1 threshold_NN1 ,_, we_PPIS2 include_VV0 all_DB vertex_VV0 labelling_NN1 whose_DDQGE percentile_NN1 is_VBZ at_RR21 most_RR22 for_IF both_DB2 the_AT transmission_NN1 number_NN1 and_CC the_AT number_NN1 of_IO unsampled_JJ lineages_NN2 ._. 
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<s>
We_PPIS2 present_VV0 two_MC types_NN2 of_IO result_NN1 :_: for_IF general_JJ modified_JJ treatment_NN1 policies_NN2 satisfying_JJ assumption_NN1 1_MC1 ,_, and_CC for_IF the_AT particular_JJ stochastic_JJ intervention_NN1 of_IO example_NN1 2_MC ._. 
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<s>
The_AT R-optimal_JJ design_NN1 <equation>_FO for_IF estimating_VVG the_AT parameters_NN2 <equation>_FO corresponding_VVG to_II the_AT terms_NN2 <equation>_FO and_CC <equation>_FO is_VBZ directly_RR obtained_VVN from_II Theorem_NN1 5_MC ,_, which_DDQ is_VBZ equally_RR supported_VVN at_II the_AT points_NN2 <equation>_FO ,_, Suppose_VV0 all_DB these_DD2 <equation>_FO factors_NN2 are_VBR at_II two_MC levels_NN2 ._. 
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<s>
The_AT arrows_NN2 indicate_VV0 the_AT points_NN2 where_RRQ the_AT events_NN2 of_IO minority_NN1 win_NN1 did_VDD occur_VVI in_II the_AT past_NN1 ._. 
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<s>
This_DD1 table_NN1 repeats_VVZ the_AT duration_NN1 analysis_NN1 used_VVN in_II Table_NN1 4_MC ,_, conditional_NN1 on_II positions_NN2 that_CST eventually_RR increase_VV0 with_IW the_AT next_MD change_NN1 ._. 
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In_II the_AT frequency_NN1 ratio_NN1 of_IO the_AT atomic_JJ transition_NN1 to_II the_AT photon_NN1 field_NN1 limit_NN1 ,_, i.e._REX ,_, →_NULL ∞_FO ,_, the_AT analytical_JJ results_NN2 show_VV0 that_CST the_AT model_NN1 undergoes_VVZ a_AT1 superradiant_JJ phase_NN1 transition_NN1 from_II the_AT normal_JJ phase_NN1 when_CS the_AT average_NN1 of_IO the_AT qubit-resonator_JJ coupling_NN1 exceeds_VVZ than_CSN a_AT1 critical_JJ value_NN1 ._. 
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All_DB regressions_NN2 include_VV0 sector-time_JJ fixed_JJ effects_NN2 ._. 
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Note_VV0 that_CST Bi+_FO and_CC Bi_NP1 have_VH0 highly_RR similar_JJ expressions_NN2 ._. 
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<s>
Displayed_VVN are_VBR 100_MC draws_NN2 from_II solution_NN1 u1(t)_FO plotted_VVN against_II t_ZZ1 for_IF values_NN2 drawn_VVN from_II the_AT the_AT prior_JJ distribution_NN1 of_IO θ_NULL ,_, for_IF each_DD1 of_IO the_AT n=7_FO placentas_NN2 and_CC treatments_NN2 given_VVN in_II Table_NN1 1_MC1 ._. 
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<s>
On_II the_AT contrary_NN1 ,_, if_CS the_AT distance_NN1 is_VBZ zero_MC ,_, the_AT groups_NN2 are_VBR identical_JJ ;_; we_PPIS2 have_VH0 no_AT reason_NN1 to_TO speak_VVI about_RG two_MC groups_NN2 because_CS actually_RR there_EX is_VBZ only_RR one_MC1 ._. 
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<s>
However_RR ,_, the_AT mean-field_JJ aspect_NN1 of_IO the_AT model_NN1 allows_VVZ a_AT1 more_RGR detailed_JJ characterisation_NN1 of_IO trajectories_NN2 within_II the_AT biased_JJ ensemble_NN1 ._. 
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<s>
In_II the_AT second_MD joint_JJ model_NN1 ,_, we_PPIS2 wrongly_RR assumed_VVD DCAR_NP1 and_CC used_JJ (_( 2a_FO )_) in_II the_AT record_NN1 linkage_NN1 parts_NN2 of_IO the_AT joint_JJ likelihood_NN1 regarding_II the_AT matches_NN2 ._. 
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The_AT set_NN1 of_IO reference_NN1 sequences_NN2 from_II RefSeq-OLD/CG/ALL_FU (_( Table_NN1 1_MC1 )_) and_CC RefSeq-CG/ALL-top-3_NP1 (_( Table_NN1 2_MC )_) were_VBDR used_VVN as_CSA inputs_VVZ to_TO generate_VVI the_AT indices_NN2 for_IF each_DD1 evaluated_VVD tool_NN1 ._. 
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<s>
Bifurcation_NN1 diagram_NN1 for_IF fractional-order_NN1 simplified_VVD Lorenz_NP1 system_NN1 with_IW different_JJ c_ZZ1 ._. 
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<s>
Table_NN1 2_MC shows_VVZ that_CST these_DD2 two_MC random_JJ effects_NN2 are_VBR present_JJ in_II this_DD1 case_NN1 –_- it_PPH1 is_VBZ in_II fact_NN1 even_RR more_RGR obvious_JJ if_CS these_DD2 tests_NN2 are_VBR done_VDN with_IW the_AT full_JJ data_NN set_VV0 ._. 
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<s>
The_AT performance_NN1 of_IO MHCflurry_NN1 is_VBZ computed_VVN without_IW those_DD2 data-points_NN2 ._. 
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<s>
Figure_VV0 1_MC1 depicts_VVZ the_AT mean_JJ and_CC 95%_NNU intervals_NN2 (_( constructed_VVN from_II the_AT sample_NN1 percentiles_NN2 )_) of_IO rO_NN1 ,_, plotted_VVN against_II N._NP1 Evidently_RR ,_, there_EX is_VBZ a_AT1 systematic_JJ underestimation_NN1 of_IO the_AT value_NN1 of_IO =1r=1_FO ,_, where_CS the_AT bias_NN1 slowly_RR diminishes_VVZ as_CSA N_ZZ1 increases_VVZ ,_, confirming_VVG the_AT assertion_NN1 by_II Meng_NP1 and_CC Wong_NP1 (_( 1996_MC )_) that_CST the_AT bias_NN1 term_NN1 is_VBZ asymptotically_RR negligible_JJ ._. 
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<s>
Rather_RR ,_, <equation>_FO is_VBZ determined_VVN by_II the_AT joint_JJ distribution_NN1 of_IO <equation>_FO ._. 
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<s>
Schematic_JJ diagram_NN1 of_IO the_AT relationship_NN1 among_II the_AT potential_JJ energy_NN1 levels_NN2 in_II the_AT components_NN2 of_IO the_AT coupled_JJ double_JJ quantum_NN1 dot_NN1 system_NN1 model_NN1 setup_NN1 ._. 
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<s>
We_PPIS2 have_VH0 <equation>_FO for_IF each_DD1 <equation>_FO ,_, and_CC as_II a_AT1 consequence_NN1 ,_, <equation>_FO also_RR takes_VVZ its_APPGE largest_JJT possible_JJ values_NN2 on_II <equation>_FO ._. 
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<s>
We_PPIS2 categorized_VVD 198_MC time_NNT1 series_NN data_NN into_II 13_MC groups_NN2 as_CSA summarized_VVN in_II Table_NN1 1_MC1 ._. 
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On_II the_AT other_JJ hand_NN1 for_IF a_AT1 small_JJ diffusion_NN1 ,_, the_AT peaks_NN2 are_VBR well_RR separated_VVN and_CC the_AT nodes_NN2 are_VBR decoupled_VVN ._. 
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<s>
Hereafter_RT ,_, we_PPIS2 move_VV0 on_RP to_II study_NN1 anyonic_JJ gases_NN2 in_II inhomogeneous_JJ settings_NN2 ._. 
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<s>
The_AT method_NN1 can_VM still_RR increase_VVI the_AT computational_JJ efficiency_NN1 of_IO such_DA algorithms_NN2 due_II21 to_II22 its_APPGE multiplicative_JJ effect_NN1 ,_, but_CCB no_AT more_DAR than_CSN it_PPH1 would_VM for_IF a_AT1 derivative-free_JJ sampler_NN1 ._. 
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Finally_RR ,_, PETs_NN2 with_IW either_DD1 tag_NN1 overlapping_VVG any_DD black_JJ listed_JJ regions_NN2 of_IO the_AT corresponding_JJ genome_NN1 are_VBR removed_VVN before_II continuing_VVG to_II the_AT next_MD stage_NN1 of_IO the_AT analysis_NN1 (_( ENCODE_NP1 Project_NN1 Consortium_NN1 ,_, 2012_MC )_) ._. 
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<s>
Time_NNT1 series_NN of_IO average_JJ portfolio_NN1 liquidity_NN1 and_CC its_APPGE components_NN2 ._. 
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<s>
MESA_NP1 is_VBZ fully_RR customizable_JJ using_VVG an_AT1 easy-to-use_JJ web_NN1 interface_NN1 ,_, without_IW requiring_VVG programming_NN1 experience_NN1 ._. 
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<s>
Proposition_VV0 1_MC1 and_CC its_APPGE proof_NN1 from_II that_DD1 paper_NN1 are_VBR repeated_VVN here_RL for_IF convenience_NN1 ._. 
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<s>
This_DD1 provides_VVZ us_PPIO2 with_IW a_AT1 way_NN1 to_TO accelerate_VVI the_AT overall_JJ computation_NN1 of_IO MwG_NP1 ._. 
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<s>
The_AT low_JJ dimensionality_NN1 is_VBZ crucial_JJ for_IF the_AT good_JJ performance_NN1 of_IO the_AT methods_NN2 ,_, since_CS they_PPHS2 suffer_VV0 heavily_RR from_II the_AT curse_NN1 of_IO dimensionality_NN1 ._. 
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<s>
Although_CS taxation_NN1 was_VBDZ a_AT1 stated_JJ topic_NN1 of_IO town_NN1 hall_NN1 meetings_NN2 ,_, as_CSA noted_VVN ,_, the_AT evaluation_NN1 form_NN1 prompts_NN2 did_VDD not_XX mention_VVI taxation_NN1 and_CC so_RR could_VM not_XX have_VHI primed_VVN citizens_NN2 about_II taxation_NN1 before_CS they_PPHS2 chose_VVD to_TO participate_VVI ._. 
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<s>
We_PPIS2 measure_VV0 children_NN2 '_NULL s_ZZ1 educational_JJ attainment_NN1 based_VVN on_II the_AT highest_JJT level_NN1 of_IO education_NN1 they_PPHS2 report_VV0 having_VHG completed_VVN in_II the_AT ACS_NN2 or_CC the_AT 2000_MC Census_NN1 long_JJ form_NN1 (_( prioritizing_VVG the_AT ACS_NN2 ,_, since_CS it_PPH1 is_VBZ more_RGR recent_JJ )_) ._. 
</s>
<s>
The_AT statement_NN1 of_IO Proposition_NN1 6.5_MC follows_VVZ now_RT immediately_RR from_II Lemma_NN1 6.3_MC ._. 
</s>
<s>
Table_NN1 2_MC presents_VVZ the_AT results_NN2 for_IF analyzing_VVG the_AT donation_NN1 and_CC deferral_JJ outcomes_NN2 separately_RR ._. 
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<s>
In_BCL21 order_BCL22 to_TO examine_VVI this_DD1 issue_NN1 ,_, we_PPIS2 re-estimate_VV0 the_AT empirical_JJ dynamic_JJ panel_NN1 model_NN1 for_IF large_JJ firms_NN2 and_CC SMEs_NN2 separately_RR ._. 
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<s>
The_AT time_NNT1 required_VVN to_TO wrap_VVI around_RP a_AT1 fixed_JJ point_NN1 for_IF one_MC1 cycle_NN1 is_VBZ called_VVN the_AT rotation_NN1 period_NN1 ._. 
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<s>
Among_II other_JJ things_NN2 ,_, Tavares_NP1 showed_VVD that_CST if_CS <equation>_FO is_VBZ an_AT1 i.i.d_NNU ._. 
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<s>
Data_NN pre-processing_JJ choices_NN2 can_VM be_VBI subjective_JJ ,_, as_II31 well_II32 as_II33 being_VBG time-consuming_JJ and_CC therefore_RR costly_JJ ._. 
</s>
<s>
It_PPH1 should_VM be_VBI noted_VVN here_RL that_DD1 ,_, for_IF many_DA2 real_JJ networks_NN2 such_II21 as_II22 protein_NN1 networks_NN2 ,_, citation_NN1 networks_NN2 ,_, and_CC social_JJ networks_NN2 ,_, their_APPGE degrees_NN2 are_VBR distributed_VVN as_CSA power-law_NN1 (_( Barabási_NP1 and_CC Albert_NP1 2002_MC )_) ,_, where_CS the_AT probability_NN1 of_IO a_AT1 node_NN1 having_VHG degree_NN1 k_ZZ1 is_VBZ proportional_JJ to_II <equation>_FO with_IW <equation>_FO ._. 
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<s>
Note_VV0 :_: For_IF BeadNet_NP1 ,_, the_AT median_NN1 of_IO five_MC trained_JJ models_NN2 is_VBZ shown_VVN ._. 
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<s>
We_PPIS2 note_VV0 this_DD1 is_VBZ because_CS for_IF each_DD1 proposal_NN1 ,_, realization_NN1 (_( 26_MC )_) is_VBZ repeated_VVN for_IF =100S=100standard_FO Brownian_JJ motion_NN1 paths_NN2 W_ZZ1 ,_, dominating_VVG the_AT total_JJ computation_NN1 of_IO the_AT sampling_NN1 algorithms_NN2 and_CC making_VVG the_AT relationships_NN2 more_RGR clearer_JJR ._. 
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<s>
In_II Sect._NP1 3_MC ,_, we_PPIS2 explore_VV0 the_AT performance_NN1 of_IO the_AT algorithm_NN1 under_II various_JJ sampler_NN1 and_CC model_NN1 settings_NN2 ,_, and_CC provide_VV0 a_AT1 real_JJ data_NN analysis_NN1 of_IO an_AT1 Airbnb_NN1 dataset_NN1 using_VVG an_AT1 intractable_JJ state-space_JJ model_NN1 with_IW a_AT1 36-dimensional_JJ latent_JJ state_NN1 observed_VVN on_II 365_MC time_NNT1 points_NN2 in_II Sect._NP1 4_MC ._. 
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<s>
In_II traditional_JJ transportation_NN1 network_NN1 ,_, goods_NN2 and_CC passengers_NN2 are_VBR usually_RR transported_VVN directly_RR to_II the_AT destination_NN1 ._. 
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<s>
Finally_RR ,_, there_EX are_VBR spontaneous_JJ offerings_NN2 ,_, made_VVN on_II a_AT1 more_RGR regular_JJ basis_NN1 ,_, which_DDQ are_VBR generally_RR anonymous_JJ and_CC the_AT amounts_NN2 given_VVN unobserved_JJ (_( though_CS during_II collections_NN2 in_II Sunday_NPD1 services_NN2 the_AT fact_NN1 of_IO going_VVG forward_RL to_TO give_VVI may_VM be_VBI very_RG visible_JJ to_II a_AT1 member_NN1 '_NULL s_ZZ1 friends_NN2 and_CC family_NN1 )_) ._. 
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<s>
Several_DA2 possible_JJ directions_NN2 exist_VV0 for_IF future_JJ research_NN1 in_II this_DD1 area_NN1 ._. 
</s>
<s>
The_AT most_RGT prominent_JJ approach_NN1 is_VBZ to_TO use_VVI Markov_NP1 chain_NN1 Monte_NP1 Carlo_NP1 (_( MCMC_NP1 )_) ,_, in_II which_DDQ a_AT1 Markov_NP1 chain_NN1 that_CST has_VHZ as_CSA its_APPGE limiting_JJ distribution_NN1 is_VBZ simulated_VVN ._. 
</s>
<s>
Centrifuge_VV0 outputs_NN2 at_II sequence_NN1 level_NN1 ,_, thus_RR ,_, an_AT1 extra_JJ step_NN1 of_IO applying_VVG an_AT1 LCA_NN1 algorithm_NN1 for_IF non-unique_JJ matches_NN2 was_VBDZ necessary_JJ to_TO generate_VVI results_NN2 at_II assembly_NN1 and_CC taxonomic_JJ levels_NN2 ._. 
</s>
<s>
Catastrophe_NN1 risk_NN1 diversification_NN1 ,_, risk_NN1 securitization_NN1 ,_, and_CC government_NN1 interventions_NN2 complement_VV0 each_PPX221 other_PPX222 to_TO benefit_VVI insurers_NN2 and_CC long-run_JJ market_NN1 equilibrium_NN1 ._. 
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<s>
The_AT above_JJ problem_NN1 may_VM be_VBI particularly_RR acute_JJ for_IF RNA_NN1 viruses_NN2 (_( Baltimore_NP1 ,_, 1971_MC )_) ,_, which_DDQ typically_RR encode_VV0 large_JJ multidomain_NN1 proteins_NN2 (_( >1000_FO aa_NNU )_) (_( Das_FW and_CC Arnold_NP1 ,_, 2015_MC )_) ._. 
</s>
<s>
Important_JJ applications_NN2 and_CC developments_NN2 in_II the_AT general_JJ area_NN1 of_IO spatial_JJ statistics_NN ,_, under_II linear_JJ and/or_CC Gaussian_JJ assumptions_NN2 ,_, can_VM be_VBI found_VVN widely_RR ;_; see_VV0 ,_, for_REX21 example_REX22 ,_, Cressie_NP1 (_( 1993_MC )_) ,_, Basawa_NP1 (_( 1996a_FO ,_, b_ZZ1 )_) ,_, Guyon_NP1 (_( 1995_MC )_) and_CC Gelfand_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2010_MC )_) for_IF comprehensive_JJ reviews_NN2 ._. 
</s>
<s>
In_II section_NN1 ,_, we_PPIS2 map_VV0 the_AT Szilárd_NP1 engine_NN1 to_II a_AT1 system_NN1 of_IO non-interacting_JJ particles_NN2 in_II q_ZZ1 energy_NN1 levels_NN2 and_CC re-derive_VV0 this_DD1 connection_NN1 in_II a_AT1 broader_JJR framework_NN1 ._. 
</s>
<s>
However_RR ,_, when_CS p_ZZ1 ≈_NULL 0.5190_MC ,_, the_AT solutions_NN2 of_IO the_AT two_MC curves_NN2 are_VBR given_VVN by_II the_AT tangent_JJ point_NN1 ,_, giving_VVG rise_NN1 to_II a_AT1 discontinuous_JJ change_NN1 in_II both_RR tAG_VV0 and_CC tBG_NNU (_( Fig._NN1 2(f)_FO )_) ._. 
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<s>
However_RR ,_, this_DD1 algorithm_NN1 performed_VVD poorly_RR (_( see_VV0 Section_NN1 4_MC )_) and_CC often_RR got_VVN trapped_VVN in_II a_AT1 local_JJ mode_NN1 ,_, which_DDQ is_VBZ due_II21 to_II22 the_AT multimodality_NN1 issues_NN2 inherent_JJ in_II fitting_JJ mixture_NN1 models_NN2 in_II a_AT1 Bayesian_JJ setting_NN1 using_VVG MCMC_NP1 simulation_NN1 (_( see_VV0 Atchadé_NP1 and_CC others_NN2 ,_, 2011_MC ;_; Altekar_NP1 and_CC others_NN2 ,_, 2004_MC )_) ._. 
</s>
<s>
Thus_RR ,_, it_PPH1 is_VBZ easily_RR seen_VVN which_DDQ variables_NN2 contribute_VV0 to_II which_DDQ component_NN1 ._. 
</s>
<s>
This_DD1 variance-based_JJ global_JJ framework_NN1 also_RR allows_VVZ to_TO extend_VVI Karabey_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2014_MC )_) measures_NN2 of_IO factor_NN1 importance_NN1 through_II the_AT calculation_NN1 of_IO Sobol_NP1 '_NULL sensitivity_NN1 indices_NN2 (_( Sobol_NP1 '_NULL ,_, 1993_MC )_) and_CC to_TO integrate_VVI the_AT results_NN2 of_IO Haberman_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2011_MC )_) accounting_VVG for_IF the_AT distributions_NN2 assigned_VVN to_II the_AT risk_NN1 factors_NN2 ._. 
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<s>
These_DD2 properties_NN2 do_VD0 not_XX hold_VVI for_IF <equation>_FO ._. 
</s>
<s>
A_AT1 significant_JJ improvement_NN1 in_II the_AT accuracy_NN1 of_IO our_APPGE fitting_NN1 could_VM be_VBI obtained_VVN by_II increasing_VVG the_AT resolution_NN1 and_CC the_AT sampling_NN1 time_NNT1 of_IO data_NN acquisition_NN1 in_II future_JJ microgravity_NN1 experiments_NN2 ._. 
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<s>
Nodes_NN2 of_IO the_AT same_DA color_NN1 belong_VV0 to_II the_AT same_DA community_NN1 ._. 
</s>
<s>
Supplementary_JJ materials_NN2 for_IF this_DD1 article_NN1 are_VBR available_JJ online_JJ ._. 
</s>
<s>
Observing_VVG the_AT table_NN1 ,_, the_AT FM-MSSN_JJ model_NN1 provides_VVZ the_AT best_JJT overall_JJ fit_JJ as_CSA it_PPH1 corresponds_VVZ to_II a_AT1 solution_NN1 with_IW the_AT highest_JJT log-likelihood_JJ value_NN1 and_CC the_AT lowest_JJT BIC_NP1 score_NN1 ._. 
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<s>
The_AT results_NN2 for_IF the_AT Lasso_NN1 estimator_NN1 in_II Table_NN1 1_MC1 show_NN1 that_CST the_AT 10-fold_JJ cross-validation_JJ method_NN1 tends_VVZ to_TO select_VVI too_RG many_DA2 valid_JJ instruments_NN2 as_CSA invalid_JJ over_II and_CC above_II the_AT invalid_JJ ones_NN2 ,_, and_CC that_CST the_AT ad_JJ21 hoc_JJ22 one-standard_JJ error_NN1 rule_NN1 does_VDZ improve_VVI the_AT selection_NN1 ._. 
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<s>
The_AT red_JJ point_NN1 in_II Fig._NN1 1_MC1 may_VM indicate_VVI noise_NN1 in_II reported_JJ data_NN ,_, changes_NN2 in_II testing_VVG policy_NN1 ,_, responses_NN2 to_II some_DD extraneous_JJ phenomena_NN2 ,_, or_CC a_AT1 combination_NN1 of_IO two_MC temporarily_RR and_CC spatially_RR separated_JJ epidemic_NN1 waves_NN2 ._. 
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<s>
This_DD1 table_NN1 reports_NN2 OLS_VVZ estimates_NN2 of_IO equation_NN1 (_( 1_MC1 )_) ,_, where_CS the_AT dependent_JJ variable_NN1 is_VBZ the_AT high_JJ school_NN1 track_NN1 recommendation_NN1 of_IO teachers_NN2 ._. 
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<s>
In_II experiments_NN2 ,_, we_PPIS2 only_RR tuned_VVN parameters_NN2 in_II the_AT first_MD loop_NN1 where_CS the_AT first_MD fold_NN1 was_VBDZ used_VVN for_IF testing_VVG and_CC the_AT remaining_JJ folds_NN2 were_VBDR used_VVN for_IF training_NN1 ,_, and_CC these_DD2 tuned_VVN parameters_NN2 were_VBDR used_VVN for_IF all_DB experiments_NN2 to_TO generate_VVI final_JJ results_NN2 ._. 
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<s>
Specifically_RR ,_, we_PPIS2 normalize_VV0 the_AT importance_NN1 of_IO constituent_NN1 stocks_NN2 of_IO the_AT SSE_ND1 50_MC (_( 180_MC )_) Index_NN1 and_CC put_VV0 them_PPHO2 into_II the_AT calculation_NN1 formula_NN1 of_IO the_AT SSE_ND1 50_MC (_( 180_MC )_) Index_NN1 (_( See_VV0 Appendix_NN1 B_ZZ1 for_IF details_NN2 )_) ,_, which_DDQ can_VM roughly_RR reflect_VVI the_AT investment_NN1 level_NN1 of_IO the_AT equity_NN1 fund_NN1 ._. 
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<s>
Each_DD1 ROC_NN1 curve_NN1 was_VBDZ smoothed_VVN over_RG 10_MC replications_NN2 ._. 
</s>
<s>
Here_RL we_PPIS2 introduce_VV0 qi_NN2 ,_, which_DDQ is_VBZ the_AT probability_NN1 that_CST infinite_JJ messages_NN2 will_VM be_VBI received_VVN after_II user_NN1 i_ZZ1 generates_VVZ a_AT1 message_NN1 ,_, to_TO quantify_VVI the_AT user_NN1 influence_NN1 in_II the_AT duplicate_JJ forwarding_JJ model_NN1 when_CS p≥_FO ,_, and_CC try_VV0 to_TO calculate_VVI qi_NN2 in_II the_AT following_JJ ._. 
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<s>
Next_MD ,_, we_PPIS2 demonstrate_VV0 that_CST subspace_VV0 stability_NN1 selection_NN1 produces_VVZ a_AT1 tangent_JJ space_NN1 which_DDQ is_VBZ different_JJ and_CC usually_RR of_IO a_AT1 higher_JJR quality_NN1 (_( e.g._REX smaller_JJR expected_JJ false_JJ discovery_NN1 )_) than_CSN the_AT base_NN1 estimator_NN1 applied_VVN to_II the_AT full_JJ data_NN set_VV0 ._. 
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<s>
See_VV0 Carkovic_JJ and_CC Levine_NP1 (_( 2002_MC )_) ,_, Kim_NP1 (_( 2008_MC )_) ,_, Wu_NP1 and_CC Hsu_NP1 (_( 2008_MC )_) ,_, Felipe_NP1 and_CC McCombie_NP1 (_( 2017_MC )_) ._. 
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<s>
Some_DD probabilistic_JJ and_CC statistical_JJ properties_NN2 are_VBR also_RR derived_VVN ._. 
</s>
<s>
However_RR ,_, for_IF an_AT1 infinite_JJ lattice_NN1 the_AT component_NN1 k_ZZ1 Q2(t)_FO can_VM be_VBI shown_VVN to_TO diverge_VVI in_II the_AT limit_NN1 t_ZZ1 →_NULL ∞_FO and_CC thus_RR can_VM not_XX model_VVI a_AT1 physically_RR meaningful_JJ contribution_NN1 to_II the_AT system_NN1 '_NULL s_ZZ1 internal_JJ energy_NN1 ._. 
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<s>
Time_NNT1 evolution_NN1 of_IO these_DD2 dimensionless_JJ phase_NN1 space_NN1 variables_NN2 can_VM be_VBI cast_VVN into_II a_AT1 compact_JJ form_NN1 ,_, These_DD2 methods_NN2 are_VBR shown_VVN to_TO improve_VVI significantly_RR on_II Gaussian_JJ variational_JJ approximation_NN1 methods_NN2 for_IF a_AT1 similar_JJ computational_JJ cost_NN1 ._. 
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<s>
A_AT1 "_" time_NNT1 of_IO flight_NN1 "_" (_( ToF_NP1 )_) mechanism_NN1 ,_, adapted_VVN from_II the_AT pioneering_JJ idea_NN1 of_IO Galileo_NP1 ,_, has_VHZ been_VBN used_VVN successfully_RR very_RG recently_RR to_TO explain_VVI the_AT length_NN1 control_NN1 of_IO flagella_NN1 by_II a_AT1 biflagellate_NN1 green_JJ algae_NN2 ._. 
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<s>
In_BCL21 order_BCL22 to_TO choose_VVI the_AT weights_NN2 in_II a_AT1 given_JJ application_NN1 ,_, it_PPH1 would_VM be_VBI useful_JJ if_CS it_PPH1 were_VBDR possible_JJ to_TO interpret_VVI the_AT weights_NN2 in_II31 terms_II32 of_II33 the_AT relative_JJ importance_NN1 of_IO the_AT desirable_JJ characteristics_NN2 ._. 
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<s>
The_AT reader_NN1 can_VM easily_RR check_VVI that_DD1 for_IF t_ZZ1 <_FO 25_MC ,_, a_AT1 growth_NN1 is_VBZ a_AT1 constant_JJ ,_, satisfies_VVZ the_AT requirement_NN1 ._. 
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<s>
Generally_RR ,_, therefore_RR ,_, single-cell_JJ multi-omics_JJ data_NN do_VD0 not_XX have_VHI any_DD correspondences_NN2 ,_, either_RR among_II samples_NN2 (_( cells_NN2 )_) or_CC among_II features_NN2 ._. 
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<s>
In_II contrast_NN1 ,_, condition_NN1 1_MC1 is_VBZ necessary_JJ for_IF us_PPIO2 to_TO be_VBI able_JK to_TO construct_VVI QSMC_NP1 methods_NN2 ._. 
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<s>
These_DD2 values_NN2 imply_VV0 that_CST BCI_NP1 has_VHZ incremental_JJ OOS_NN2 predictive_JJ power_NN1 for_IF future_NN1 <equation>_FO and_CC <equation>_FO after_II using_VVG the_AT control_NN1 variables_NN2 ._. 
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<s>
Following_VVG Autor_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2017b_FO )_) ,_, Figure_NN1 IV_MC plots_NN2 the_AT sales-weighted_JJ average_JJ sales-_NN1 and_CC employment-based_NN1 CR4_FO and_CC CR20_FO measures_NN2 of_IO concentration_NN1 across_II four-digit_JJ industries_NN2 for_IF the_AT six_MC major_JJ sectors_NN2 using_VVG updated_JJ data_NN from_II the_AT census_NN1 ._. 
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<s>
In_II contrast_NN1 ,_, to_TO process_VVI adjacent_JJ large_JJ contigs_NN2 (_( e.g._REX >1_FO Mb_NNU in_II size_NN1 )_) ,_, contacts_NN2 between_II the_AT two_MC contigs_NN2 would_VM be_VBI sufficient_JJ ._. 
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<s>
The_AT results_NN2 of_IO the_AT estimation_NN1 are_VBR shown_VVN in_II Table_NN1 4_MC ,_, Figs._NN2 9_MC ,_, and_CC 10_MC ._. 
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<s>
Using_VVG microdata_NN1 on_II the_AT performance_NN1 of_IO sales_NN workers_NN2 at_II 131_MC firms_NN2 ,_, we_PPIS2 find_VV0 evidence_NN1 consistent_JJ with_IW the_AT Peter_NP1 Principle_NN1 ,_, which_DDQ proposes_VVZ that_CST firms_NN2 prioritize_VV0 current_JJ job_NN1 performance_NN1 in_II promotion_NN1 decisions_NN2 at_II the_AT expense_NN1 of_IO other_JJ observable_JJ characteristics_NN2 that_DD1 better_RRR predict_VVI managerial_JJ performance_NN1 ._. 
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<s>
We_PPIS2 used_VVD a_AT1 disease–disease_NN1 network_NN1 from_II Menche_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2015_MC )_) with_IW 299_MC nodes_NN2 (_( diseases_NN2 )_) ,_, created_VVD based_VVN on_II human_JJ interactome_NN1 data_NN (_( as_CSA detailed_VVN earlier_RRR )_) ,_, gene_NN1 expression_NN1 data_NN (_( Su_NP1 et_RA21 al._RA22 ,_, 2004_MC )_) ,_, disease–gene_NN1 associations_NN2 (_( Hamosh_NP1 et_RA21 al._RA22 ,_, 2005_MC ;_; Mottaz_NP1 et_RA21 al._RA22 ,_, 2008_MC ;_; Ramos_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) ,_, GO_VV0 (_( Ashburner_NP1 et_RA21 al._RA22 ,_, 2000_MC )_) ,_, symptom_NN1 similarity_NN1 (_( Zhou_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) and_CC comorbidity_NN1 (_( Hidalgo_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ._. 
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<s>
In_II practice_NN1 ,_, the_AT LLSA_NN1 is_VBZ reliable_JJ and_CC can_VM be_VBI applied_VVN to_II a_AT1 large_JJ variety_NN1 of_IO settings_NN2 ,_, such_II21 as_II22 price_NN1 forecasting_VVG ,_, portfolio_NN1 selection_NN1 ,_, and_CC risk_NN1 management_NN1 ,_, and_CC especially_RR it_PPH1 can_VM be_VBI combined_VVN with_IW other_JJ models_NN2 or_CC methods_NN2 ._. 
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<s>
This_DD1 is_VBZ similar_JJ to_II the_AT specification_NN1 of_IO the_AT survival_NN1 process_NN1 of_IO a_AT1 firm_NN1 ,_, but_CCB we_PPIS2 do_VD0 not_XX require_VVI that_CST <equation>_FO is_VBZ nonincreasing_VVG ._. 
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<s>
Our_APPGE results_NN2 show_VV0 that_CST different_JJ types_NN2 of_IO randomization_NN1 that_CST could_VM be_VBI present_JJ during_II pattern_NN1 generation_NN1 lower_VV0 the_AT inference_NN1 capabilities_NN2 in_II very_RG different_JJ ways_NN2 ._. 
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<s>
The_AT insurer_NN1 can_VM subscribe_VVI a_AT1 generic_JJ reinsurance_NN1 contract_NN1 with_IW retention_NN1 level_NN1 u∈_FO &lsqb;_( 0_MC ,_, I_ZZ1 &rsqb;_) ,_, where_CS I>0_FO (_( eventually_RR I=+∞_FO )_) ,_, transferring_VVG part_NN1 of_IO her_APPGE risks_NN2 to_II the_AT reinsurer_NN1 ._. 
</s>
<s>
This_DD1 suggests_VVZ that_CST the_AT autoregressive_JJ sieve_NN1 bootstrap_NN1 is_VBZ likely_JJ to_TO yield_VVI reasonably_RR good_JJ approximations_NN2 within_II a_AT1 class_NN1 of_IO processes_NN2 larger_JJR than_CSN that_DD1 associated_VVN with_IW (_( 1_MC1 )_) or_CC (_( 6_MC )_) ._. 
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<s>
Alternatively_RR ,_, the_AT null_JJ hypothesis_NN1 of_IO no_AT pleiotropy_NN1 can_VM be_VBI tested_VVN by_II simultaneously_RR testing_VVG <equation>_FO (_( i.e._REX ,_, no_AT associated_JJ traits_NN2 )_) and_CC testing_VVG the_AT null_JJ hypotheses_NN2 that_CST only_RR one_MC1 <equation>_FO holds_VVZ for_IF <equation>_FO (_( i.e_REX ,_, only_RR one_MC1 associated_JJ trait_NN1 )_) ._. 
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<s>
In_II the_AT velocity_NN1 space_NN1 transport_NN1 ,_, the_AT momentum_NN1 exchange_NN1 and_CC the_AT energy_NN1 exchange_NN1 correspond_VV0 to_II the_AT different_JJ Coulomb_NN1 cross_NN1 sections_NN2 ,_, respectively_RR &lsqb;_( 2_MC &rsqb;_) ._. 
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<s>
This_DD1 was_VBDZ a_AT1 future_NN1 on_II an_AT1 index_NN1 built_VVN of_IO catastrophic_JJ losses_NN2 of_IO certain_JJ insurance_NN1 companies_NN2 from_II catastrophes_NN2 in_II a_AT1 determined_JJ period_NN1 reported_VVN to_II the_AT insurer_NN1 until_CS a_AT1 given_JJ deadline_NN1 ._. 
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<s>
But_CCB ICVARIF_NP1 performs_VVZ better_JJR than_CSN TVICVARIF_NP1 ._. 
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<s>
Croux_VV0 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2012_MC ,_, p._NN1 33_MC )_) suggest_VV0 using_VVG c=1.345_FO for_IF both_DB2 estimating_VVG equations_NN2 for_IF the_AT mean_JJ and_CC the_AT dispersion_NN1 ,_, borrowing_VVG from_II the_AT Gaussian_JJ regression_NN1 setting_NN1 and_CC stating_VVG that_CST "_" this_DD1 value_NN1 gives_VVZ reasonable_JJ results_NN2 for_IF other_JJ models_NN2 as_RR21 well_RR22 "_" ._. 
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<s>
Normally_RR ,_, nothing_PN1 happens_VVZ in_II none_PN of_IO the_AT cohorts_NN2 ._. 
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<s>
This_DD1 can_VM yield_VVI final_JJ direct_JJ evidence_NN1 ,_, as_RG well_RR as_CSA suggests_VVZ more_RGR sophisticated_JJ solutions_NN2 to_II the_AT problem_NN1 ._. 
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<s>
Our_APPGE approach_NN1 is_VBZ based_VVN on_II a_AT1 penalisation_NN1 method_NN1 ;_; we_PPIS2 show_VV0 that_CST the_AT solution_NN1 to_II the_AT liquidation_NN1 problem_NN1 can_VM be_VBI approximated_VVN by_II a_AT1 sequence_NN1 of_IO solutions_NN2 to_II unconstrained_JJ problems_NN2 ,_, where_CS the_AT terminal_JJ state_NN1 constraint_NN1 is_VBZ replaced_VVN by_II an_AT1 increased_JJ penalisation_NN1 of_IO open_JJ positions_NN2 at_II the_AT terminal_JJ time_NNT1 ._. 
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<s>
On_II each_DD1 graph_NN1 ,_, the_AT shaded_JJ area_NN1 indicates_VVZ the_AT integral_JJ of_IO V_ZZ1 '_NULL (_( x_ZZ1 )_) over_II the_AT interval_NN1 &lsqb;_( X(z)_NP1 ,_, X(z)_NP1 +_FO z_ZZ1 &rsqb;_) ._. 
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<s>
In_II other_JJ words_NN2 ,_, it_PPH1 becomes_VVZ possible_JJ to_TO answer_VVI the_AT question_NN1 of_IO whether_CSW labor-market_JJ developments_NN2 among_II those_DD2 employed_VVN in_II the_AT security-guard_JJ industry_NN1 may_VM attest_VVI to_II something_PN1 unique_JJ about_II this_DD1 sector_NN1 as_II21 against_II22 all_DB others_NN2 ,_, irrespective_II21 of_II22 time_NNT1 ._. 
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<s>
There_EX were_VBDR three_MC unavoidable_JJ changes_NN2 to_II the_AT main_JJ protocol_NN1 between_II wave_NN1 1_MC1 and_CC wave_NN1 2_MC ._. 
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<s>
The_AT results_NN2 reported_VVN in_II Columns_NN2 1_MC1 and_CC 2_MC indicate_VV0 that_CST HY-NEIO_NP1 positively_RR predicts_VVZ future_JJ discount_NN1 rate_NN1 changes_NN2 ,_, even_RR after_II controlling_VVG for_IF lagged_JJ monetary_JJ policy_NN1 changes_NN2 and_CC other_JJ control_NN1 variables_NN2 ._. 
</s>
<s>
We_PPIS2 simulated_VVD the_AT following_JJ five_MC missing_JJ data_NN mechanisms_NN2 for_IF this_DD1 situation_NN1 :_: MCAR_NP1 ,_, MAR_VV0 ,_, MNAR_NP1 ,_, MARY_NP1 ,_, and_CC MNARY_NP1 ._. 
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<s>
We_PPIS2 consider_VV0 additional_JJ simulation_NN1 settings_NN2 with_IW correlated_JJ (_( Appendix_NN1 B.1_FO )_) and_CC higher-dimensional_JJR (_( Appendix_NN1 B.2_FO )_) covariates_VVZ in_II the_AT online_JJ supplement_NN1 ._. 
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<s>
We_PPIS2 present_VV0 a_AT1 high-dimensional_JJ changepoint_NN1 detection_NN1 method_NN1 that_CST takes_VVZ inspiration_NN1 from_II geometry_NN1 to_II map_NN1 a_AT1 high-dimensional_JJ time_NNT1 series_NN to_II two_MC dimensions_NN2 ._. 
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<s>
Hamiltonian_JJ type_NN1 SDEs_NN2 have_VH0 been_VBN investigated_VVN in_II molecular_JJ dynamics_NN ,_, where_CS they_PPHS2 are_VBR typically_RR referred_VVN to_II as_CSA Langevin_NP1 equations_NN2 ;_; see_VV0 ,_, e.g._REX Leimkuhler_NP1 and_CC Matthews_NP1 (_( 2015_MC )_) ._. 
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<s>
To_II this_DD1 end_NN1 ,_, it_PPH1 is_VBZ important_JJ to_TO discuss_VVI the_AT symmetries_NN2 of_IO the_AT model_NN1 ._. 
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<s>
The_AT performance_NN1 of_IO the_AT <equation>_FO though_CS is_VBZ somewhat_RR exceptional_JJ in_II that_DD1 ,_, although_CS generally_RR being_VBG quite_RG powerful_JJ ,_, its_APPGE power_NN1 is_VBZ not_XX monotonic_JJ with_II31 respect_II32 to_II33 the_AT shape_NN1 parameter_NN1 ._. 
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<s>
Additive_JJ noise_NN1 is_VBZ the_AT internal_JJ fluctuations_NN2 ,_, and_CC its_APPGE origin_NN1 is_VBZ the_AT active_JJ nature_NN1 of_IO the_AT system_NN1 ._. 
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<s>
Such_DA factors_NN2 would_VM be_VBI unspanned_JJ by_II the_AT term_NN1 structures_NN2 of_IO defaultable_JJ bonds_NN2 and_CC CDS_NN2 and_CC give_VV0 rise_NN1 to_II unspanned_JJ stochastic_JJ volatility_NN1 ,_, as_CSA described_VVN in_II Filipovi_NP1 et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 25_MC &rsqb;_) ._. 
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These_DD2 models_NN2 provide_VV0 useful_JJ guidelines_NN2 and_CC have_VH0 shown_VVN consistency_NN1 with_IW their_APPGE observed_JJ data_NN ._. 
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<s>
Applying_VVG the_AT same_DA reasoning_NN1 as_CSA Pástor_NN1 et_RA21 al_RA22 ._. 
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<s>
(_( 2017_MC )_) ,_, we_PPIS2 expect_VV0 the_AT turnover-performance_JJ relation_NN1 to_TO be_VBI stronger_JJR for_IF less-liquid_JJ portfolios_NN2 ._. 
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Figure_NN1 D.4_FO in_II the_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR ._. 
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<s>
Quantum_NN1 clock_NN1 models_NN2 have_VH0 recently_RR attracted_VVN a_AT1 strong_JJ interest_NN1 ._. 
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The_AT main_JJ results_NN2 are_VBR the_AT following_JJ :_: (_( i_ZZ1 )_) an_AT1 overall_JJ convergence_NN1 process_NN1 has_VHZ been_VBN at_II work_NN1 among_II advanced_JJ countries_NN2 ,_, mainly_RR after_II WWII_NN1 ,_, first_MD through_II capital_NN1 intensity_NN1 and_CC then_RT through_II TFP_NP1 ,_, while_CS trends_NN2 in_II hours_NNT2 worked_VVN and_CC even_RR more_RGR so_RR employment_NN1 rates_NN2 are_VBR more_RGR disparate_JJ ;_; (_( ii_MC )_) however_RR ,_, this_DD1 convergence_NN1 process_NN1 is_VBZ not_XX continuous_JJ ._. 
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<s>
An_AT1 alternative_JJ dimension_NN1 reduction_NN1 method_NN1 is_VBZ the_AT factor_NN1 model_NN1 ,_, which_DDQ summarizes_VVZ the_AT information_NN1 in_II a_AT1 high-dimensional_JJ set_NN1 of_IO explanatory_JJ variables_NN2 by_II lower-dimensional_JJR latent_JJ (_( unobservable_JJ )_) common_JJ factors_NN2 ._. 
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Classifying_VVG stock_NN1 markets_NN2 by_II measuring_VVG the_AT similarity_NN1 between_II them_PPHO2 can_VM provide_VVI a_AT1 reliable_JJ reference_NN1 for_IF investors_NN2 and_CC help_VV0 them_PPHO2 earn_VVI more_DAR profits_NN2 ._. 
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<s>
A_AT1 covenant_NN1 violation_NN1 occurs_VVZ when_RRQ a_AT1 firms_NN2 reports_VVZ a_AT1 covenant_NN1 violation_NN1 in_II a_AT1 SEC_NP1 10-K_NP1 or_CC 10-Q_JJ filing_NN1 in_II the_AT current_JJ but_CCB not_XX in_II the_AT previous_JJ year_NNT1 ._. 
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Echoing_VVG the_AT findings_NN2 in_II manufacturing_NN1 ,_, we_PPIS2 find_VV0 that_CST the_AT between-survivor_JJ reallocation_NN1 effect_NN1 contributes_VVZ to_II the_AT decline_NN1 in_II the_AT payroll_NN1 share_NN1 in_II each_DD1 of_IO the_AT other_JJ five_MC sectors_NN2 ._. 
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The_AT bank_NN1 can_VM make_VVI up_RP for_IF the_AT loss_NN1 by_II borrowing_NN1 and_CC other_JJ investment_NN1 returns_NN2 ._. 
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<s>
Within_II the_AT linear_JJ framework_NN1 ,_, we_PPIS2 define_VV0 the_AT linear_JJ hypercube_NN1 (_( LHC_NP1 )_) model_NN1 which_DDQ is_VBZ a_AT1 single-name_JJ model_NN1 ._. 
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<s>
The_AT processes_NN2 we_PPIS2 identified_VVD play_VV0 a_AT1 role_NN1 in_II the_AT immune_JJ system_NN1 ,_, mitochondrial_JJ respiration_NN1 ,_, translation_NN1 initiation_NN1 ,_, chromosome_NN1 segregation_NN1 ,_, intracellular_JJ signaling_NN1 ,_, protein_NN1 transport_NN1 and_CC muscle_NN1 contraction_NN1 ._. 
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<s>
For_IF each_DD1 of_IO the_AT simulations_NN2 ,_, UnionCom_NP1 integrates_VVZ the_AT two_MC datasets_NN2 with_IW well-aligned_JJ geometrical_JJ structures_NN2 (_( see_VV0 upper_JJ right_JJ panels_NN2 of_IO Fig._NN1 2a_FO and_CC b_ZZ1 )_) and_CC well-matched_JJ branches_NN2 (_( see_VV0 lower_JJR right_NN1 panels_NN2 of_IO Fig._NN1 2a_FO and_CC b_ZZ1 )_) ._. 
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By_II measuring_VVG these_DD2 shadow_NN1 prices_NN2 of_IO raising_VVG revenue_NN1 from_II different_JJ groups_NN2 ,_, the_AT MVPF_NP1 provides_VVZ a_AT1 unified_JJ method_NN1 of_IO welfare_NN1 analysis_NN1 that_CST can_VM be_VBI applied_VVN both_RR across_RL and_CC within_II diverse_JJ policy_NN1 domains_NN2 ._. 
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<s>
With_IW g_ZZ1 computed_VVN as_CSA in_II Eq_NN1 ._. 
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(_( 37_MC )_) ,_, we_PPIS2 estimate_VV0 the_AT regression_NN1 corresponding_VVG to_II Eq_NN1 ._. 
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(_( 36_MC )_) ._. 
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<s>
We_PPIS2 observe_VV0 similarities_NN2 between_II clones_NN2 in_II the_AT discretized_JJ reconstruction_NN1 of_IO Ling_NN1 et_RA21 al_RA22 ._. 
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<s>
(_( 2015_MC )_) '_NULL s_ZZ1 figure_NN1 (_( Fig._NN1 4a_FO )_) and_CC the_AT spatial_JJ plot_NN1 with_IW real_JJ frequencies_NN2 ;_; namely_REX ,_, mutation_NN1 clusters_NN2 containing_VVG MUC16_FO ,_, MLL_NP1 and_CC CHUK_NP1 ,_, and_CC RIMS2_FO appear_VV0 in_II similar_JJ regions_NN2 of_IO the_AT grid_NN1 ._. 
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<s>
We_PPIS2 also_RR observe_VV0 that_CST in_II both_DB2 regimes_NN2 ,_, the_AT value_NN1 of_IO exponent_NN1 z_ZZ1 grows_VVZ with_IW the_AT number_NN1 of_IO habitats_NN2 and_CC then_RT drops_VVZ when_RRQ the_AT number_NN1 of_IO habitats_NN2 becomes_VVZ large_JJ (_( see_VV0 Table_NN1 1_MC1 ,_, Table_NN1 2_MC ,_, Table_NN1 3_MC )_) ._. 
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<s>
Firstly_RR ,_, we_PPIS2 discuss_VV0 the_AT transmission_NN1 coefficient_NN1 T_ZZ1 which_DDQ depends_VVZ on_II the_AT element_NN1 M22_FO of_IO the_AT transfer_NN1 matrix_NN1 and_CC no_AT phase_NN1 consideration_NN1 is_VBZ necessary_JJ ._. 
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<s>
Moreover_RR ,_, the_AT percentage_NN1 of_IO trucks_NN2 and_CC truck_NN1 impact_NN1 have_VH0 a_AT1 significant_JJ influence_NN1 on_II the_AT fundamental_JJ diagram_NN1 ,_, congestion_NN1 rate_NN1 ,_, lane-changing_JJ rate_NN1 and_CC traffic_NN1 stability_NN1 ._. 
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<s>
Bernoulli_NN2 random_JJ variables_NN2 with_IW parameter_NN1 <equation>_FO ,_, independent_JJ of_IO <equation>_FO and_CC <equation>_FO ._. 
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<s>
It_PPH1 is_VBZ plain_JJ to_TO check_VVI that_CST the_AT supremum_NN1 is_VBZ attained_VVN for_IF <equation>_FO ._. 
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<s>
It_PPH1 should_VM be_VBI noticed_VVN that_CST fewer_DAR predictable_JJ nodes_NN2 do_VD0 not_XX necessarily_RR mean_VVI higher_JJR accuracy_NN1 ._. 
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<s>
First_MD ,_, actuarial_JJ pricing_NN1 of_IO the_AT residual_JJ risk_NN1 remaining_VVG after_II conditioning_NN1 on_II the_AT future_JJ development_NN1 of_IO prices_NN2 of_IO traded_JJ assets_NN2 is_VBZ done_VDN ._. 
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<s>
These_DD2 issuance_NN1 costs_NN2 include_VV0 underwriting_NN1 fees_NN2 and_CC dilution_NN1 costs_VVZ to_II shareholders_NN2 due_II21 to_II22 asymmetric_JJ information_NN1 ._. 
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The_AT Markov_NP1 chain_NN1 approximation_NN1 method_NN1 locates_VVZ the_AT initial_NN1 guesses_VVZ with_IW coarse_JJ scale_NN1 ._. 
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<s>
To_TO make_VVI the_AT comparison_NN1 of_IO mmcollapse_NN1 and_CC terminus_NN1 as_RG consistent_JJ as_CSA possible_JJ ,_, we_PPIS2 have_VH0 used_VVN Salmon-produced_JJ BAM_NN1 files_NN2 for_IF running_VVG the_AT mmcollapse_NN1 pipeline_NN1 ._. 
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<s>
The_AT absolute_JJ bias_NN1 and_CC MSE_NN1 of_IO <equation>_FO are_VBR both_RR smaller_JJR than_CSN those_DD2 of_IO <equation>_FO ._. 
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<s>
For_IF every_AT1 initialising_NN1 pair<equation>_FO ,_, any_DD convergent_JJ subsequence_NN1 produced_VVN by_II the_AT algorithm_NN1 of_IO (_( 4.6_MC )_) converges_VVZ to_II some_DD stationary_JJ point_NN1 of_IO ._. 
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<s>
Setting_VVG max=0_FO ,_, the_AT basic_JJ reproduction_NN1 number_NN1 becomes_VVZ :_: <equation>_FO ._. 
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<s>
Essentially_RR ,_, then_RT ,_, the_AT investor_NN1 can_VM ignore_VVI the_AT presence_NN1 of_IO the_AT liquid_JJ risky_JJ asset_NN1 ,_, reducing_VVG the_AT dimensionality_NN1 of_IO the_AT problem_NN1 ._. 
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<s>
And_CC ,_, for_IF the_AT restricted_JJ group_NN1 ,_, G(M1)=8542725_FO ,_, P(M1)=7917319_FO ,_, and_CC G(M2)=739435_FO ,_, P(M2)=2247120_FO ._. 
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<s>
Industry_NN1 is_VBZ estimated_VVN contemporaneously_RR using_VVG the_AT ten_MC industry_NN1 classification_NN1 from_II Fama_NP1 and_CC French_NN1 ._. 
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<s>
However_RR ,_, the_AT design_NN1 was_VBDZ also_RR found_VVN to_TO provide_VVI benefits_NN2 in_II the_AT setting_NN1 of_IO phase_NN1 I_ZZ1 clinical_JJ trials_NN2 seeking_VVG to_TO select_VVI the_AT maximum_NN1 tolerated_VVD dose_NN1 (_( i.e._REX the_AT target_NN1 probability_NN1 γ_NULL is_VBZ the_AT toxicity_NN1 probability_NN1 at_II the_AT maximum_NN1 tolerated_VVD dose_NN1 )_) ,_, particularly_RR when_CS the_AT assumption_NN1 of_IO monotonicity_NN1 is_VBZ questionable_JJ ._. 
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<s>
Plug-and-play_JJ SMC_NN1 techniques_NN2 have_VH0 been_VBN central_JJ to_II solving_VVG the_AT other_JJ five_MC challenges_NN2 of_IO Bj?rnstad_NP1 and_CC Grenfell_NP1 (_( 2001_MC )_) ,_, all_DB of_IO which_DDQ can_VM be_VBI represented_VVN in_II the_AT framework_NN1 of_IO inference_NN1 for_IF low-dimensional_JJ nonlinear_JJ non-Gaussian_JJ POMP_NN1 models_NN2 ._. 
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<s>
In_II this_DD1 paper_NN1 we_PPIS2 propose_VV0 a_AT1 generalization_NN1 of_IO the_AT FD_NP1 ,_, called_VVN the_AT extended_JJ flexible_JJ Dirichlet_NN1 (_( EFD_NP1 )_) ,_, aimed_VVN at_II coping_VVG with_IW the_AT above_JJ issues_NN2 ._. 
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This_DD1 figure_NN1 plots_NN2 the_AT aggregate_JJ labor_NN1 share_NN1 in_II manufacturing_NN1 from_II 1982_MC to_II 2012_MC ._. 
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<s>
We_PPIS2 next_MD compare_VV0 the_AT proposed_JJ new_JJ dataadaptive_JJ methods_NN2 with_IW other_JJ techniques_NN2 in_II31 terms_II32 of_II33 change_NN1 point_NN1 detection_NN1 ._. 
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<s>
For_IF Bordogna_NP1 and_CC Albano_NP1 &lsqb;_( 21_MC &rsqb;_) ,_, knowledge_NN1 increases_VVZ over_II time_NNT1 and_CC is_VBZ assumed_VVN to_TO be_VBI discrete_JJ ._. 
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<s>
We_PPIS2 used_VVD a_AT1 reconstruction_NN1 error_NN1 with_IW RMSE_NN1 as_II an_AT1 objective_JJ function_NN1 for_IF our_APPGE model_NN1 ._. 
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<s>
This_DD1 finding_NN1 suggests_VVZ that_DD1 business_NN1 confidence_NN1 innovations_NN2 clearly_RR convey_VV0 important_JJ information_NN1 about_II the_AT future_JJ paths_NN2 of_IO investment_NN1 growth_NN1 ,_, most_RGT notably_RR at_II shorter_JJR horizons_NN2 ._. 
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<s>
Recapitalizing_VVG the_AT bank_NN1 by_II selling_VVG some_DD of_IO the_AT assets_NN2 at_II a_AT1 discount_NN1 is_VBZ feasible_JJ if_CS only_RR if_CS δ_NULL >_FO 0_MC ,_, which_DDQ implies_VVZ the_AT following_JJ restriction_NN1 on_II the_AT fire_NN1 sale_NN1 discount_NN1 :_: <equation>_FO ._. 
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<s>
Similarly_RR ,_, a_AT1 GI_NN1 index_NN1 is_VBZ defined_VVN for_IF multinomial_JJ outcomes_NN2 (_( Glazebrook_NP1 ,_, 1978_MC )_) that_CST could_VM be_VBI an_AT1 alternative_JJ approach_NN1 for_IF the_AT problem_NN1 with_IW coprimary_JJ outcome_NN1 studied_VVN in_II Section_NN1 5_MC ._. 
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<s>
Then_RT ,_, we_PPIS2 decrease_VV0 γ_NULL 0_MC by_II a_AT1 small_JJ amount_NN1 and_CC run_VV0 rVAMP_NN1 until_CS convergence_NN1 ._. 
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Although_CS promising_JJ ,_, HBA_NP1 needs_VVZ improvements_NN2 on_II convergence_NN1 at_II late_JJ stages_NN2 for_IF optimality_NN1 proof_NN1 ._. 
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The_AT optimal_JJ set_NN1 of_IO tuning_VVG parameters_NN2 is_VBZ then_RT determined_VVN based_VVN on_II the_AT information_NN1 criterion_NN1 (_( AIC_NP1 ,_, BIC_NP1 ,_, or_CC AICc_NP1 )_) ._. 
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Nodes_NN2 connected_VVN by_II these_DD2 new_JJ edges_NN2 can_VM be_VBI either_RR newly_RR added_VVN or_CC existing_JJ ones_NN2 in_II both_DB2 networks_NN2 ._. 
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We_PPIS2 generated_VVD data_NN sets_VVZ under_RG two_MC simulation_NN1 scenarios_NN2 ._. 
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<s>
As_II a_AT1 result_NN1 ,_, there_EX is_VBZ seemingly_RR no_AT more_RGR simple_JJ rule_NN1 of_IO thumb_NN1 as_II21 to_II22 how_RRQ the_AT risk_NN1 capital_NN1 allocation_NN1 values_NN2 shape_VV0 up_RP when_CS the_AT PH-MBR_JJ portfolios_NN2 are_VBR considered_VVN ._. 
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<s>
In_II words_NN2 ,_, the_AT complete_JJ information_NN1 allows_VVZ the_AT insurer_NN1 to_TO improve_VVI her_APPGE result_NN1 ._. 
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<s>
Hence_RR <equation>_FO is_VBZ the_AT number_NN1 of_IO asymptotically_RR dominant_JJ objects_NN2 with_IW the_AT minimum_JJ tail_NN1 parameter_NN1 <equation>_FO ._. 
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<s>
This_DD1 allows_VVZ an_AT1 interpretation_NN1 of_IO the_AT topics_NN2 in_II31 terms_II32 of_II33 the_AT raw_JJ data_NN ,_, and_CC the_AT display_NN1 reinforces_VVZ the_AT findings_NN2 of_IO Figure_NN1 3_MC and_CC Figure_NN1 12_MC of_IO supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR ._. 
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For_REX21 example_REX22 ,_, when_CS Chen_NP1 and_CC Cox_NP1 (_( 2009_MC )_) used_VVD their_APPGE extended_JJ Lee–Carter_NN1 model_NN1 with_IW transitory_JJ jump_NN1 effects_NN2 to_TO price_VVI a_AT1 mortality_NN1 bond_NN1 ,_, they_PPHS2 were_VBDR required_VVN to_TO estimate_VVI three_MC parameters_NN2 in_II the_AT Wang_NP1 transform_VV0 ._. 
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<s>
Let_VV0 us_PPIO2 now_RT focus_VVI on_II conditionals_NN2 ._. 
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<s>
In_II our_APPGE sample_NN1 ,_, about_RG 57%_NNU of_IO participants_NN2 received_VVD transfers_NN2 for_IF the_AT second_MD benefit_NN1 period_NN1 ._. 
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<s>
Furthermore_RR ,_, (_( 0_MC ,_, )_) can_VM capture_VVI the_AT alternative_JJ pattern_NN1 by_II adopting_VVG the_AT (_( 0_MC ,_, )_) norm_NN1 ._. 
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However_RR ,_, most_DAT of_IO the_AT above_JJ methods_NN2 fail_VV0 on_RP non-normally_RR distributed_VVN or_CC heteroskedastic_JJ data_NN ._. 
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<s>
The_AT statistical_JJ effectiveness_NN1 of_IO the_AT sticky_JJ regions_NN2 is_VBZ presented_VVN in_II the_AT probability_NN1 distributions_NN2 obtained_VVN for_IF the_AT z_ZZ1 >_FO 1_MC1 systems_NN2 ,_, i.e._REX especially_RR for_IF the_AT (_( K_ZZ1 =_FO 0.2_MC ,_, z_ZZ1 =_FO 5_MC )_) case_NN1 which_DDQ is_VBZ explained_VVN in_II detail_NN1 below_RL ._. 
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In_II the_AT same_DA table_NN1 ,_, we_PPIS2 replicate_VV0 the_AT exercise_NN1 for_IF nonpolluting_VVG firms_NN2 and_CC find_VV0 that_CST the_AT estimated_JJ RD_NN1 coefficient_NN1 fluctuates_VVZ around_RG zero_MC and_CC is_VBZ not_XX statistically_RR significant_JJ in_II any_DD year_NNT1 ._. 
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It_PPH1 is_VBZ clear_JJ that_CST this_DD1 is_VBZ the_AT reason_NN1 for_IF the_AT appearance_NN1 of_IO two_MC modes_NN2 in_II the_AT distributions_NN2 in_II the_AT lower_JJR panels_NN2 of_IO Fig._NN1 10_MC ._. 
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Therefore_RR ,_, the_AT Eq_NN1 ._. 
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(_( iii_MC )_) is_VBZ true_JJ as_CS31 long_CS32 as_CS33 Tr2Det>0_FO ,_, the_AT solution_NN1 is<equation>.In_FO a_AT1 nutshell_NN1 ,_, E_ZZ1 is_VBZ locally_RR stable_JJ if_CS adjustment_NN1 speeds_NN2 of_IO two_MC airlines_NN2 satisfy_VV0 the_AT stability_NN1 condition_NN1 that(20)<equation>_FO ._. 
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<s>
We_PPIS2 demonstrate_VV0 the_AT sampler_NN1 '_NULL s_ZZ1 performance_NN1 via_II two_MC simulated_JJ examples_NN2 ,_, and_CC a_AT1 real_JJ analysis_NN1 of_IO Airbnb_NP1 rental_NN1 prices_NN2 using_VVG a_AT1 intractable_JJ high-dimensional_JJ multivariate_JJ nonlinear_JJ state-space_JJ model_NN1 with_IW a_AT1 36-dimensional_JJ latent_JJ state_NN1 observed_VVN on_II 365_MC time_NNT1 points_NN2 ,_, which_DDQ presents_VVZ a_AT1 real_JJ challenge_NN1 to_II standard_JJ ABC_NN1 techniques_NN2 ._. 
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This_DD1 article_NN1 presents_VVZ a_AT1 novel_JJ Laplace-based_JJ algorithm_NN1 that_CST can_VM be_VBI used_VVN to_TO find_VVI Bayesian_JJ adaptive_JJ designs_NN2 under_II model_NN1 and_CC parameter_NN1 uncertainty_NN1 ._. 
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Admittedly_RR ,_, the_AT fact_NN1 that_CST the_AT job_NN1 market_NN1 suddenly_RR shrunk_VVN in_II 2000_MC could_VM contribute_VVI to_TO alter_VVI individual_JJ preferences_NN2 to_TO choose_VVI an_AT1 academic_JJ job_NN1 ,_, particularly_RR for_IF those_DD2 graduates_NN2 in_II fields_NN2 with_IW more_DAR connection_NN1 to_II industry_NN1 ._. 
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In_II sum_NN1 ,_, this_DD1 analysis_NN1 shows_VVZ that_CST most_DAT of_IO the_AT theories_NN2 affect_VV0 government_NN1 expenditure_NN1 directly_RR as_II31 well_II32 as_II33 indirectly_RR ._. 
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<s>
In_II Sect._NP1 2_MC ,_, we_PPIS2 introduce_VV0 the_AT class_NN1 of_IO affine_JJ forward_JJ variance_NN1 models_NN2 and_CC show_VV0 that_CST a_AT1 forward_JJ variance_NN1 model_NN1 has_VHZ an_AT1 affine_JJ cumulant-generating_JJ function_NN1 (_( CGF_NP1 )_) if_CS and_CC only_RR if_CS it_PPH1 can_VM be_VBI written_VVN in_II a_AT1 very_RG specific_JJ form_NN1 ._. 
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We_PPIS2 add_VV0 industry_NN1 fixed_JJ effects_NN2 in_II column_NN1 2_MC and_CC various_JJ controls_NN2 in_II columns_NN2 3_MC through_II 5_MC ._. 
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Simulated_JJ series_NN SIMPASS_VV0 and_CC DISC_NN1 are_VBR investigated_VVN in_II Sect5_FO ._. 
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We_PPIS2 try_VV0 to_TO locate_VVI the_AT position_NN1 of_IO the_AT crossover_NN1 points_NN2 and_CC percolation_NN1 thresholds_NN2 of_IO both_DB2 network_NN1 AG_FO and_CC network_NN1 BG_NP1 in_II the_AT following_JJ ._. 
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It_PPH1 is_VBZ however_RR not_XX invariant_JJ under_II permutation_NN1 of_IO both_DB2 axes_NN2 ._. 
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Conditionally_RR to_II 1_MC1 ,_, Yx1_FO ,_, Yxn_NP1 ,_, the_AT process_NN1 Y_ZZ1 is_VBZ still_RR Gaussian_JJ except_CS21 that_CS22 we_PPIS2 add_VV0 the_AT variances_NN2 2=1_FO τ_NULL i2i=1n_FO to_II the_AT diagonal_JJ elements_NN2 of_IO the_AT covariance_NN1 matrix_NN1 ._. 
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We_PPIS2 consider_VV0 that_CST each_DD1 site_NN1 of_IO the_AT lattice_NN1 holds_VVZ 10_MC distinct_JJ resources_NN2 and_CC can_VM be_VBI occupied_VVN by_II at_RR21 most_RR22 one_MC1 individual_NN1 ._. 
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This_DD1 impact_NN1 is_VBZ more_RGR pronounced_JJ for_IF SMEs_NN2 and_CC private_JJ firms_NN2 ._. 
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Arguably_RR ,_, it_PPH1 is_VBZ the_AT most_RGT important_JJ aspect_NN1 of_IO nonparametric_JJ density_NN1 estimation_NN1 ._. 
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Thus_RR in_II our_APPGE formula_NN1 for_IF the_AT shadow_NN1 price_NN1 in_II (_( 20_MC )_) ,_, the_AT second_MD term_NN1 in_II the_AT bracket_NN1 ,_, which_DDQ should_VM dominate_VVI as_CSA C_ZZ1 grows_VVZ ,_, is_VBZ divided_VVN by_II (_( <equation>_FO )_) which_DDQ is_VBZ almost_RR dividing_VVG by_II zero_MC ._. 
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We_PPIS2 find_VV0 that_CST the_AT performance_NN1 of_IO the_AT CPM_NP1 and_CC Laplace_NP1 methods_NN2 is_VBZ strongly_RR effected_VVN by_II the_AT typical_JJ posterior_JJ model_NN1 size_NN1 ._. 
</s>
<s>
Our_APPGE main_JJ result_NN1 says_VVZ that_CST the_AT agent_NN1 often_RR behaves_VVZ as_CS21 if_CS22 she_PPHS1 had_VHD separate_JJ mental_JJ budgets_NN2 for_IF separate_JJ categories_NN2 :_: (_( i_ZZ1 )_) consumption_NN1 in_II a_AT1 category_NN1 is_VBZ independent_JJ of_IO shocks_NN2 to_II other_JJ categories_NN2 ,_, and_CC (_( ii_MC )_) total_JJ consumption_NN1 is_VBZ unresponsive_JJ ,_, but_CCB individual_JJ consumption_NN1 levels_NN2 are_VBR smoothly_RR responsive_JJ ,_, to_II shocks_NN2 within_II the_AT category_NN1 ._. 
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<s>
Thirdly_RR ,_, it_PPH1 is_VBZ exhibited_VVN visually_RR that_CST the_AT autocorrelations_NN2 of_IO the_AT two_MC systems_NN2 and_CC the_AT cross-correlation_NN1 between_II the_AT two_MC systems_NN2 present_VV0 different_JJ multifractal_JJ characteristics_NN2 at_II different_JJ time_NNT1 scales_NN2 ._. 
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<s>
In_II the_AT statistic_NN1 literature_NN1 ,_, such_DA banded_JJ structure_NN1 can_VM be_VBI exploited_VVN by_II tapering_JJ techniques_NN2 ,_, which_DDQ significantly_RR improve_VV0 covariance_NN1 estimation_NN1 ._. 
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<s>
Parametric_JJ statistical_JJ models_NN2 of_IO the_AT sort_NN1 used_VVN in_II retrievals_NN2 (_( L2_FO )_) ,_, mapping_VVG (_( L3_FO )_) ,_, and_CC flux_NN1 inversion_NN1 (_( L4_FO )_) have_VH0 parameters_NN2 ,_, and_CC these_DD2 require_VV0 as_RG much_DA1 thought_NN1 as_CSA do_VD0 models_NN2 for_IF &lsqb;_( Y_ZZ1 |_NULL X_ZZ1 &rsqb;_) and_CC &lsqb;_( X_ZZ1 &rsqb;_) ;_; in_II this_DD1 article_NN1 ,_, parameters_NN2 are_VBR notated_VVN generically_RR as_CSA θ_NULL ._. 
</s>
<s>
That_REX21 is_REX22 ,_, the_AT indices_NN2 <equation>_FO correspond_VV0 to_II the_AT sub-hypothesis_NN1 <equation>_FO ._. 
</s>
<s>
The_AT contrast_NN1 matrix_NN1 <equation>_FO is_VBZ contructed_VVN by_II constituting_VVG an_AT1 identity_NN1 matrix_NN1 whose_DDQGE dimension_NN1 is_VBZ the_AT number_NN1 of_IO estimated_JJ parameters_NN2 ,_, then_RT deleting_VVG the_AT rows_NN2 that_CST correspond_VV0 to_TO intercepts_VVZ (_( to_TO exclude_VVI <equation>_FO intercepts_VVZ )_) ,_, and_CC then_RT deleting_VVG rows_NN2 with_IW indices_NN2 <equation>_FO for_IF <equation>_FO '_NULL s_ZZ1 not_XX constrained_VVN to_II equal_JJ zero_NN1 ._. 
</s>
<s>
Temperature_NN1 dependence_NN1 of_IO the_AT energy_NN1 per_II monomer_NN1 unit_NN1 for_IF various_JJ bending_NN1 energies_NN2 εbend_FO as_CSA indicated_VVN ._. 
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<s>
From_II figure_NN1 (_( d_ZZ1 )_) increasing_VVG the_AT value_NN1 of_IO β_NULL makes_NN2 two_MC tricritical_JJ points_NN2 (_( from_II continuous_JJ to_II multiple_JJ discontinuous_JJ as_II31 well_II32 as_II33 from_II multiple_JJ discontinuous_JJ to_II discontinuous_JJ )_) become_VV0 large_JJ ,_, which_DDQ provides_VVZ help_NN1 for_IF controlling_VVG the_AT width_NN1 of_IO phase_NN1 transition_NN1 regions_NN2 in_II random_JJ networks_NN2 ._. 
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<s>
Market_VV0 state_NN1 2_MC shows_NN2 in_II the_AT correlation_NN1 matrix_NN1 ansatz_NN1 more_RGR negative_JJ inter-sector_JJ correlations_NN2 ._. 
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<s>
The_AT random_JJ variable_NN1 X_ZZ1 (_( "_" number_NN1 of_IO borrowers_NN2 with_IW repayment_NN1 difficulties_NN2 "_" )_) is_VBZ therefore_RR Hypergeometric_JJ distributed_JJ ,_, i.e._REX <equation>_FO ._. 
</s>
<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 evaluate_VV0 our_APPGE method_NN1 on_II the_AT task_NN1 of_IO multi-label_JJ node_NN1 classification_NN1 ,_, which_DDQ is_VBZ another_DD1 important_JJ mission_NN1 in_II network_NN1 analysis_NN1 ._. 
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<s>
A_AT1 limitation_NN1 of_IO this_DD1 study_NN1 is_VBZ that_CST we_PPIS2 only_RR examined_VVN a_AT1 few_DA2 methods_NN2 ,_, and_CC future_JJ studies_NN2 should_VM also_RR evaluate_VVI other_JJ methods_NN2 ,_, including_II guenomu_NN1 (_( discussed_VVN earlier_RRR )_) and_CC MixTreEM_NP1 (_( Ullah_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) ,_, to_TO discover_VVI the_AT places_NN2 in_II the_AT parameter_NN1 space_NN1 of_IO model_NN1 species_NN trees_NN2 where_CS each_DD1 method_NN1 outperforms_VVZ the_AT others_NN2 ._. 
</s>
<s>
The_AT precise_JJ binding_JJ location_NN1 is_VBZ assumed_VVN to_TO be_VBI between_II the_AT two_MC peak_NN1 modes_NN2 ,_, that_DD1 is_VBZ (_( xg+yg_FO )_) /2_MF ._. 
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<s>
As_CSA shown_VVN in_II the_AT numerical_JJ results_NN2 (_( see_VV0 Fig._NN1 8_MC )_) ,_, a_AT1 variety_NN1 of_IO term_NN1 structures_NN2 can_VM be_VBI achieved_VVN by_II choosing_VVG the_AT value_NN1 of_IO <equation>_FO ._. 
</s>
<s>
It_PPH1 has_VHZ been_VBN observed_VVN that_CST different_JJ cancer_NN1 types_NN2 have_VH0 different_JJ rates_NN2 of_IO CNAs_NP2 (_( Ciriello_NP1 et_RA21 al._RA22 ,_, 2013_MC ;_; Zack_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) ,_, and_CC even_RR within_II a_AT1 cancer_NN1 type_NN1 ,_, different_JJ chromosomes_NN2 show_VV0 varying_JJ patterns_NN2 of_IO aneuploidy_NN1 (_( Taylor_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
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<s>
To_TO address_VVI scalability_NN1 requirements_NN2 ,_, new_JJ methods_NN2 based_VVN on_II variational_JJ autoencoders_NN2 have_VH0 been_VBN developed_VVN ;_; these_DD2 leverage_NN1 the_AT large_JJ amounts_NN2 of_IO available_JJ data_NN to_TO learn_VVI non-linear_JJ maps_NN2 ,_, and_CC crucially_RR scale_VV0 well_JJ thanks_NN2 to_II efficient_JJ algorithms_NN2 for_IF inference_NN1 that_CST leverage_NN1 the_AT structure_NN1 of_IO autoencoders_NN2 (_( Eraslan_NP1 et_RA21 al._RA22 ,_, 2019_MC ;_; Lopez_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
</s>
<s>
Using_VVG 1=2N1=N2_FO corresponds_VVZ to_II the_AT original_JJ bridge_NN1 sampling_NN1 estimate_NN1 recommended_VVN by_II Meng_NP1 and_CC Wong_NP1 (_( 1996_MC )_) ._. 
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<s>
The_AT model_NN1 improves_VVZ the_AT traditional_JJ SIR_NN1 ,_, and_CC it_PPH1 is_VBZ applied_VVN to_TO study_VVI the_AT Brazilian_JJ epidemic_NN1 considering_II data_NN up_RG21 to_RG22 05/26/2020_MF ,_, and_CC analyzing_VVG possible_JJ future_JJ actions_NN2 and_CC their_APPGE consequences_NN2 ._. 
</s>
<s>
This_DD1 was_VBDZ done_VDN in_II &lsqb;_( 23_MC &rsqb;_) ,_, where_CS the_AT authors_NN2 developed_VVD a_AT1 probabilistic_JJ approach_NN1 based_VVN on_II ergodic_JJ BSDEs_NN2 (_( see_VV0 &lsqb;_( 4_MC ,_, 5_MC ,_, 12_MC ,_, 19_MC ,_, 23_MC &rsqb;_) for_IF recent_JJ developments_NN2 of_IO ergodic_JJ BSDEs_NN2 )_) ._. 
</s>
<s>
These_DD2 cover_VV0 several_DA2 types_NN2 of_IO distributions_NN2 :_: unimodal_JJ and_CC symmetric_JJ ,_, as_II31 well_II32 as_II33 bimodal_JJ and_CC asymmetric_JJ ._. 
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<s>
Further_RRR ,_, we_PPIS2 proposed_VVD an_AT1 extension_NN1 in_II computing_VVG the_AT additional_JJ canonical_JJ pairs_NN2 ._. 
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<s>
This_DD1 percentage_NN1 increases_VVZ to_II 99.40%_FO for_IF transactions_NN2 occurred_VVD within_II a_AT1 5-day_JJ time_NNT1 span_NN1 ,_, and_CC 99.73%_FO for_IF transactions_NN2 within_II a_AT1 10-day_JJ time_NNT1 span_NN1 ._. 
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<s>
These_DD2 studies_NN2 are_VBR ,_, however_RR ,_, conducted_VVN at_II the_AT aggregate_JJ level_NN1 ._. 
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<s>
As_CSA observed_VVN in_II Fig._NN1 10(c)_FO and_CC (_( d_ZZ1 )_) ,_, with_IW greater_JJR ,_, the_AT results_NN2 of_IO Monte_NP1 Carlo_NP1 simulation_NN1 are_VBR more_RGR unstable_JJ ._. 
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<s>
We_PPIS2 formally_RR model_VV0 this_DD1 credibility_NN1 as_CSA arising_VVG in_II a_AT1 dynamic_JJ reputation_NN1 model_NN1 ,_, assess_VV0 its_APPGE impact_NN1 using_VVG a_AT1 structural_JJ estimation_NN1 ,_, and_CC use_VV0 activist-friendly_JJ actions_NN2 to_TO capture_VVI both_RR formal_JJ and_CC informal_JJ settlements_NN2 ._. 
</s>
<s>
This_DD1 corresponds_VVZ to_II the_AT intuition_NN1 that_CST a_AT1 process_NN1 must_VM remain_VVI in_II a_AT1 state_NN1 at_RR21 least_RR22 for_IF some_DD time_NNT1 to_TO be_VBI naturally_RR interpreted_VVN as_II a_AT1 regime_NN1 ._. 
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<s>
Perturbation_NN1 experiments_NN2 are_VBR frequently_RR used_VVN to_TO infer_VVI and_CC quantify_VVI interactions_NN2 in_II biological_JJ networks_NN2 ._. 
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<s>
Suppose_VV0 we_PPIS2 observe_VV0 data_NN (_( Xi_NN1 ,_, Yi_NP1 )_) for_IF a_AT1 large_JJ number_NN1 of_IO unemployment_NN1 benefit_NN1 receivers_NN2 i=1_FO ,_, ,_, n_ZZ1 ,_, where_CS Xi_NN1 is_VBZ the_AT time_NNT1 point_NN1 where_RRQ individual_JJ i_ZZ1 started_VVD to_TO receive_VVI benefits_NN2 and_CC Yi_NP1 is_VBZ the_AT benefit_NN1 duration_NN1 ._. 
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<s>
Suppose_VV0 that_DD1 is_VBZ a_AT1 Markov_NP1 tree-shift_JJ with_IW for_CS some_DD ._. 
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<s>
Both_DB2 models_NN2 introduced_VVN in_II this_DD1 paper_NN1 have_VH0 dependent_JJ innovation_NN1 processes_NN2 ,_, where_CS one_PN1 has_VHZ innovation_NN1 processes_NN2 driven_VVN by_II the_AT bivariate_JJ Poisson_NP1 distribution_NN1 (_( PBINAR(1)_FO )_) ,_, and_CC the_AT other_JJ by_II the_AT bivariate_JJ negative_JJ binomial_JJ distribution_NN1 (_( NBBINAR(1)_FO )_) ._. 
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<s>
We_PPIS2 encode_VV0 uniqueness_NN1 of_IO the_AT label_NN1 of_IO each_DD1 vertex_NN1 with_IW the_AT following_JJ formula_NN1 ._. 
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<s>
By_II embedding_VVG the_AT enhanced_JJ network_NN1 ,_, we_PPIS2 obtain_VV0 the_AT final_JJ node_NN1 embedding_NN1 vectors_NN2 with_IW enhanced_JJ community_NN1 structures_NN2 ._. 
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<s>
The_AT volatility_NN1 of_IO bitcoin_NN1 prices_NN2 is_VBZ very_RG high_RR compared_VVN to_II that_DD1 of_IO other_JJ financial_JJ assets_NN2 ,_, and_CC the_AT price_NN1 of_IO bitcoin_NN1 (_( 1BTC_FO )_) varies_VVZ depending_II21 on_II22 the_AT country_NN1 or_CC cryptocurrency_NN1 exchange_NN1 ,_, which_DDQ facilitates_VVZ profit-taking_NN1 &lsqb;_( 12_MC &rsqb;_) ._. 
</s>
<s>
This_DD1 is_VBZ a_AT1 sample_NN1 period_NN1 that_CST has_VHZ received_VVN substantial_JJ attention_NN1 ,_, mainly_RR because_II21 of_II22 the_AT policy_NN1 relevance_NN1 of_IO the_AT surrounding_JJ issues_NN2 &lsqb;_( 31_MC &rsqb;_) ._. 
</s>
<s>
Thus_RR ,_, withdrawing_VVG resources_NN2 from_II these_DD2 establishments_NN2 and_CC refocusing_VVG may_VM improve_VVI operating_NN1 efficiency_NN1 and_CC decrease_VVI the_AT risk_NN1 of_IO failure_NN1 ,_, thus_RR improving_VVG firm_JJ performance_NN1 and_CC value_NN1 (_( Schoar_NP1 ,_, 2002_MC )_) ._. 
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<s>
The_AT goal_NN1 is_VBZ to_TO estimate_VVI the_AT nonlinear_JJ function_NN1 τ_NULL ._. 
</s>
<s>
Appendix_NN1 D_ZZ1 provides_VVZ the_AT detailed_JJ derivation_NN1 process_NN1 ._. 
</s>
<s>
The_AT basins_NN2 of_IO attraction_NN1 corresponds_VVZ to_II different_JJ values_NN2 of_IO parameter_NN1 v_ZZ1 ,_, when_CS the_AT other_JJ parameters_NN2 are_VBR fixed_VVN as_CSA =11.9119_FO ,_, β_NULL =1.3976_FO ,_, γ_NULL =0.2778_FO and_CC θ_NULL =0.0667_FO ._. 
</s>
<s>
In_II the_AT row_NN1 marked_VVN by_II 1_MC1 SD_NP1 HY-NEIO_NP1 we_PPIS2 show_VV0 the_AT one-standard-deviation_JJ effect_NN1 of_IO HY-NEIO_NN1 on_II future_JJ market_NN1 returns_NN2 ._. 
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<s>
The_AT response_NN1 of_IO output_NN1 growth_NN1 to_II the_AT sign_NN1 of_IO oil_NN1 price_NN1 shock_NN1 is_VBZ found_VVN to_TO behave_VVI asymmetrically_RR ._. 
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<s>
In_II the_AT third_MD and_CC last_MD stage_NN1 of_IO RL_NP1 model_NN1 training_NN1 ,_, we_PPIS2 start_VV0 from_II the_AT stage_NN1 2_MC model_NN1 and_CC generate_VV0 drug_NN1 combinations_NN2 for_IF a_AT1 fixed_JJ target_NN1 disease_NN1 and_CC can_VM choose_VVI scaffold_NN1 libraries_NN2 specific_JJ to_II the_AT disease_NN1 ._. 
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<s>
The_AT instrument_NN1 is_VBZ not_XX significantly_RR correlated_VVN with_IW manager_NN1 value_NN1 added_VVN ,_, nor_CC is_VBZ manager_NN1 value_NN1 added_VVN correlated_VVN with_IW other_JJ factors_NN2 that_CST may_VM drive_VVI promotion_NN1 opportunities_NN2 (_( see_VV0 Online_JJ Appendix_NN1 Table_NN1 A5_FO )_) ._. 
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<s>
Hence_RR ,_, I_PPIS1 term_VV0 this_DD1 finding_VVG "_" the_AT Duffee_NN1 Puzzle_NN1 ._. "_" 
</s>
<s>
We_PPIS2 notice_VV0 that_CST the_AT performance_NN1 of_IO Bayesian_JJ MLE_NN1 is_VBZ more_RGR similar_JJ to_II that_DD1 of_IO L1000_FO than_CSN the_AT Bayesian_JJ method_NN1 ._. 
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<s>
GIRF_NP1 can_VM be_VBI successfully_RR applied_VVN to_II highly_RR nonlinear_JJ models_NN2 for_IF which_DDQ the_AT ensemble_NN1 Kalman_NN1 filter_NN1 fails_VVZ ._. 
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<s>
The_AT network_NN1 structure_NN1 of_IO couplings_NN2 is_VBZ assumed_VVN to_TO be_VBI locally_RR tree-like_JJ ,_, and_CC our_APPGE theoretical_JJ result_NN1 is_VBZ expected_VVN to_TO be_VBI exact_JJ on_II those_DD2 networks_NN2 in_II the_AT thermodynamic_JJ limit_NN1 ._. 
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<s>
The_AT functionality_NN1 of_IO alona_NN1 is_VBZ comparable_JJ to_II the_AT aforementioned_JJ services_NN2 ,_, with_IW some_DD notable_JJ differences_NN2 :_: alona_NN1 offers_VVZ more_DAR choices_NN2 in_II31 terms_II32 of_II33 algorithms_NN2 ;_; the_AT clustering_NN1 strategy_NN1 is_VBZ graph-based_JJ ;_; cell_NN1 type_NN1 prediction_NN1 is_VBZ always_RR performeda_NN1 key_JJ goal_NN1 in_II most_DAT single-cell_JJ experiments_NN2 ._. 
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<s>
In_RR21 addition_RR22 ,_, the_AT dark_JJ colors_NN2 (_( blue_JJ and_CC green_JJ )_) represent_VV0 individuals_NN2 who_PNQS want_VV0 to_TO join_VVI other_JJ cooperative_JJ groups_NN2 and_CC the_AT light_JJ colors_NN2 are_VBR individuals_NN2 who_PNQS are_VBR not_XX willing_JJ to_TO join_VVI other_JJ cooperative_JJ groups_NN2 ._. 
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<s>
We_PPIS2 will_VM further_RRR analyze_VVI the_AT issue_NN1 of_IO discontinuity_NN1 in_II Section_NN1 2.3_MC ._. 
</s>
<s>
Thus_RR <equation>_FO is_VBZ a_AT1 positive_JJ classical_JJ solution_NN1 of_IO the_AT problem_NN1 (_( 2.17_MC )_) ._. 
</s>
<s>
As_CSA some_DD observers_NN2 have_VH0 suggested_VVN ,_, companies_NN2 may_VM have_VHI been_VBN more_RGR careful_JJ with_IW licensing_VVG compounds_NN2 and_CC gotten_VVN better_RRR at_II identifying_VVG potential_JJ failures_NN2 (_( see_VV0 Smietana_NP1 and_CC others_NN2 ,_, 2016_MC )_) ,_, thus_RR leading_VVG to_II higher_JJR productivity_NN1 ._. 
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<s>
We_PPIS2 note_VV0 that_CST USDT_NP1 and_CC TUSD_NP1 did_VDD not_XX stand_VVI out_RP as_RG clear_JJ outliers_NN2 ,_, nor_CC did_VDD they_PPHS2 cluster_VVI together_RL ,_, in_II Fig._NN1 2_MC ,_, the_AT focus_NN1 of_IO Section_NN1 3.3_MC ._. 
</s>
<s>
The_AT next_MD example_NN1 shows_VVZ that_CST it_PPH1 does_VDZ not_XX hold_VVI in_RR21 general_RR22 even_CS21 when_CS22 the_AT pdf_NNU is_VBZ decreasing_VVG ._. 
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<s>
The_AT second-stage_JJ optimization_NN1 problem_NN1 as_CSA summarized_VVN by_II the_AT conditional_JJ indirect_JJ utility_NN1 function_NN1 (_( 4_MC )_) is_VBZ derived_VVN conditional_NN1 on_II the_AT level_NN1 of_IO consumption_NN1 expenditure_NN1 <equation>_FO ._. 
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<s>
Hanushek_VV0 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2017_MC )_) find_VV0 that_CST countries_NN2 emphasizing_VVG apprenticeships_NN2 and_CC vocational_JJ training_NN1 have_VH0 lower_JJR youth_NN1 unemployment_NN1 rates_NN2 at_II labor_NN1 market_NN1 entry_NN1 but_CCB higher_JJR rates_NN2 later_RRR in_II life_NN1 ,_, suggesting_VVG a_AT1 trade-off_NN1 between_II general_NN1 and_CC specific_JJ skills_NN2 ._. 
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<s>
Let_VV0 Xj_NP1 denote_VVI the_AT subset_NN1 of_IO d1_FO predictors_NN2 excluding_II Xj_NP1 ,_, i.e._REX <equation>_FO ._. 
</s>
<s>
For_IF these_DD2 reasons_NN2 ,_, we_PPIS2 establish_VV0 the_AT above_JJ results_NN2 working_VVG directly_RR with_IW the_AT function_NN1 <equation>_FO in_II (_( 3.15_MC )_) ._. 
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<s>
In_CS21 Case_CS22 III_MC and_CC Case_NN1 IV_MC ,_, the_AT distribution_NN1 of_IO grades_NN2 condenses_VVZ at_II the_AT maximum_JJ value_NN1 ,_, showing_VVG that_CST they_PPHS2 reached_VVD the_AT maximum_JJ information_NN1 needed_VVD to_TO complete_VVI a_AT1 learning_NN1 task_NN1 or_CC objectives_NN2 ._. 
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<s>
The_AT stochastic_JJ behaviour_NN1 comes_VVZ from_II future_JJ fluctuations_NN2 of_IO the_AT mortality_NN1 rates_NN2 ._. 
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<s>
Markov_NP1 chain_NN1 Monte_NP1 Carlo_NP1 (_( MCMC_NP1 )_) methods_NN2 constitute_VV0 a_AT1 popular_JJ class_NN1 of_IO algorithms_NN2 to_TO approximate_VVI high_JJ dimensional_JJ integrals_NN2 arising_VVG in_II statistics_NN and_CC other_JJ fields_NN2 (_( Liu_NP1 ,_, 2008_MC ;_; Robert_NP1 and_CC Casella_NP1 ,_, 2004_MC ;_; Brooks_NP1 et_RA21 al._RA22 ,_, 2011_MC ;_; Green_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) ._. 
</s>
<s>
The_AT first_MD class_NN1 seeks_VVZ to_TO determine_VVI whether_CSW a_AT1 defined_JJ subset_NN1 (_( temporal_JJ ,_, spatial_JJ ,_, or_CC spatio-temporal_JJ )_) is_VBZ unusual_JJ compared_VVN to_II the_AT incidence_NN1 in_II the_AT study_NN1 region_NN1 as_II a_AT1 whole_NN1 ._. 
</s>
<s>
We_PPIS2 index_VV0 vertices_NN2 in_II this_DD1 graph_NN1 as_CSA (_( b_ZZ1 ,_, i_ZZ1 ,_, j_ZZ1 )_) using_VVG three_MC indices_NN2 (_( b_ZZ1 represents_VVZ a_AT1 block_NN1 ,_, i_ZZ1 represents_VVZ a_AT1 position_NN1 in_II the_AT block_NN1 b_ZZ1 and_CC j_ZZ1 represents_VVZ a_AT1 position_NN1 in_II string_NN1 R_ZZ1 )_) except_II21 for_II22 vertices_NN2 in_II the_AT 0-th_JJ row_NN1 that_CST are_VBR indexed_VVN simply_RR as_CSA (_( 0_MC ,_, j_ZZ1 )_) since_CS all_DB blocks_NN2 share_VV0 the_AT same_DA '_NULL glued_JJ '_NULL 0-th_JJ row_NN1 ._. 
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<s>
As_CSA a_AT1 result_NN1 ,_, a_AT1 one-time_JJ dividend_NN1 event_NN1 unique_JJ and_CC anticipated_VVD never_RR to_TO recur_VVI should_VM be_VBI excluded_VVN from_II the_AT analysis_NN1 because_CS such_DA an_AT1 event_NN1 is_VBZ not_XX drawn_VVN from_II the_AT distribution_NN1 relevant_JJ to_II current_JJ and_CC future_JJ prices_NN2 ._. 
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<s>
In_II real_JJ life_NN1 ,_, parking_VVG lots_PN are_VBR often_RR nearly_RR full_JJ ,_, which_DDQ corresponds_VVZ to_II large_JJ in_II our_APPGE model_NN1 ._. 
</s>
<s>
Then_RT ,_, the_AT learning_NN1 rate_NN1 depends_VVZ on_II the_AT so-called_JJ signal-to-noise_JJ ratio_NN1 <equation>_FO and_CC on_II the_AT current_JJ belief_NN1 <equation>_FO ,_, which_DDQ appear_VV0 in_II the_AT diffusion_NN1 coefficient_NN1 in_II (_( 2.5_MC )_) ._. 
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<s>
It_PPH1 is_VBZ clear_JJ from_II the_AT definition_NN1 that_CST <equation>_FO as_CSA <equation>_FO ._. 
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<s>
Controller_NN1 executives_NN2 comprise_VV0 about_RG a_AT1 quarter_NN1 of_IO the_AT executives_NN2 in_II the_AT sample_NN1 ._. 
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<s>
The_AT forecasting_VVG and_CC backcasting_VVG steps_NN2 will_VM be_VBI described_VVN in_II Sects_NP1 ._. 
</s>
<s>
Therefore_RR ,_, we_PPIS2 can_VM obtain_VVI a_AT1 symmetric_JJ similarity_NN1 coefficient_NN1 matrix_NN1 with_IW the_AT main_JJ diagonal_JJ of_IO 1_MC1 on_II average_JJ DCCA_NN1 ,_, and_CC transfer_VV0 it_PPH1 into_II a_AT1 distance_NN1 matrix_NN1 for_IF MDS_NN2 analysis_NN1 ._. 
</s>
<s>
Unless_CS otherwise_RR stated_VVN ,_, the_AT sample_NN1 size_NN1 is_VBZ chosen_VVN to_TO be_VBI =600n=600_FO ,_, and_CC the_AT quantiles_NN2 under_II consideration_NN1 are_VBR =0.1,0.25,0.5,0.75_FO τ_NULL =0.1,0.25,0.5,0.75_FO ,_, and_CC 0.9_MC ._. 
</s>
<s>
The_AT variable_JJ "_" Fem_NN1 "_" indicates_VVZ the_AT gender_NN1 of_IO the_AT student_NN1 and_CC "_" Stereotypes_NN2 "_" is_VBZ the_AT IAT_NN1 score_NN1 of_IO the_AT teacher_NN1 ._. 
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<s>
The_AT temperature_NN1 dependence_NN1 of_IO the_AT specific_JJ heat_NN1 can_VM exhibit_VVI one_MC1 or_CC two_MC maxima_NN2 in_II31 addition_II32 to_II33 the_AT jump_NN1 in_RP at_II the_AT adsorption_NN1 (_( second_MD order_NN1 )_) transition_NN1 point_NN1 ._. 
</s>
<s>
Considering_CS the_AT ratio_NN1 of_IO diagnosed_JJ cases_NN2 ,_, patients_NN2 who_PNQS are_VBR asymptomatic_JJ or_CC with_IW mild_JJ symptoms_NN2 of_IO COVID-19_MC may_VM not_XX seek_VVI health_NN1 care_NN1 ,_, which_DDQ leads_VVZ to_II underestimating_VVG the_AT burden_NN1 of_IO COVID-19_MC ._. 
</s>
<s>
We_PPIS2 considered_VVD this_DD1 specific_JJ problem_NN1 and_CC found_VVD that_CST the_AT clustering_NN1 threshold_NN1 occurs_VVZ on_II the_AT scale_NN1 2k1_NN1 (_( lnk_NNU +_FO lnlnk_NNU +_FO γ_NULL )_) /k_FU with_IW γ_NULL constant_JJ ,_, and_CC more_RGR precisely_RR that_DD1 for_IF the_AT uniform_JJ measure_NN1 γ_NULL d_ZZ1 ,_, u_ZZ1 ≈_NULL 0.871_MC ,_, which_DDQ falls_VVZ into_II the_AT range_NN1 allowed_VVN by_II the_AT previous_JJ bounds_NN2 ._. 
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<s>
The_AT dashed_JJ vertical_JJ lines_NN2 separate_VV0 the_AT data_NN into_II two_MC groups_NN2 :_: age_NN1 at_II move_NN1 m_ZZ1 ≤_FO 23_MC and_CC m_ZZ1 >_FO 23_MC ._. 
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<s>
It_PPH1 is_VBZ an_AT1 interesting_JJ finding_NN1 and_CC worth_NN1 to_TO be_VBI solved_VVN ._. 
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<s>
Numerical_JJ tests_NN2 and_CC rigorous_JJ analysis_NN1 in_II Gaussian_JJ settings_NN2 have_VH0 revealed_VVN that_CST MwG_NP1 has_VHZ dimension-independent_JJ MCMC_NP1 convergence_NN1 rate_NN1 when_CS the_AT underlying_JJ distributions_NN2 are_VBR spatially_RR localized_VVN ._. 
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<s>
Similarly_RR ,_, Cavallo_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2015_MC )_) find_VV0 that_CST there_EX is_VBZ an_AT1 immediate_JJ price_NN1 convergence_NN1 in_II studied_JJ products_NN2 after_II Latvia_NP1 '_NULL s_ZZ1 adoption_NN1 of_IO the_AT euro_NN1 in_II 2014_MC ._. 
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<s>
Each_DD1 sub-process_NN1 is_VBZ based_VVN on_II the_AT following_JJ steps_NN2 :_: (_( i_ZZ1 )_) substrings_NN2 beginning_VVG with_IW a_AT1 common_JJ prefix_NN1 of_IO length_NN1 k_ZZ1 are_VBR searched_VVN through_II all_DB reads_VVZ in_II memory_NN1 ,_, and_CC suffixes_NN2 with_IW the_AT prefix_NN1 in_II the_AT substrings_NN2 are_VBR generated_VVN and_CC stored_VVN in_II memory_NN1 as_CSA additional_JJ components_NN2 for_IF subsequent_JJ analysis_NN1 ._. 
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<s>
In_II this_DD1 paper_NN1 ,_, we_PPIS2 have_VH0 studied_VVN the_AT estimation_NN1 ,_, hypothesis_NN1 testing_NN1 ,_, variable_JJ selection_NN1 ,_, and_CC model_NN1 checking_VVG for_IF linear_JJ models_NN2 with_IW additive_JJ distortion_NN1 measurement_NN1 errors_NN2 ._. 
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<s>
We_PPIS2 next_MD focus_NN1 on_II the_AT forecast_NN1 revision_NN1 and_CC examine_VV0 how_RRQ all_DB the_AT new_JJ information_NN1 is_VBZ incorporated_VVN into_II the_AT GDP_NN1 forecasts_NN2 ._. 
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<s>
The_AT effect_NN1 on_II prices_NN2 of_IO monetary_JJ policy_NN1 shocks_NN2 is_VBZ traditionally_RR unconstrained_JJ as_CSA to_TO be_VBI able_JK to_TO identify_VVI if_CSW there_EX exists_VVZ a_AT1 price_NN1 puzzle_NN1 within_II the_AT system_NN1 (_( given_VVN the_AT fact_NN1 that_CST getting_VVG rid_VVN of_IO this_DD1 puzzle_NN1 is_VBZ one_MC1 of_IO the_AT original_JJ motivations_NN2 for_IF using_VVG FAVAR_NN1 models_NN2 )_) ._. 
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<s>
The_AT forecasting_VVG error_NN1 is_VBZ defined_VVN as_II the_AT difference_NN1 Ykt+h(T)Ykt+h(T)_FO between_II the_AT actual_JJ value_NN1 Ykt+h(T)_FO and_CC the_AT predicted_JJ value_NN1 Ykt+h(T)_FO of_IO the_AT bond_NN1 yield_NN1 with_IW time-to-maturity_JJ T_ZZ1 related_JJ to_TO curve_VVI k_ZZ1 and_CC forecasted_JJ business_NN1 days_NNT2 h_ZZ1 ._. 
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<s>
I_PPIS1 randomly_RR resampled_VVD cases_NN2 from_II each_DD1 cancer_NN1 (_( their_APPGE Table_NN1 S4_FO )_) in_II31 proportion_II32 to_II33 their_APPGE incidence_NN1 rates_NN2 (_( L._NP1 Danilova_NP1 ,_, personal_JJ communication_NN1 )_) ._. 
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<s>
Then_RT ,_, the_AT time-t_NNT1 fair_JJ value_NN1 of_IO the_AT death_NN1 benefit_NN1 with_IW a_AT1 cash_NN1 flow_NN1 stream_NN1 Ct_NN1 ,_, payable_JJ in_CS21 case_CS22 the_AT insured_JJ dies_VVZ before_II time_NNT1 T_ZZ1 and_CC 0≤t≤T_FO ,_, is_VBZ given_VVN by_II <equation>_FO ._. 
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<s>
In_II fact_NN1 ,_, Turkish_JJ industrial_JJ production_NN1 is_VBZ highly_RR dependent_JJ on_II imported_JJ inputs_NN2 ._. 
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<s>
Our_APPGE GIRF_NN1 implementation_NN1 used_VVD the_AT guide_NN1 function_NN1 constructed_VVN via_II forty_MC guide_NN1 simulations_NN2 ,_, according_II21 to_II22 the_AT quantile-based_JJ method_NN1 (_( 19_MC )_) and_CC (_( 20_MC )_) with_IW =2L=2_FO and_CC =8K=8_FO ._. 
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<s>
Considering_CS the_AT space_NN1 occupied_VVN by_II luggage_NN1 ,_, the_AT number_NN1 of_IO pedestrians_NN2 in_II each_DD1 row_NN1 is_VBZ different_JJ ._. 
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<s>
Due_II21 to_II22 restrictions_NN2 related_VVN to_II the_AT availability_NN1 of_IO some_DD of_IO the_AT additional_JJ aggregate-level_JJ variables_NN2 (_( e.g._REX ,_, the_AT two_MC objective-level_JJ Gini_JJ coefficients_NN2 )_) ,_, it_PPH1 is_VBZ not_XX possible_JJ to_TO use_VVI the_AT full_JJ set_NN1 of_IO aggregate_JJ cells_NN2 in_II most_DAT parts_NN2 of_IO the_AT empirical_JJ analysis_NN1 ._. 
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<s>
We_PPIS2 observed_VVD a_AT1 slight_JJ decrease_NN1 in_II correlation_NN1 for_IF this_DD1 artificial_JJ dataset_NN1 (_( Spearman_NP1 '_NULL s_ZZ1 rho=0.47_FO ,_, P=3.67×10176_FO )_) ,_, which_DDQ may_VM be_VBI due_II21 to_II22 the_AT effects_NN2 of_IO His-tags_NN2 in_II solubility_NN1 and/or_CC the_AT limitation(s)_NN2 of_IO our_APPGE approach_NN1 that_CST may_VM overfit_VVI to_II His-tag_JJ fusion_NN1 proteins_NN2 ._. 
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<s>
Configurations_NN2 can_VM then_RT be_VBI generated_VVN using_VVG standard_JJ Metropolis_NN1 Monte_NP1 Carlo_NP1 techniques_NN2 ._. 
</s>
<s>
The_AT first_MD eight_MC time_NNT1 series_NN were_VBDR simulated_VVN from_II an_AT1 AR(2)_FO process_VV0 with_IW modulus_NN1 0.95_MC and_CC frequency_NN1 =2.07_FO ,_, while_CS the_AT last_MD seven_MC time_NNT1 series_NN were_VBDR simulated_VVN from_II an_AT1 AR(2)_FO process_VV0 with_IW the_AT same_DA modulus_NN1 of_IO 0.95_MC but_CCB with_IW frequency_NN1 =1.08_FO ._. 
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<s>
We_PPIS2 performed_VVD several_DA2 experiments_NN2 to_TO elucidate_VVI our_APPGE guiding_JJ question_NN1 from_II different_JJ angles_NN2 ,_, namely_REX whether_CSW there_EX is_VBZ a_AT1 general_JJ difficulty_NN1 of_IO using_VVG Sankoff-like_JJ scores_NN2 for_IF the_AT simultaneous_JJ local_JJ alignment_NN1 and_CC folding_NN1 of_IO RNAs_NN2 ._. 
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<s>
Another_DD1 set_NN1 of_IO variables_NN2 revolves_VVZ around_RP quantities_NN2 of_IO credit_NN1 :_: We_PPIS2 show_VV0 that_CST HY-NEIO_NP1 predicts_VVZ balance_NN1 sheet_NN1 growth_NN1 in_II financial_JJ intermediaries_NN2 and_CC total_JJ net_JJ amounts_NN2 of_IO corporate_JJ bonds_NN2 issued_VVN in_II the_AT economy_NN1 ._. 
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<s>
To_TO filter_VVI out_RP such_DA rare_JJ k-mers_NN2 ,_, we_PPIS2 analyze_VV0 their_APPGE frequencies_NN2 in_II the_AT read-set_NN1 ._. 
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<s>
One_MC1 recent_JJ study_NN1 by_II deHaan_NN1 et_RA21 al_RA22 ._. 
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<s>
(_( 2018_MC )_) investigates_VVZ the_AT impact_NN1 of_IO non-additive_JJ errors_NN2 of_IO the_AT dependent_JJ variable_NN1 ,_, especially_RR the_AT noise_NN1 in_II accounting_VVG measures_NN2 ._. 
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<s>
First_MD ,_, we_PPIS2 will_VM explore_VVI more_RGR sophisticated_JJ weight_NN1 functions_NN2 ,_, e.g._REX down-weighting_JJ erroneous_JJ k-mers_NN2 in_II31 addition_II32 to_II33 repetitive_JJ k-mers_NN2 ._. 
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<s>
G1_FO ,_, G2_FO ,_, G3_FO ,_, G4andG5_FO show_VV0 the_AT results_NN2 of_IO GSuper_NP1 ,_, GSp_NP1 ,_, Gmax_NP1 ,_, GGreyandGER_NP1 ,_, respectively_RR ._. 
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There_EX exists_VVZ a_AT1 constant_JJ M_ZZ1 satisfying_JJ that_CST <equation>_FO asymptotically_RR ._. 
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<s>
The_AT independent_JJ bypassing_VVG agents_NN2 are_VBR not_XX affected_VVN by_II propaganda_NN1 "_" 0_MC "_" ,_, while_CS the_AT unswerving_JJ bypassing_VVG agents_NN2 are_VBR still_RR affected_VVN by_II it_PPH1 ,_, and_CC Bt_NP1 should_VM be_VBI closer_JJR to_II their_APPGE propaganda_NN1 opinion_NN1 "_" 0_MC "_" than_CSN is_VBZ It_PPH1 ._. 
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<s>
It_PPH1 is_VBZ shown_VVN that_CST ,_, compared_VVN with_IW LR_NP1 ,_, the_AT new_JJ regression_NN1 results_NN2 in_II a_AT1 significantly_RR improved_VVN adjusted_VVN <equation>_FO ,_, increasing_VVG from_II less_DAR than_CSN <equation>_FO to_II over_II <equation>_FO ._. 
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Finally_RR ,_, we_PPIS2 elaborate_VV0 on_II our_APPGE findings_NN2 for_IF the_AT growth_NN1 constant_NN1 ._. 
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<s>
On_II the_AT one_MC1 hand_NN1 ,_, the_AT results_NN2 imply_VV0 that_CST high-potential_JJ entrepreneurs_NN2 face_VV0 barriers_NN2 to_II growth_NN1 besides_II financial_JJ constraints_NN2 ,_, which_DDQ can_VM be_VBI mitigated_VVN by_II business_NN1 accelerators_NN2 ._. 
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<s>
From_II Fig._NN1 12(a)_FO ,_, at_II some_DD hours_NNT2 (_( e.g._REX around_II hour_NNT1 0_MC ,_, which_DDQ is_VBZ midnight_NNT1 )_) as_CSA weather_NN1 situation_NN1 increases_NN2 ._. 
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<s>
We_PPIS2 did_VDD not_XX include_VVI the_AT specialized_JJ tools_NN2 that_CST model_NN1 protein_NN1 structural_JJ information_NN1 such_II21 as_II22 surface_NN1 geometry_NN1 ,_, surface_NN1 charges_NN2 and_CC solvent_NN1 accessibility_NN1 because_CS these_DD2 tools_NN2 require_VV0 prior_JJ knowledge_NN1 of_IO protein_NN1 tertiary_JJ structure_NN1 ._. 
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<s>
Since_CS the_AT development_NN1 of_IO high-throughput_JJ sequencing_NN1 ,_, a_AT1 multitude_NN1 of_IO other_JJ types_NN2 of_IO -omics_JJ experiments_NN2 have_VH0 appeared_VVN ._. 
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<s>
Specifically_RR ,_, Fulvestrant_JJ targets_NN2 estrogen_NN1 receptor_NN1 in_II estrogen_NN1 signaling_VVG pathway_NN1 and_CC Palbociclib_NP1 targets_NN2 cyclin-dependent_JJ kinases_NN2 4_MC and_CC 6_MC (_( CDK4_FO and_CC CDK6_FO )_) in_II cell_NN1 cycle_NN1 pathway_NN1 (_( Turner_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) ._. 
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<s>
The_AT Intermediate_JJ Scattering_NN1 Function_NN1 (_( ISF_NP1 )_) of_IO each_DD1 IMF_NP1 was_VBDZ used_VVN for_IF computing_VVG the_AT structure_NN1 factor_NN1 and_CC the_AT relaxation_NN1 time_NNT1 of_IO fluctuations_NN2 ._. 
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<s>
But_CCB due_II21 to_II22 the_AT high_JJ concentration_NN1 of_IO cellular_JJ crowding_JJ ,_, we_PPIS2 ignore_VV0 this_DD1 possibility_NN1 and_CC assume_VV0 that_CST the_AT specific/non_FU specific_JJ sites_NN2 on_II the_AT DNA_NN1 chain_NN1 in_II the_AT crowded_JJ region_NN1 can_VM be_VBI reached_VVN only_RR by_II sliding_VVG ._. 
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<s>
However_RR ,_, the_AT international_JJ finance_NN1 literature_NN1 has_VHZ shown_VVN that_CST the_AT presence_NN1 of_IO credit_NN1 constraints_NN2 can_VM reverse_VVI the_AT direction_NN1 of_IO capital_NN1 flows_VVZ relative_II21 to_II22 the_AT prediction_NN1 of_IO neoclassical_JJ models_NN2 ._. 
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<s>
In_II this_DD1 section_NN1 we_PPIS2 are_VBR establishing_VVG relations_NN2 between_II H-MIN_NNU and_CC its_APPGE weak_JJ counterpart_NN1 with_IW other_JJ correlation_NN1 measures_NN2 ._. 
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<s>
We_PPIS2 then_RT compute_VV0 the_AT MDC_MC score_NN1 (_( denoted_VVN as_CSA MDCp_NP1 )_) on_II T._NP1 Step_NN1 3_MC computes_VVZ a_AT1 trinucleotide_NN1 composition_NN1 profile_NN1 for_IF each_DD1 sampled_VVD long_RR read_VVN ._. 
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<s>
The_AT pioneering_JJ works_NN of_IO Lyons_NP1 &lsqb;_( 33_MC &rsqb;_) and_CC Avellaneda_NP1 et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 4_MC &rsqb;_) on_II Knightian_JJ uncertainty_NN1 in_II mathematical_JJ finance_NN1 consider_VV0 models_NN2 with_IW uncertain_JJ volatility_NN1 in_II continuous_JJ time_NNT1 ._. 
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<s>
Nevertheless_RR ,_, Monte_NP1 Carlo_NP1 converges_VVZ very_RG slowly_RR taking_VVG more_DAR than_CSN 1_MC1 hour_NNT1 for_IF a_AT1 comparable_JJ level_NN1 of_IO accuracy_NN1 ._. 
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<s>
The_AT turnover_NN1 ratio_NN1 reflects_VVZ the_AT total_JJ number_NN1 of_IO shares_NN2 traded_VVN relative_II21 to_II22 the_AT average_JJ number_NN1 of_IO shares_NN2 outstanding_JJ ._. 
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<s>
Institutional_JJ changes_NN2 and_CC technological_JJ advances_NN2 ,_, however_RR ,_, may_VM alter_VVI the_AT supply_NN1 and_CC demand_VVI relationships_NN2 in_II the_AT natural_JJ gas_NN1 sector_NN1 inducing_VVG structural_JJ changes_NN2 in_II price_NN1 relationships_NN2 among_II natural_JJ gas_NN1 markets_NN2 ._. 
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<s>
If_CS we_PPIS2 compare_VV0 the_AT condition_NN1 (_( 4.18_MC )_) with_IW the_AT condition_NN1 (_( 5.4_MC )_) of_IO &lsqb;_( 14_MC ,_, Example_NN1 5.5_MC &rsqb;_) ,_, i.e._REX ,_, In_II this_DD1 model_NN1 ,_, both_DB2 parts_NN2 of_IO rainfall_NN1 process_NN1 occurrence_NN1 and_CC intensity_NN1 ,_, are_VBR determined_VVN by_II a_AT1 censored_JJ power-transformed_JJ Ornstein–Uhlenbeck_NN1 (_( OU_FW )_) process_VV0 ._. 
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<s>
Under_II each_DD1 height_NN1 constraint_NN1 condition_NN1 ,_, six_MC groups_NN2 of_IO tests_NN2 were_VBDR performed_VVN ._. 
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<s>
The_AT first_MD period_NN1 accounts_VVZ for_IF 82_MC observations_NN2 (_( January_NPM1 2001–October_NN1 2007_MC )_) ,_, and_CC the_AT second_MD accounts_VVZ for_IF 101_MC (_( November_NPM1 2007–April_VV0 2016_MC )_) ._. 
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<s>
Data_NN cleaning_VVG techniques_NN2 such_II21 as_II22 removing_VVG features_NN2 with_IW low_JJ gene_NN1 expression_NN1 and_CC variance_NN1 were_VBDR used_VVN ,_, leaving_VVG us_PPIO2 with_IW a_AT1 remaining_JJ of_IO 2250_MC genes_NN2 and_CC 5164_MC methylation_NN1 sites_NN2 ._. 
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<s>
The_AT red_JJ edges_NN2 are_VBR a_AT1 maximum_JJ matching_NN1 of_IO the_AT network_NN1 ._. 
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<s>
M.S._NN1 and_CC M.B._NNU acknowledge_VV0 financial_JJ support_NN1 through_II the_AT Northern_JJ Netherlands_NP1 Region_NN1 of_IO Smart_NP1 Factories_NN2 (_( RoSF_NP1 )_) consortium_NN1 ,_, led_VVN by_II the_AT Noordelijke_NP1 Ontwikkelings_NP1 en_FW Investerings_NP1 Maatschappij_NP1 (_( NOM_NP1 )_) ._. 
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<s>
First_MD ,_, the_AT devaluation_NN1 of_IO host_NN1 currency_NN1 decreases_VVZ the_AT cost_NN1 of_IO production_NN1 relatively_RR in_II31 terms_II32 of_II33 foreign_JJ currency_NN1 ._. 
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<s>
Further_JJR investigations_NN2 are_VBR required_VVN to_TO elucidate_VVI the_AT molecular_JJ mechanisms_NN2 of_IO this_DD1 novel_JJ miRNA_NN1 in_II regulating_VVG cell_NN1 cycle_NN1 and_CC the_AT potential_JJ role_NN1 of_IO its_APPGE isomiRs_NN2 in_II cervical_JJ carcinogenesis_NN1 and_CC progression_NN1 ._. 
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<s>
SSIF_NP1 contains_VVZ three_MC main_JJ components_NN2 :_: (_( i_ZZ1 )_) a_AT1 sequence-based_JJ representation_NN1 of_IO GO_VV0 concepts_NN2 constructed_VVN using_VVG part-of-speech_NN1 (_( POS_NN2 )_) tagging_VVG ,_, sub-concept_JJ matching_NN1 and_CC antonym_NN1 tagging_VVG ;_; (_( ii_MC )_) a_AT1 formulation_NN1 of_IO algebraic_JJ operations_NN2 for_IF the_AT development_NN1 of_IO a_AT1 term-algebra_NN1 based_VVN on_II the_AT sequence-based_JJ representation_NN1 ,_, that_CST leverages_NN2 subsumption-based_JJ longest_JJT subsequence_NN1 alignment_NN1 ;_; and_CC (_( iii_MC )_) the_AT construction_NN1 of_IO a_AT1 set_NN1 of_IO conditional_JJ rules_NN2 for_IF backward_JJ subsumption_NN1 inference_NN1 aimed_VVN at_II uncovering_VVG problematic_JJ is-a_VBZ relations_NN2 in_II GO_VV0 ._. 
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<s>
In_II Section_NN1 3_MC ,_, a_AT1 series_NN of_IO computational_JJ analyses_NN2 based_VVN on_II related_JJ mathematical_JJ models_NN2 are_VBR made_VVN to_TO testify_VVI and_CC complement_VVI the_AT derived_JJ theoretical_JJ results_NN2 in_II Section_NN1 2_MC ._. 
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<s>
As_II the_AT initial_JJ condition_NN1 (_( x_ZZ1 =_FO 5.654566893_MC ..._... ,_, p_ZZ1 =_FO 1.627640289_MC ..._... )_) a_AT1 red_JJ curve_NN1 is_VBZ located_VVN in_II the_AT sticky_JJ region_NN1 ,_, and_CC as_II the_AT initial_JJ condition_NN1 (_( x_ZZ1 =_FO 5.668539896_MC ..._... ,_, p_ZZ1 =_FO 4.509105458_MC ..._... )_) a_AT1 black_JJ curve_NN1 is_VBZ located_VVN in_II the_AT strongly_RR chaotic_JJ sea_NN1 ._. 
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<s>
The_AT Joe_NP1 ,_, Gumbel_NP1 ,_, and_CC t_ZZ1 copulas_NN2 appear_VV0 better_RRR than_CSN the_AT rest_NN1 in_II the_AT sense_NN1 that_CST their_APPGE distances_NN2 are_VBR mostly_RR distributed_VVN around_II small_JJ values_NN2 ._. 
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<s>
Such_DA a_AT1 feasibility_NN1 analysis_NN1 relates_VVZ to_II whether_CSW the_AT buyer_NN1 and_CC the_AT seller_NN1 would_VM keep_VVI the_AT status_NN121 quo_NN122 with_IW no-insurance_JJ and_CC no-premium_JJ strategy_NN1 ,_, when_CS A_ZZ1 is_VBZ an_AT1 empty_JJ set_NN1 ._. 
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<s>
We_PPIS2 first_MD consider_VV0 their_APPGE size_NN1 properties_NN2 ._. 
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<s>
For_IF this_DD1 experiment_NN1 ,_, we_PPIS2 simulated_VVD data_NN from_II a_AT1 linear_JJ regression_NN1 model_NN1 ._. 
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<s>
If_CS there_EX is_VBZ dependence_NN1 between_II traits_NN2 ,_, it_PPH1 makes_VVZ sense_NN1 to_TO model_VVI them_PPHO2 jointly_RR ._. 
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<s>
We_PPIS2 defer_VV0 supply-side_JJ and_CC general-equilibrium_JJ assumptions_NN2 to_II Section_NN1 V._II The_AT GARCH_NN1 equation_NN1 is_VBZ shown_VVN in_II (_( 4c_FO )_) for_IF which_DDQ <equation>_FO ,_, <equation>_FO and_CC <equation>_FO ._. 
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<s>
If_CS X_ZZ1 (_( ._MC )_) is_VBZ an_AT1 MSS_NP1 with_IW parameter_NN1 space_NN1 and_CC Hurst_NP1 vector_NN1 ,_, then_RT it_PPH1 is_VBZ easy_JJ to_TO show_VVI that_CST its_APPGE stationary_JJ counterpart_NN1 Y_ZZ1 (_( ._MC )_) has_VHZ a_AT1 parameter_NN1 space_NN1 ._. 
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<s>
That_REX21 is_REX22 ,_, we_PPIS2 consider_VV0 that_CST "_" the_AT multiple_JJ datasets_NN2 have_VH0 a_AT1 common_JJ eigenvector_NN1 structure_NN1 but_CCB with_IW different_JJ sets_NN2 of_IO eigenvalues_NN2 "_" (_( Pepler_NP1 2014_MC )_) ._. 
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<s>
Let_VV0 and_CC be_VBI samples_NN2 of_IO the_AT stationary_JJ processes_NN2 Y1()_FO and_CC Y2()_FO introduced_VVN in_II remark_NN1 4_MC ._. 
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Prior_II21 to_II22 cell_NN1 division_NN1 ,_, it_PPH1 also_RR assembles_VVZ an_AT1 additional_JJ flagellum_NN1 ._. 
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<s>
A_AT1 banking_NN1 network_NN1 system_NN1 is_VBZ a_AT1 complex_JJ network_NN1 system_NN1 composed_VVN of_IO a_AT1 series_NN of_IO banks_NN2 and_CC their_APPGE interconnections_NN2 ._. 
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<s>
The_AT fact_NN1 that_CST the_AT clusterings_NN2 estimated_VVN on_II some_DD data_NN types_NN2 are_VBR strongly_RR dependent_JJ over_II time_NNT1 provides_VVZ evidence_NN1 that_CST they_PPHS2 are_VBR scientifically_RR meaningful_JJ ._. 
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<s>
There_EX are_VBR other_JJ algorithmic_JJ efforts_NN2 to_TO speed_VVI up_RP RNA_NN1 folding_NN1 and_CC partition_NN1 function_NN1 calculation_NN1 ,_, including_II sparsification_NN1 (_( Backofen_NP1 et_RA21 al._RA22 ,_, 2011_MC ;_; Chitsaz_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) ._. 
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<s>
Several_DA2 tools_NN2 for_IF assembly-free_JJ genome_NN1 comparison_NN1 have_VH0 pursued_VVN this_DD1 ambition_NN1 (_( e.g._REX Dai_NP1 et_RA21 al._RA22 ,_, 2008_MC ;_; Fan_VV0 et_RA21 al._RA22 ,_, 2015_MC ;_; Roychowdhury_NP1 et_RA21 al._RA22 ,_, 2013_MC ;_; Ulitsky_NP1 et_RA21 al._RA22 ,_, 2006_MC ;_; Yang_NP1 and_CC Zhang_NP1 ,_, 2008_MC ;_; Yi_NP1 and_CC Jin_NP1 ,_, 2013_MC )_) ._. 
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<s>
The_AT gray_JJ lines_NN2 are_VBR the_AT various_JJ trajectories_NN2 at_II fixed_JJ energy_NN1 ._. 
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<s>
Open-source_JJ image_NN1 analysis_NN1 software_NN1 available_JJ from_II TINA_NP1 Vision_NN1 ,_, www.tina-vision.net_NNU ._. 
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<s>
We_PPIS2 know_VV0 from_II Figure_NN1 VII_MC that_CST the_AT fixed_JJ cost_NN1 is_VBZ sizable_JJ and_CC has_VHZ gone_VVN up_RP ._. 
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<s>
The_AT dielectric_JJ susceptibility_NN1 (_( ionic_JJ contribution_NN1 to_II dielectric_JJ constant_JJ )_) as_II a_AT1 function_NN1 of_IO temperature_NN1 T._NP1 Moreover_RR ,_, the_AT possibility_NN1 of_IO a_AT1 heterogenous_JJ error_NN1 structure_NN1 suggests_VVZ the_AT presence_NN1 of_IO an_AT1 additional_JJ discrete_JJ nominal_JJ latent_JJ variable_NN1 S._NN1 Since_CS the_AT number_NN1 of_IO categories_NN2 for_IF the_AT latent_JJ trait_NN1 ,_, method_NN1 ,_, and_CC error_NN1 structure_NN1 variables_NN2 is_VBZ unknown_JJ ,_, we_PPIS2 compare_VV0 the_AT fit_NN1 of_IO models_NN2 with_IW differing_JJ numbers_NN2 of_IO categories_NN2 for_IF each_DD1 of_IO these_DD2 ._. 
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<s>
Table_NN1 2_MC summarizes_VVZ the_AT microscopy_NN1 platforms_NN2 as_II31 well_II32 as_II33 objectives_NN2 used_VVN in_II this_DD1 work_NN1 ._. 
</s>
<s>
Particularly_RR ,_, counties_NN2 which_DDQ belong_VV0 to_II Central_JJ Henan_JJ Urban_JJ Agglomeration_NN1 are_VBR more_RGR likely_JJ to_TO be_VBI members_NN2 of_IO a_AT1 club_NN1 with_IW a_AT1 higher_JJR mean_JJ income_NN1 per_RR21 capita_RR22 ._. 
</s>
<s>
For_IF SVD_NP1 of_IO the_AT matrix_NN1 <equation>_FO ,_, <equation>_FO ,_, because_CS <equation>_FO is_VBZ computed_VVN as_CSA <equation>_FO in_II (_( 6_MC )_) ._. 
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<s>
In_II41 the_II42 light_II43 of_II44 economic_JJ theory_NN1 ,_, the_AT results_NN2 can_VM be_VBI seen_VVN either_RR expected_VVN or_CC surprising_JJ ._. 
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<s>
The_AT confinement_NN1 of_IO the_AT transition_NN1 paths_NN2 between_II absorbing_JJ boundaries_NN2 results_NN2 in_II a_AT1 narrower_JJR distribution_NN1 of_IO the_AT TPTDs_NP1 as_CSA compared_VVN to_II broader_JJR distribution_NN1 curves_NN2 for_IF the_AT free_JJ boundary_NN1 condition_NN1 ._. 
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<s>
We_PPIS2 draw_VV0 the_AT observations_NN2 in_II the_AT lth_NNU data_NN view_NN1 from_II a_AT1 Gaussian_JJ mixture_NN1 model_NN1 ,_, for_IF which_DDQ the_AT kth_NNU mixture_NN1 component_NN1 is_VBZ a_AT1 Np_NP1 (_( (_( l_ZZ1 )_) k_ZZ1 ,_, (_( l_ZZ1 )_) )_) distribution_NN1 ,_, with_IW p=10_FO ,_, and_CC with_IW (_( l_ZZ1 )_) k_ZZ1 given_VVN in_II Appendix_NN1 C.1_FO of_IO the_AT supplementary_JJ material_NN1 available_JJ at_II Biostatistics_NP1 online_RR ._. 
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<s>
We_PPIS2 hope_VV0 that_CST our_APPGE results_NN2 ,_, comparing_VVG a_AT1 variety_NN1 of_IO deep_JJ learning_NN1 models_NN2 ,_, and_CC this_DD1 discussion_NN1 will_VM be_VBI helpful_JJ for_IF future_JJ deep_JJ learning_NN1 applications_NN2 in_II imaging_VVG MS_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, the_AT probability_NN1 that_CST marital_JJ status_NN1 agrees_VVZ in_II nonmatches_NN2 could_VM depend_VVI on_II the_AT age_NN1 of_IO the_AT individual_NN1 since_CS younger_JJR individuals_NN2 are_VBR less_RGR likely_JJ to_TO be_VBI married_JJ ._. 
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<s>
Second_MD ,_, differences_NN2 in_II parental_JJ marital_JJ status_NN1 ,_, education_NN1 ,_, and_CC wealth_NN1 explain_VV0 little_DA1 of_IO the_AT black-white_JJ income_NN1 gap_NN1 conditional_NN1 on_II parent_NN1 income_NN1 ._. 
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<s>
As_CSA shown_VVN in_II brackets_NN2 ,_, the_AT statistical_JJ significance_NN1 does_VDZ not_XX have_VHI any_DD substantial_JJ change_NN1 for_IF the_AT two_MC outcome_NN1 variables_NN2 of_IO interest_NN1 ._. 
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<s>
This_DD1 density_NN1 is_VBZ concentrated_VVN around_RG 0.5_MC years_NNT2 ._. 
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<s>
Additionally_RR ,_, we_PPIS2 use_VV0 re-estimation_NN1 when_RRQ possible_JJ as_CSA in_II Gertheiss_NP1 and_CC Tutz_NP1 (_( 2010_MC )_) to_TO reduce_VVI the_AT bias_NN1 of_IO the_AT regularized_JJ estimates_NN2 ._. 
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<s>
This_DD1 also_RR allows_VVZ to_TO use_VVI approaches_NN2 ,_, which_DDQ are_VBR computer_NN1 based_VVN and_CC nuisance_NN1 parameter_NN1 free_JJ ._. 
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<s>
Or_CC yet_RR ,_, the_AT constant_JJ decrease_NN1 of_IO isolation_NN1 levels_NN2 in_II the_AT country_NN1 (_( below_RG 50%_NNU for_IF most_DAT days_NNT2 of_IO the_AT past_JJ month_NNT1 )_) ._. 
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<s>
The_AT measure_NN1 for_IF CBI_NP1 is_VBZ Cukierman_NP1 '_NULL s_ZZ1 unweighted_JJ index_NN1 of_IO de_JJ21 jure_JJ22 CB_NN1 autonomy_NN1 (_( Cukierman_NP1 1992_MC )_) ._. 
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<s>
With_IW no_AT interaction_NN1 between_II the_AT quantum_NN1 dots_NN2 ,_, U_ZZ1 =_FO 0_MC ,_, the_AT four_MC probabilities_NN2 of_IO the_AT states_NN2 almost_RR equivalently_RR share_VV0 the_AT pie_NN1 ,_, q_ZZ1 (_( x_ZZ1 ,_, y_ZZ1 )_) =_FO 0.25_MC ._. 
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<s>
Extensive_JJ Monte_NP1 Carlo_NP1 computer_NN1 simulations_NN2 fully_RR support_VV0 our_APPGE theoretical_JJ predictions_NN2 ._. 
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<s>
The_AT dataset_NN1 X_ZZ1 is_VBZ first_MD divided_VVN into_II disjoint_JJ subsets_NN2 X1_FO ,_, ,_, Xd_NP1 using_VVG Principal_JJ Component_NN1 Trees_NN2 (_( PC-trees_NN2 )_) ,_, which_DDQ hierarchically_RR split_VV0 the_AT data_NN into_II equal_JJ halves_NN2 along_II the_AT leading_JJ principal_JJ component_NN1 (_( Verma_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ._. 
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<s>
These_DD2 formats_NN2 also_RR support_VV0 remote_JJ file_NN1 access_NN1 ,_, allowing_VVG multiple_JJ parallel_JJ requests_NN2 to_TO process_VVI at_II the_AT same_DA time_NNT1 ._. 
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<s>
In_II contrast_NN1 ,_, the_AT additional_JJ information_NN1 <equation>_FO yields_VVZ arbitrage_NN1 opportunities_NN2 ._. 
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<s>
Sun_NN1 et_RA21 al_RA22 ._. 
</s>
<s>
propose_VV0 a_AT1 new_JJ wavelet-based_JJ methodology_NN1 ,_, the_AT generalized_JJ optimal_JJ wavelet_NN1 decomposition_NN1 algorithm_NN1 ,_, to_TO deconstruct_VVI prices_NN2 series_NN into_II the_AT true_JJ efficient_JJ price_NN1 and_CC microstructural_JJ noise_NN1 &lsqb;_( 20_MC &rsqb;_) ._. 
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<s>
A_AT1 few_DA2 studies_NN2 also_RR apply_VV0 IV_MC regression_NN1 and_CC treat_VV0 the_AT probability_NN1 of_IO arrest_NN1 as_CSA endogenous_JJ ,_, but_CCB all_DB remaining_JJ variables_NN2 as_CSA exogenous_JJ (_( Cornwell_NP1 and_CC Trumbull_NP1 1994_MC ;_; Entorf_NP1 and_CC Spengler_NP1 2008_MC ,_, 2015_MC )_) ._. 
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<s>
First_MD ,_, we_PPIS2 determine_VV0 the_AT reference_NN1 and_CC comparison_NN1 series_NN to_TO explore_VVI the_AT effect_NN1 between_II stocks_NN2 ._. 
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<s>
In_II section_NN1 4_MC we_PPIS2 argue_VV0 that_CST the_AT position_NN1 of_IO the_AT chosen_JJ parking_NN1 spot_NN1 is_VBZ spatially_RR uniform_JJ ,_, independent_JJ of_IO the_AT threshold_NN1 τ_NULL ._. 
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<s>
For_REX21 example_REX22 ,_, for_IF SU(M)_NN1 spin_NN1 systems_NN2 on_II the_AT triangular_JJ lattice_NN1 with_IW a_AT1 self-conjugate_JJ representation_NN1 on_II each_DD1 site_NN1 ,_, using_VVG the_AT fermionic_JJ spinon_NN1 formalism_NN1 ,_, when_CS there_EX is_VBZ a_AT1 -flux_NN1 through_II half_DB of_IO the_AT triangles_NN2 ,_, there_EX are_VBR N_ZZ1 =_FO 2M_NNU components_NN2 of_IO Dirac_NP1 fermions_NN2 at_II low_JJ energy_NN1 ._. 
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<s>
Note_VV0 that_CST G_ZZ1 contains_VVZ missing_JJ values_NN2 for_IF all_DB entries_NN2 Gijwith_NP1 maxi_JJ ,_, j>n_FO ._. 
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<s>
In_II this_DD1 study_NN1 ,_, K_ZZ1 corresponds_VVZ to_II a_AT1 similarity_NN1 matrix_NN1 of_IO diseases_NN2 with_IW omics_NN1 data_NN ,_, and_CC G_ZZ1 corresponds_VVZ to_II an_AT1 adjacency_NN1 matrix_NN1 in_II which_DDQ each_DD1 element_NN1 indicate_VV0 if_CS two_MC diseases_NN2 share_VV0 the_AT same_DA therapeutic_JJ targets/drugs_NN2 or_CC not_XX ._. 
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<s>
Table_NN1 7_MC shows_VVZ the_AT results_NN2 for_IF a_AT1 model_NN1 specification_NN1 that_CST includes_VVZ seven_MC interaction_NN1 terms_NN2 ._. 
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<s>
The_AT emergent_JJ structure_NN1 given_VVN by_II the_AT Gauss-like_JJ |_NULL u_ZZ1 |_NULL -distribution_JJ with_IW zero_NN1 electron_NN1 current_NN1 will_VM appear_VVI for_IF higher_JJR disorder_NN1 values_NN2 ._. 
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<s>
The_AT pseudocode_NN1 in_II Algorithm_NN1 2_MC shows_VVZ the_AT case_NN1 where_RRQ τ_NULL is_VBZ drawn_VVN once_RR per_II iteration_NN1 and_CC the_AT same_DA value_NN1 is_VBZ used_VVN for_IF all_DB ∈1_FO :_: n∈1:N_FO ,_, but_CCB τ_NULL can_VM also_RR be_VBI drawn_VVN separately_RR for_IF each_DD1 n_ZZ1 ,_, provided_CS21 that_CS22 the_AT draws_NN2 are_VBR independent_JJ of_IO each_PPX221 other_PPX222 and_CC of_IO all_DB other_JJ random_JJ draws_NN2 in_II the_AT algorithm_NN1 ._. 
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<s>
Thus_RR ,_, edges_NN2 of_IO a_AT1 tumor_NN1 graph_NN1 Gp_NN1 capture_VV0 the_AT complete_JJ available_JJ information_NN1 about_II partial_JJ ordering_NN1 of_IO alteration_NN1 events_NN2 in_II tumor_NN1 p_ZZ1 (_( Fig._NN1 1_MC1 )_) ._. 
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<s>
Our_APPGE results_NN2 show_VV0 that_CST MetaRib_NP1 can_VM deal_VVI with_IW larger_JJR datasets_NN2 and_CC recover_VVI more_DAR rRNA_NN1 genes_NN2 ,_, which_DDQ achieve_VV0 around_RG 60_MC times_NNT2 speedup_VV0 and_CC higher_JJR F1_FO score_NN1 compared_VVN to_II EMIRGE_NP1 in_II simulated_JJ datasets_NN2 ._. 
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Thus_RR by_II the_AT induction_NN1 hypothesis_NN1 ,_, <equation>_FO ._. 
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<s>
Similarly_RR ,_, denote_VV0 by_II <equation>_FO the_AT family_NN1 of_IO disjoint_JJ open_JJ intervals_NN2 on_II which_DDQ <equation>_FO ._. 
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<s>
It_PPH1 can_VM be_VBI easily_RR installed_VVN from_II source_NN1 code_NN1 or_CC using_VVG stand-alone_JJ installers_NN2 ._. 
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<s>
The_AT two_MC regimes_NN2 distinguish_VV0 themselves_PPX2 by_II the_AT behavior_NN1 of_IO the_AT limit_NN1 K_ZZ1 →_NULL ∞_FO :_: in_II regime_NN1 IIb_VV0 this_DD1 limit_NN1 is_VBZ accompanied_VVN by_II both_RR n_ZZ1 →_NULL ∞_FO and_CC ?_ZZ1 →_NULL ∞_FO ,_, whereas_CS in_II regime_NN1 IIa_NP1 we_PPIS2 have_VH0 n_ZZ1 →_NULL ∞_FO but_CCB ?_ZZ1 remains_VVZ finite_JJ ._. 
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<s>
Trio_NN1 WES_NP1 identified_VVD a_AT1 de_NP1 novo_NN1 intronic_JJ SNV_NP1 (_( c.4026-9A>G_FO )_) in_II EP300_FO (_( transcript_NN1 NM001429.3_FO )_) ._. 
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<s>
The_AT IDE_NN1 kernel_NN1 k_ZZ1 (_( us_PPIO2 |_NULL θ_NULL )_) in_II equation_NN1 1_MC1 )_) can_VM be_VBI interpreted_VVN as_II a_AT1 weighting_NN1 function_NN1 that_CST maps_VVZ the_AT process_NN1 at_II location_NN1 u_ZZ1 and_CC time_NNT1 t_ZZ1 to_II the_AT process_NN1 at_II location_NN1 s_ZZ1 and_CC time_NNT1 t+1_FO ._. 
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<s>
Intuitively_RR ,_, consider_VV0 the_AT negative_NN1 of_IO the_AT logarithm_NN1 of_IO the_AT p_NN1 value_NN1 as_II the_AT linear_JJ function_NN1 of_IO the_AT sample_NN1 size_NN1 ._. 
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<s>
This_DD1 is_VBZ the_AT motivation_NN1 for_IF Section_NN1 7_MC where_RRQ we_PPIS2 introduce_VV0 recent_JJ experimental_JJ work_NN1 for_IF the_AT lifetime_NNT1 statistics_NN of_IO soap_NN1 films_NN2 ,_, which_DDQ shows_VVZ high_JJ initial_JJ failure_NN1 rates_NN2 due_II21 to_II22 well-identified_JJ defects_NN2 ._. 
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<s>
The_AT second_MD approach_NN1 is_VBZ based_VVN on_II the_AT mutational_JJ spectrum_NN1 of_IO 96_MC trinucleotides_NN2 (_( immediate_JJ 5_MC and_CC 3_MC bases_NN2 of_IO each_DD1 mutated_JJ base_NN1 ,_, named_VVN MS96_FO )_) in_II each_DD1 patient_NN1 or_CC the_AT decomposed_JJ mutational_JJ signatures_NN2 using_VVG non-negative_JJ matrix_NN1 factorization_NN1 (_( NMF_NP1 )_) (_( Alexandrov_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) ._. 
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Relevant_JJ proofs_NN2 are_VBR given_VVN to_II certificate_NN1 the_AT above_JJ two_MC conclusions_NN2 ._. 
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<s>
For_IF a_AT1 large_JJ system_NN1 size_NN1 ,_, the_AT relative_JJ density_NN1 fluctuations_NN2 become_VV0 small_JJ ,_, and_CC the_AT density_NN1 A_ZZ1 evolves_VVZ according_II21 to_II22 a_AT1 low_JJ noise_NN1 dynamics_NN in_II this_DD1 limit_NN1 ._. 
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<s>
The_AT mean_JJ correlation_NN1 according_II21 to_II22 figure_NN1 can_VM also_RR become_VVI weaker_JJR for_IF more_RGR recent_JJ times_NNT2 for_IF the_AT standard_JJ correlation_NN1 matrices_NN2 ._. 
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In_II Fig._NN1 4_MC ,_, we_PPIS2 also_RR show_VV0 some_DD statistical_JJ properties_NN2 of_IO the_AT simulated_JJ networks_NN2 ._. 
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<s>
Instead_RR ,_, cars_NN2 keep_VV0 accelerating_VVG by_II alc_NN1 as_CSA shown_VVN in_II <equation>_FO and_CC trucks_NN2 drive_VV0 at_II a_AT1 constant_JJ velocity_NN1 as_CSA shown_VVN in_II <equation>_FO ._. 
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The_AT force_NN1 is_VBZ the_AT sine_NN1 model_NN1 of_IO equation_NN1 with_IW ,_, and_CC varies_VVZ in_RP ._. 
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<s>
The_AT latter_DA can_VM be_VBI obtained_VVN from_II the_AT scalar_JJ recursion_NN1 ,_, it_PPH1 depends_VVZ on_II γ_NULL and_CC b_ZZ1 ,_, and_CC the_AT asymptotic_JJ expansion_NN1 of_IO the_AT rigidity_NN1 threshold_NN1 is_VBZ of_IO the_AT form_NN1 with_IW a_AT1 constant_JJ γ_NULL r(b)_NNU easily_RR determined_VVN from_II the_AT large_JJ n_ZZ1 behavior_NN1 of_IO :_: for_IF γ_NULL <_FO γ_NULL r(b)_NNU one_PN1 has_VHZ <equation>_FO as_CSA n_ZZ1 →_NULL ∞_FO ,_, while_CS remains_NN2 bounded_VVN for_IF γ_NULL ≥_FO γ_NULL r(b)_NNU ._. 
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<s>
For_IF the_AT all-or-nothing_JJ market_NN1 ,_, they_PPHS2 find_VV0 that_CST the_AT optimal_JJ annuitisation_NN1 time_NNT1 is_VBZ deterministic_JJ as_II an_AT1 artifact_NN1 of_IO CRRA_NP1 utility_NN1 ._. 
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<s>
Indeed_RR ,_, a_AT1 growing_JJ literature_NN1 witnesses_VVZ that_CST a_AT1 common_JJ feature_NN1 of_IO systems_NN2 with_IW confinement_NN1 is_VBZ their_APPGE anomalous_JJ quantum_NN1 dynamics_NN with_IW signatures_NN2 of_IO non-thermal_JJ behavior_NN1 ._. 
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Second_MD ,_, when_CS used_VVN as_II a_AT1 diagnostic_JJ tool_NN1 ,_, the_AT nonparametric_JJ estimator_NN1 can_VM exclude_VVI false_JJ models_NN2 easily_RR when_CS the_AT dependence_NN1 is_VBZ high_JJ and_CC the_AT discreteness_NN1 level_NN1 is_VBZ low_JJ ._. 
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Generally_RR speaking_VVG ,_, the_AT long-range_JJ correlations_NN2 for_IF small_JJ and_CC large_JJ fluctuations_NN2 and_CC the_AT fat-tailed_JJ probability_NN1 distribution_NN1 in_II fluctuations_NN2 are_VBR the_AT main_JJ sources_NN2 for_IF the_AT multifractality_NN1 &lsqb;_( 23_MC &rsqb;_) ._. 
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<s>
If_CS we_PPIS2 impose_VV0 the_AT condition_NN1 <equation>_FO ,_, the_AT asymptotic_JJ normality_NN1 of_IO Theorem_NN1 5_MC (_( b_ZZ1 )_) is_VBZ in_II31 accordance_II32 with_II33 Theorem_NN1 1_MC1 as_CS21 if_CS22 we_PPIS2 had_VHD known_VVN those_DD2 non-zero_JJ components_NN2 beforehand_RR ._. 
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<s>
The_AT simulation_NN1 library_NN1 RSSALib_NP1 provides_VVZ a_AT1 full_JJ implementation_NN1 of_IO all_DB known_JJ RSSA_NN1 formulations_NN2 to_TO offer_VVI their_APPGE computational_JJ advantages_NN2 in_II dealing_VVG with_IW varying_JJ complexities_NN2 of_IO biological_JJ networks_NN2 ._. 
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<s>
We_PPIS2 refer_VV0 to_II the_AT results_NN2 obtained_VVN under_II such_DA an_AT1 assumption_NN1 as_CSA the_AT baseline_NN1 case_NN1 in_II this_DD1 paper_NN1 and_CC the_AT corresponding_JJ valuation_NN1 becomes_VVZ simple_JJ ._. 
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Table_NN1 1_MC1 shows_VVZ proteins_NN2 that_CST have_VH0 less_DAR than_CSN 10_MC taxonomic_JJ assignments_NN2 ._. 
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An_AT1 automated_JJ counting_NN1 of_IO beads_NN2 is_VBZ required_VVN for_IF many_DA2 high-throughput_JJ experiments_NN2 such_II21 as_II22 studying_VVG mimicked_JJ bacterial_JJ invasion_NN1 processes_NN2 ._. 
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The_AT adjustment_NN1 of_IO the_AT open_JJ market_NN1 operating_NN1 rate_NN1 directly_RR affects_VVZ the_AT supply_NN1 of_IO money_NN1 and_CC interest_NN1 rates_NN2 and_CC further_RRR affects_VVZ the_AT securities_NN2 market_VV0 ._. 
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<s>
These_DD2 ideas_NN2 prompt_VV0 the_AT initial_JJ motivation_NN1 of_IO this_DD1 study_NN1 ,_, where_CS we_PPIS2 investigate_VV0 growth_NN1 path_NN1 heterogeneity_NN1 in_II China_NP1 '_NULL s_ZZ1 provincial_JJ economies_NN2 and_CC the_AT roles_NN2 that_CST geofigurey_NN1 and_CC institutions_NN2 play_VV0 ._. 
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More_DAR examples_NN2 can_VM be_VBI found_VVN in_II Cs?rg?_NP1 and_CC Horváth_NP1 (_( 1997_MC )_) ._. 
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<s>
The_AT results_NN2 in_II Table_NN1 5_MC agree_VV0 with_IW those_DD2 obtained_VVN for_IF locally_RR optimal_JJ designs_NN2 ._. 
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<s>
Transfer_VV0 learning_NN1 addresses_VVZ this_DD1 challenge_NN1 with_IW the_AT goal_NN1 to_TO improve_VVI the_AT generalization_NN1 on_II a_AT1 target_NN1 task_NN1 TT_UH using_VVG the_AT knowledge_NN1 in_II DMS_NNU2 and_CC DMT_NP1 ,_, as_II31 well_II32 as_II33 their_APPGE corresponding_JJ tasks_NN2 TS_ZZ2 and_CC TT_UH ._. 
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<s>
Transfer_VV0 learning_NN1 addresses_VVZ this_DD1 challenge_NN1 with_IW the_AT goal_NN1 to_TO improve_VVI the_AT generalization_NN1 on_II a_AT1 target_NN1 task_NN1 TT_UH using_VVG the_AT knowledge_NN1 in_II DMS_NNU2 and_CC DMT_NP1 ,_, as_II31 well_II32 as_II33 their_APPGE corresponding_JJ tasks_NN2 TS_ZZ2 and_CC TT_UH ._. 
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Transfer_VV0 learning_NN1 can_VM be_VBI categorized_VVN into_II three_MC categories_NN2 :_: (_( i_ZZ1 )_) unsupervised_JJ transfer_NN1 learning_NN1 ,_, (_( ii_MC )_) transductive_JJ transfer_NN1 learning_NN1 and_CC (_( iii_MC )_) inductive_JJ transfer_NN1 learning_NN1 ._. 
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<s>
With_IW the_AT use_NN1 of_IO CaSQ_NP1 ,_, as_CSA demonstrated_VVN in_II this_DD1 study_NN1 ,_, we_PPIS2 can_VM now_RT obtain_VVI large-scale_JJ Boolean_NN1 models_NN2 that_CST can_VM be_VBI executed_VVN using_VVG popular_JJ modelling_NN1 software_NN1 that_CST can_VM import_VVI SBML-qual_JJ files_NN2 ._. 
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<s>
Alternative_JJ approaches_NN2 to_II estimation_NN1 of_IO stable_JJ regression_NN1 models_NN2 are_VBR provided_VVN by_II Lambert_NP1 and_CC Lindsey_NP1 (_( 1999_MC )_) and_CC Achcar_NP1 and_CC Lopes_NP1 (_( 2016_MC )_) ._. 
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<s>
One_MC1 could_VM avoid_VVI such_DA issues_NN2 by_II only_RR fitting_VVG the_AT data_NN at_II large_JJ wavenumbers_NN2 with_IW the_AT reduced_JJ formula_NN1 given_VVN by_II Eq_NN1 ._. 
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(_( 1_MC1 )_) ._. 
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<s>
Therefore_RR ,_, finding_VVG (_( 1_MC1 )_) j*_FO (_( θ_NULL Mj1_FO )_) in_II equation_NN1 17_MC is_VBZ exactly_RR equivalent_JJ to_II finding_VVG an_AT1 augmented_JJ optimal_JJ design_NN1 as_CSA defined_VVN in_II equation_NN1 15_MC ._. 
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<s>
The_AT popular_JJ choice_NN1 of_IO this_DD1 utility_NN1 having_VHG enough_DD justifications_NN2 is_VBZ the_AT logarithmic_JJ entropy(4)u(r)=log(r)_FO ,_, which_DDQ leads_VVZ to_II the_AT constraint(5)E_NN1 (_( log_NN1 (_( r_ZZ1 )_) )_) =r=1Nlog(r)f(r)=c1_NN1 (_( some_DD constant_JJ )_) ._. 
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<s>
The_AT most_RGT important_JJ justification_NN1 behind_II the_AT consideration_NN1 of_IO this_DD1 logarithmic_JJ utility_NN1 in_II (_( 4_MC )_) can_VM be_VBI understood_VVN by_II re-expressing_VVG the_AT associated_JJ constraint_NN1 in_II (_( 5_MC )_) that_CST the_AT left_JJ hand_NN1 side_NN1 of_IO the_AT above_JJ form_NN1 of_IO the_AT constraint_NN1 is_VBZ nothing_PN1 but_II the_AT (_( weighted_JJ )_) geometric_JJ mean_NN1 of_IO the_AT ranks_NN2 with_IW weights_NN2 being_VBG the_AT corresponding_JJ model_NN1 probabilities_NN2 ._. 
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Fourth_MD ,_, we_PPIS2 exploit_VV0 that_CST the_AT boundedness_NN1 of_IO terminal_JJ portfolio_NN1 values_NN2 in_II an_AT1 appropriate_JJ sense_NN1 implies_VVZ boundedness_NN1 of_IO the_AT strategies_NN2 themselves_PPX2 (_( again_RT ,_, in_II an_AT1 appropriate_JJ sense_NN1 )_) ;_; this_DD1 is_VBZ false_JJ in_II continuous-time_JJ frictionless_JJ markets_NN2 ,_, but_CCB true_JJ in_II our_APPGE setting_NN1 ._. 
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It_PPH1 will_VM be_VBI determined_VVN later_RRR ,_, see_VV0 equation_NN1 (_( 66_MC )_) ._. 
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<s>
Our_APPGE new_JJ method_NN1 QDeep_NN1 strikes_VVZ an_AT1 ideal_JJ balance_NN1 to_TO deliver_VVI top-notch_JJ performance_NN1 across_II various_JJ facets_NN2 of_IO model_NN1 quality_NN1 estimation_NN1 simultaneously_RR ._. 
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In_II discriminant_JJ analysis_NN1 ,_, the_AT group-conditional_JJ distribution_NN1 of_IO variables_NN2 is_VBZ commonly_RR assumed_VVN to_TO be_VBI Gaussian_JJ ._. 
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<s>
This_DD1 risk_NN1 management_NN1 activity_NN1 will_VM be_VBI repeated_VVN sequentially_RR ,_, and_CC as_II a_AT1 consequence_NN1 ,_, a_AT1 chain_NN1 of_IO reinsurance_NN1 will_VM be_VBI formed_VVN ._. 
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More_RGR recently_RR ,_, Zeira_NP1 et_RA21 al_RA22 ._. 
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(_( 2017_MC )_) showed_VVD that_CST the_AT CND_NP1 between_II a_AT1 pair_NN of_IO profiles_NN2 can_VM be_VBI computed_VVN in_II linear_JJ time_NNT1 and_CC El-Kebir_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2017_MC )_) gave_VVD an_AT1 integer_NN1 linear_JJ programming_NN1 formulation_NN1 for_IF reconstructing_VVG a_AT1 phylogenetic_JJ tree_NN1 between_II CNPs_NP1 with_IW the_AT minimum_JJ number_NN1 of_IO events_NN2 ._. 
</s>
<s>
We_PPIS2 call_VV0 the_AT reduced_JJ genealogies_NN2 T._NP1 MLEs_NP2 ,_, standard_JJ deviations_NN2 (_( SD_NP1 )_) of_IO bootstrap_NN1 replications_NN2 ,_, and_CC approximate_VV0 95%_NNU confidence_NN1 intervals_NN2 (_( CI_FO )_) for_IF parameters_NN2 of_IO our_APPGE model_NN1 (_( 4_MC )_) (_( left_JJ )_) and_CC the_AT Gaussian_JJ process_NN1 (_( right_RR )_) ._. 
</s>
<s>
The_AT same_DA terminology_NN1 is_VBZ also_RR applied_VVN to_II the_AT notations_NN2 for_IF the_AT objective_JJ functions_NN2 in_II Eq_NN1 ._. 
</s>
<s>
(_( 6_MC )_) ._. 
</s>
<s>
In_II the_AT case_NN1 of_IO 0<_FO qn_NNU <1_FO ,_, the_AT average_JJ collision_NN1 frequency_NN1 in_II the_AT q-distributed_JJ plasma_NN1 is_VBZ slightly_RR less_DAR than_CSN that_DD1 in_II the_AT Maxwell-distributed_JJ plasma_NN1 ,_, but_CCB in_II the_AT case_NN1 of_IO 1<_FO qn_NNU <3/2_FU ,_, the_AT average_JJ collision_NN1 frequency_NN1 in_II the_AT q-distributed_JJ plasma_NN1 is_VBZ more_DAR than_CSN that_DD1 in_II the_AT Maxwell-distributed_JJ plasma_NN1 ,_, and_CC increases_VVZ rapidly_RR with_IW the_AT q-parameter_JJ increases_NN2 ._. 
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<s>
Moreover_RR ,_, the_AT extension_NN1 of_IO modeling_VVG piecewise_RR linear_JJ membership_NN1 functions_NN2 is_VBZ proposed_VVN regarding_II user_NN1 '_NULL s_ZZ1 (_( dis-_NN1 )_) satisfaction_NN1 or_CC economic_JJ preferences_NN2 in_II31 relation_II32 to_II33 (_( marginal_JJ )_) costs_NN2 of_IO acceptance/rejection_NN1 of_IO particular_JJ hypothesis_NN1 elements_NN2 ._. 
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<s>
For_IF unbounded_JJ loss_NN1 functions_NN2 ,_, such_II21 as_II22 the_AT absolute_JJ error_NN1 loss_NN1 or_CC Huber_NP1 loss_NN1 ,_, a_AT1 penalized_JJ cost_NN1 approach_NN1 will_VM place_VVI an_AT1 outlier_JJR in_II a_AT1 segment_NN1 on_II its_APPGE own_DA if_CS that_DD1 outlier_JJR is_VBZ sufficiently_RR extreme_JJ ._. 
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<s>
Finally_RR ,_, the_AT feature_NN1 vectors_NN2 obtained_VVN were_VBDR flattened_VVN to_II a_AT1 single_JJ vector_NN1 ._. 
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<s>
Design_NN1 2_MC (_( middle_JJ right_NN1 )_) is_VBZ ,_, just_RR like_II the_AT baseline_NN1 design_NN1 ,_, a_AT1 data_NN fusion_NN1 design_NN1 ,_, but_CCB the_AT core_NN1 component_NN1 is_VBZ increased_VVN by_II two_MC variables_NN2 ._. 
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<s>
Therefore_RR ,_, we_PPIS2 define_VV0 a_AT1 canonical_JJ representation_NN1 of_IO the_AT chains_NN2 corresponding_VVG to_II a_AT1 minimal_JJ k-instance_NN1 :_: Given_VVN two_MC strings_NN2 P_ZZ1 and_CC T_ZZ1 ,_, a_AT1 chain_NN1 of_IO P_ZZ1 versus_II T_ZZ1 is_VBZ canonical_JJ if_CS each_DD1 prefix_NN1 of_IO length_NN1 i_MC1 of_IO this_DD1 chain_NN1 ,_, for_IF i=1_FO |_NULL P_ZZ1 |_NULL ,_, corresponds_VVZ to_II some_DD minimal_JJ k-instance_NN1 of_IO P&lsqb;1i&rsqb;_FO in_II T._NP1 Table_NN1 summarizes_VVZ detailed_JJ information_NN1 about_II the_AT bidirectional_JJ cases_NN2 ._. 
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<s>
Wage_NN1 (_( <equation>_FO )_) defined_VVD as_CSA employee_NN1 '_NULL s_ZZ1 compensation_NN1 per_II hour_NNT1 worked_VVD ._. 
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<s>
The_AT user_NN1 preferences_NN2 vector_NN1 for_IF user_NN1 i_ZZ1 is_VBZ defined_VVN as_II :_: <equation>_FO ,_, where<equation>_FO ._. 
</s>
<s>
Another_DD1 type_NN1 of_IO measures_NN2 are_VBR those_DD2 relying_VVG on_II counting_VVG the_AT number_NN1 of_IO connected_JJ clusters_NN2 in_II the_AT colored_JJ subgraph_NN1 c_ZZ1 ._. 
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<s>
In_II this_DD1 latter_DA model_NN1 ,_, data_NN also_RR remains_VVZ secret_JJ to_II the_AT possibly_RR untrusted_JJ curator_NN1 ._. 
</s>
<s>
In_II what_DDQ follows_VVZ ,_, we_PPIS2 first_MD difference_NN1 the_AT data_NN to_TO remove_VVI any_DD trend_NN1 ,_, as_CSA is_VBZ commonplace_JJ prior_II21 to_II22 secondary_JJ analysis_NN1 (_( Ahrabian_JJ et_RA21 al_RA22 ._. 
</s>
<s>
2017_MC )_) ._. 
</s>
<s>
Our_APPGE universe_NN1 includes_VVZ only_RR primary_JJ schools_NN2 as_II a_AT1 reference_NN1 ._. 
</s>
<s>
In_II fact_NN1 ,_, for_REX21 example_REX22 for_IF stochastic_JJ volatility_NN1 or_CC rough_JJ volatility_NN1 models_NN2 ,_, it_PPH1 turns_VVZ out_RP that_CST the_AT classical_JJ superhedging_JJ price_NN1 coincides_VVZ with_IW the_AT model-independent_JJ one_PN1 and_CC is_VBZ so_RG high_JJ that_CST for_IF Markovian_JJ payoffs_NN2 of_IO the_AT form_NN1 <equation>_FO ,_, like_II e.g._REX European_JJ call_NN1 and_CC put_VV0 options_NN2 ,_, the_AT optimal_JJ superhedging_JJ strategy_NN1 must_VM be_VBI chosen_VVN to_TO be_VBI of_IO buy-and-hold_JJ type_NN1 ;_; see_VV0 e.g._REX Cvitani_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
&lsqb;_( 8_MC &rsqb;_) ,_, Frey_NP1 and_CC Sin_NN1 &lsqb;_( 15_MC &rsqb;_) ,_, Dolinsky_NP1 and_CC Neufeld_NP1 &lsqb;_( 10_MC &rsqb;_) and_CC Neufeld_NP1 &lsqb;_( 25_MC &rsqb;_) ._. 
</s>
<s>
In_II31 terms_II32 of_II33 reducing_VVG noise_NN1 and_CC extracting_VVG signal_NN1 ,_, Chapter_NN1 6_MC explores_VVZ the_AT scaling_NN1 of_IO ultrametric_JJ through_II metric_JJ mapping_NN1 ._. 
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<s>
In_II31 addition_II32 to_II33 gravity_NN1 factors_NN2 ,_, they_PPHS2 control_VV0 for_IF host_NN1 country_NN1 policy_NN1 variables_NN2 as_CSA FDI_NP1 determinants_NN2 ._. 
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<s>
Overall_RR speaking_VVG ,_, 3-hop-based_JJ indices_NN2 outperform_VV0 2-hop-based_JJ indices_NN2 on_II ROC-AUC_NP1 ,_, and_CC 3-hop-based_JJ indices_NN2 and_CC 2-hop-based_JJ indices_NN2 are_VBR competitive_JJ on_II precision_NN1 ._. 
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<s>
To_TO facilitate_VVI comparison_NN1 to_II other_JJ studies_NN2 ,_, the_AT following_JJ text_NN1 discusses_VVZ these_DD2 parameter_NN1 estimates_VVZ in_II the_AT context_NN1 of_IO two_MC recent_JJ studies_NN2 ,_, one_MC1 with_IW a_AT1 similar_JJ sample_NN1 and_CC one_PN1 with_IW a_AT1 similar_JJ model_NN1 ._. 
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<s>
One_PN1 might_VM expect_VVI an_AT1 increase_NN1 in_II bribes_NN2 in_II future_JJ rounds_NN2 of_IO property_NN1 tax_NN1 collection_NN1 ._. 
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<s>
It_PPH1 is_VBZ very_RG cost-effective_JJ to_TO bring_VVI into_II use_NN1 group_NN1 rewarding_VVG as_CS31 long_CS32 as_CS33 r_ZZ1 is_VBZ not_XX very_RG small_JJ ._. 
</s>
<s>
What_DDQ are_VBR the_AT mechanisms_NN2 that_CST result_VV0 in_II these_DD2 critical_JJ value_NN1 of_IO ?_? 
</s>
<s>
Moreover_RR ,_, in_II31 line_II32 with_II33 the_AT original_JJ TITE-CRM_NN1 which_DDQ showed_VVD that_CST the_AT linear_JJ weight_NN1 function_NN1 yielded_VVD similar_JJ operating_NN1 characteristics_NN2 compared_VVN to_II more_RGR complicated_JJ weight_NN1 functions_NN2 ,_, we_PPIS2 assume_VV0 that_CST the_AT weight_NN1 functions_NN2 are_VBR linear_JJ ,_, that_REX21 is_REX22 ,_, <equation>_FO ._. 
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<s>
Dose_NN1 skipping_NN1 was_VBDZ not_XX allowed_VVN ._. 
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<s>
We_PPIS2 were_VBDR interested_JJ in_II the_AT probability_NN1 of_IO a_AT1 second_MD delivery_NN1 given_VVN the_AT characteristics_NN2 of_IO the_AT mother_NN1 (_( age_NN1 and_CC social_JJ economic_JJ status_NN1 )_) at_II the_AT first_MD delivery_NN1 and_CC characteristics_NN2 of_IO the_AT first_MD delivery_NN1 (_( gender_NN1 of_IO the_AT child_NN1 ,_, pregnancy_NN1 induced_VVN with_IW assisted_JJ reproductive_JJ technology_NN1 ,_, and_CC pre-term_JJ birth_NN1 defined_VVD as_RG gestational_JJ age_NN1 <_FO 37_MC weeks_NNT2 )_) ._. 
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<s>
This_DD1 version_NN1 of_IO the_AT grid_NN1 is_VBZ much_RR more_RGR straightforward_JJ ;_; each_DD1 clone_NN1 is_VBZ clearly_RR distinguished_VVN on_II the_AT grid_NN1 (_( Fig._NN1 5b_FO and_CC c_ZZ1 )_) ._. 
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<s>
First_MD ,_, a_AT1 global_JJ edge_NN1 weight_NN1 threshold_NN1 is_VBZ applied_VVN ._. 
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<s>
Then_RT ,_, we_PPIS2 develop_VV0 a_AT1 direct_JJ and_CC deterministic_JJ method_NN1 ,_, Soft_JJ K-indicators_NN2 Alternative_JJ Projection_NN1 (_( SKAP_NP1 )_) algorithm_NN1 ,_, which_DDQ can_VM be_VBI solved_VVN by_II a_AT1 double-layer_JJ alternating_JJ projection_NN1 framework_NN1 ._. 
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<s>
It_PPH1 can_VM be_VBI mathematically_RR proved_VVN that_CST as_CS31 long_CS32 as_CS33 the_AT Zipf_NN1 pattern_NN1 of_IO city_NN1 size_NN1 distribution_NN1 remains_VVZ unchanged_JJ ,_, the_AT analytical_JJ conclusion_NN1 will_VM not_XX change_VVI due_II21 to_II22 different_JJ urban_JJ boundaries_NN2 ._. 
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<s>
The_AT goal_NN1 is_VBZ to_TO maximize_VVI the_AT expected_JJ utility_NN1 of_IO terminal_JJ wealth_NN1 ._. 
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<s>
The_AT performances_NN2 of_IO estimates_NN2 are_VBR studied_VVN over_II repeated_JJ samples_NN2 ,_, drawn_VVN from_II the_AT surrogate_NN1 population_NN1 ._. 
</s>
<s>
That_REX21 is_REX22 ,_, <equation>_FO it_PPH1 is_VBZ <equation>_FO ,_, i.e._REX a_AT1 permutation_NN1 invariable_JJ likelihood_NN1 ._. 
</s>
<s>
Antai_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2015_MC )_) focus_VV0 on_II estimating_VVG a_AT1 dynamic_JJ spatial_JJ panel_NN1 data_NN model_NN1 with_IW a_AT1 specified_JJ source_NN1 of_IO endogeneity_NN1 for_IF the_AT time-varying_JJ spatial_JJ weight_NN1 matrices_NN2 when_RRQ the_AT time_NNT1 period_NN1 T_ZZ1 is_VBZ short_JJ ._. 
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<s>
In_II Section_NN1 2_MC ,_, we_PPIS2 present_VV0 our_APPGE new_JJ methodology_NN1 for_IF the_AT general_JJ hypotheses_NN2 (_( 1.1_MC )_) ._. 
</s>
<s>
Our_APPGE results_NN2 were_VBDR discussed_VVN in_II the_AT case_NN1 of_IO an_AT1 observable_JJ 1-dimensional_JJ output_NN1 process_NN1 ._. 
</s>
<s>
The_AT 2L2-consistency_NN1 of_IO E_ZZ1 is_VBZ proven_VVN in_II Penrose_NP1 and_CC Yukich_NP1 (_( 2013_MC ,_, Theorem_NN1 2.4_MC )_) for_IF i.i.d_NNU ._. 
</s>
<s>
The_AT computation_NN1 time_NNT1 of_IO BAQR_NN1 is_VBZ averaged_VVN over_RG 100_MC repetitions_NN2 and_CC its_APPGE standard_JJ deviation_NN1 is_VBZ included_VVN in_II parentheses_NN2 ._. 
</s>
<s>
The_AT Mundell–Fleming_JJ model_NN1 ,_, with_IW two_MC core_NN1 assumptions_NN2 of_IO perfect_JJ capital_NN1 mobility_NN1 and_CC sticky_JJ domestic_JJ price_NN1 ,_, suggests_VVZ that_CST higher_JJR interest_NN1 rates_NN2 produce_VV0 a_AT1 greater_JJR demand_NN1 for_IF domestic_JJ assets_NN2 and_CC hence_RR lead_VV0 to_II a_AT1 negative_JJ relationship_NN1 between_II the_AT two_MC variables_NN2 (_( Fleming_NP1 1962_MC ;_; Mundell_NP1 1963_MC )_) ._. 
</s>
<s>
We_PPIS2 find_VV0 evidence_NN1 of_IO bank_NN1 deposits_NN2 increasing_VVG and_CC credit_NN1 contracting_VVG in_II areas_NN2 experiencing_VVG more_RGR severe_JJ demonetization_NN1 ._. 
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<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 cover_VV0 the_AT required_JJ stability_NN1 and_CC tightness_NN1 results_NN2 ._. 
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<s>
Consequently_RR ,_, we_PPIS2 derived_VVD an_AT1 algorithm_NN1 which_DDQ iteratively_RR converges_VVZ to_II this_DD1 proximal_JJ operator_NN1 ._. 
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<s>
We_PPIS2 remind_VV0 that_DD1 PRAM_NN1 was_VBDZ introduced_VVN by_II Kooiman_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 1997_MC )_) and_CC further_RRR explored_VVN by_II Gouweleeuw_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 1997_MC )_) and_CC De_NP1 Wolf_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 1997_MC )_) ._. 
</s>
<s>
The_AT results_NN2 are_VBR not_XX driven_VVN by_II trend-chasing_NN1 in_II flows_NN2 that_CST might_VM drive_VVI both_RR HY-NEIO_JJ and_CC contemporaneous_JJ bond_NN1 returns_NN2 ,_, as_CSA we_PPIS2 control_VV0 for_IF cumulative_JJ returns_NN2 of_IO each_DD1 asset_NN1 class_NN1 ._. 
</s>
<s>
In_II contrast_NN1 ,_, item-based_NN1 CF_VV0 methods_NN2 &lsqb;_( 5_MC &rsqb;_) ,_, &lsqb;_( 25_MC &rsqb;_) group_NN1 items_NN2 based_VVN on_II item-item_JJ similarity_NN1 matrix_NN1 ._. 
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<s>
At_II the_AT meantime_NNT1 ,_, the_AT total_JJ quantity_NN1 of_IO energy_NN1 and_CC water_NN1 consumption_NN1 will_VM also_RR be_VBI low_JJ ._. 
</s>
<s>
Working_VVG in_II the_AT ground_NN1 state_NN1 ,_, the_AT entanglement_NN1 Hamiltonian_JJ describes_VVZ again_RT free_JJ bosons_NN2 or_CC fermions_NN2 and_CC is_VBZ obtained_VVN from_II the_AT correlation_NN1 functions_NN2 via_II high-precision_JJ numerics_NN2 for_IF up_II21 to_II22 several_DA2 hundred_NNO sites_NN2 ._. 
</s>
<s>
Chromosomal_JJ conformation_NN1 capture_NN1 experiments_NN2 (_( Hi-C_FW )_) provide_VV0 a_AT1 quantitative_JJ way_NN1 to_TO infer_VVI the_AT spatial_JJ proximity_NN1 of_IO DNA_NN1 segments_NN2 (_( Dekker_NP1 et_RA21 al._RA22 ,_, 2002_MC ;_; Lieberman-Aiden_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ._. 
</s>
<s>
At_II each_DD1 base_NN1 position_NN1 ,_, we_PPIS2 set_VV0 the_AT score_NN1 to_TO be_VBI the_AT larger_JJR of_IO the_AT two_MC scores_NN2 at_II that_DD1 position_NN1 ._. 
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<s>
A_AT1 cylindrical_JJ sample_NN1 with_IW an_AT1 inner_JJ diameter_NN1 of_IO 12_MC mm_NNU and_CC a_AT1 thickness_NN1 of_IO 4.34_MC mm_NNU was_VBDZ filled_VVN with_IW electronic_JJ quality_NN1 SF6_FO corresponding_VVG to_II 99.98_MC %_NNU purity_NN1 (_( from_II Alphagaz-Air_NP1 Liquide_NP1 )_) ._. 
</s>
<s>
The_AT algorithmic_JJ simplicity_NN1 of_IO sequential-proposal_JJ facilitates_VVZ the_AT use_NN1 of_IO a_AT1 large_JJ number_NN1 of_IO proposals_NN2 in_II each_DD1 iteration_NN1 ._. 
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<s>
Clearly_RR ,_, taking_VVG into_II account_NN1 such_DA an_AT1 inhibitory_JJ function_NN1 ,_, the_AT valid_JJ question_NN1 is_VBZ the_AT safety_NN1 of_IO fluoride_NN1 for_IF humans_NN2 ,_, especially_RR since_CS in_II many_DA2 countries_NN2 tap_VV0 water_NN1 and_CC table_NN1 salt_NN1 come_VV0 fluorinated_JJ ._. 
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<s>
The_AT R_NP1 package_NN1 of_IO 2DImpute_FO is_VBZ freely_RR available_JJ at_II GitHub_NP1 (_( https_NNU :_: )_) ._. 
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<s>
There_EX is_VBZ now_RT a_AT1 wide_JJ literature_NN1 on_II SSL_NP1 techniques_NN2 ,_, for_REX21 example_REX22 ,_, Grandvalet_NP1 and_CC Bengio_NP1 (_( 2005_MC )_) ,_, Elkan_NP1 and_CC Neto_NP1 (_( 2008_MC )_) ,_, and_CC Berthelot_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2019_MC )_) ,_, which_DDQ are_VBR too_RG numerous_JJ to_TO discuss_VVI here_RL ;_; see_VV0 van_NP1 Engelen_NP1 and_CC Hoos_NP2 (_( 2020_MC )_) for_IF a_AT1 recent_JJ survey_NN1 of_IO SSL_NP1 techniques_NN2 ._. 
</s>
<s>
The_AT number_NN1 of_IO second-level_JJ hubs_NN2 will_VM increase_VVI ,_, and_CC the_AT ratio_NN1 of_IO hub_NN1 costs_VVZ to_TO total_VVI costs_NN2 will_VM increase_VVI ._. 
</s>
<s>
The_AT estimation_NN1 of_IO reinsurance_NN1 premiums_NN2 under_II the_AT net_JJ premium_JJ principle_NN1 (_( 1_MC1 )_) using_VVG univariate_NN1 extreme_JJ value_NN1 methods_NN2 was_VBDZ studied_VVN in_II Beirlant_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2001_MC )_) ._. 
</s>
<s>
Besides_RR ,_, firm_JJ growth_NN1 and_CC firm_JJ business_NN1 risk_NN1 have_VH0 significant_JJ negative_JJ associations_NN2 with_IW both_DB2 short-term_JJ and_CC long-term_JJ leverages_NN2 ._. 
</s>
<s>
This_DD1 automated_JJ procedure_NN1 is_VBZ used_VVN in_II the_AT comparison_NN1 of_IO the_AT proposed_JJ jackstraw_NN1 to_TO feature_VVI selection_NN1 methods_NN2 (_( Supplementary_JJ Material_NN1 )_) ._. 
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<s>
This_DD1 section_NN1 introduces_VVZ our_APPGE data_NN and_CC analyzes_VVZ the_AT empirical_JJ performance_NN1 of_IO FCS_NP2 portfolios_NN2 ._. 
</s>
<s>
The_AT authors_NN2 identified_VVN two_MC marker_NN1 genes_NN2 (_( chuA_NN1 and_CC yjaA_NN1 )_) and_CC an_AT1 anonymous_JJ DNA_NN1 fragment_NN1 (_( TspE4.C2_FO )_) whose_DDQGE combination_NN1 of_IO presence_NN1 or_CC absence_NN1 in_II the_AT genome_NN1 can_VM determine_VVI the_AT phylogenetic_JJ group_NN1 ._. 
</s>
<s>
These_DD2 topological_JJ similarities_NN2 between_II nodes_NN2 have_VH0 also_RR been_VBN used_VVN to_TO define_VVI the_AT graphlet_NN1 correlation_NN1 distance_NN1 (_( GCD_NP1 )_) ,_, which_DDQ is_VBZ the_AT most_RGT sensitive_JJ measure_NN1 of_IO topological_JJ similarity_NN1 between_II networks_NN2 (_( Yaverolu_NP1 et_RA21 al._RA22 ,_, 2014_MC ,_, 2015a_FO )_) ._. 
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<s>
Under_II Assumption_NN1 4.1_MC ,_, solving_VVG (_( 4.2_MC )_) is_VBZ equivalent_JJ to_II solving_VVG the_AT original_JJ problem_NN1 (_( 2.5_MC )_) ._. 
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<s>
Among_II models_NN2 of_IO individual_JJ enhancers_NN2 ,_, we_PPIS2 chose_VVD Kim_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2013_MC )_) for_IF reimplementation_NN1 as_II an_AT1 DNN_NP1 because_CS it_PPH1 has_VHZ a_AT1 sufficiently_RR rich_JJ set_NN1 of_IO mechanisms_NN2 with_IW which_DDQ to_TO model_VVI stripes_NN2 2_MC and_CC 3_MC and_CC is_VBZ thus_RR a_AT1 suitable_JJ test_NN1 bed_NN1 ._. 
</s>
<s>
Finally_RR ,_, the_AT –vblock_NN1 and_CC –sblock_NN1 options_NN2 allow_VV0 the_AT user_NN1 to_TO control_VVI the_AT tradeoff_NN1 between_II compression_NN1 and_CC speed_NN1 related_VVN to_II subsetting_VVG regions_NN2 and_CC samples_NN2 ._. 
</s>
<s>
Then_RT ,_, the_AT average_JJ collision_NN1 frequency_NN1 of_IO the_AT charged_JJ particle_NN1 (_( =e_FO ,_, i_ZZ1 )_) in_II the_AT weakly_RR ionized_VVD plasmas_NN2 with_IW the_AT velocity_NN1 q-distribution_NN1 is_VBZ made_VVN by(17)<equation>_FO ._. 
</s>
<s>
Since_CS <equation>_FO ,_, however_RR ,_, the_AT consumption_NN1 levels_NN2 y1_FO and_CC y2_FO are_VBR not_XX fixedthe_VV0 agent_NN1 does_VDZ think_VVI about_II the_AT problem_NN1 ,_, but_CCB not_XX by_II changing_VVG the_AT ratio_NN1 in_II which_DDQ she_PPHS1 buys_VVZ the_AT products_NN2 ._. 
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<s>
This_DD1 paper_NN1 is_VBZ indeed_RR the_AT first_MD work_NN1 within_II the_AT optimal_JJ insurance_NN1 contract_NN1 design_NN1 literature_NN1 to_TO address_VVI both_RR minimum_JJ charge_NN1 and_CC premium_JJ budget_NN1 constraints_NN2 ._. 
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<s>
Blue_NN1 indicates_VVZ a_AT1 free_JJ traffic_NN1 state_NN1 while_CS red_NN1 indicates_VVZ a_AT1 congested_JJ traffic_NN1 state_NN1 ._. 
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<s>
Impact_NN1 funds_NN2 have_VH0 diverse_JJ goals_NN2 ,_, so_CS it_PPH1 is_VBZ useful_JJ to_TO consider_VVI specific_JJ examples_NN2 of_IO impact_NN1 funds_NN2 in_II our_APPGE final_JJ sample_NN1 ._. 
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<s>
If_CS the_AT scenario_NN1 at_II hand_NN1 is_VBZ thought_VVN to_TO be_VBI particularly_RR "_" easy_JJ "_" with_IW high_JJ r_ZZ1 or_CC SNR_NP1 and_CC covariates_NN2 are_VBR uncorrelated_JJ or_CC very_RG weakly_RR correlated_VVN ,_, SCAD_NP1 may_VM provide_VVI the_AT best_JJT PPV_NP1 while_CS retaining_VVG a_AT1 competitive_JJ TPR_NP1 ._. 
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<s>
We_PPIS2 propose_VV0 two_MC other_JJ possible_JJ reasons_NN2 for_IF the_AT trend_NN1 ._. 
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<s>
Thus_RR ,_, corporate_JJ leverage_NN1 is_VBZ expected_VVN to_TO be_VBI increasing_VVG with_IW industry_NN1 median_NN1 leverage_NN1 according_II21 to_II22 TOT_NN1 while_CS the_AT said_JJ relation_NN1 is_VBZ not_XX certain_JJ according_II21 to_II22 POT_NN1 ._. 
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<s>
Finally_RR ,_, 99.77%_FO of_IO the_AT banks_NN2 were_VBDR active_JJ within_II a_AT1 15-day_JJ span_NN1 ._. 
</s>
<s>
Super_JJ spreaders_NN2 publish_VV0 information_NN1 preferential_JJ to_II their_APPGE followers_NN2 ,_, who_PNQS may_VM then_RT forward_RL it_PPH1 to_II other_JJ users_NN2 who_PNQS may_VM not_XX currently_RR be_VBI a_AT1 follower_NN1 of_IO the_AT super_JJ spreader_NN1 ._. 
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<s>
The_AT set_NN1 of_IO countries_NN2 considered_VVN in_II our_APPGE analysis_NN1 are_VBR Australia_NP1 and_CC its_APPGE five_MC largest_JJT trading_NN1 partners_NN2 :_: China_NP1 ,_, Japan_NP1 ,_, the_AT EU_NP1 ,_, (_( the_AT Republic_NN1 of_IO )_) Korea_NP1 and_CC the_AT USA_NP1 ._. 
</s>
<s>
While_CS the_AT forecasting_VVG results_NN2 of_IO the_AT multiple-curve_JJ PCA_NN1 model_NN1 are_VBR comparable_JJ to_II those_DD2 of_IO the_AT individual-curve_JJ PCA_NN1 approach_NN1 for_IF forecasting_VVG horizons_NN2 of_IO 1_MC1 month_NNT1 or_CC longer_RRR ,_, it_PPH1 produces_VVZ much_DA1 better_JJR predictions_NN2 of_IO future_JJ yields_NN2 over_II shorter_JJR horizons_NN2 as_CSA 1_MC1 day_NNT1 or_CC 1_MC1 week_NNT1 ,_, especially_RR for_IF the_AT risky_JJ curves_NN2 ._. 
</s>
<s>
Figure_NN1 2_MC shows_VVZ an_AT1 exemplar_JJ vascular_JJ morphology_NN1 visualized_VVD with_IW the_AT different_JJ builders_NN2 ._. 
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The_AT mean_JJ velocity_NN1 〈_NULL v_ZZ1 〉_NULL vs._II t_ZZ1 ._. 
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As_CSA 20_MC countries_NN2 and_CC regions_NN2 are_VBR included_VVN ,_, removing_VVG data_NN on_II non-coincident_JJ market_NN1 days_NNT2 causes_VVZ a_AT1 nearly_RR 50%_NNU reduction_NN1 of_IO the_AT sample_NN1 ._. 
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If_CS <equation>_FO (_( cf._VV0 Fig._NN1 2_MC )_) ,_, i.e._REX ,_, if_CS it_PPH1 is_VBZ optimal_JJ to_TO invest_VVI all_DB money_NN1 in_II the_AT stock_NN1 in_II the_AT absence_NN1 of_IO transaction_NN1 costs_NN2 ,_, then_RT two_MC cases_NN2 must_VM be_VBI distinguished_VVN in_II the_AT presence_NN1 of_IO costs_NN2 ._. 
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<s>
This_DD1 suggests_VVZ that_CST the_AT use_NN1 of_IO a_AT1 BNB_NP1 conditional_JJ distribution_NN1 is_VBZ not_XX relevant_JJ for_IF point_NN1 forecasts_NN2 ._. 
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This_DD1 poor_JJ outcome_NN1 represents_VVZ a_AT1 limitation_NN1 of_IO the_AT IBSS_NN1 algorithm_NN1 ,_, not_XX a_AT1 limitation_NN1 of_IO SuSiE_NP1 or_CC the_AT variational_JJ approximation_NN1 ._. 
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<s>
Rather_RG paradoxically_RR ,_, we_PPIS2 show_VV0 that_CST the_AT classifier_NN1 so_RR formed_VVN from_II the_AT partially_RR classified_JJ sample_NN1 may_VM have_VHI smaller_JJR expected_JJ error_NN1 rate_NN1 than_CSN that_DD1 if_CS the_AT sample_NN1 were_VBDR completely_RR classified_VVN ._. 
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<s>
Table_NN1 9_MC reports_VVZ the_AT overnight_JJ and_CC weekly_JJ capital_NN1 commitment_NN1 regression_NN1 results_NN2 for_IF bond_NN1 groups_NN2 sorted_VVD based_VVN on_II the_AT 2003_MC trading_NN1 volume_NN1 ._. 
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Lastly_RR ,_, although_CS it_PPH1 was_VBDZ not_XX our_APPGE main_JJ objective_NN1 ,_, we_PPIS2 examined_VVD the_AT top_JJ hits_NN2 in_II the_AT association_NN1 result_NN1 ._. 
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The_AT main_JJ theoretical_JJ result_NN1 regarding_II the_AT performance_NN1 of_IO LOAD_NN1 is_VBZ presented_VVN in_II the_AT following_JJ theorem_NN1 and_CC corollary_NN1 ._. 
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For_IF this_DD1 section_NN1 we_PPIS2 shall_VM work_VVI with_IW the_AT specific_JJ form_NN1 of_IO the_AT killing_NN1 rate_NN1 in_II Theorem_NN1 1_MC1 ,_, namely_REX (_( x_ZZ1 )_) ._. 
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In_II this_DD1 article_NN1 ,_, we_PPIS2 are_VBR able_JK to_TO make_VVI further_RRR mathematical_JJ progress_NN1 on_II the_AT mid-p-value_NN1 by_II using_VVG a_AT1 stochastic_JJ order_NN1 known_VVN as_II the_AT convex_JJ order_NN1 ._. 
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SAS_NP1 is_VBZ supported_VVN by_II the_AT Australian_JJ Research_NN1 Council_NN1 through_II the_AT Discovery_NN1 Project_NN1 Scheme_NN1 (_( FT170100079_FO )_) ,_, and_CC the_AT Australian_JJ Centre_NN1 of_IO Excellence_NN1 for_IF Mathematical_JJ and_CC Statistical_JJ Frontiers_NN2 (_( ACEMS_NP2 ,_, CE140100049_FO )_) ._. 
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<s>
The_AT model_NN1 has_VHZ only_RR 4_MC parameters_NN2 ,_, so_CS this_DD1 is_VBZ again_RT a_AT1 quite_RG simple_JJ example_NN1 ._. 
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Comparison_NN1 of_IO mean_JJ and_CC standard_JJ deviation_NN1 (_( STD_NN1 )_) of_IO each_DD1 evaluation_NN1 metric_JJ averaged_JJ over_II all_DB the_AT datasets_NN2 for_IF each_DD1 tool_NN1 ._. 
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After_II that_DD1 ,_, we_PPIS2 study_VV0 the_AT case_NN1 in_II which_DDQ each_DD1 spin_NN1 interacts_VVZ with_IW all_DB the_AT others_NN2 ,_, with_IW interaction_NN1 between_II two_MC spins_NN2 placed_VVN n_ZZ1 sites_NN2 apart_RL on_II the_AT chain_NN1 decaying_VVG either_RR exponentially_RR or_CC as_II 1/n_FU (_( or_CC more_RGR generally_RR as_II 1/n1+p_FU )_) ._. 
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Essentially_RR ,_, the_AT stepwise_JJ approach_NN1 can_VM be_VBI viewed_VVN as_II a_AT1 first_MD (_( selection_NN1 )_) step_NN1 used_VMK to_TO identify_VVI those_DD2 funds_NN2 whose_DDQGE alphas_NN2 we_PPIS2 can_VM most_RGT confidently_RR trust_VVI are_VBR truly_RR positive_JJ ._. 
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This_DD1 allows_VVZ us_PPIO2 to_TO obtain_VVI an_AT1 exact_JJ description_NN1 of_IO the_AT thermodynamic_JJ and_CC spatial_JJ correlation_NN1 quantities_NN2 ._. 
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A_AT1 second_MD takeaway_NN1 from_II these_DD2 works_NN is_VBZ that_CST some_DD patients_NN2 prefer_VV0 extremely_RR simple_JJ dashboards_NN2 ._. 
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We_PPIS2 illustrate_VV0 the_AT approach_NN1 by_II replicating_VVG it_PPH1 for_IF cohorts_NN2 of_IO patients_NN2 for_IF which_DDQ stage_NN1 at_II diagnosis_NN1 and_CC other_JJ important_JJ prognosis_NN1 factors_NN2 are_VBR available_JJ ._. 
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Political_JJ transparency_NN1 is_VBZ significantly_RR negatively_RR related_VVN to_II unemployment_NN1 rates_NN2 ._. 
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The_AT following_JJ notation_NN1 is_VBZ used_VVN in_II the_AT remainder_NN1 of_IO the_AT article_NN1 ._. 
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Moreover_RR ,_, estimation_NN1 by_II ordered_JJ probit_NN1 also_RR yields_VVZ qualitatively_RR identical_JJ results_NN2 ._. 
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Our_APPGE spectral_JJ investigation_NN1 was_VBDZ able_JK to_TO distinguish_VVI very_RG sharp_JJ peaks_NN2 ,_, corresponding_VVG to_II different_JJ nearby_JJ frequencies_NN2 ,_, that_CST are_VBR responsible_JJ for_IF the_AT different_JJ actions_NN2 of_IO the_AT rodent_NN1 ._. 
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Finally_RR ,_, half_DB of_IO the_AT dams_NN2 operational_JJ system_NN1 is_VBZ regulated_VVN separately_RR by_II Romanian_JJ planners_NN2 ,_, with_IW real_JJ time_NNT1 monitoring_NN1 and_CC yearly_JJ arbitrage_NN1 according_II21 to_II22 the_AT common_JJ dispatching_VVG protocol_NN1 &lsqb;_( 34_MC &rsqb;_) ._. 
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TLR9_FO has_VHZ also_RR been_VBN shown_VVN to_TO drive_VVI the_AT fibrosis_NN1 progression_NN1 in_II IPF_NP1 in_II another_DD1 study_NN1 (_( Hogaboam_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ._. 
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<s>
One_MC1 possible_JJ reason_NN1 for_IF such_DA improvement_NN1 is_VBZ that_DD1 partitioned_JJ assemblies_NN2 allow_VV0 assemblers_NN2 to_TO estimate_VVI more_RGR appropriate_JJ parameters_NN2 for_IF reads_NN2 in_II each_DD1 bin_NN1 rather_II21 than_II22 applying_VVG the_AT same_DA parameters_NN2 to_II the_AT entire_JJ dataset_NN1 ._. 
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Specifically_RR ,_, <equation>_FO ,_, where_RRQ (_( )_) is_VBZ the_AT cumulative_JJ distribution_NN1 function_NN1 of_IO the_AT standard_JJ normal_JJ distribution_NN1 ._. 
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Consequently_RR ,_, we_PPIS2 consider_VV0 the_AT adaptation_NN1 of_IO the_AT SUR_NP1 strategy_NN1 for_IF noisy_JJ observations_NN2 (_( see_VV0 Sect._NP1 4.3_MC )_) ._. 
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Plainly_RR speaking_VVG ,_, the_AT only_JJ difference_NN1 between_II the_AT two_MC aforementioned_JJ reinsurance_NN1 chains_NN2 is_VBZ that_CST the_AT positions_NN2 of_IO the_AT (_( k1_FO )_) th_NNU and_CC kth_NNU level_JJ reinsurers_NN2 are_VBR interchanged_VVN ._. 
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As_CSA seen_VVN ,_, NIHBA_NP1 can_VM obtain_VVI diverse_JJ solutions_NN2 forming_VVG a_AT1 good_JJ representative_NN1 of_IO the_AT trade-off_NN1 between_II cell_NN1 growth_NN1 and_CC succinate_JJ production_NN1 ._. 
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Here_RL ,_, we_PPIS2 go_VV0 one_MC1 step_NN1 further_RRR by_II checking_VVG for_IF the_AT presence_NN1 of_IO stocks_NN2 with_IW atypical_JJ temporal_JJ behavior_NN1 ._. 
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The_AT left_JJ panel_NN1 shows_VVZ the_AT posterior_JJ probability_NN1 that_CST each_DD1 area_NN1 is_VBZ assigned_VVN to_II each_DD1 trend_NN1 ,_, with_IW the_AT three_MC parts_NN2 of_IO that_DD1 figure_NN1 grouping_NN1 areas_NN2 according_II21 to_II22 their_APPGE maximum_JJ a_JJ21 posteriori_JJ22 trend_NN1 ._. 
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We_PPIS2 can_VM see_VVI that_CST the_AT results_NN2 are_VBR good_JJ considering_II the_AT intrinsic_JJ difficulty_NN1 of_IO this_DD1 inverse_JJ statistical_JJ problem_NN1 that_CST is_VBZ in_II very_RG high_JJ dimension_NN1 ._. 
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Section_NN1 3_MC describes_VVZ our_APPGE method_NN1 ,_, first_MD with_IW an_AT1 illustrative_JJ example_NN1 in_II Section_NN1 3.1_MC ,_, and_CC then_RT with_IW formulas_NN2 and_CC pseudocode_VV0 in_II Section_NN1 3.2_MC ._. 
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Before_II iterating_VVG (_( 10_MC )_) ,_, (_( 11_MC )_) ,_, we_PPIS2 need_VV0 to_TO compute_VVI qix_NN1 and_CC qijx_NN1 ,_, y_ZZ1 at_RR21 first_RR22 ._. 
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The_AT stability_NN1 of_IO (_( self-normalised_NN1 )_) importance_NN1 sampling_NN1 can_VM be_VBI improved_VVN by_II replacing_VVG the_AT largest_JJT weights_NN2 with_IW order_NN1 statistics_NN of_IO the_AT generalized_JJ Pareto_NP1 distribution_NN1 estimated_VVD already_RR for_IF the_AT diagnostic_JJ purposes_NN2 ._. 
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Even_CS21 when_CS22 formula_NN1 (_( 4.8_MC )_) is_VBZ only_RR valid_JJ in_II the_AT case_NN1 <equation>_FO ,_, Theorem_NN1 3.2_MC gives_VVZ us_PPIO2 that_CST ,_, in_II the_AT uncorrelated_JJ case_NN1 <equation>_FO ,_, the_AT ATM_NN1 implied_VVD volatility_NN1 (_( which_DDQ coincides_VVZ in_II this_DD1 case_NN1 with_IW (_( 4.8_MC )_) )_) must_VM be_VBI an_AT1 accurate_JJ approximation_NN1 for_IF the_AT volatility_NN1 swap_VV0 fair_JJ price_NN1 ._. 
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The_AT rapid_JJ proliferation_NN1 of_IO single-cell_JJ RNA-sequencing_NN1 (_( scRNA-Seq_NP1 )_) technologies_NN2 has_VHZ spurred_VVN the_AT development_NN1 of_IO diverse_JJ computational_JJ approaches_NN2 to_TO detect_VVI transcriptionally_RR coherent_JJ populations_NN2 ._. 
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Since_CS the_AT latent_JJ factors_NN2 are_VBR estimated_VVN from_II a_AT1 large_JJ panel_NN1 of_IO time_NNT1 series_NN ,_, they_PPHS2 contain_VV0 not_XX only_RR fast-moving_JJ monetary/financial_JJ variables_NN2 but_CCB also_RR slow-moving_JJ macro_JJ variables_NN2 ._. 
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The_AT trend_NN1 (_( <equation>_FO )_) ensures_VVZ the_AT presence_NN1 of_IO this_DD1 effect_NN1 ._. 
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In_II the_AT analysis_NN1 ,_, such_DA nuisance_NN1 entities_NN2 are_VBR to_TO be_VBI removed_VVN in_II some_DD way_NN1 or_CC to_TO work_VVI with_IW nonparametrically_RR ._. 
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In_RR21 brief_RR22 ,_, ?3000_FO cells_NN2 were_VBDR placed_VVN into_II each_DD1 well_NN1 of_IO 96-well_JJ plates_NN2 after_II transfection_NN1 for_IF 24h_FO ,_, and_CC CCK-8_MC solution_NN1 was_VBDZ added_VVN after_II cells_NN2 attached_VVN to_II the_AT wall_NN1 (_( 0h_FO )_) ._. 
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We_PPIS2 refer_VV0 the_AT reader_NN1 to_II Mazumder_NP1 et_RA21 al_RA22 ._. 
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(_( 2010_MC )_) for_IF a_AT1 detailed_JJ study_NN1 of_IO the_AT algorithm_NN1 ._. 
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Specifically_RR ,_, the_AT detection_NN1 of_IO aberrant_NN1 splicing_VVG in_II many_DA2 rare_JJ disease_NN1 patients_NN2 suggests_VVZ that_CST identifying_JJ RNA_NN1 splicing_VVG outliers_NN2 is_VBZ particularly_RR useful_JJ for_IF determining_VVG causal_JJ Mendelian_JJ disease_NN1 genes_NN2 ._. 
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Again_RT ,_, we_PPIS2 focus_VV0 on_II situation_NN1 where_RRQ 12p2_FO θ_NULL 1_MC1 is_VBZ constructed_VVN to_TO be_VBI close_RR to_II 1p1_FO (_( using_VVG method_NN1 of_IO moments_NN2 )_) ._. 
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The_AT estimation_NN1 from_II EPS_NP1 adjustment_NN1 is_VBZ almost_RR identical_JJ to_II the_AT regression_NN1 approach_NN1 which_DDQ directly_RR includes_VVZ <equation>_FO as_CSA covariates_VVZ ._. 
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In_II summary_NN1 ,_, <equation>_FO has_VHZ been_VBN changed_VVN to_II <equation>_FO ._. 
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There_EX are_VBR two_MC critical_JJ facets_NN2 to_II this_DD1 ._. 
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A_AT1 second_MD approach_NN1 ,_, implemented_VVN in_II the_AT software_NN1 ai_NNU (_( Gutenkunst_NP1 et_RA21 al_RA22 ._. 
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<s>
2009_MC )_) ,_, computes_VVZ x_ZZ1 by_II numerically_RR solving_VVG PDEs_NN2 arising_VVG from_II the_AT Wright–Fisher_NN1 diffusion_NN1 (_( Ewens_NP2 2004_MC )_) ,_, which_DDQ is_VBZ dual_JJ to_II the_AT coalescent_JJ process_NN1 described_VVN above_RL ._. 
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As_II the_AT right-hand_JJ side_NN1 of_IO (_( 4.33_MC )_) depends_VVZ only_RR on_II <equation>_FO (_( and_CC not_XX on_II <equation>_FO )_) ,_, the_AT assertion_NN1 of_IO the_AT lemma_NN1 follows_VVZ from_II the_AT dominated_JJ convergence_NN1 theorem_NN1 ._. 
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The_AT performance_NN1 of_IO BUS_NN1 remains_VVZ the_AT same_DA ,_, taking_VVG 1.32_MC hr_NNU on_II a_AT1 2.6GHz_FO processor_NN1 (_( the_AT same_DA processor_NN1 used_VVN across_II the_AT article_NN1 )_) and_CC resulting_VVG in_II zero_MC FDR_NP1 (_( =_FO 0.5_MC )_) and_CC an_AT1 ARI_NP1 of_IO one_MC1 ,_, whereas_CS the_AT original_JJ MetaSparseKmeans_NN2 algorithm_NN1 fails_VVZ to_TO work_VVI using_VVG its_APPGE exhaustive_JJ version_NN1 ._. 
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However_RR ,_, communication_NN1 only_RR through_II inner_JJ chains_NN2 without_IW considering_VVG cooperation_NN1 between_II inter_JJ chains_NN2 (_( q=0_FO )_) will_VM lead_VVI to_II a_AT1 longer_JJR time_NNT1 to_TO achieve_VVI consensus_NN1 for_IF the_AT whole_JJ system_NN1 ._. 
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The_AT resulting_JJ signature_NN1 1_MC1 should_VM then_RT be_VBI driven_VVN by_II the_AT molecular_JJ feature_NN1 used_VVD ._. 
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This_DD1 more_RGR realistically_RR reflects_VVZ circumstances_NN2 in_II Weibo_NP1 ,_, where_RRQ individuals_NN2 '_NULL information_NN1 dissemination_NN1 contribution_NN1 status_NN1 continuously_RR changes_NN2 ._. 
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Figure_NN1 III_MC shows_VVZ that_CST students_NN2 who_PNQS major_VV0 in_II these_DD2 subjects_NN2 go_VV0 into_II a_AT1 narrow_JJ range_NN1 of_IO technology-intensive_JJ careers_NN2 with_IW high_JJ rates_NN2 of_IO change_NN1 (_( as_CSA shown_VVN in_II Table_NN1 I_ZZ1 )_) ._. 
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Note_VV0 that_CST C_ZZ1 needs_VVZ to_TO be_VBI positive_JJ definite_JJ ._. 
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We_PPIS2 find_VV0 that_CST for_CS E=3_FO and_CC 4_MC ,_, HAPLEXD_NP1 has_VHZ statistically_RR significantly_RR higher_JJR classification_NN1 accuracy_NN1 as_CSA determined_VVN by_II paired_JJ one-tailed_JJ t-tests_NN2 against_II each_PPX221 other_PPX222 method_NN1 ;_; in_II each_DD1 test_NN1 ,_, we_PPIS2 found_VVD that_CST p<8.14×108_FO (_( Fig._NN1 5_MC )_) ._. 
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Under_II time_NNT1 evolution_NN1 the_AT scalar_JJ field_NN1 will_VM decay_VVI by_II '_NULL falling_VVG through_II the_AT horizon_NN1 '_NULL ,_, eventually_RR leading_VVG us_PPIO2 back_RP to_II the_AT pure_JJ gravity_NN1 solution_NN1 ,_, in_II31 accordance_II32 with_II33 the_AT no-hair_JJ theorem_NN1 ._. 
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A_ZZ1 MDS_NN2 method_NN1 based_VVN on_II Hurst-surface_JJ distance_NN1 is_VBZ proposed_VVN in_II this_DD1 paper_NN1 ._. 
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On_II the_AT other_JJ hand_NN1 ,_, if_CS the_AT p_NN1 value_NN1 is_VBZ smaller_JJR ,_, it_PPH1 is_VBZ reasonable_JJ to_TO believe_VVI that_CST the_AT underlying_JJ model_NN1 performs_VVZ worse_JJR than_CSN the_AT comparison_NN1 model_NN1 under_II consideration_NN1 ._. 
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Figure_VV0 3d_NNU ,_, e_ZZ1 show_VV0 the_AT empirical_JJ within-cluster_JJ variances_NN2 for_IF each_DD1 dimension_NN1 ._. 
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For_IF this_DD1 set_NN1 of_IO examples_NN2 ,_, we_PPIS2 compared_VVD logistic_JJ scoring_NN1 rules_NN2 and_CC brier_NN1 scores_NN2 ._. 
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To_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, this_DD1 paper_NN1 is_VBZ the_AT first_MD work_NN1 that_CST applies_VVZ extended_JJ weak_JJ convergence_NN1 to_II continuous-time_JJ portfolio_NN1 optimisation_NN1 problems_NN2 ._. 
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The_AT increased_JJ accuracy_NN1 upon_II exclusion_NN1 of_IO small_JJ (_( N<150_FO )_) structures_NN2 could_VM be_VBI attributed_VVN to_II the_AT fact_NN1 that_CST sequence/structure_VV0 data_NN in_II this_DD1 range_NN1 might_VM be_VBI incomplete_JJ and_CC not_XX representative_JJ of_IO the_AT intact_JJ protein_NN1 ._. 
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The_AT absolute_JJ error_NN1 loss_NN1 (_( full-line_NN1 )_) ,_, and_CC its_APPGE generalization_NN1 for_IF detecting_VVG change_NN1 in_II quantiles_NN2 for_IF u_ZZ1 =_FO 0.1_MC (_( red_JJ dashed_JJ )_) and_CC u_ZZ1 =_FO 0.25_MC (_( blue_JJ dotted_JJ )_) ._. 
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Here_RL and_CC is_VBZ the_AT standard_JJ triple_NN1 of_IO spin-1/2_FU operators_NN2 acting_VVG in_II the_AT corresponding_JJ copy_NN1 of_IO the_AT space_NN1 associated_VVN with_IW nth_MD site_NN1 ._. 
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To_TO describe_VVI our_APPGE dataset_NN1 ,_, let_VV0 D_ZZ1 denotes_VVZ the_AT protein_NN1 and_CC clustering_NN1 dataset_NN1 in_II our_APPGE study_NN1 :_: D=P_FO ,_, C_ZZ1 ,_, τ_NULL ,_, ._. 
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Here_RL ,_, P=P1_FO ,_, P2_FO ,_, ,_, Pm_NP1 is_VBZ a_AT1 set_NN1 of_IO all_DB the_AT proteins_NN2 in_II the_AT NR_II database_NN1 ._. 
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The_AT patterns_NN2 of_IO treatment_NN1 heterogeneity_NN1 show_VV0 that_DD1 selection_NN1 lies_VVZ at_II the_AT heart_NN1 of_IO accelerators_NN2 '_NULL success_NN1 ,_, as_CSA impacts_NN2 are_VBR visible_JJ only_RR for_IF high-potential_JJ entrepreneurs_NN2 ._. 
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Table_NN1 VI_MC summarizes_VVZ the_AT associations_NN2 between_II participation_NN1 and_CC these_DD2 different_JJ complier_NN1 margins_NN2 in_II treatment_NN1 neighborhoods_NN2 ._. 
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The_AT values_NN2 in_II the_AT set_NN1 POTU_NN1 were_VBDR then_RT arranged_VVN in_II a_AT1 decreasing_JJ order_NN1 and_CC a_AT1 new_JJ vector_NN1 POTU*_FO was_VBDZ created_VVN containing_VVG cumulative_JJ correlation_NN1 coefficients_NN2 in_II decreasing_JJ order_NN1 which_DDQ were_VBDR further_RRR re-indexed_VVN from_II 1_MC1 to_II p_ZZ1 ._. 
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However_RR ,_, there_EX could_VM be_VBI intergenerational_JJ transfers_NN2 from_II an_AT1 ex_NN1 post_NN1 point_NN1 of_IO view_NN1 ._. 
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The_AT daily_JJ closing_JJ prices_NN2 of_IO the_AT 1229_MC stocks_NN2 from_II 2013_MC to_II 2018_MC are_VBR extracted_VVN ,_, and_CC then_RT the_AT threshold_NN1 method_NN1 &lsqb;_( 5_MC &rsqb;_) ,_, &lsqb;_( 8_MC &rsqb;_) is_VBZ used_VVN to_TO construct_VVI the_AT stock_NN1 correlation_NN1 network_NN1 ._. 
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Details_NN2 on_II data_NN ,_, models_NN2 ,_, and_CC simulations_NN2 are_VBR described_VVN in_II Table_NN1 8_MC ._. 
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Previous_JJ studies_NN2 present_VV0 mixed_JJ results_NN2 ,_, and_CC no_AT single_JJ theory_NN1 seems_VVZ to_TO be_VBI adequate_JJ in_II explaining_VVG leverage_NN1 dynamics_NN of_IO companies_NN2 ._. 
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This_DD1 is_VBZ a_AT1 modified_JJ version_NN1 of_IO the_AT classic_JJ EM_FU which_DDQ is_VBZ likely_JJ to_TO explore_VVI a_AT1 large_JJ region_NN1 of_IO the_AT parameter_NN1 space_NN1 ._. 
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Also_RR ,_, one_PN1 typically_RR resorts_VVZ to_II thinning_VVG the_AT output_NN1 of_IO an_AT1 MCMC_NP1 sampler_NN1 if_CS the_AT memory_NN1 cost_NN1 of_IO storing_VVG chains_NN2 is_VBZ prohibitive_JJ ,_, or_CC if_CS the_AT cost_NN1 of_IO evaluating_VVG the_AT test_NN1 function_NN1 of_IO interest_NN1 is_VBZ significant_JJ compared_VVN with_IW the_AT cost_NN1 of_IO each_DD1 MCMC_NP1 iteration_NN1 (_( e.g._REX Owen_NP1 (_( 2017_MC )_) )_) ._. 
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Social_JJ media_NN can_VM serve_VVI as_II an_AT1 important_JJ channel_NN1 for_IF investors_NN2 to_TO obtain_VVI relevant_JJ information_NN1 quickly_RR and_CC conveniently_RR ._. 
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We_PPIS2 note_VV0 that_CST this_DD1 is_VBZ a_AT1 special_JJ case_NN1 of_IO the_AT joint_JJ model_NN1 presented_VVD earlier_RRR ,_, see_VV0 Equation_NN1 (_( 3_MC )_) ._. 
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In_BCL21 order_BCL22 to_TO assess_VVI the_AT robustness_NN1 of_IO our_APPGE findings_NN2 in_II the_AT previous_JJ section_NN1 ,_, we_PPIS2 next_MD conduct_NN1 additional_JJ analysis_NN1 that_CST covers_VVZ some_DD relevant_JJ aspects_NN2 given_VVN our_APPGE empirical_JJ setting_NN1 ._. 
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This_DD1 approach_NN1 is_VBZ somewhat_RR similar_JJ to_II the_AT bootstrap_NN1 approach_NN1 but_CCB is_VBZ different_JJ in_II spirit_NN1 ._. 
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Only_RR in_II the_AT case_NN1 of_IO unit_NN1 elasticity_NN1 demand_NN1 will_VM sales_NN be_VBI invariant_JJ for_IF different_JJ markups_NN2 ._. 
</s>
<s>
I_PPIS1 crosschecked_VVD the_AT list_NN1 with_II31 respect_II32 to_II33 the_AT list_NN1 of_IO communes_NN2 in_II each_DD1 French_JJ Metropolitan_JJ department.7_FO N.B._FO There_EX are_VBR 101_MC departments_NN2 in_II France_NP1 :_: 96_MC in_II "_" Metropole_NP1 "_" ,_, counting_VVG 2_MC departments_NN2 in_II Corsica_NP1 ,_, and_CC 5_MC away_II21 from_II22 the_AT "_" Metropole_NP1 "_" ,_, in_II DOM-TOM_NP1 ._. 
</s>
<s>
In_RR21 particular_RR22 ,_, the_AT difference_NN1 in_II time_NNT1 evolution_NN1 of_IO y(t)_NN1 and_CC w(t)_NN1 is_VBZ important_JJ to_II setup_NN1 medical_JJ care_NN1 systems_NN2 ._. 
</s>
