{"id":"W2478801192","doi":"10.1103/physreve.94.042418","title":"Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem","year":2016,"lang":"en","type":"article","venue":"Physical review. E","topic":"Diffusion and Search Dynamics","field":"Biochemistry, Genetics and Molecular Biology","cited_by":30,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"National Science Foundation","keywords":"Laplace transform; Helmholtz equation; Bounded function; Superposition principle; Mathematical analysis; Mathematics; Probability density function; Inverse Laplace transform; Helmholtz free energy; First-hitting-time model; Boundary value problem; Physics; Statistics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001706658,0.0006055035,0.0006396531,0.001675685,0.0004961059,0.0006833705,0.001504535,0.001157754,0.001390677],"category_scores_gemma":[0.006964326,0.0003935795,0.0007731469,0.0006324011,0.001069674,0.0009466828,0.001482322,0.001111767,0.0003963053],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007941683,"about_ca_system_score_gemma":0.001367001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003223569,"about_ca_topic_score_gemma":0.001744869,"domain_scores_codex":[0.9994552,0.0002020781,0.00002580759,0.00004897047,0.0002217109,0.00004624914],"domain_scores_gemma":[0.9968807,0.002090929,0.0002776641,0.0002494392,0.0004072976,0.0000939765],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00005142863,0.00008744191,0.001456819,0.0001566076,0.00005624292,0.0001433549,0.000108034,0.8715563,0.01124187,0.08164904,0.0005017361,0.03299124],"study_design_scores_gemma":[0.000001613402,0.000006001895,0.00004827041,0.000003356524,0.000001356973,0.00002031534,0.000003749329,0.9962137,0.0004035989,0.003106026,0.0001872375,0.000004725452],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.005205086,0.00005238982,0.9937171,0.00003006191,0.00001101665,0.00001967343,0.00001360618,0.0001623216,0.0007887757],"genre_scores_gemma":[0.2886579,0.000195905,0.70751,0.00009844014,0.00006348019,0.0004740914,0.0001570886,0.0001897534,0.002653257],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003223569,"threshold_uncertainty_score":0.009025812,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009298321034386357,"score_gpt":0.2760551249740364,"score_spread":0.26675680393965,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}