{"id":"W2982496310","doi":"10.1103/physreve.100.042413","title":"Locally and globally optimal configurations of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>N</mml:mi></mml:math> particles on the sphere with applications in the narrow escape and narrow capture problems","year":2019,"lang":"en","type":"article","venue":"Physical review. E","topic":"Diffusion and Search Dynamics","field":"Biochemistry, Genetics and Molecular Biology","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Maxima and minima; Saddle point; Energy (signal processing); Physics; Combinatorics; Algorithm; Mathematics; Statistical physics; Geometry; Mathematical analysis; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000189863,0.00009768082,0.00009150938,0.000005730993,0.00008326842,0.00004689692,0.0001848483,0.00005931869,0.000008113965],"category_scores_gemma":[0.00005723003,0.00006560042,0.00006446124,0.00008837182,0.0001576704,0.00001011293,0.00006916573,0.0001279348,0.00002145251],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000001540478,"about_ca_system_score_gemma":0.00007009708,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001988158,"about_ca_topic_score_gemma":0.00006303327,"domain_scores_codex":[0.9992744,0.00005493298,0.0001408228,0.00019794,0.0001891815,0.000142711],"domain_scores_gemma":[0.9994437,0.00006663168,0.00009248094,0.0003100818,0.00003560318,0.00005157882],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00002966431,0.0001076378,0.00002867035,0.0002207627,0.00002380304,0.000001455143,0.0002022029,0.0001766936,0.02440243,0.9737868,0.0003061474,0.0007137351],"study_design_scores_gemma":[0.001981551,0.003381983,0.002681441,0.002167261,0.0004459964,0.00015295,0.003652442,0.8919162,0.03747556,0.003977729,0.05120198,0.0009648748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9954216,0.001616912,0.00009978183,0.001018839,0.000008736794,0.0001550056,0.00001790101,0.000005124298,0.001656071],"genre_scores_gemma":[0.9981135,0.0007752195,0.0001372473,0.0007115185,0.00003257052,0.0001435885,0.00004942609,0.00001302492,0.00002390845],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9698091,"threshold_uncertainty_score":0.2675107,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01063206616985537,"score_gpt":0.2527416928287975,"score_spread":0.2421096266589421,"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."}}