{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006091705,0.0004825214,0.0006701081,0.001479037,0.001038964,0.001053911,0.0005146462,0.000972165,0.005455007],"category_scores_gemma":[0.003444012,0.0004161682,0.0006643843,0.0007994491,0.001391288,0.001204201,0.0008752084,0.0005501741,0.0004377515],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001184725,"about_ca_system_score_gemma":0.001133934,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004341789,"about_ca_topic_score_gemma":0.007652009,"domain_scores_codex":[0.9998573,0.00003285646,0.000009607442,0.00002937994,0.00002949136,0.00004135124],"domain_scores_gemma":[0.999034,0.000538229,0.0001227145,0.00006494962,0.0001296577,0.0001104803],"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":[0.000158062,0.00007923496,0.005191058,0.0001536057,0.00005815315,0.0002361038,0.0001974971,0.9192348,0.002407657,0.05828199,0.003266683,0.01073529],"study_design_scores_gemma":[0.0000519893,0.00007844649,0.002705249,0.00007663806,0.00003015627,0.0001017455,0.0003655212,0.9307141,0.001790792,0.06256769,0.001465944,0.00005167798],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8856584,0.001052196,0.08328488,0.0008579903,0.00005787984,0.00008032234,0.001053703,0.0002919857,0.02766273],"genre_scores_gemma":[0.9637842,0.000294125,0.03170397,0.00005956735,0.000009314444,0.0001465975,0.0007506483,0.000168014,0.00308359],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005455007,"threshold_uncertainty_score":0.01824886,"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."}}