{"id":"W2949297942","doi":"10.2969/jmsj/80268026","title":"Optimal problem for mixed $p$-capacities","year":2019,"lang":"en","type":"article","venue":"Journal of the Mathematical Society of Japan","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"Hubei University; National Natural Science Foundation of China","keywords":"Mathematics; Isoperimetric inequality; Regular polygon; Type (biology); Mixed volume; Pure mathematics; Inequality; Convex function; Combinatorics; Mathematical analysis; Convex optimization; Convex combination; Geometry; Geology","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":[0.001830159,0.001597203,0.001430525,0.001141539,0.0008432062,0.00257973,0.002028203,0.002410125,0.01043595],"category_scores_gemma":[0.004222327,0.000731563,0.001145736,0.001420014,0.001536377,0.004696591,0.002543718,0.002998808,0.0009270851],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002140229,"about_ca_system_score_gemma":0.001593227,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001783359,"about_ca_topic_score_gemma":0.001481514,"domain_scores_codex":[0.9988449,0.0003941419,0.00005391879,0.0002920451,0.0001881341,0.0002268759],"domain_scores_gemma":[0.9988217,0.0006891487,0.0001002361,0.00007626744,0.0001924361,0.0001202598],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000225639,0.00009994888,0.0005757923,0.0006067779,0.00009719044,0.0001991553,0.00012484,0.3574336,0.003712795,0.5916921,0.006435139,0.03879698],"study_design_scores_gemma":[0.00003764172,0.0001157311,0.0004162198,0.0001028558,0.00004385998,0.0001649365,0.0001572002,0.7317019,0.002516432,0.25766,0.007036146,0.00004721159],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04689835,0.0009296642,0.9209859,0.001374915,0.0001519647,0.000126914,0.0004749696,0.0001763815,0.02888091],"genre_scores_gemma":[0.7511572,0.001699929,0.2188037,0.0006025626,0.0002371339,0.0006041161,0.0008191655,0.0003271447,0.02574906],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01043595,"threshold_uncertainty_score":0.03491169,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04337013773032308,"score_gpt":0.2961310398395032,"score_spread":0.2527609021091801,"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."}}