{"id":"W4317493516","doi":"10.1007/s11228-023-00664-5","title":"Limiting Behaviour of the Generalized Simplex Gradient as the Number of Points Tends to Infinity on a Fixed Shape in IRn","year":2023,"lang":"en","type":"article","venue":"Set-Valued and Variational Analysis","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia, Okanagan Campus; Kelowna General Hospital; University of British Columbia","funders":"","keywords":"Simplex; Mathematics; Infinity; Position (finance); Function (biology); Limiting; Fixed point; Mathematical analysis; Finite set; Upper and lower bounds; Work (physics); Point (geometry); Sample (material); Applied mathematics; Combinatorics; Geometry; Physics","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":[0.003906656,0.001332732,0.001701164,0.003424082,0.001781205,0.003875216,0.003976944,0.002521092,0.006267113],"category_scores_gemma":[0.02719895,0.001431249,0.001313992,0.001355864,0.004895474,0.004868648,0.004344145,0.002912281,0.0008018886],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003136034,"about_ca_system_score_gemma":0.001311066,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.007780871,"about_ca_topic_score_gemma":0.0061099,"domain_scores_codex":[0.9988127,0.0005653604,0.00004372708,0.0001675522,0.0002551788,0.0001555452],"domain_scores_gemma":[0.9860339,0.007994589,0.001152214,0.0006700585,0.001807368,0.002341971],"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":[0.000317701,0.000139051,0.002927655,0.000605815,0.0001212635,0.0004374735,0.0005114251,0.1992377,0.006470806,0.7755905,0.003969574,0.009670884],"study_design_scores_gemma":[0.00002866986,0.0000673733,0.0014317,0.0001393411,0.00003127108,0.0002847683,0.0001889272,0.8066791,0.001023541,0.1887018,0.001360087,0.00006346519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4984298,0.002955359,0.4319214,0.003854805,0.0003030543,0.0001890003,0.0005103112,0.0008914205,0.06094491],"genre_scores_gemma":[0.9021106,0.001482712,0.07208237,0.0005531749,0.0002393474,0.0002547945,0.0005658547,0.0007039026,0.02200716],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007780871,"threshold_uncertainty_score":0.02275366,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0724339798274549,"score_gpt":0.3897422809007294,"score_spread":0.3173083010732745,"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."}}