{"id":"W4388767802","doi":"10.1142/s0219199723500554","title":"Persistent homology for functionals","year":2023,"lang":"en","type":"article","venue":"Communications in Contemporary Mathematics","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Innosuisse - Schweizerische Agentur für Innovationsförderung; Agence Nationale de la Recherche","keywords":"Mathematics; Persistent homology; Morse theory; Morse code; Homology (biology); Pure mathematics; Filtration (mathematics); Class (philosophy); Algorithm; Computer science","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":[0.001234459,0.0004132273,0.0005214697,0.002588142,0.001301542,0.002405516,0.000748724,0.0009357802,0.006909398],"category_scores_gemma":[0.004086392,0.0002382721,0.0006019914,0.0008043828,0.002835992,0.00634993,0.003413441,0.0017917,0.0006112832],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00120357,"about_ca_system_score_gemma":0.0005919732,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006651104,"about_ca_topic_score_gemma":0.0006695502,"domain_scores_codex":[0.9993786,0.0001009991,0.00003374844,0.0001452849,0.0001853161,0.0001560051],"domain_scores_gemma":[0.9981766,0.0006334163,0.0002187213,0.000289639,0.0003330756,0.0003485889],"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":[0.000003760151,0.000006267908,0.0002380287,0.00001470137,0.000002270742,0.00005295561,0.0001460622,0.0003458374,0.001062065,0.9963231,0.0001964897,0.001608435],"study_design_scores_gemma":[0.000007643658,0.00003144417,0.0007141966,0.00002646759,0.000007034292,0.0001868747,0.0002289842,0.0086002,0.001459782,0.9825017,0.006224005,0.00001174007],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5235571,0.001359068,0.3713375,0.002378914,0.0002723928,0.00009940084,0.0003822985,0.0004804046,0.100133],"genre_scores_gemma":[0.9702834,0.000422109,0.01832729,0.0003166734,0.0002178103,0.0000858717,0.0002123319,0.0001055761,0.01002884],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006909398,"threshold_uncertainty_score":0.02311426,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2859288559465944,"score_gpt":0.3720454033289617,"score_spread":0.08611654738236735,"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."}}