{"id":"W4226052975","doi":"10.1007/s41884-022-00070-0","title":"Laplacian operator on statistical manifold","year":2022,"lang":"en","type":"article","venue":"Information Geometry","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia, Okanagan Campus; Kelowna General Hospital; University of British Columbia; Carleton University","funders":"","keywords":"Laplace operator; Vector Laplacian; Mathematics; Manifold (fluid mechanics); Manifold alignment; Operator (biology); Statistical manifold; Pure mathematics; Laplacian matrix; Kernel (algebra); Heat kernel; Computer science; Mathematical analysis; Artificial intelligence; Nonlinear dimensionality reduction; Physics; Vector potential; Information geometry; Chemistry; Geometry","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":[0.001437356,0.0008179009,0.0009581795,0.003987147,0.001158056,0.002894395,0.0008801529,0.001509391,0.005061218],"category_scores_gemma":[0.004269217,0.000371652,0.0006319372,0.002058871,0.003306416,0.005280643,0.001675791,0.002021868,0.0004622688],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001687882,"about_ca_system_score_gemma":0.0008255623,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00161146,"about_ca_topic_score_gemma":0.001095564,"domain_scores_codex":[0.9993297,0.0002699652,0.00002838425,0.0001490732,0.0001651254,0.00005782909],"domain_scores_gemma":[0.9974324,0.001186066,0.0002938768,0.0002289658,0.0005530475,0.0003056282],"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":[0.00000395752,0.000005416366,0.00009128593,0.00001247128,0.000004679792,0.00002412874,0.000087102,0.0008584935,0.000301424,0.996299,0.0006040815,0.001707922],"study_design_scores_gemma":[0.000002306942,0.000007253313,0.0002066534,0.00000481539,0.000003466894,0.00004678406,0.00002558938,0.01099311,0.00009112606,0.9869866,0.00162408,0.000008204944],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2460761,0.007180679,0.6582579,0.01475962,0.0008070102,0.0000655779,0.0008143949,0.0005079922,0.07153074],"genre_scores_gemma":[0.9185593,0.003968094,0.04324134,0.001197475,0.001841806,0.0001009436,0.0004402264,0.0001939594,0.03045692],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005061218,"threshold_uncertainty_score":0.01693141,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01980564271858374,"score_gpt":0.2725252397428656,"score_spread":0.2527195970242819,"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."}}