{"id":"W4401387153","doi":"10.4310/ajm.2023.v27.n6.a2","title":"A note on heat kernel estimates, resistance bounds and Poincaré inequality","year":2023,"lang":"en","type":"article","venue":"Asian Journal of Mathematics","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Inequality; Heat kernel; Kernel (algebra); Poincaré inequality; Applied mathematics; Pure mathematics; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00121786,0.0002114137,0.0005142615,0.0002221137,0.000136791,0.00009978333,0.0002388188,0.00009528925,0.00004398675],"category_scores_gemma":[0.002762772,0.0001737802,0.0001432831,0.0003484846,0.00009314068,0.0001379,0.00006742843,0.0003074028,0.00007420049],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006340475,"about_ca_system_score_gemma":0.00009254934,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001625184,"about_ca_topic_score_gemma":0.0000304443,"domain_scores_codex":[0.9979697,0.0000968453,0.0009208058,0.0001486994,0.0005793814,0.0002845821],"domain_scores_gemma":[0.9978905,0.0009307252,0.0004390808,0.0003681895,0.0001885879,0.0001829585],"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":[0.0004704399,0.003861558,0.001493869,0.00567694,0.001079814,0.0009285565,0.05357677,0.0001551817,0.01126069,0.8618153,0.04894513,0.01073579],"study_design_scores_gemma":[0.001134478,0.0002791196,0.001646485,0.00103125,0.0002178394,0.0001284009,0.00137417,0.005731175,0.001751523,0.9856744,0.0007095169,0.0003215775],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8873179,0.0001240094,0.0979062,0.006596205,0.0005322703,0.0004787347,0.00006575555,0.0002183802,0.006760548],"genre_scores_gemma":[0.8166671,0.00004194894,0.1819304,0.00008472621,0.000310444,0.000006704508,0.000006848506,0.00008221036,0.000869612],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1238592,"threshold_uncertainty_score":0.7086549,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06500814321921038,"score_gpt":0.3601771768925229,"score_spread":0.2951690336733125,"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."}}