{"id":"W2069359224","doi":"10.2969/jmsj/1149166785","title":"Stability of parabolic Harnack inequalities on metric measure spaces","year":2006,"lang":"en","type":"article","venue":"Journal of the Mathematical Society of Japan","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":59,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Ministry of Education, Culture, Sports, Science and Technology; National Science Foundation","keywords":"Harnack's inequality; Harnack's principle; Measure (data warehouse); Metric (unit); Dirichlet form; Divergence (linguistics); Stability (learning theory); Poincaré inequality; Elliptic operator; Exponent","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002387104,0.0006077631,0.0007312145,0.001387845,0.001341986,0.002615837,0.001106278,0.001099885,0.003423369],"category_scores_gemma":[0.009287047,0.0003588242,0.0008563856,0.0006977222,0.00293295,0.004675101,0.003332956,0.001970591,0.0004031309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001626507,"about_ca_system_score_gemma":0.0006582553,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000853525,"about_ca_topic_score_gemma":0.0005260913,"domain_scores_codex":[0.9984859,0.000358936,0.0001081438,0.0003205485,0.0003590949,0.0003673222],"domain_scores_gemma":[0.9951766,0.002144232,0.0007310067,0.0003533305,0.0008552412,0.0007395872],"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":[0.0001037822,0.00002103081,0.001316233,0.00005854966,0.00002831671,0.0003234263,0.000374743,0.004650628,0.007249675,0.9807544,0.0007639735,0.004355263],"study_design_scores_gemma":[0.00003145356,0.00009805246,0.001646486,0.00002287123,0.00001373317,0.0002560655,0.0002811031,0.1002273,0.002856739,0.8926716,0.001848417,0.00004622514],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7633377,0.001232235,0.1954031,0.002700837,0.0001692221,0.00008327176,0.000311721,0.0002181721,0.03654369],"genre_scores_gemma":[0.9858164,0.0002763756,0.009424585,0.0002254426,0.000122492,0.00006670162,0.0001568724,0.00003212454,0.00387921],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003423369,"threshold_uncertainty_score":0.01262438,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05058455057789514,"score_gpt":0.2845758973885409,"score_spread":0.2339913468106458,"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."}}