{"id":"W3110657852","doi":"10.1090/tran/8356","title":"On 𝐿_{𝑝}-Brunn-Minkowski type and 𝐿_{𝑝}-isoperimetric type inequalities for measures","year":2020,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"National Science Foundation","keywords":"Mathematics; Isoperimetric inequality; Type (biology); Inequality; Pure mathematics; Minkowski space; Mathematical analysis; Combinatorics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004227218,0.0002235089,0.000597167,0.00005572214,0.0002144466,0.00003593501,0.000313242,0.00006639276,0.0001236205],"category_scores_gemma":[0.002262849,0.0001506094,0.0003142888,0.001754094,0.0004415831,0.00008299856,0.00002824963,0.0002217124,0.000009965196],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000341155,"about_ca_system_score_gemma":0.00008121908,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000312379,"about_ca_topic_score_gemma":0.000001387592,"domain_scores_codex":[0.9985204,0.00006929956,0.0004782685,0.0002442616,0.0004050951,0.0002827233],"domain_scores_gemma":[0.9967225,0.002266413,0.0002724654,0.0003210198,0.0002992022,0.0001184241],"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":[0.001315154,0.001922541,0.0001536367,0.01002721,0.002103025,0.000001139535,0.04119937,0.0003989535,0.00456899,0.892439,0.02669303,0.01917792],"study_design_scores_gemma":[0.001741679,0.003806554,0.0001880509,0.0003222969,0.0009854636,0.00001752859,0.02250037,0.007367672,0.01769048,0.9398972,0.004431529,0.001051136],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5227377,0.0005154244,0.4657304,0.006734274,0.0002139437,0.001221538,0.0001873061,0.0002566737,0.002402822],"genre_scores_gemma":[0.9684647,0.000131384,0.02968153,0.0009513559,0.00006263456,0.00003078934,0.000001676192,0.00004324228,0.0006327087],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.445727,"threshold_uncertainty_score":0.6141672,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1037853208974032,"score_gpt":0.3350403374943361,"score_spread":0.2312550165969329,"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."}}