{"id":"W2113306869","doi":"10.24033/ast.937","title":"Fractional Sobolev Inequalities :Symmetrization, Isoperimetry and Interpolation","year":2018,"lang":"en","type":"article","venue":"Astérisque","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Sobolev inequality; Sobolev space; Isoperimetric inequality; Pure mathematics; Embedding; Gaussian; Metric (unit); Mathematical analysis; Interpolation (computer graphics); Interpolation space; Functional analysis; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001899006,0.000106439,0.0001309685,0.0001088258,0.0001535527,0.00005988928,0.00006730352,0.00007512421,0.0006514657],"category_scores_gemma":[0.0009040239,0.0001027726,0.0000314131,0.0002414743,0.0001038457,0.0002290782,0.0000560315,0.00009218256,0.0001312502],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002521666,"about_ca_system_score_gemma":0.00002984925,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008734844,"about_ca_topic_score_gemma":0.0001148684,"domain_scores_codex":[0.9991717,0.00008323966,0.000263964,0.0001697286,0.0001752352,0.0001361536],"domain_scores_gemma":[0.9992484,0.000234317,0.0000996303,0.0001642698,0.0001938059,0.00005952675],"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":[0.0000799307,0.0003407608,0.011846,0.00008647407,0.0001610463,0.000001339114,0.002837311,0.000004162553,0.01619567,0.9460062,0.009462322,0.01297873],"study_design_scores_gemma":[0.002208924,0.0007537215,0.04189743,0.0002179531,0.0002381268,0.00004083607,0.002137957,0.08033732,0.06135662,0.7876621,0.02187399,0.001274967],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3434198,0.00003894475,0.6484854,0.0004666433,0.0003775029,0.0001883704,0.00003049369,0.0001377944,0.006855074],"genre_scores_gemma":[0.9800551,0.000004604626,0.01849418,0.0001236516,0.0006584959,0.00001142349,0.00003326525,0.00002226547,0.0005970368],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6366352,"threshold_uncertainty_score":0.7133092,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06462924322897937,"score_gpt":0.3574942628963715,"score_spread":0.2928650196673921,"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."}}