{"id":"W2064402426","doi":"10.1051/cocv/2014031","title":"Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere","year":2015,"lang":"en","type":"article","venue":"ESAIM Control Optimisation and Calculus of Variations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; Centre de Recherches Mathématiques","keywords":"Isoperimetric inequality; Rotational symmetry; Criticality; Curvature; Mathematics; Rigidity (electromagnetism); Class (philosophy); Mathematical analysis; Term (time); Physics; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0009002609,0.001292527,0.0009692877,0.00141169,0.001020762,0.001655711,0.0009653461,0.001536642,0.00249826],"category_scores_gemma":[0.003317094,0.0004004786,0.0006438015,0.0003752239,0.002523675,0.001351195,0.002134546,0.001109794,0.000193255],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001442598,"about_ca_system_score_gemma":0.0007990672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002721273,"about_ca_topic_score_gemma":0.00166449,"domain_scores_codex":[0.9997182,0.0000967824,0.00001241784,0.00005663494,0.00005911644,0.0000568553],"domain_scores_gemma":[0.9987955,0.0004512364,0.0002973148,0.00004954827,0.0001493953,0.0002569848],"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":[0.0002084142,0.0001190258,0.001587158,0.0002680065,0.0001388316,0.0005750939,0.0002623555,0.3527066,0.0123306,0.6240048,0.002115791,0.005683321],"study_design_scores_gemma":[0.00003571597,0.00009217302,0.0008445854,0.00003999869,0.00002088012,0.0001004766,0.0001493446,0.8538664,0.001696654,0.1420835,0.001037518,0.00003276913],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6909794,0.0008786856,0.2755256,0.001694771,0.000117577,0.0001227075,0.0001996732,0.00009637138,0.03038515],"genre_scores_gemma":[0.9720427,0.0003711565,0.01963909,0.0001159606,0.00008945136,0.0001362562,0.0001418771,0.00006781227,0.007395647],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002721273,"threshold_uncertainty_score":0.01046681,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07261705316050004,"score_gpt":0.3424553178029734,"score_spread":0.2698382646424733,"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."}}