{"id":"W2064643400","doi":"10.4171/ifb/252","title":"On the global minimizers of a nonlocal isoperimetric problem in two dimensions","year":2011,"lang":"en","type":"article","venue":"Interfaces and Free Boundaries Mathematical Analysis Computation and Applications","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":49,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"National Science Foundation","keywords":"Isoperimetric inequality; Mathematics; Boundary (topology); Torus; Constraint (computer-aided design); Interval (graph theory); Quantum nonlocality; Mathematical analysis; Boundary value problem; Physics; Geometry; Combinatorics; Quantum mechanics","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":[0.0002283115,0.0001377799,0.0003359932,0.0001709356,0.0002242817,0.0001151104,0.00015576,0.00003647495,0.0001252769],"category_scores_gemma":[0.0001749175,0.00009286917,0.00008136974,0.001005018,0.0006169931,0.00005306179,0.0001160573,0.0000954821,0.000008581263],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002101724,"about_ca_system_score_gemma":0.00003064187,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000196803,"about_ca_topic_score_gemma":0.0005474802,"domain_scores_codex":[0.9988773,0.00007878715,0.0005104461,0.0002205839,0.0001823661,0.0001305192],"domain_scores_gemma":[0.9986982,0.0007221792,0.0001698498,0.0002511047,0.00009173188,0.00006687402],"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":[0.00001930251,0.00036869,0.0004230852,0.00003669478,0.0002101623,2.244269e-7,0.001129166,0.00008029461,0.00002114379,0.9961326,0.00004316235,0.001535475],"study_design_scores_gemma":[0.0002955468,0.00005360392,0.0006132286,0.00002896771,0.0003667571,0.000001730427,0.0006272628,0.1004264,0.0001519014,0.8972974,0.0000370952,0.0001001495],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2726016,0.00005016444,0.7236665,0.0003583855,0.000007908364,0.0004289933,0.0000444382,0.00002577056,0.002816259],"genre_scores_gemma":[0.951569,0.000005146173,0.04824181,0.00003901767,0.000007443432,0.00009484866,0.000007010939,0.000006802322,0.00002888533],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6789674,"threshold_uncertainty_score":0.3787095,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0586734422926119,"score_gpt":0.3369137017848705,"score_spread":0.2782402594922586,"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."}}