{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001253885,0.001140567,0.0009005441,0.0009397048,0.0005397656,0.001054966,0.0007747488,0.001252101,0.001319933],"category_scores_gemma":[0.003754117,0.0003920595,0.0005614667,0.0003122599,0.001873937,0.001326078,0.001755104,0.0007036102,0.0001283907],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000577363,"about_ca_system_score_gemma":0.0004013777,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008516346,"about_ca_topic_score_gemma":0.0006355966,"domain_scores_codex":[0.9997188,0.0001251348,0.00001327393,0.00005948769,0.00004214642,0.0000411067],"domain_scores_gemma":[0.9989269,0.0005767321,0.0002022444,0.00004019626,0.0001089407,0.0001449016],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0004321703,0.0002110636,0.002994026,0.0005600377,0.0001941759,0.0008354706,0.0004502562,0.649891,0.01755955,0.3112682,0.002390794,0.01321334],"study_design_scores_gemma":[0.00004769323,0.0001831803,0.001386691,0.00004307886,0.00002406607,0.0001242609,0.000198779,0.8822653,0.001497462,0.1134217,0.0007712235,0.00003652727],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7375275,0.001174449,0.2466578,0.001057181,0.00006613108,0.00008076381,0.0001341655,0.00007231817,0.01322957],"genre_scores_gemma":[0.9546304,0.0004855054,0.03898814,0.0001175538,0.00008906537,0.0001932364,0.0002058186,0.0000980492,0.005192254],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001319933,"threshold_uncertainty_score":0.006631255,"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."}}