{"id":"W2963789438","doi":"10.3934/dcds.2016023","title":"Periodic solutions of the planar N-center problem with topological constraints","year":2016,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Guidance and Control Systems","field":"Engineering","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Homotopy; Center (category theory); Planar; Mathematics; Class (philosophy); Topology (electrical circuits); Pure mathematics; Space (punctuation); Mathematical analysis; Combinatorics; 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":[0.0003396172,0.0005700616,0.0005124083,0.0005147279,0.0007138369,0.0007874078,0.0007628556,0.001126156,0.002455359],"category_scores_gemma":[0.001558842,0.0002792038,0.0003755136,0.0003209799,0.001313205,0.0008244511,0.001300547,0.0004983069,0.000135043],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005644121,"about_ca_system_score_gemma":0.0007055861,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001820032,"about_ca_topic_score_gemma":0.001795241,"domain_scores_codex":[0.9998709,0.00002537867,0.000005550582,0.00003030248,0.00002591646,0.00004194243],"domain_scores_gemma":[0.9997311,0.0001108898,0.00006933313,0.00001686108,0.00002645865,0.00004535189],"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":[0.0001687402,0.00006907791,0.00111197,0.0001737556,0.0000655981,0.0005367939,0.0002072921,0.2746202,0.006215717,0.7018421,0.001999647,0.01298902],"study_design_scores_gemma":[0.0001024796,0.000114315,0.0007509444,0.00003050971,0.00001955707,0.0002199789,0.0003220156,0.6588345,0.002250893,0.3359139,0.001394729,0.00004612403],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7133014,0.0003765103,0.2586904,0.0006695307,0.00006904051,0.0000698088,0.000130666,0.00007218526,0.02662046],"genre_scores_gemma":[0.9679421,0.0001855125,0.0248581,0.00007134754,0.00003917225,0.000112021,0.0001190849,0.00003631652,0.006636446],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002455359,"threshold_uncertainty_score":0.008213997,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005307637207479678,"score_gpt":0.1742145843184044,"score_spread":0.1689069471109247,"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."}}