{"id":"W1996952380","doi":"10.3934/dcds.2010.28.789","title":"A structural condition for microscopic convexity principle","year":2010,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Convexity; Nonlinear system; Mathematics; Natural (archaeology); Mathematical economics; Mathematical analysis; Applied mathematics; Calculus (dental); Physics; Geology; Economics","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":[0.0007967736,0.0003729277,0.0005126961,0.0007184719,0.00144185,0.001176547,0.0008509613,0.001146842,0.009763962],"category_scores_gemma":[0.001985247,0.0004275283,0.0006809709,0.0002958601,0.002560979,0.002964094,0.002631895,0.002772114,0.0008852797],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009648376,"about_ca_system_score_gemma":0.001265732,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001102894,"about_ca_topic_score_gemma":0.001324352,"domain_scores_codex":[0.9993078,0.00008691595,0.00002468906,0.0001302833,0.0003042081,0.0001461382],"domain_scores_gemma":[0.9990656,0.000256327,0.0000962527,0.0001804222,0.0002595105,0.0001419459],"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":[0.000007498691,0.000007932487,0.0002044977,0.00001891088,0.000005131709,0.00007754464,0.00004230799,0.001606134,0.002471769,0.9929726,0.0008493772,0.001736292],"study_design_scores_gemma":[0.00003497123,0.00006614486,0.002089952,0.00003007357,0.00001385367,0.0004917811,0.0001300267,0.04188768,0.005074643,0.9385836,0.01156635,0.0000309135],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2132118,0.000540084,0.5528309,0.006645516,0.00039504,0.0001746618,0.0006674319,0.0003776767,0.2251568],"genre_scores_gemma":[0.9533105,0.0003373731,0.02518961,0.0006333429,0.0002915575,0.0001973234,0.000381538,0.0001297746,0.01952893],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009763962,"threshold_uncertainty_score":0.0326637,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02301611046836846,"score_gpt":0.3380462380250357,"score_spread":0.3150301275566673,"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."}}