{"id":"W2080199983","doi":"10.1016/j.disc.2008.02.005","title":"A criterion for the half-plane property","year":2008,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":37,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Matroid; Property (philosophy); Homogeneous; Plane (geometry); Polynomial; Combinatorics; Pure mathematics; Discrete mathematics; Mathematical analysis; Geometry","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":[0.00140794,0.0006424724,0.001153263,0.002293004,0.00203008,0.003497848,0.001675572,0.002408868,0.01639498],"category_scores_gemma":[0.008685842,0.0004903488,0.0009278618,0.001524701,0.003855481,0.007971032,0.003349389,0.00411533,0.003624906],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008968569,"about_ca_system_score_gemma":0.0008345665,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007277466,"about_ca_topic_score_gemma":0.0004373642,"domain_scores_codex":[0.9989864,0.0001586308,0.00008425571,0.0002920979,0.0003064736,0.0001721492],"domain_scores_gemma":[0.9950469,0.002150633,0.0002743453,0.0006479636,0.001365534,0.0005146114],"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":[0.00005261515,0.00001797006,0.0003097352,0.00003871991,0.000006070576,0.00008292253,0.00008165943,0.0002814365,0.00208677,0.9879051,0.00304407,0.006092903],"study_design_scores_gemma":[0.00004136373,0.00004815183,0.0005574053,0.00003501416,0.00001246481,0.0003838924,0.0001684894,0.006915725,0.003847179,0.9718482,0.01611761,0.00002443546],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1526778,0.001281185,0.5902788,0.007673558,0.0009099228,0.0002469041,0.001513296,0.0008078859,0.2446106],"genre_scores_gemma":[0.8550645,0.001079012,0.09898496,0.002245757,0.001074925,0.0004234157,0.001907317,0.0006614299,0.03855862],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01639498,"threshold_uncertainty_score":0.05484664,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03454349146865929,"score_gpt":0.2535597875582731,"score_spread":0.2190162960896138,"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."}}