{"id":"W2153170581","doi":"10.4153/cjm-2009-010-4","title":"Representations of Non-Negative Polynomials, Degree Bounds and Applications to Optimization","year":2009,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":72,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Degree (music); Set (abstract data type); Polynomial; Point (geometry); Explained sum of squares; Section (typography); Discrete mathematics; Combinatorics; Mathematical optimization; Mathematical analysis; Statistics; Computer science; 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":[0.002327128,0.0009457701,0.0007764287,0.001670224,0.0007158857,0.002298051,0.0008594507,0.0008747173,0.004837594],"category_scores_gemma":[0.01374738,0.0003243193,0.0006555286,0.001814666,0.00364899,0.004164982,0.002525538,0.003215512,0.0006347207],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001416022,"about_ca_system_score_gemma":0.0005463741,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008767471,"about_ca_topic_score_gemma":0.0008615338,"domain_scores_codex":[0.9988463,0.0004412084,0.00005387322,0.0001530515,0.0003597844,0.0001457257],"domain_scores_gemma":[0.9958059,0.002462774,0.0005986766,0.0003689761,0.0004403976,0.0003233624],"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":[0.00002293776,0.000008880903,0.0001245816,0.00004056015,0.000003764085,0.00003378298,0.00009012713,0.01059538,0.000523751,0.9800354,0.0006769705,0.007843878],"study_design_scores_gemma":[0.000007394369,0.00002049988,0.0001258141,0.00002264024,0.000004316896,0.00006910657,0.0000498402,0.05849407,0.0003372614,0.9383637,0.002492938,0.0000124661],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07053979,0.003817319,0.8798984,0.002374505,0.00032416,0.00003781906,0.0001580684,0.0001622516,0.04268763],"genre_scores_gemma":[0.9068617,0.002818171,0.07860877,0.0003153545,0.0005361667,0.000072424,0.0001567202,0.0001160664,0.01051456],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004837594,"threshold_uncertainty_score":0.01618338,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0592822340303602,"score_gpt":0.3639287664330567,"score_spread":0.3046465324026965,"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."}}