{"id":"W1592751003","doi":"10.1090/surv/146/02","title":"Positive polynomials and sums of squares","year":2008,"lang":"en","type":"book-chapter","venue":"Mathematical surveys and monographs","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":274,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Algebraic number; Pure mathematics; Semidefinite programming; Explained sum of squares; Moment (physics); Algebra over a field; Isotropy; Real algebraic geometry; Quadratic equation; Discrete mathematics; Combinatorics; Mathematical analysis; Physics; Mathematical optimization; Quantum mechanics; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001145984,0.0003995658,0.0009875454,0.0003152109,0.0001184831,0.00003675674,0.0001443464,0.0003527232,0.0003510815],"category_scores_gemma":[0.0004274407,0.0003364048,0.0001670498,0.00007537245,0.0007261036,0.00008252994,0.0001991224,0.000314649,0.000009135596],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001771277,"about_ca_system_score_gemma":0.00003429932,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009079934,"about_ca_topic_score_gemma":0.000007650639,"domain_scores_codex":[0.9979489,0.0001903109,0.0007026541,0.0004090924,0.0004522456,0.0002967528],"domain_scores_gemma":[0.9968463,0.002020584,0.0003129831,0.0003660572,0.0002274464,0.0002266752],"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":[0.00007668995,0.0003029805,0.0002053451,0.002438199,0.0009086681,0.00009288877,0.002068587,0.00000466519,0.00008721825,0.9238131,0.004583255,0.06541838],"study_design_scores_gemma":[0.0008937852,0.0003254792,0.0004142152,0.0008023717,0.0001558605,0.0001041698,0.00008245108,0.0007811054,0.0004328116,0.9931419,0.002037667,0.0008281334],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.007376033,0.008907424,0.3815655,0.0003450419,0.0001660705,0.004202819,0.001994477,0.0003484822,0.5950941],"genre_scores_gemma":[0.0390182,0.04199374,0.4728407,0.0001562657,0.0003576675,0.0001901837,0.0004155168,0.001021968,0.4440057],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.1510884,"threshold_uncertainty_score":0.9999088,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05852086305204175,"score_gpt":0.3177076905527647,"score_spread":0.2591868275007229,"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."}}