{"id":"W2049085908","doi":"10.1515/advg.2005.5.4.583","title":"Positivity, sums of squares and the multi-dimensional moment problem II","year":2005,"lang":"en","type":"article","venue":"Advances in Geometry","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":45,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lemma (botany); Mathematics; Section (typography); Algebraic number; Mathematical proof; Moment problem; Moment (physics); Discrete mathematics; Explained sum of squares; Combinatorics; Algebra over a field; Pure mathematics; Mathematical analysis; Computer science; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002157964,0.0006009936,0.001018993,0.001578705,0.001466722,0.003246404,0.001381333,0.001251577,0.007970602],"category_scores_gemma":[0.008607997,0.0005309805,0.0009670924,0.001393604,0.004483468,0.007259994,0.00345418,0.002769107,0.0007268515],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001300476,"about_ca_system_score_gemma":0.0004872378,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004117845,"about_ca_topic_score_gemma":0.0002278399,"domain_scores_codex":[0.9980564,0.0006476095,0.00009755724,0.0003735841,0.0005159469,0.000308895],"domain_scores_gemma":[0.9940608,0.003416497,0.0007191097,0.0004473795,0.0005588395,0.0007974041],"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":[0.00005053147,0.00001758228,0.0004227883,0.00005522759,0.00001199643,0.0001066767,0.0001867417,0.003204682,0.000777887,0.9890632,0.001314525,0.004788222],"study_design_scores_gemma":[0.000006898516,0.0000176914,0.0004340483,0.00001503192,0.000004537569,0.000182961,0.0001010966,0.01262829,0.0004407234,0.9848107,0.001343408,0.0000146314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6231568,0.002579686,0.2768016,0.004222571,0.0004509579,0.00006827556,0.000355608,0.0001510392,0.09221337],"genre_scores_gemma":[0.975831,0.0006384284,0.01205506,0.0002564404,0.0005324645,0.00005589613,0.0001704948,0.00007230599,0.01038804],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007970602,"threshold_uncertainty_score":0.02666432,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005438372741447335,"score_gpt":0.2505785019273996,"score_spread":0.2451401291859522,"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."}}