{"id":"W1483432773","doi":"10.1090/s0002-9947-02-03075-1","title":"Positivity, sums of squares and the multi-dimensional moment problem","year":2002,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":86,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Moment (physics); Least-squares function approximation; Applied mathematics; Combinatorics; Statistics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002559848,0.0008398843,0.001060399,0.001809562,0.00153902,0.003783329,0.001538418,0.001387949,0.01209177],"category_scores_gemma":[0.009357251,0.0006256269,0.00162034,0.001520973,0.004375333,0.006592404,0.003417927,0.003040968,0.002095729],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00182332,"about_ca_system_score_gemma":0.001013178,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001325566,"about_ca_topic_score_gemma":0.001264029,"domain_scores_codex":[0.9982449,0.0006754245,0.00007797816,0.0003435099,0.0004534236,0.0002048351],"domain_scores_gemma":[0.9958556,0.002390216,0.0004318849,0.000389808,0.0005704258,0.0003620134],"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":[0.00001944472,0.000006067593,0.00008976345,0.00004331794,0.000008595872,0.00003948174,0.00007932648,0.001996549,0.0002823343,0.9915558,0.002055086,0.003824303],"study_design_scores_gemma":[0.000003779633,0.000006228714,0.00009237458,0.000008558807,0.000003320492,0.00004650688,0.00003056457,0.009825152,0.0001875511,0.987983,0.001802314,0.00001067929],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1268968,0.003685246,0.6894802,0.006662218,0.0008154213,0.00005949525,0.0007234766,0.0007108969,0.1709664],"genre_scores_gemma":[0.8382134,0.002030612,0.08903898,0.001084938,0.001050647,0.0001482835,0.000577993,0.0007223125,0.06713273],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01209177,"threshold_uncertainty_score":0.04045093,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03519699289673154,"score_gpt":0.2804487899602526,"score_spread":0.2452517970635211,"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."}}