{"id":"W2079678340","doi":"10.1093/imrn/rnm086","title":"Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints","year":2007,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":104,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Queen (butterfly); Mathematics; Operator (biology)","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":[],"consensus_categories":[],"category_scores_codex":[0.00727646,0.0001767545,0.0001948483,0.0004271345,0.0002939794,0.0007399213,0.001387441,0.00006813907,0.000181155],"category_scores_gemma":[0.0007795907,0.0001450777,0.00005606733,0.0004814594,0.0002406941,0.001038639,0.000338798,0.0003575643,0.0001814852],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001985214,"about_ca_system_score_gemma":0.0001669472,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002424714,"about_ca_topic_score_gemma":0.00001987665,"domain_scores_codex":[0.9964448,0.0002196716,0.0005166522,0.0004099208,0.001874367,0.0005345538],"domain_scores_gemma":[0.9971325,0.001256246,0.0001978205,0.0004572385,0.0007992918,0.0001568947],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003317713,0.0004806947,0.0004131867,0.000150641,0.0001822538,0.0001924229,0.002668869,0.0003966701,0.008946283,0.9798146,0.00006366315,0.006657525],"study_design_scores_gemma":[0.001147749,0.0002713956,0.0003853932,0.0005600827,0.00001979668,0.0001258609,0.001770423,0.8969936,0.02062406,0.07730495,0.000329097,0.0004675834],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1178003,0.00004510463,0.8717145,0.0005405999,0.0002048111,0.0004109397,0.000008463094,0.00009856676,0.009176708],"genre_scores_gemma":[0.788003,0.000004095889,0.2114829,0.00005655182,0.0001156092,0.00001900523,0.000007725728,0.00001416308,0.0002969565],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9025096,"threshold_uncertainty_score":0.7135078,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06121214032924077,"score_gpt":0.3893041851664276,"score_spread":0.3280920448371868,"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."}}