{"id":"W2070248864","doi":"10.1016/j.laa.2008.12.028","title":"Extreme points and optimal measures","year":2009,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Guelph","funders":"","keywords":"Mathematics; Extreme point; Toeplitz matrix; Trinomial; Unit sphere; Norm (philosophy); Multiplier (economics); Trigonometry; Combinatorics; Elementary proof; Discrete mathematics; Pure mathematics; Mathematical analysis","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":[0.00004834494,0.0001008263,0.0001139136,0.00001847197,0.0002071464,0.00002972702,0.00006948843,0.00002285068,0.00009385551],"category_scores_gemma":[0.000005025621,0.00008787929,0.00002613122,0.0001010562,0.00004331923,0.00008187014,0.00002691659,0.00007614122,0.00003901501],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000002508218,"about_ca_system_score_gemma":0.00000725545,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000148604,"about_ca_topic_score_gemma":1.122881e-7,"domain_scores_codex":[0.9994603,0.000006680198,0.0001396507,0.0001965436,0.00006192041,0.0001348771],"domain_scores_gemma":[0.9996037,0.00005194658,0.00004097705,0.0001575306,0.00004077004,0.000105048],"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":[0.000001760507,0.00005559922,0.00002856803,0.000003096248,0.000007229635,3.113156e-8,0.00004915324,0.000003519327,0.000925685,0.9550313,0.00004800392,0.04384605],"study_design_scores_gemma":[0.0002860128,0.00003464612,0.0005016655,0.00001002492,0.00003513743,0.000002439073,0.0002066452,0.002130275,0.002713359,0.8998763,0.09398634,0.0002171851],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06936724,0.0007048147,0.9035428,0.004187473,0.00001212088,0.000835682,0.00007743567,0.0001164004,0.02115605],"genre_scores_gemma":[0.9794609,0.00004606735,0.01935219,0.0001675609,0.0002069801,0.0001415147,0.00002281017,0.000009748367,0.0005922203],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9100937,"threshold_uncertainty_score":0.3583614,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01923416937430849,"score_gpt":0.2704013110146985,"score_spread":0.25116714164039,"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."}}