{"id":"W1480611495","doi":"10.1109/iscas.1990.112515","title":"Extension of the Toeplitz theorem to the 2-D case and its application to information theory","year":2002,"lang":"en","type":"article","venue":"","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Toeplitz matrix; Extension (predicate logic); Eigenvalues and eigenvectors; Mathematics; Omega; Levinson recursion; Entropy (arrow of time); Pure mathematics; Discrete mathematics; Algebra over a field; Computer science; Physics; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008246381,0.0005515122,0.0004532494,0.001415583,0.0003987575,0.001608811,0.0004292295,0.0006455083,0.003131537],"category_scores_gemma":[0.00360419,0.0002522307,0.0006979114,0.001311827,0.001149438,0.001911331,0.0009648982,0.001122782,0.0006491297],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007139059,"about_ca_system_score_gemma":0.000439775,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007677305,"about_ca_topic_score_gemma":0.0006790914,"domain_scores_codex":[0.9995387,0.0001205478,0.00003380355,0.00008459028,0.0001815994,0.00004079665],"domain_scores_gemma":[0.9979783,0.001283567,0.0001344786,0.0002496665,0.0002995492,0.00005452346],"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":[0.00007807715,0.00004904074,0.0006819671,0.0001675602,0.00006704571,0.0006940489,0.0002565983,0.09216888,0.0106608,0.7898139,0.003891853,0.1014704],"study_design_scores_gemma":[0.000008631084,0.0001069344,0.0009428681,0.00003551121,0.00001779966,0.0008037144,0.0000753612,0.3995198,0.004671303,0.5790877,0.01468165,0.00004864024],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01094056,0.001017187,0.9739615,0.000374243,0.000298162,0.0000193808,0.00008206584,0.0001294322,0.01317739],"genre_scores_gemma":[0.6619091,0.004903032,0.3078115,0.0009167463,0.001122036,0.0001172701,0.0002174406,0.0001497132,0.02285307],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003131537,"threshold_uncertainty_score":0.01047605,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04029717953150559,"score_gpt":0.3115668595845267,"score_spread":0.2712696800530211,"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."}}