{"id":"W2088187808","doi":"10.5539/jmr.v5n4p52","title":"On Positive Integer Powers of Toeplitz Matrices","year":2013,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Toeplitz matrix; Mathematics; Integer (computer science); Matrix (chemical analysis); Combinatorics; Levinson recursion; Integer matrix; Shalom; Discrete mathematics; Algebra over a field; Pure mathematics; Nonnegative matrix; Symmetric matrix; Theology; Chemistry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.001428987,0.0009953016,0.0005525476,0.001149953,0.00082246,0.001553785,0.000628941,0.0007191559,0.008189474],"category_scores_gemma":[0.01258106,0.0003331908,0.0004829243,0.0008775552,0.002995946,0.005725421,0.001513152,0.002145132,0.001817073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003946074,"about_ca_system_score_gemma":0.0003788724,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004099589,"about_ca_topic_score_gemma":0.0003213382,"domain_scores_codex":[0.9988626,0.0002630174,0.00007318727,0.0002304417,0.0003576252,0.0002131524],"domain_scores_gemma":[0.99459,0.003155085,0.0004896757,0.0005074171,0.0008554972,0.000402311],"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":[0.0001287625,0.00004576677,0.000805059,0.0001238541,0.000008249579,0.001321221,0.0004661835,0.006160463,0.01140638,0.9612842,0.001818835,0.01643114],"study_design_scores_gemma":[0.00002605822,0.000114563,0.0004098474,0.000062827,0.00001318423,0.0009175272,0.000248964,0.03763694,0.00647897,0.9456724,0.008379794,0.00003896392],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2551216,0.001640654,0.6386367,0.001090003,0.0005727478,0.00009928368,0.000240132,0.000241626,0.1023572],"genre_scores_gemma":[0.9244937,0.001797196,0.05516006,0.0005742569,0.0008580264,0.0000894588,0.0002839104,0.0001597628,0.0165836],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008189474,"threshold_uncertainty_score":0.0273965,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04163628422797602,"score_gpt":0.3575452078759446,"score_spread":0.3159089236479686,"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."}}