{"id":"W2042593547","doi":"10.1016/j.laa.2014.06.045","title":"The principal rank characteristic sequence over various fields","year":2014,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria; University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada; Banff International Research Station for Mathematical Innovation and Discovery; Iowa State University","keywords":"Rank (graph theory); Mathematics; Sequence (biology); Combinatorics; Principal (computer security); Field (mathematics); Order (exchange); Matrix (chemical analysis); Principal component analysis; Position (finance); Pure mathematics; Statistics; Chemistry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001329344,0.00008292155,0.00007997065,0.00001607542,0.0002126466,0.00004015132,0.0001251845,0.00005578817,0.00001866192],"category_scores_gemma":[0.00001595173,0.00006192061,0.00002503503,0.00008794476,0.00003026411,0.00004329989,0.00001725372,0.0001113507,0.00008175845],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005115362,"about_ca_system_score_gemma":0.000004246884,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002746652,"about_ca_topic_score_gemma":0.000005244693,"domain_scores_codex":[0.9995423,0.00002015908,0.0001362214,0.0001086801,0.00005769795,0.0001349241],"domain_scores_gemma":[0.9995641,0.0001215935,0.00002094455,0.0002196338,0.00001860462,0.00005519648],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000008679832,0.00001993118,0.0001974128,0.0001006294,0.0000492056,5.662134e-7,0.000410069,0.0002840518,0.0066482,0.9726384,0.0003035839,0.01933931],"study_design_scores_gemma":[0.0003562579,0.00005104397,0.006212028,0.00002632383,0.00004385847,0.00002622738,0.00004042746,0.1787951,0.001714487,0.02119384,0.7911648,0.000375649],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9170928,0.001038164,0.07058379,0.000353257,0.0003366852,0.0007248003,0.00003289475,0.0004322516,0.009405358],"genre_scores_gemma":[0.9989566,0.0001379394,0.00004321459,0.00007955296,0.0001982541,0.0001782866,0.000009149355,0.00001247333,0.000384565],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9514445,"threshold_uncertainty_score":0.2525049,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008323045199526983,"score_gpt":0.219224699725822,"score_spread":0.210901654526295,"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."}}