{"id":"W2967425770","doi":"10.1080/03081087.2019.1684873","title":"Higher rank numerical ranges of Jordan-like matrices","year":2019,"lang":"en","type":"preprint","venue":"Linear and Multilinear Algebra","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Rank (graph theory); Eigenvalues and eigenvectors; Mathematics; Characterization (materials science); Block (permutation group theory); Combinatorics; Numerical range; Range (aeronautics); Jordan matrix; Alpha (finance); Numerical analysis; Physics; Pure mathematics; Mathematical analysis; Statistics; Materials science; Optics; Quantum mechanics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004650672,0.0004334122,0.0007851704,0.000192035,0.00007659812,0.000121966,0.001178402,0.0003873829,0.0001158471],"category_scores_gemma":[0.00004247031,0.0003661751,0.0002717579,0.0002406014,0.0001196883,0.0001915016,0.001636003,0.0006573705,0.0001217171],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001438652,"about_ca_system_score_gemma":0.0001057409,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009656235,"about_ca_topic_score_gemma":9.532465e-7,"domain_scores_codex":[0.9975978,0.000179969,0.000571403,0.0008677273,0.0004049207,0.0003782355],"domain_scores_gemma":[0.997944,0.0002939287,0.000338783,0.001103408,0.0001494419,0.0001704122],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001906875,0.004308207,0.007313434,0.01776054,0.00335521,0.0005628044,0.01355064,0.0202199,0.005016912,0.2614639,0.01498159,0.6495599],"study_design_scores_gemma":[0.003205135,0.0003085207,0.002220179,0.0004433169,0.0001948077,0.00003846404,0.0000568989,0.8872923,0.01038438,0.01233673,0.08192474,0.001594499],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3005197,0.02276615,0.6495379,0.002465961,0.01463684,0.002912487,0.0003839312,0.001240216,0.005536826],"genre_scores_gemma":[0.8039077,0.00170687,0.18663,0.0005432796,0.001233293,0.00004068817,0.00007252065,0.00008611666,0.005779533],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8670724,"threshold_uncertainty_score":0.999879,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01607395792606067,"score_gpt":0.2677448405882698,"score_spread":0.2516708826622092,"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."}}