{"id":"W2130417105","doi":"10.1007/pl00021726","title":"Optimal Stability and Eigenvalue Multiplicity","year":2001,"lang":"en","type":"article","venue":"Foundations of Computational Mathematics","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":48,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Multiplicity (mathematics); Eigenvalues and eigenvectors; Stability (learning theory); Numerical analysis; Applied mathematics; Mathematical analysis; Physics; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002032189,0.000970735,0.001689967,0.001871036,0.001773637,0.003822044,0.001464298,0.001631529,0.01088704],"category_scores_gemma":[0.0180906,0.0007376373,0.0007629443,0.001330286,0.003992462,0.006295036,0.003860412,0.002903438,0.001440264],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001463477,"about_ca_system_score_gemma":0.0009534627,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003736271,"about_ca_topic_score_gemma":0.000327519,"domain_scores_codex":[0.9982077,0.0006159842,0.00007327165,0.0004248131,0.0004369082,0.000241285],"domain_scores_gemma":[0.9907724,0.005674243,0.000832379,0.0008904916,0.00110752,0.000722909],"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":[0.00007875857,0.00002652185,0.0002191231,0.00003662918,0.00001300462,0.00001901239,0.00008121408,0.01084722,0.0009321414,0.9785188,0.001699407,0.007528197],"study_design_scores_gemma":[0.000009753236,0.00001089169,0.0001082424,0.000006387745,0.000004074588,0.00001905899,0.00002529297,0.02646263,0.0004084283,0.9723913,0.0005445869,0.000009383362],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2353407,0.002755791,0.6439716,0.006388979,0.0007472077,0.00009084528,0.000282348,0.0005686528,0.1098539],"genre_scores_gemma":[0.960607,0.0007767814,0.02055353,0.0003633069,0.0007494371,0.0001413961,0.0001121139,0.0001950513,0.01650134],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01088704,"threshold_uncertainty_score":0.03642076,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03108360772005937,"score_gpt":0.2848674620295977,"score_spread":0.2537838543095383,"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."}}