{"id":"W2952370829","doi":"10.48550/arxiv.1409.7081","title":"Root locii for systems defined on Hilbert spaces","year":2014,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Root locus; Interlacing; Mathematics; Unit circle; Hilbert space; Distributed parameter system; Mathematical analysis; Hermitian matrix; Linear system; Differential equation; Pure mathematics; Control system; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004521395,0.0004360428,0.0007526629,0.0002498417,0.0001861469,0.00009878466,0.00067626,0.0004555598,0.00005204234],"category_scores_gemma":[0.001058608,0.0004497129,0.0004560602,0.0002328955,0.00009771733,0.00006133603,0.0004003266,0.000482745,0.0001042858],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002808665,"about_ca_system_score_gemma":0.00008818392,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000169026,"about_ca_topic_score_gemma":0.00007240455,"domain_scores_codex":[0.9978923,0.0003468244,0.0003361017,0.000885885,0.0001290402,0.0004098034],"domain_scores_gemma":[0.9957697,0.002213156,0.0005122572,0.00109518,0.0002144481,0.0001952724],"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":[0.0001360216,0.0002445417,0.0002798357,0.0008084167,0.000289113,0.00001042135,0.00007737676,0.03249754,0.00003597288,0.9637935,0.001417833,0.0004094898],"study_design_scores_gemma":[0.0007600567,0.0001802477,0.00009484986,0.0003126193,0.0005308355,0.00000111021,0.00006649094,0.0983256,0.0001043867,0.8958141,0.003231073,0.0005786571],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1694666,0.00001929727,0.8251538,0.0001199709,0.001189383,0.001079088,0.00008582112,0.0002439089,0.002642104],"genre_scores_gemma":[0.9764215,0.00001175807,0.01657773,0.00003006976,0.0002568599,0.0000159698,0.00005873641,0.00008448966,0.00654289],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8085761,"threshold_uncertainty_score":0.9997954,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1892503571773777,"score_gpt":0.2680169479761293,"score_spread":0.07876659079875167,"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."}}