{"id":"W2273579192","doi":"10.4236/am.2015.68132","title":"Universality in Statistical Measures of Trajectories in Classical Billiard Systems","year":2015,"lang":"en","type":"article","venue":"Applied Mathematics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Dynamical billiards; Universality (dynamical systems); Integrable system; Random matrix; Chaotic; Rigidity (electromagnetism); Statistical physics; Dirac comb; Mathematics; Random walk; Classical mechanics; Physics; Mathematical analysis; Mathematical physics; Quantum mechanics; Geometry; Eigenvalues and eigenvectors","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":[0.0004068869,0.0001161576,0.0004042384,0.00005195031,0.000009632588,0.00001941114,0.0001093624,0.00005305311,0.00001123542],"category_scores_gemma":[0.00001725604,0.00009422365,0.00002841189,0.0001717282,0.00007700059,0.00003036461,0.0000296443,0.0001225886,0.00001269287],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005638,"about_ca_system_score_gemma":0.00006690519,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007539747,"about_ca_topic_score_gemma":0.00005066295,"domain_scores_codex":[0.9989365,0.00003443432,0.0004481942,0.0001415289,0.0002527101,0.0001866056],"domain_scores_gemma":[0.9994054,0.0001927199,0.0001065173,0.0001707476,0.0000358473,0.00008875017],"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":[0.00001638849,0.0002824659,0.00827491,0.0001044533,0.00001286668,0.000001723419,0.001029911,0.0004484185,0.0001870573,0.9892485,0.0001148082,0.0002785496],"study_design_scores_gemma":[0.005542667,0.0001955875,0.007054524,0.0004656689,0.0000771744,0.0000026511,0.04262403,0.1492187,0.0006960102,0.7904172,0.002700373,0.001005384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8339052,0.00002902357,0.1368004,0.00003229859,0.0001517396,0.0005213062,0.00007750853,0.00002500454,0.02845746],"genre_scores_gemma":[0.997813,3.76055e-7,0.002057368,0.000001484035,0.00004769751,0.00002442328,0.00001019805,0.00001140864,0.00003408625],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1988313,"threshold_uncertainty_score":0.3842329,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04661032910118178,"score_gpt":0.2613530918378723,"score_spread":0.2147427627366905,"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."}}