{"id":"W2049481015","doi":"10.1007/s00041-014-9355-0","title":"Gaussian Cubature Arising from Hybrid Characters of Simple Lie Groups","year":2014,"lang":"en","type":"article","venue":"Journal of Fourier Analysis and Applications","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal; University of Victoria","funders":"","keywords":"Mathematics; Simple (philosophy); Lie group; Simple Lie group; Gaussian; Homomorphism; Weyl group; Lie algebra; Pure mathematics; Sign (mathematics); Root (linguistics); Lie theory; Order (exchange); Fundamental representation; Mathematical analysis; Physics; Weight; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009297879,0.0009996017,0.00151504,0.002767627,0.001983231,0.003763359,0.001455121,0.002216677,0.007512788],"category_scores_gemma":[0.002949222,0.0006362649,0.0009252028,0.001291798,0.003592534,0.00381674,0.002876824,0.002235166,0.00106361],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001452671,"about_ca_system_score_gemma":0.0007724208,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001253293,"about_ca_topic_score_gemma":0.001117675,"domain_scores_codex":[0.999216,0.0001906319,0.00003106466,0.0001149872,0.000256249,0.0001910611],"domain_scores_gemma":[0.9985246,0.0003852367,0.0002220738,0.000136115,0.0002492009,0.0004826465],"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":[0.00003302881,0.00001724509,0.0001536843,0.00001226739,0.000007686361,0.00009226938,0.0001441864,0.0008977428,0.0006511655,0.9957243,0.0005187493,0.001747661],"study_design_scores_gemma":[0.00001943059,0.0000266238,0.0002327633,0.000008638783,0.000006252817,0.0001685318,0.0001076193,0.01815765,0.0003864078,0.9796428,0.001219723,0.00002347938],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7483594,0.0006348811,0.1747597,0.001860748,0.0008349017,0.0001025079,0.0002958393,0.0006350489,0.07251684],"genre_scores_gemma":[0.9623396,0.0002318187,0.01042503,0.0004392232,0.0005831351,0.00007295666,0.0001642092,0.0001952999,0.02554863],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007512788,"threshold_uncertainty_score":0.02513278,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01054048227274391,"score_gpt":0.2812573883446404,"score_spread":0.2707169060718965,"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."}}