{"id":"W2609909975","doi":"10.1090/amsip/025/15","title":"Applications of shift-invariant space theory to some problems of multi-resolution analysis of 𝐿²(ℝ^{𝕕})","year":2002,"lang":"en","type":"book-chapter","venue":"AMS/IP studies in advanced mathematics","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Invariant (physics); Resolution (logic); Mathematics; Pure mathematics; Computer science; Calculus (dental); Artificial intelligence; Mathematical physics; Medicine","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":[0.0008935662,0.00100604,0.001043645,0.00228099,0.001662369,0.002221121,0.001204734,0.001188935,0.006016322],"category_scores_gemma":[0.001832854,0.0005228962,0.001483534,0.002416654,0.004005943,0.003568113,0.001400945,0.003970849,0.000796309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001768572,"about_ca_system_score_gemma":0.000507027,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00128534,"about_ca_topic_score_gemma":0.001249229,"domain_scores_codex":[0.9997074,0.0001112226,0.00002016817,0.0000475379,0.00008765465,0.00002594679],"domain_scores_gemma":[0.9994931,0.0003183573,0.00003550727,0.0000508624,0.00006542638,0.00003669097],"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":[0.000003086951,0.000007027352,0.00001973928,0.00002694718,0.000005963888,0.00003108785,0.0001003997,0.000608175,0.000174094,0.991555,0.0015374,0.00593113],"study_design_scores_gemma":[0.000001492943,0.000002861057,0.00003705586,0.000006494194,0.000002175434,0.00003206853,0.00002209071,0.001358876,0.00008498188,0.9945666,0.003881622,0.000003781446],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.03854972,0.04810656,0.5229182,0.01069745,0.003081888,0.00005581004,0.0001741655,0.0003793378,0.3760368],"genre_scores_gemma":[0.5866176,0.02755324,0.2385894,0.002248336,0.006078881,0.0001640724,0.0003102109,0.0003560987,0.1380821],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.006016322,"threshold_uncertainty_score":0.02012658,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08866506154649458,"score_gpt":0.3653148497849684,"score_spread":0.2766497882384739,"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."}}