{"id":"W2165804617","doi":"10.1017/s0308210500000445","title":"Local linear independence of refinable vectors of functions","year":2000,"lang":"en","type":"article","venue":"Proceedings of the Royal Society of Edinburgh Section A Mathematics","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":18,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Independence (probability theory); Mathematics; Characterization (materials science); Bounded function; Sequence (biology); Wavelet; Pure mathematics; Nonlinear system; Discrete mathematics; Mathematical analysis; Computer science; Physics; Artificial intelligence; Statistics","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":[],"consensus_categories":[],"category_scores_codex":[0.0002544504,0.0001399481,0.0003997702,0.000042928,0.00004591287,0.000003267275,0.0002469333,0.000147727,0.0003123674],"category_scores_gemma":[0.00006318273,0.0001115724,0.0003605835,0.0006237014,0.0002241195,0.000110119,0.00004909921,0.0002327041,4.383877e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006045692,"about_ca_system_score_gemma":0.00001247032,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004218121,"about_ca_topic_score_gemma":5.53503e-7,"domain_scores_codex":[0.9987393,0.000001880513,0.0005866073,0.0001160219,0.000412224,0.0001439824],"domain_scores_gemma":[0.9991083,0.00005330859,0.0003278699,0.0001292371,0.0003473744,0.00003390178],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0001247722,0.001975367,0.005155556,0.009049213,0.001712482,1.31966e-7,0.01250309,0.4516016,0.4362114,0.0008960893,0.06350641,0.01726382],"study_design_scores_gemma":[0.0002236622,0.0001679138,0.0002020793,0.000427137,0.0001948922,0.00000290991,0.002052579,0.3824688,0.608806,0.004186535,0.001068741,0.0001987884],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8937554,0.0001550721,0.0994876,0.00004908993,0.000107075,0.0002691549,0.00001252804,0.0001995145,0.005964554],"genre_scores_gemma":[0.9692615,0.0001327845,0.02937124,0.000005012505,0.00004460242,0.00001153731,5.854672e-7,0.00002018159,0.001152589],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1725945,"threshold_uncertainty_score":0.4549792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007510136256152562,"score_gpt":0.216184114158693,"score_spread":0.2086739779025404,"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."}}