{"id":"W2025239200","doi":"10.3390/sym5010047","title":"A Note on Lower Bounds for Colourful Simplicial Depth","year":2013,"lang":"en","type":"article","venue":"Symmetry","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University; McMaster University","funders":"Universidad de Cantabria; Natural Sciences and Engineering Research Council of Canada; Mitacs; Canada Research Chairs","keywords":"Combinatorics; Convex hull; Mathematics; Dimension (graph theory); Upper and lower bounds; Regular polygon; Simplicial complex; Point (geometry); Set (abstract data type); Computer science; Geometry; Mathematical analysis","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":[0.000105037,0.0001258455,0.0001445207,0.00007716469,0.00006395745,0.00004715816,0.0001166155,0.0001072868,0.00008707045],"category_scores_gemma":[0.00002817158,0.0001161552,0.00009620057,0.000134984,0.00001904052,0.00006995087,0.000009441736,0.0001006849,0.0005294594],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003445727,"about_ca_system_score_gemma":0.000006540703,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001530404,"about_ca_topic_score_gemma":0.00001433317,"domain_scores_codex":[0.9993676,0.000014514,0.0001424792,0.0001255119,0.00008517452,0.0002647041],"domain_scores_gemma":[0.9995859,0.0001050546,0.00001744534,0.0001948703,0.00002580142,0.00007094162],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0003574555,0.0004782663,0.004207673,0.001109472,0.0006076751,0.00002684153,0.001677021,0.003967782,0.07113039,0.4122172,0.3446918,0.1595284],"study_design_scores_gemma":[0.005179269,0.002070136,0.03195033,0.0003563721,0.0001532959,0.00004722283,0.0008809968,0.05321687,0.05715537,0.1645406,0.6815218,0.002927672],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9395057,0.00007987081,0.004493019,0.00007283557,0.002043326,0.0005207839,0.00001817553,0.0003197994,0.05294647],"genre_scores_gemma":[0.9987106,0.000001416522,0.0001645029,0.0001953317,0.0003057512,0.000116625,0.000005463909,0.00003644414,0.0004638293],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.33683,"threshold_uncertainty_score":0.6805307,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007351167647369117,"score_gpt":0.2223952436063858,"score_spread":0.2150440759590167,"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."}}