{"id":"W2314740108","doi":"10.1515/advgeom-2014-0021","title":"The harmonic mean measure of symmetry for convex bodies","year":2015,"lang":"en","type":"article","venue":"Advances in Geometry","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Mixed volume; Convex body; Simplex; Measure (data warehouse); Harmonic mean; Volume (thermodynamics); Ball (mathematics); Combinatorics; Intersection (aeronautics); Regular polygon; Mathematical analysis; Harmonic; Geometry; Convex hull; Physics; 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":[0.00212043,0.0003849247,0.000759928,0.002972837,0.0008782349,0.002559912,0.001343764,0.000647318,0.00316024],"category_scores_gemma":[0.008948318,0.000269828,0.0007116734,0.0009671283,0.004864709,0.003016525,0.002574372,0.001241967,0.0002595737],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001755203,"about_ca_system_score_gemma":0.0004887801,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007320163,"about_ca_topic_score_gemma":0.0004048453,"domain_scores_codex":[0.9985961,0.0003299903,0.00005079883,0.0002327742,0.0005839133,0.0002063233],"domain_scores_gemma":[0.9955527,0.002138292,0.0006886379,0.0003545619,0.0007208417,0.0005448845],"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":[0.00006746377,0.00001709419,0.001315348,0.00004517225,0.0000329572,0.00006625727,0.0001685095,0.007087043,0.002994417,0.9797199,0.000500824,0.007985071],"study_design_scores_gemma":[0.00002693053,0.0001024765,0.004492589,0.0000396105,0.00002310712,0.0002534217,0.0002765661,0.07893017,0.002893563,0.910126,0.002791773,0.00004372107],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5420633,0.001150425,0.4233439,0.0008440496,0.0002092436,0.00006049874,0.0003215815,0.0001556129,0.03185131],"genre_scores_gemma":[0.9847343,0.0002193532,0.01294453,0.00006002481,0.0001832357,0.00005395434,0.000126059,0.00004279169,0.001635653],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00316024,"threshold_uncertainty_score":0.01273501,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07834743652979254,"score_gpt":0.3554747423666126,"score_spread":0.2771273058368201,"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."}}