{"id":"W2794316066","doi":"10.1007/978-3-319-71834-7_6","title":"Discrete Centro-Affine Curvature for Convex Polygons","year":2017,"lang":"en","type":"book-chapter","venue":"Springer INdAM series","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"","keywords":"Affine transformation; Isoperimetric inequality; Mathematics; Curvature; Regular polygon; Affine hull; Combinatorics; Pure mathematics; Geometry; Affine space","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003306419,0.0006532966,0.001011426,0.0002720865,0.0004743371,0.0002963523,0.0006617463,0.0006489171,0.0008419401],"category_scores_gemma":[0.0008879679,0.0005694609,0.0004106564,0.00002863708,0.0002792793,0.0003715588,0.0003112415,0.0005745546,0.00005892744],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007237142,"about_ca_system_score_gemma":0.0001886282,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001555429,"about_ca_topic_score_gemma":0.00009025542,"domain_scores_codex":[0.9978526,0.000009457019,0.0005917333,0.0005378281,0.0004159378,0.0005924849],"domain_scores_gemma":[0.9973765,0.0003325855,0.0007664084,0.001056365,0.0003325555,0.0001356019],"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":[0.0001187451,0.00001598063,0.00001713002,0.001542035,0.0003300666,0.00001339654,0.0005137815,1.090527e-7,0.00001182121,0.9801415,0.0154961,0.00179938],"study_design_scores_gemma":[0.0002867751,0.00009925619,0.00001177367,0.0003520016,0.0001689431,0.00001099707,0.00005264027,0.000001693763,0.0003087388,0.3777858,0.6204401,0.0004813151],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0002659257,0.004419219,0.00188486,0.00301428,0.002646457,0.001571299,0.002780185,0.00045775,0.98296],"genre_scores_gemma":[0.003391001,0.0004971899,0.00424819,0.0001403655,0.00164538,0.0000758374,0.0001619237,0.0002029512,0.9896371],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.604944,"threshold_uncertainty_score":0.9996757,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07135697515924005,"score_gpt":0.3258677882239183,"score_spread":0.2545108130646782,"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."}}