{"id":"W2009319947","doi":"10.1016/s0012-365x(01)00108-x","title":"On the existence of a point subset with a specified number of interior points","year":2001,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Combinatorics; Integer (computer science); Convex hull; Point (geometry); Boundary (topology); Plane (geometry); Set (abstract data type); Finite set; Interior point method; Regular polygon; Discrete mathematics; Geometry; Mathematical analysis; Algorithm","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":[0.004055564,0.0009922406,0.00214417,0.002270206,0.00162479,0.002900157,0.002085651,0.00321634,0.007178921],"category_scores_gemma":[0.0291995,0.00108069,0.001452841,0.001734016,0.004856364,0.006121664,0.006218006,0.003044374,0.001098552],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009175429,"about_ca_system_score_gemma":0.0008583569,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004516065,"about_ca_topic_score_gemma":0.0003912827,"domain_scores_codex":[0.9983663,0.0005506416,0.0001274571,0.0003010506,0.0004678295,0.0001866929],"domain_scores_gemma":[0.971467,0.02273024,0.001250178,0.001716852,0.001906063,0.0009296463],"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":[0.00213185,0.0002268666,0.005440983,0.0008738228,0.00009807321,0.001095848,0.001335206,0.1764662,0.02705191,0.7098553,0.004530755,0.07089316],"study_design_scores_gemma":[0.000136319,0.0003767218,0.001397023,0.0003740977,0.00008102966,0.00088154,0.0007866951,0.5722776,0.01968072,0.3986473,0.005274486,0.00008643234],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1526774,0.0004549067,0.8261158,0.001339488,0.00008290674,0.0001661569,0.0003435906,0.000190897,0.01862893],"genre_scores_gemma":[0.6999457,0.001456419,0.2859291,0.0003409842,0.0001886772,0.0005551701,0.001019439,0.0003782596,0.01018625],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007178921,"threshold_uncertainty_score":0.0240159,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02746433403006654,"score_gpt":0.2678415786168757,"score_spread":0.2403772445868092,"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."}}