{"id":"W2341520074","doi":"10.1017/mag.2016.19","title":"100.10 Dice problems with generating function solutions","year":2016,"lang":"en","type":"article","venue":"The Mathematical Gazette","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Dice; Computer science; Content (measure theory); Function (biology); Information retrieval; Mathematics; Statistics; Mathematical analysis; Biology","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":[0.001555216,0.001153151,0.001033809,0.003047147,0.002124388,0.004110702,0.001236592,0.003175587,0.08453127],"category_scores_gemma":[0.007240101,0.0005717106,0.001217839,0.001312933,0.002166863,0.003408021,0.002637154,0.003591428,0.01238974],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00258754,"about_ca_system_score_gemma":0.001094669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001619118,"about_ca_topic_score_gemma":0.001150322,"domain_scores_codex":[0.9988856,0.0003732617,0.00004675176,0.0001837699,0.0003659689,0.0001446748],"domain_scores_gemma":[0.9983713,0.0007181303,0.0001398025,0.0001814968,0.0003720275,0.000217216],"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":[0.00002220325,0.00001928673,0.0001516223,0.00007564321,0.000009914577,0.00007791432,0.00004950538,0.001665699,0.0002477831,0.9598206,0.02828465,0.009575251],"study_design_scores_gemma":[0.00002727597,0.00001182828,0.0002759805,0.00005176222,0.000008312657,0.0003285158,0.00006824949,0.01166501,0.0003595077,0.9617767,0.02540759,0.00001933741],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04413799,0.002935426,0.1208933,0.01111848,0.002155389,0.0001778654,0.001787886,0.0004375846,0.816356],"genre_scores_gemma":[0.4526433,0.00273753,0.05744954,0.003009818,0.002672471,0.0004406564,0.003061377,0.001070484,0.4769149],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.08453127,"threshold_uncertainty_score":0.2827853,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0792498113184131,"score_gpt":0.276746548745693,"score_spread":0.1974967374272799,"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."}}