{"id":"W2612145187","doi":"","title":"Recounting the number of peaks and valleys in compositions of integers.","year":2017,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Integer (computer science); Combinatorics; Set (abstract data type); Discrete mathematics; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005863588,0.0001358689,0.0003873887,0.00004053518,0.0001543348,0.00003272481,0.0004855508,0.00007918943,0.00001885922],"category_scores_gemma":[0.001339014,0.0001101069,0.00006098301,0.00008472518,0.0002789869,0.0001778439,0.0002618116,0.0002147169,0.000003553625],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000334659,"about_ca_system_score_gemma":0.00002852719,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007627988,"about_ca_topic_score_gemma":0.0000132341,"domain_scores_codex":[0.9989049,0.00007026691,0.0004886494,0.0001481889,0.000216402,0.000171553],"domain_scores_gemma":[0.9974746,0.0008944113,0.0006359972,0.0008086227,0.0001537268,0.00003270757],"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":[0.00001136317,0.0001678266,0.00677802,0.0001510303,0.0000255036,0.000002161078,0.001135345,9.669599e-7,0.0006491309,0.990814,0.00009573311,0.0001688923],"study_design_scores_gemma":[0.0007982158,0.0000310171,0.002373759,0.0002548359,0.00002958384,0.000007989375,0.0003658131,0.0001642452,0.002543336,0.993281,0.00004397063,0.0001062086],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9893481,0.00003007486,0.0001216869,0.0002115061,0.0007142003,0.0002491428,0.000002977359,0.00001878249,0.009303546],"genre_scores_gemma":[0.9950812,0.00002095259,0.004790686,0.000006714703,0.000006767196,0.00001500258,6.254805e-7,0.00002316106,0.00005488731],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009248658,"threshold_uncertainty_score":0.4490029,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03600574116603807,"score_gpt":0.3414195245162259,"score_spread":0.3054137833501879,"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."}}