{"id":"W2552556533","doi":"10.1016/j.aam.2017.09.003","title":"Pfaffians and nonintersecting paths in graphs with cycles: Grassmann algebra methods","year":2017,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":31,"is_retracted":false,"has_abstract":false,"ca_institutions":"Perimeter Institute","funders":"Agence Nationale de la Recherche; Innovation, Science and Economic Development Canada","keywords":"Mathematics; Exterior algebra; Grassmannian; Algebra over a field; Schubert calculus; Algebraic number; Graph; Generalization; Combinatorics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001328311,0.0005468783,0.001042346,0.0002994488,0.0003090933,0.000169996,0.0008191959,0.0001904944,0.000007863345],"category_scores_gemma":[0.001459855,0.0004721115,0.00007014565,0.0002851973,0.0004241131,0.0005765269,0.0003719228,0.0005933214,0.000006308711],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001312691,"about_ca_system_score_gemma":0.00003944114,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007627753,"about_ca_topic_score_gemma":0.0003147045,"domain_scores_codex":[0.9972396,0.00005925882,0.0009735886,0.0006317734,0.000409463,0.0006863496],"domain_scores_gemma":[0.9950485,0.002332704,0.0009917204,0.001442989,0.0000542746,0.00012983],"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":[0.00004333167,0.0004060502,0.001479966,0.001256549,0.00002551205,0.0000492073,0.004826564,0.00005263841,0.0003712684,0.9716142,0.000006231189,0.01986841],"study_design_scores_gemma":[0.001742068,0.00008550187,0.0001789069,0.000832618,0.00004448128,0.0000463099,0.005756687,0.001306863,0.001791441,0.9875267,0.0001145212,0.0005738917],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.5235347,0.0006545337,0.4097051,0.000126742,0.0005928849,0.002552912,0.000009579526,0.0003916577,0.06243183],"genre_scores_gemma":[0.4385009,0.0001546597,0.5610024,0.00001770121,0.00002922843,0.0001768331,9.371571e-7,0.0000875093,0.00002973649],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.1512973,"threshold_uncertainty_score":0.9997731,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02961173959000027,"score_gpt":0.3745098303551216,"score_spread":0.3448980907651213,"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."}}