{"id":"W2950339429","doi":"10.48550/arxiv.0811.0208","title":"Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones","year":2008,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Combinatorics; Nabla symbol; Mathematics; Lipschitz continuity; Compact space; Function (biology); Laplace operator; Discrete mathematics; Physics; Pure mathematics; Omega; Mathematical analysis","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":[0.002350117,0.001023291,0.0008248892,0.001312656,0.001361517,0.002513333,0.001676369,0.00122636,0.007941236],"category_scores_gemma":[0.01139607,0.0002946227,0.001140399,0.0007208641,0.003759432,0.005725966,0.003088471,0.002587596,0.0005478523],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002672729,"about_ca_system_score_gemma":0.001315355,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00277468,"about_ca_topic_score_gemma":0.001635601,"domain_scores_codex":[0.9991152,0.0002940968,0.00002740054,0.0001103846,0.0002149995,0.0002379403],"domain_scores_gemma":[0.9953915,0.002466353,0.0005096591,0.0002772266,0.0005049931,0.0008502791],"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":[0.00001192776,0.00001050517,0.0002179352,0.00001604588,0.000005663179,0.00005208338,0.00005692916,0.006561701,0.0002091734,0.9909051,0.000474328,0.00147865],"study_design_scores_gemma":[0.0000119945,0.00001957205,0.0001631971,0.00002714482,0.000005726821,0.00005071585,0.00009990911,0.1192585,0.0002482213,0.8783958,0.001704965,0.00001422633],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2678117,0.002680671,0.5840011,0.003924774,0.0002591139,0.0001225362,0.0002236294,0.0002190028,0.1407575],"genre_scores_gemma":[0.9479923,0.001040403,0.02353956,0.0006625513,0.0001901416,0.000148305,0.0001331964,0.0001245879,0.02616877],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007941236,"threshold_uncertainty_score":0.02656609,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2299699849408838,"score_gpt":0.256374555288751,"score_spread":0.02640457034786717,"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."}}