{"id":"W4302227484","doi":"10.4230/lipics.socg.2024.5","title":"Communication Complexity and Discrepancy of Halfplanes","year":2024,"lang":"en","type":"preprint","venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University; Marianopolis College","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Upper and lower bounds; Mathematics; Hypercube; Omega; Factorization; Order (exchange); Norm (philosophy); Polynomial; Discrete mathematics; Physics; Mathematical analysis; Algorithm","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":[0.0009618064,0.0005399421,0.0009997766,0.0002843967,0.0001717553,0.0003239915,0.0006402883,0.0005176693,0.000131461],"category_scores_gemma":[0.0005137956,0.0004354668,0.00034138,0.0001425432,0.0003706955,0.0002968663,0.001366282,0.001004929,0.00004747682],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009249854,"about_ca_system_score_gemma":0.00008468322,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004004677,"about_ca_topic_score_gemma":0.00006909014,"domain_scores_codex":[0.9966311,0.00008142395,0.002111724,0.0002940638,0.0005178142,0.0003638069],"domain_scores_gemma":[0.9966505,0.0005173953,0.001087609,0.00118033,0.0004175127,0.0001467254],"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":[0.00005714128,0.0003600708,0.00009158567,0.01985462,0.0002562492,4.867712e-7,0.01110001,0.000002941415,0.00001101233,0.9602669,0.005963126,0.002035859],"study_design_scores_gemma":[0.000699166,0.00008577379,0.00005610865,0.002090696,0.0002178908,0.0000237014,0.0015971,0.07760619,0.0004975179,0.9125449,0.004131568,0.0004493938],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7896073,0.0009736543,0.1031702,0.003323294,0.001472746,0.009193907,0.008392148,0.001052536,0.08281419],"genre_scores_gemma":[0.5883448,0.0003244739,0.4042732,0.0002768689,0.0001659075,0.0006412925,0.004500901,0.0001602643,0.001312279],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.301103,"threshold_uncertainty_score":0.9998097,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08719177781554249,"score_gpt":0.3545731149878742,"score_spread":0.2673813371723317,"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."}}