{"id":"W2543706324","doi":"10.19086/da.3118","title":"Rank bounds for design matrices with block entries and geometric applications","year":2018,"lang":"en","type":"preprint","venue":"Discrete Analysis","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Collinearity; Combinatorics; Linear subspace; Rank (graph theory); Upper and lower bounds; Matrix (chemical analysis); Scalar (mathematics); Scaling; Discrete mathematics; Pure mathematics; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.0004756761,0.0002444337,0.0004086099,0.001582386,0.0003445529,0.0007602458,0.0005964204,0.0001191581,0.000009990924],"category_scores_gemma":[0.00005027766,0.0002052869,0.0002119533,0.004022629,0.00007957464,0.0002129279,0.0003788639,0.0001115757,0.00000614836],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003725526,"about_ca_system_score_gemma":0.0001516359,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003156256,"about_ca_topic_score_gemma":0.00001910744,"domain_scores_codex":[0.9982408,0.00007163652,0.0003134539,0.0007960483,0.0003537073,0.0002243382],"domain_scores_gemma":[0.9980805,0.0004507368,0.0003066362,0.0006307251,0.0004274257,0.0001039997],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001822419,0.0002420972,0.005369647,0.000600842,0.01203364,0.000006771534,0.001367566,0.8891901,0.00008729706,0.02376463,0.003655955,0.06349918],"study_design_scores_gemma":[0.0005071153,0.0002226622,0.002938926,0.000026747,0.00388752,0.000005350925,0.00003537024,0.9613285,0.0007277469,0.01939954,0.01019043,0.0007300954],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.003231737,0.001904662,0.9934852,0.0004048389,0.00005749992,0.0006805191,0.00005612583,0.00008619323,0.00009321074],"genre_scores_gemma":[0.5546066,0.0003385523,0.4431068,0.00009896146,0.0002830411,0.0007112085,0.0004108111,0.00001448381,0.0004295504],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5513749,"threshold_uncertainty_score":0.8371356,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01731660051463633,"score_gpt":0.2698239929125862,"score_spread":0.2525073923979499,"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."}}