{"id":"W3000977365","doi":"10.1002/rsa.21085","title":"The rank of sparse random matrices","year":2022,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Cooperative Communication and Network Coding","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematical proof; Random matrix; Mathematics; Rank (graph theory); Conjecture; Sparse matrix; Matrix (chemical analysis); Discrete mathematics; Combinatorics; Computer science; Physics","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":[0.002574971,0.0005355066,0.0006103098,0.00158992,0.0004938873,0.001355011,0.001029957,0.000788225,0.003138932],"category_scores_gemma":[0.03055945,0.0004513283,0.0002936899,0.0006312143,0.002948457,0.003255227,0.001271799,0.001235641,0.0005425748],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001146341,"about_ca_system_score_gemma":0.000894579,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008617456,"about_ca_topic_score_gemma":0.0006033053,"domain_scores_codex":[0.9982589,0.0008205256,0.00005055394,0.0002294387,0.0004270776,0.0002134818],"domain_scores_gemma":[0.9800565,0.01245036,0.002163157,0.002324373,0.002132019,0.0008736445],"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":[0.0002839462,0.00007127322,0.002924453,0.0001638635,0.00003763472,0.0002206168,0.0002165572,0.1337336,0.01382327,0.8309419,0.003463792,0.01411905],"study_design_scores_gemma":[0.00003115307,0.00009497313,0.001445111,0.00005721681,0.00001198455,0.0002476,0.00007587032,0.6095103,0.006024768,0.381074,0.00136517,0.0000618932],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5542246,0.0009647483,0.418916,0.001772444,0.0001741838,0.00006579683,0.0005326558,0.0006882838,0.0226613],"genre_scores_gemma":[0.983949,0.0003429701,0.01224859,0.0001451886,0.0001832494,0.00005910985,0.0002061321,0.00009402219,0.002771794],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003138932,"threshold_uncertainty_score":0.01361787,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01743487275880538,"score_gpt":0.2567832990242409,"score_spread":0.2393484262654355,"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."}}