{"id":"W6994304677","doi":"","title":"Ramanujan graphs","year":2014,"lang":"en","type":"dissertation","venue":"eScholarship@McGill (McGill)","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Ramanujan's sum; Expander graph; Mathematical proof; Graph theory; Topological graph theory; Graph","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":[0.0006457529,0.0007330232,0.0006311577,0.00208049,0.002379335,0.002151719,0.001058618,0.001097775,0.02071527],"category_scores_gemma":[0.001832611,0.0003631346,0.0009286374,0.001554019,0.002210488,0.003808452,0.002010756,0.00244271,0.004157416],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00137589,"about_ca_system_score_gemma":0.0006476563,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001235224,"about_ca_topic_score_gemma":0.001197443,"domain_scores_codex":[0.9991284,0.0002108991,0.00003270731,0.0001868099,0.0002958792,0.0001452736],"domain_scores_gemma":[0.9991938,0.0003728606,0.0000793272,0.0001258403,0.0001618654,0.00006628712],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00000373611,0.00000514432,0.0000408194,0.00002491773,0.000002271275,0.00003367804,0.0001056794,0.0002792768,0.0002802873,0.992265,0.001782105,0.005177091],"study_design_scores_gemma":[0.000003929829,0.00001306815,0.0001518864,0.00003658121,0.000004230574,0.0002466263,0.0001033449,0.001686038,0.0003262398,0.9165164,0.08090102,0.00001066456],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.06206531,0.01541219,0.2170221,0.004701746,0.001549988,0.0002452662,0.001182684,0.0005026669,0.6973181],"genre_scores_gemma":[0.6123173,0.02078469,0.1287709,0.003490626,0.002663449,0.0005656545,0.001581952,0.0004485625,0.2293768],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.02071527,"threshold_uncertainty_score":0.06929946,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02535069051174987,"score_gpt":0.2787685394117108,"score_spread":0.2534178488999609,"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."}}