{"id":"W2966843155","doi":"10.1088/1475-7516/2019/09/052","title":"Stochastic homology of Gaussian vs. non-Gaussian random fields: graphs towards Betti numbers and persistence diagrams","year":2019,"lang":"en","type":"article","venue":"Journal of Cosmology and Astroparticle Physics","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":44,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute","funders":"Ministero dello Sviluppo Economico; Institut Périmètre de physique théorique; Industry Canada; Government of Canada; John Templeton Foundation","keywords":"Betti number; Euler characteristic; Persistent homology; Gaussian; Topology (electrical circuits); Random field; Minkowski space; Topological data analysis; Homology (biology)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001239501,0.0003981087,0.0007735814,0.004323251,0.00130241,0.002979991,0.001158955,0.001516669,0.005081932],"category_scores_gemma":[0.009726088,0.0005093354,0.0005377603,0.001135995,0.003069786,0.005357667,0.001795813,0.001567195,0.0003560226],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001326247,"about_ca_system_score_gemma":0.0006412513,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00122008,"about_ca_topic_score_gemma":0.001136362,"domain_scores_codex":[0.9995509,0.0001522205,0.00001491147,0.00009060345,0.0001006125,0.00009080136],"domain_scores_gemma":[0.9910262,0.00502683,0.001320223,0.0004478254,0.0007307308,0.001448219],"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":[0.00002356111,0.00002426305,0.001144391,0.00002772174,0.000005503081,0.00006562334,0.0003035918,0.003967764,0.0006824936,0.9908699,0.0004821054,0.00240297],"study_design_scores_gemma":[0.000008096573,0.00001328628,0.0009764427,0.00001851631,0.000006542681,0.0000820786,0.000117125,0.04714505,0.0002863918,0.9508256,0.0005091656,0.0000117308],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8609136,0.0005883822,0.1134262,0.002512793,0.00007208811,0.00004370059,0.0002519839,0.00016573,0.02202552],"genre_scores_gemma":[0.9917467,0.0002686481,0.003992441,0.0001693091,0.0001169431,0.00002789562,0.00012835,0.00005010956,0.003499661],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005081932,"threshold_uncertainty_score":0.01700073,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01090830763408355,"score_gpt":0.2280337714204822,"score_spread":0.2171254637863987,"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."}}