{"id":"W1986609638","doi":"10.1214/009117906000001015","title":"A note on multitype branching processes with immigration in a random environment","year":2007,"lang":"en","type":"article","venue":"The Annals of Probability","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Eidgenössische Technische Hochschule Zürich","keywords":"Branching process; Complement (music); Branching (polymer chemistry); Limit (mathematics); Branching random walk; Stochastic process; Extinction probability; Central limit theorem","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001785989,0.0001136563,0.0002199493,0.00003169095,0.00005018861,0.000009020626,0.0001365477,0.00004281869,0.00001610277],"category_scores_gemma":[0.003254401,0.00006503092,0.00002891817,0.0001587231,0.00007740479,0.00005183166,0.0000267986,0.0001354318,0.000004282564],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002015239,"about_ca_system_score_gemma":0.00006723269,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004750321,"about_ca_topic_score_gemma":0.0007038704,"domain_scores_codex":[0.9989513,0.00005211909,0.0003363746,0.000185608,0.0002740409,0.0002005746],"domain_scores_gemma":[0.9972197,0.002233678,0.0001465021,0.0002691752,0.00009332797,0.00003763667],"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":[0.02103893,0.005386265,0.001330942,0.005994735,0.0001309127,0.00002345908,0.01953967,0.00236202,0.002630999,0.8664043,0.000137082,0.0750207],"study_design_scores_gemma":[0.001050008,0.000526369,0.001664173,0.0002420595,0.00002053779,0.00000227948,0.0001103215,0.001517451,0.01255135,0.9821416,0.00003756863,0.0001362444],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3898512,0.00004352137,0.6086604,0.0005676782,0.00001364018,0.0005697518,0.00001005291,0.00001558898,0.0002681872],"genre_scores_gemma":[0.9829268,0.00001689396,0.01690134,0.00009404604,0.00001764433,0.00002220817,0.000001302075,0.000008788682,0.00001093651],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5930756,"threshold_uncertainty_score":0.3896057,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09342150145699844,"score_gpt":0.3561155320795067,"score_spread":0.2626940306225082,"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."}}