{"id":"W2982262031","doi":"10.1007/s00211-022-01291-2","title":"Rigorous numerics for nonlinear heat equations in the complex plane of time","year":2022,"lang":"en","type":"article","venue":"Numerische Mathematik","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Japan Society for the Promotion of Science; National Institutes of Health","keywords":"Mathematics; Initial value problem; Cauchy problem; Nonlinear system; Heat equation; Cauchy distribution; Fixed point; Banach space; Mathematical analysis; Singularity; Applied mathematics","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":[0.002479338,0.0007010879,0.0008289717,0.001687513,0.0006256803,0.00124303,0.0009568038,0.0008117511,0.00184948],"category_scores_gemma":[0.005932385,0.0002886378,0.000799821,0.0004121305,0.002230192,0.002059508,0.002343666,0.001649566,0.0002919883],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009918635,"about_ca_system_score_gemma":0.0009169696,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001311041,"about_ca_topic_score_gemma":0.001122349,"domain_scores_codex":[0.9992448,0.000252464,0.00003583553,0.00003792748,0.0003733011,0.00005569712],"domain_scores_gemma":[0.9981903,0.0007972813,0.00023159,0.0001728531,0.000488599,0.0001193231],"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":[0.00005812629,0.00009536543,0.0008904919,0.0001601519,0.00004987976,0.0002245244,0.0003090603,0.3589894,0.01635875,0.6124455,0.0006515173,0.009767344],"study_design_scores_gemma":[0.000005142975,0.00001469738,0.0001083849,0.000009142309,0.000002591267,0.00002019815,0.00001978045,0.9745402,0.001181053,0.02347655,0.0006155991,0.000006640409],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04906824,0.0002920351,0.944397,0.0002373715,0.00006248341,0.00004852593,0.00003135783,0.0001608648,0.005702099],"genre_scores_gemma":[0.7857114,0.0003689904,0.2065674,0.000109228,0.00007416439,0.0001935337,0.00008419858,0.0002810289,0.006610033],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002479338,"threshold_uncertainty_score":0.01311219,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02612422237683499,"score_gpt":0.241937234614109,"score_spread":0.215813012237274,"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."}}