{"id":"W4235635581","doi":"10.1002/9781119517566.ch16","title":"Differentiation and Integration on Smooth Manifolds","year":2019,"lang":"en","type":"other","venue":"","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Atlas (anatomy); Vector field; Diffeomorphism; Curl (programming language); Manifold (fluid mechanics); Mathematics; Pure mathematics; Volume form; Mathematical analysis; Divergence (linguistics); Differential form; Geometry; Geology; Computer science; Scalar curvature; Hermitian manifold; Paleontology; Curvature","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":[0.00002702737,0.0001244979,0.0001195037,0.0001102942,0.000008053146,0.00004713803,0.0001719929,0.00007304567,0.00003448843],"category_scores_gemma":[0.0000147749,0.00009623439,0.00001413904,0.00004205055,0.000004679052,0.00005977421,0.00006168844,0.00008316247,0.000118644],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001739544,"about_ca_system_score_gemma":0.000003762413,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004338345,"about_ca_topic_score_gemma":0.000003312619,"domain_scores_codex":[0.9994895,0.000005650386,0.00008185625,0.0002214489,0.0001175037,0.00008396696],"domain_scores_gemma":[0.999576,0.00003510582,0.00004432116,0.0003131873,0.000007262743,0.00002410877],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[5.355849e-7,0.00002109373,6.679818e-7,0.00007192248,0.000007493571,4.768222e-7,0.00002683486,0.0003765455,0.00009707848,0.9729037,0.0114708,0.01502288],"study_design_scores_gemma":[0.0001841583,0.0001099326,0.00003005034,0.0004230474,0.000006507908,0.000001536797,0.000002739349,0.9676499,0.0001612751,0.01761232,0.01350303,0.0003154354],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.000003565153,0.00002323876,0.6927814,0.0000298799,0.0001815416,0.00009896395,3.906986e-7,0.0002843826,0.3065966],"genre_scores_gemma":[0.01232922,0.00004307721,0.3592289,0.0001115668,0.00009432634,0.00001450792,0.000004752949,0.0001683213,0.6280053],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9672734,"threshold_uncertainty_score":0.3924325,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01273093888524384,"score_gpt":0.2329646269153135,"score_spread":0.2202336880300696,"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."}}