{"id":"W3177351760","doi":"10.1098/rspa.2020.0908","title":"Differential invariant method for seeking nonlocally related systems and nonlocal symmetries. I: General theory and examples","year":2021,"lang":"en","type":"article","venue":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ode; Homogeneous space; Mathematics; Invariant (physics); Conservation law; Ordinary differential equation; Invertible matrix; Partial differential equation; Symmetry (geometry); Applied mathematics; Mathematical analysis; Differential equation; Pure mathematics; Mathematical physics","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":[0.0008356443,0.0004865106,0.0005701002,0.0009967592,0.000466774,0.0006825068,0.0009930619,0.0009330782,0.002023363],"category_scores_gemma":[0.001096892,0.0002886284,0.0007661537,0.0005159525,0.001454676,0.001120072,0.001506938,0.001005715,0.0003948669],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006234575,"about_ca_system_score_gemma":0.0004896431,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005150931,"about_ca_topic_score_gemma":0.0005132562,"domain_scores_codex":[0.9997134,0.00009748575,0.00001732132,0.00003389844,0.0001159071,0.00002204978],"domain_scores_gemma":[0.9996613,0.0001393632,0.00005202729,0.0000611946,0.00005621362,0.00002978905],"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":[0.00003814746,0.00005323794,0.0006903883,0.0002307603,0.00003579135,0.0002867033,0.000212041,0.05364911,0.01653001,0.885152,0.00158456,0.04153726],"study_design_scores_gemma":[0.00002015349,0.0000430444,0.0002050445,0.00001859429,0.0000102339,0.0002400829,0.00004182823,0.8226095,0.002966,0.1687282,0.005097511,0.000019803],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.009765071,0.0003114614,0.9843519,0.0001237985,0.00004815599,0.00004857397,0.00001769461,0.00009805524,0.005235147],"genre_scores_gemma":[0.2818247,0.0006554337,0.7076249,0.000159738,0.00007802944,0.000231984,0.00008436495,0.0001539599,0.009186932],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002023363,"threshold_uncertainty_score":0.006768823,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009730768674545896,"score_gpt":0.2399172528157485,"score_spread":0.2301864841412026,"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."}}