{"id":"W2297951637","doi":"10.1007/s00023-016-0536-z","title":"Bifurcations of Standing Localized Waves on Periodic Graphs","year":2016,"lang":"en","type":"article","venue":"Annales Henri Poincaré","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":46,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Mathematical analysis; Nonlinear Schrödinger equation; Periodic boundary conditions; Standing wave; Homogenization (climate); Exponential function; Amplitude; Nonlinear system; Breather; Physics; Schrödinger equation; Boundary value problem; Quantum mechanics","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":[0.0002603567,0.000207031,0.0003876935,0.0001440794,0.0001070376,0.0000140084,0.0002311874,0.00006713874,0.0001548305],"category_scores_gemma":[0.000547534,0.0001356575,0.000177849,0.0002463314,0.0002599856,0.0001718233,0.00006804481,0.00009792529,0.000109677],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005132781,"about_ca_system_score_gemma":0.00004628026,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002297523,"about_ca_topic_score_gemma":0.000003557415,"domain_scores_codex":[0.998515,0.00006342081,0.0004821456,0.0002667289,0.0003609745,0.0003117708],"domain_scores_gemma":[0.9977877,0.001160204,0.0002372742,0.0005672352,0.0001400535,0.0001075353],"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":[0.00003395938,0.0002257097,0.00009373583,0.0001898502,0.00005477239,0.000002466476,0.0005760905,0.000003318896,0.01446311,0.9794134,0.001647403,0.003296159],"study_design_scores_gemma":[0.0005734555,0.0001390431,0.00005441986,0.0003987941,0.00003188239,0.000003305608,0.0001359998,0.00003964839,0.01644106,0.9803877,0.00160256,0.0001920987],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7101809,0.0003898354,0.2472788,0.002697282,0.0002073333,0.001101316,0.000170758,0.0004724975,0.03750129],"genre_scores_gemma":[0.9834404,0.00007793625,0.01535172,0.00009681908,0.00003732968,0.00003602961,0.00000330834,0.00004967222,0.0009068072],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2732595,"threshold_uncertainty_score":0.5531952,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05666607067887016,"score_gpt":0.3298647194367878,"score_spread":0.2731986487579177,"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."}}