{"id":"W2036807344","doi":"10.1007/s00332-014-9206-9","title":"Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction–Diffusion Systems in $${\\mathbb {R}}^2$$ R 2","year":2014,"lang":"en","type":"article","venue":"Journal of Nonlinear Science","topic":"Nonlinear Dynamics and Pattern Formation","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia; Dalhousie University","funders":"","keywords":"Lattice (music); Eigenvalues and eigenvectors; Reaction–diffusion system; Mathematical physics; Mathematical analysis; Mathematics; Combinatorics; Physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006264723,0.0007029612,0.000480509,0.001148916,0.0004662183,0.001564483,0.001044119,0.0009805098,0.006408119],"category_scores_gemma":[0.006187786,0.000325736,0.0004257149,0.0003503315,0.001682336,0.001632829,0.0009592153,0.000915735,0.0006116486],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007775101,"about_ca_system_score_gemma":0.0004232337,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008311242,"about_ca_topic_score_gemma":0.0005198816,"domain_scores_codex":[0.9998221,0.00005736142,0.000008867925,0.000035013,0.00004586166,0.00003089675],"domain_scores_gemma":[0.9980275,0.001130512,0.0003339899,0.00007788851,0.0002383097,0.0001918442],"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":[0.0004707323,0.0001877889,0.002517654,0.0003557548,0.00006791528,0.0007035609,0.0006274973,0.1538349,0.06127051,0.7527567,0.0043576,0.02284949],"study_design_scores_gemma":[0.00004640138,0.00005476009,0.001197954,0.00002572307,0.00001671524,0.0002185052,0.00008832147,0.7957721,0.002507874,0.1992182,0.0008114945,0.00004192799],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7344156,0.001631929,0.213019,0.003848486,0.0002216434,0.00006971492,0.0002304687,0.0005738299,0.0459893],"genre_scores_gemma":[0.9845067,0.0003535394,0.005455954,0.0001209057,0.00007802316,0.00004539936,0.00007218763,0.0001117942,0.009255563],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006408119,"threshold_uncertainty_score":0.02143729,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01477982420182347,"score_gpt":0.2554765263739625,"score_spread":0.240696702172139,"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."}}