{"id":"W3008604955","doi":"10.3934/dcdsb.2020039","title":"Hexagonal spike clusters for some PDE's in 2D","year":2020,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems - B","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Lattice (music); Combinatorics; Mathematics; Separable space; Ode; Cluster (spacecraft); Hexagonal crystal system; Hexagonal lattice; Mathematical analysis; Physics; Condensed matter physics; Crystallography; Antiferromagnetism","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":[0.000183356,0.0002059194,0.0005397911,0.00003132557,0.00006244126,0.00008608585,0.0001583043,0.0001100462,0.000007583304],"category_scores_gemma":[0.0006810426,0.0001705059,0.00007968995,0.00009379229,0.00004698337,0.00008149631,0.0000760426,0.0001597622,0.000004292142],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003005811,"about_ca_system_score_gemma":0.00002364394,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004345167,"about_ca_topic_score_gemma":0.00001679885,"domain_scores_codex":[0.9985203,0.00003953361,0.0004792494,0.0003770583,0.0002040608,0.0003798564],"domain_scores_gemma":[0.9989276,0.0005655678,0.0001050426,0.0001228881,0.00004461955,0.0002342767],"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":[0.0001764572,0.00004458144,0.00008731306,0.0008701468,0.00003849084,0.00002871969,0.0003683267,0.00001244269,0.0002180115,0.9949924,0.0004801347,0.002683018],"study_design_scores_gemma":[0.002085161,0.0005955041,0.00007940188,0.0002636624,0.00009412151,0.00002635966,0.00131103,0.7879581,0.00001613181,0.205993,0.001092396,0.0004851863],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.101134,0.0004298245,0.8950385,0.001363271,0.0002912149,0.001036682,0.0002774451,0.00009264649,0.0003364005],"genre_scores_gemma":[0.9968227,0.000008071245,0.002248055,0.0003663862,0.000197709,0.000129044,0.00002556108,0.00003345758,0.0001689817],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8956888,"threshold_uncertainty_score":0.695303,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02879530975457721,"score_gpt":0.2874600531465698,"score_spread":0.2586647433919926,"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."}}