{"id":"W2082350986","doi":"10.4153/cmb-2008-026-2","title":"On the Inner Radius of a Nodal Domain","year":2008,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Eigenfunction; RADIUS; Dimension (graph theory); Domain (mathematical analysis); Type (biology); Manifold (fluid mechanics); Eigenvalues and eigenvectors; Upper and lower bounds; Pure mathematics; Riemannian manifold; Mathematical analysis; Combinatorics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001719523,0.0005978408,0.000734847,0.001808159,0.0006296614,0.001410668,0.0009316999,0.0006070568,0.002958814],"category_scores_gemma":[0.007090849,0.0003078211,0.0003572234,0.0003170998,0.002910145,0.002213514,0.002545523,0.001108496,0.0008506082],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006590092,"about_ca_system_score_gemma":0.0001895491,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000405276,"about_ca_topic_score_gemma":0.0002091493,"domain_scores_codex":[0.9993408,0.0002732638,0.00002175233,0.0001188316,0.0001440077,0.0001011977],"domain_scores_gemma":[0.9942135,0.003352216,0.0005643043,0.0004128679,0.0006841674,0.0007728861],"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":[0.0003002147,0.00004510388,0.003408648,0.0002818848,0.00005939982,0.0005329989,0.0006557859,0.04559764,0.02817956,0.9078909,0.002736336,0.01031143],"study_design_scores_gemma":[0.00003079977,0.0001819018,0.006237132,0.0001897614,0.00005830028,0.0008588817,0.0005170907,0.4364102,0.01667848,0.5302852,0.008444173,0.0001080291],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6311243,0.004437789,0.2873978,0.001161811,0.0001212962,0.00004219187,0.0002048106,0.0004428745,0.07506713],"genre_scores_gemma":[0.9861755,0.0006461734,0.00917934,0.00006054619,0.00008616795,0.00002742917,0.00007869346,0.0001177774,0.003628319],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002958814,"threshold_uncertainty_score":0.009898186,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05517958439604307,"score_gpt":0.2677561826126426,"score_spread":0.2125765982165995,"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."}}