{"id":"W3134204343","doi":"10.1090/proc/15543","title":"Refinements of the Gauss-Lucas theorem using rational lemniscates and polar convexity","year":2021,"lang":"lv","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Convexity; Mathematics; Gauss; Polar; Pure mathematics; Algebra over a field; Physics; Economics; Quantum mechanics","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":[0.001825282,0.001115504,0.0009538343,0.002754761,0.001740424,0.003214173,0.001165532,0.0008317489,0.01489051],"category_scores_gemma":[0.007351493,0.000574205,0.001938385,0.001597999,0.004883331,0.005055144,0.003199474,0.003387017,0.003172291],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003066785,"about_ca_system_score_gemma":0.00123852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005669798,"about_ca_topic_score_gemma":0.004755931,"domain_scores_codex":[0.9990175,0.0002721026,0.00005261454,0.0001969075,0.0002957437,0.0001651634],"domain_scores_gemma":[0.9981288,0.0008600974,0.0001321295,0.0002578536,0.0004507694,0.0001704292],"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":[0.00001710219,0.000004143639,0.00007255055,0.00002322174,0.000003557358,0.00004367984,0.00006812302,0.00124336,0.00016048,0.9931572,0.00155486,0.003651687],"study_design_scores_gemma":[0.00001621283,0.00001234673,0.0001508366,0.00002356414,0.00000913433,0.00006692165,0.00009396361,0.01187464,0.0004654767,0.9764225,0.01084825,0.00001610732],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07312348,0.002552681,0.4654534,0.003965931,0.001016119,0.000134827,0.000662862,0.0007081788,0.4523827],"genre_scores_gemma":[0.783484,0.003344728,0.1192423,0.001153071,0.001353577,0.0001917315,0.0007928361,0.0008582651,0.08957963],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01489051,"threshold_uncertainty_score":0.04981375,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01641405568117211,"score_gpt":0.2791535082060397,"score_spread":0.2627394525248676,"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."}}