{"id":"W4416192305","doi":"10.3934/dcds.2025181","title":"A special concavity property for positive Hessian quotient operators","year":2025,"lang":"","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hessian matrix; Quotient; Hessian equation; Property (philosophy); Tensor (intrinsic definition)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007238647,0.0007431404,0.001635594,0.0001861758,0.0007628119,0.0008601439,0.0004725207,0.0005231317,0.00006238434],"category_scores_gemma":[0.0002674435,0.0005248602,0.0004468124,0.0004632361,0.0004528077,0.0002107396,0.0003591861,0.0004364293,0.00001340892],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002292592,"about_ca_system_score_gemma":0.0001821903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005933892,"about_ca_topic_score_gemma":0.000210334,"domain_scores_codex":[0.9956785,0.0004625249,0.001339753,0.00110066,0.0004170607,0.001001546],"domain_scores_gemma":[0.9977841,0.0004728451,0.0003701194,0.0006138859,0.0004009043,0.0003581969],"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":[0.001280966,0.001119624,0.004865794,0.004668495,0.001625784,0.00007016282,0.002332285,0.00002517508,0.0005157483,0.9515845,0.01283755,0.01907394],"study_design_scores_gemma":[0.02649479,0.008824312,0.01613666,0.01652415,0.006621901,0.0002896008,0.05007748,0.4262238,0.0006235991,0.04835681,0.3915397,0.008287133],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7344924,0.004025074,0.09075394,0.004442519,0.01625099,0.01867601,0.003072179,0.0003808955,0.127906],"genre_scores_gemma":[0.9644067,0.00003539642,0.0002169587,0.0001683315,0.001972686,0.0003740734,0.00008444262,0.00005556325,0.03268582],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9032277,"threshold_uncertainty_score":0.9997203,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0124673428987518,"score_gpt":0.2675442049688279,"score_spread":0.2550768620700761,"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."}}