{"paper":{"title":"On a voltage-conductance kinetic system for integrate and fire neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.AP","authors_text":"Benoit Perthame (LJLL, Delphine Salort (IJM), INRIA Rocquencourt)","submitted_at":"2013-10-10T09:26:21Z","abstract_excerpt":"The voltage-conductance kinetic equation for integrate and fire neurons has been used in neurosciences since a decade and describes the probability density of neurons in a network. It is used when slow conductance receptors are activated and noticeable applications to the visual cortex have been worked-out. In the simplest case, the derivation also uses the assumption of fully excitatory and moderately all-to-all coupled networks; this is the situation we consider here. We study properties of solutions of the kinetic equation for steady states and time evolution and we prove several global a p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2742","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}