{"paper":{"title":"Hydrodynamic Limits for Spatially Structured Interacting Neurons","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aline Duarte, Andr\\'es Rodr\\'iguez, Guilherme Ost","submitted_at":"2015-03-20T01:03:58Z","abstract_excerpt":"In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We do not impose on the neurons mean-field type interactions. The values of the membrane potentials evolve under the effect of chemical and electrical synapses and leak currents. The system consists of $\\epsilon^{-2}$ neurons embedded in $[0,1)^2$, each spiking randomly according to a point process with rate depending on both its membrane potential and position. When neuron $i$ spikes, its membrane potential is reset to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05974","kind":"arxiv","version":3},"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"}