Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a finite-size neuronal population equation   Population equations for infinitely large networks of spiking neurons have a
long tradition in theoretical neuroscience. In this work, we analyze a recent
generalization of these equations to populations of finite size, which takes
the form of a nonlinear stochastic integral equation. We prove that, in the
case of leaky integrate-and-fire (LIF) neurons with escape noise and for a
slightly simplified version of the model, the equation is well-posed and stable
in the sense of Br\'emaud-Massouli\'e. The proof combines methods from Markov
processes taking values in the space of positive measures and nonlinear Hawkes
processes. For applications, we also provide an efficient simulation algorithm
for interacting populations of LIF neurons.

7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas