Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
From spiking neurons to rate models: A cascade model as an approximation to spiking neuron models with refractoriness
 

Summary: From spiking neurons to rate models: A cascade model as an approximation to spiking neuron
models with refractoriness
Yuval Aviel and Wulfram Gerstner*
Ecole Polytechnique Fédérale de Lausanne (EPFL), School of Computer and Communication Sciences and Brain Mind Institute,
CH 1015 Lausanne, Switzerland
Received 26 October 2005; published 16 May 2006
A neuron that is stimulated repeatedly by the same time-dependent stimulus exhibits slightly different spike
timing at each trial. We compared the exact solution of the time-dependent firing rate for a stochastically
spiking neuron model with refractoriness spike response model with that of an inhomogeneous Poisson
process subject to the same stimulus. To arrive at a mapping between the two models we used alternatively i
a systematic parameter-free Volterra expansion of the exact solution or ii a linear filter combined with
nonlinear Poisson rate model linear-nonlinear Poisson cascade model with a single free parameter. Both the
cascade model and the second-order Volterra model showed excellent agreement with the exact rate dynamics
of the spiking neuron model with refractoriness even for strong and rapidly changing input. Cascade rate
models are widely used in systems neuroscience. Our method could help to connect experimental rate mea-
surements to the theory of spiking neurons.
DOI: 10.1103/PhysRevE.73.051908 PACS number s : 87.19.La, 05.10.Gg
I. INTRODUCTION
Descriptions of neuronal activity range from detailed bio-
physical neuron models 1 to formal neurons used in artifi-

  

Source: Aviel, Yuval - Interdisciplinary Center for Neural Computation, Hebrew University of Jerusalem
Gerstner, Wulfram - Laboratory of Computational Neuroscience, Faculté Informatique et Communications, Ecole Polytechnique Fédérale de Lausanne

 

Collections: Biology and Medicine; Computer Technologies and Information Sciences