78,459 research outputs found
A mean-field model for conductance-based networks of adaptive exponential integrate-and-fire neurons
Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of
neocortical processing at mesoscopic scales. Since VSDi signals report the
average membrane potential, it seems natural to use a mean-field formalism to
model such signals. Here, we investigate a mean-field model of networks of
Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based
synaptic interactions. The AdEx model can capture the spiking response of
different cell types, such as regular-spiking (RS) excitatory neurons and
fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism,
together with a semi-analytic approach to the transfer function of AdEx
neurons. We compare the predictions of this mean-field model to simulated
networks of RS-FS cells, first at the level of the spontaneous activity of the
network, which is well predicted by the mean-field model. Second, we
investigate the response of the network to time-varying external input, and
show that the mean-field model accurately predicts the response time course of
the population. One notable exception was that the "tail" of the response at
long times was not well predicted, because the mean-field does not include
adaptation mechanisms. We conclude that the Master Equation formalism can yield
mean-field models that predict well the behavior of nonlinear networks with
conductance-based interactions and various electrophysiolgical properties, and
should be a good candidate to model VSDi signals where both excitatory and
inhibitory neurons contribute.Comment: 21 pages, 7 figure
How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation
This paper addresses two questions in the context of neuronal networks
dynamics, using methods from dynamical systems theory and statistical physics:
(i) How to characterize the statistical properties of sequences of action
potentials ("spike trains") produced by neuronal networks ? and; (ii) what are
the effects of synaptic plasticity on these statistics ? We introduce a
framework in which spike trains are associated to a coding of membrane
potential trajectories, and actually, constitute a symbolic coding in important
explicit examples (the so-called gIF models). On this basis, we use the
thermodynamic formalism from ergodic theory to show how Gibbs distributions are
natural probability measures to describe the statistics of spike trains, given
the empirical averages of prescribed quantities. As a second result, we show
that Gibbs distributions naturally arise when considering "slow" synaptic
plasticity rules where the characteristic time for synapse adaptation is quite
longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure
A statistical model for in vivo neuronal dynamics
Single neuron models have a long tradition in computational neuroscience.
Detailed biophysical models such as the Hodgkin-Huxley model as well as
simplified neuron models such as the class of integrate-and-fire models relate
the input current to the membrane potential of the neuron. Those types of
models have been extensively fitted to in vitro data where the input current is
controlled. Those models are however of little use when it comes to
characterize intracellular in vivo recordings since the input to the neuron is
not known. Here we propose a novel single neuron model that characterizes the
statistical properties of in vivo recordings. More specifically, we propose a
stochastic process where the subthreshold membrane potential follows a Gaussian
process and the spike emission intensity depends nonlinearly on the membrane
potential as well as the spiking history. We first show that the model has a
rich dynamical repertoire since it can capture arbitrary subthreshold
autocovariance functions, firing-rate adaptations as well as arbitrary shapes
of the action potential. We then show that this model can be efficiently fitted
to data without overfitting. Finally, we show that this model can be used to
characterize and therefore precisely compare various intracellular in vivo
recordings from different animals and experimental conditions.Comment: 31 pages, 10 figure
Statistics of spike trains in conductance-based neural networks: Rigorous results
We consider a conductance based neural network inspired by the generalized
Integrate and Fire model introduced by Rudolph and Destexhe. We show the
existence and uniqueness of a unique Gibbs distribution characterizing spike
train statistics. The corresponding Gibbs potential is explicitly computed.
These results hold in presence of a time-dependent stimulus and apply therefore
to non-stationary dynamics.Comment: 42 pages, 1 figure, to appear in Journal of Mathematical Neuroscienc
Multi-layered Spiking Neural Network with Target Timestamp Threshold Adaptation and STDP
Spiking neural networks (SNNs) are good candidates to produce
ultra-energy-efficient hardware. However, the performance of these models is
currently behind traditional methods. Introducing multi-layered SNNs is a
promising way to reduce this gap. We propose in this paper a new threshold
adaptation system which uses a timestamp objective at which neurons should
fire. We show that our method leads to state-of-the-art classification rates on
the MNIST dataset (98.60%) and the Faces/Motorbikes dataset (99.46%) with an
unsupervised SNN followed by a linear SVM. We also investigate the sparsity
level of the network by testing different inhibition policies and STDP rules
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Mean-field systems have been previously derived for networks of coupled,
two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting
exponential (AdEx) and quartic integrate and fire (QIF), among others.
Unfortunately, the mean-field systems have a degree of frequency error and the
networks analyzed often do not include noise when there is adaptation. Here, we
derive a one-dimensional partial differential equation (PDE) approximation for
the marginal voltage density under a first order moment closure for coupled
networks of integrate-and-fire neurons with white noise inputs. The PDE has
substantially less frequency error than the mean-field system, and provides a
great deal more information, at the cost of analytical tractability. The
convergence properties of the mean-field system in the low noise limit are
elucidated. A novel method for the analysis of the stability of the
asynchronous tonic firing solution is also presented and implemented. Unlike
previous attempts at stability analysis with these network types, information
about the marginal densities of the adaptation variables is used. This method
can in principle be applied to other systems with nonlinear partial
differential equations.Comment: 26 Pages, 6 Figure
- …