144 research outputs found
Auto and crosscorrelograms for the spike response of LIF neurons with slow synapses
An analytical description of the response properties of simple but realistic
neuron models in the presence of noise is still lacking. We determine
completely up to the second order the firing statistics of a single and a pair
of leaky integrate-and-fire neurons (LIFs) receiving some common slowly
filtered white noise. In particular, the auto- and cross-correlation functions
of the output spike trains of pairs of cells are obtained from an improvement
of the adiabatic approximation introduced in \cite{Mor+04}. These two functions
define the firing variability and firing synchronization between neurons, and
are of much importance for understanding neuron communication.Comment: 5 pages, 3 figure
Response of Spiking Neurons to Correlated Inputs
The effect of a temporally correlated afferent current on the firing rate of
a leaky integrate-and-fire (LIF) neuron is studied. This current is
characterized in terms of rates, auto and cross-correlations, and correlation
time scale of excitatory and inhibitory inputs. The output rate
is calculated in the Fokker-Planck (FP) formalism in the limit of
both small and large compared to the membrane time constant of
the neuron. By simulations we check the analytical results, provide an
interpolation valid for all and study the neuron's response to rapid
changes in the correlation magnitude.Comment: 4 pages, 3 figure
Simple model for 1/f noise
We present a simple stochastic mechanism which generates pulse trains
exhibiting a power law distribution of the pulse intervals and a
power spectrum over several decades at low frequencies with close to
one. The essential ingredient of our model is a fluctuating threshold which
performs a Brownian motion. Whenever an increasing potential hits the
threshold, is reset to the origin and a pulse is emitted. We show that
if increases linearly in time, the pulse intervals can be approximated
by a random walk with multiplicative noise. Our model agrees with recent
experiments in neurobiology and explains the high interpulse interval
variability and the occurrence of noise observed in cortical
neurons and earthquake data.Comment: 4 pages, 4 figure
Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?
Many complex systems display self-organized critical states characterized by
1/f frequency scaling of power spectra. Global variables such as the
electroencephalogram, scale as 1/f, which could be the sign of self-organized
critical states in neuronal activity. By analyzing simultaneous recordings of
global and neuronal activities, we confirm the 1/f scaling of global variables
for selected frequency bands, but show that neuronal activity is not consistent
with critical states. We propose a model of 1/f scaling which does not rely on
critical states, and which is testable experimentally.Comment: 3 figures, 6 page
An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings
An associative memory has been discussed of neural networks consisting of
spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which
memorize P patterns in their synaptic weights. In addition to excitatory
synapses whose strengths are modified after the Willshaw-type learning rule
with the 0/1 code for quiescent/active states, the network includes uniform
inhibitory synapses which are introduced to reduce cross-talk noises. Our
simulations of the HH neuron network for the noise-free state have shown to
yield a fairly good performance with the storage capacity of for the low neuron activity of . This
storage capacity of our temporal-code network is comparable to that of the
rate-code model with the Willshaw-type synapses. Our HH neuron network is
realized not to be vulnerable to the distribution of time delays in couplings.
The variability of interspace interval (ISI) of output spike trains in the
process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl
Population coding by globally coupled phase oscillators
A system of globally coupled phase oscillators subject to an external input
is considered as a simple model of neural circuits coding external stimulus.
The information coding efficiency of the system in its asynchronous state is
quantified using Fisher information. The effect of coupling and noise on the
information coding efficiency in the stationary state is analyzed. The
relaxation process of the system after the presentation of an external input is
also studied. It is found that the information coding efficiency exhibits a
large transient increase before the system relaxes to the final stationary
state.Comment: 7 pages, 9 figures, revised version, new figures added, to appear in
JPSJ Vol 75, No.
A Markovian event-based framework for stochastic spiking neural networks
In spiking neural networks, the information is conveyed by the spike times,
that depend on the intrinsic dynamics of each neuron, the input they receive
and on the connections between neurons. In this article we study the Markovian
nature of the sequence of spike times in stochastic neural networks, and in
particular the ability to deduce from a spike train the next spike time, and
therefore produce a description of the network activity only based on the spike
times regardless of the membrane potential process.
To study this question in a rigorous manner, we introduce and study an
event-based description of networks of noisy integrate-and-fire neurons, i.e.
that is based on the computation of the spike times. We show that the firing
times of the neurons in the networks constitute a Markov chain, whose
transition probability is related to the probability distribution of the
interspike interval of the neurons in the network. In the cases where the
Markovian model can be developed, the transition probability is explicitly
derived in such classical cases of neural networks as the linear
integrate-and-fire neuron models with excitatory and inhibitory interactions,
for different types of synapses, possibly featuring noisy synaptic integration,
transmission delays and absolute and relative refractory period. This covers
most of the cases that have been investigated in the event-based description of
spiking deterministic neural networks
Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings
Model calculations have been performed on the spike-train response of a pair
of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory
couplings with time delay. The coupled, excitable HH neurons are assumed to
receive the two kinds of spike-train inputs: the transient input consisting of
impulses for the finite duration (: integer) and the sequential input
with the constant interspike interval (ISI). The distribution of the output ISI
shows a rich of variety depending on the coupling strength and the
time delay. The comparison is made between the dependence of the output ISI for
the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure
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