469 research outputs found
Can Attractor Network Models Account for the Statistics of Firing During Persistent Activity in Prefrontal Cortex?
Persistent activity observed in neurophysiological experiments in monkeys is thought to be the neuronal correlate of working memory. Over the last decade, network modellers have strived to reproduce the main features of these experiments. In particular, attractor network models have been proposed in which there is a coexistence between a non-selective attractor state with low background activity with selective attractor states in which sub-groups of neurons fire at rates which are higher (but not much higher) than background rates. A recent detailed statistical analysis of the data seems however to challenge such attractor models: the data indicates that firing during persistent activity is highly irregular (with an average CV larger than 1), while models predict a more regular firing process (CV smaller than 1). We discuss here recent proposals that allow to reproduce this feature of the experiments
Parameter estimation of ODE's via nonparametric estimators
Ordinary differential equations (ODE's) are widespread models in physics,
chemistry and biology. In particular, this mathematical formalism is used for
describing the evolution of complex systems and it might consist of
high-dimensional sets of coupled nonlinear differential equations. In this
setting, we propose a general method for estimating the parameters indexing
ODE's from times series. Our method is able to alleviate the computational
difficulties encountered by the classical parametric methods. These
difficulties are due to the implicit definition of the model. We propose the
use of a nonparametric estimator of regression functions as a first-step in the
construction of an M-estimator, and we show the consistency of the derived
estimator under general conditions. In the case of spline estimators, we prove
asymptotic normality, and that the rate of convergence is the usual
-rate for parametric estimators. Some perspectives of refinements of
this new family of parametric estimators are given.Comment: Published in at http://dx.doi.org/10.1214/07-EJS132 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mechanisms of Induction and Maintenance of Spike-Timing Dependent Plasticity in Biophysical Synapse Models
We review biophysical models of synaptic plasticity, with a focus on spike-timing dependent plasticity (STDP). The common property of the discussed models is that synaptic changes depend on the dynamics of the intracellular calcium concentration, which itself depends on pre- and postsynaptic activity. We start by discussing simple models in which plasticity changes are based directly on calcium amplitude and dynamics. We then consider models in which dynamic intracellular signaling cascades form the link between the calcium dynamics and the plasticity changes. Both mechanisms of induction of STDP (through the ability of pre/postsynaptic spikes to evoke changes in the state of the synapse) and of maintenance of the evoked changes (through bistability) are discussed
Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks
Networks of randomly connected neurons are among the most popular models in
theoretical neuroscience. The connectivity between neurons in the cortex is
however not fully random, the simplest and most prominent deviation from
randomness found in experimental data being the overrepresentation of
bidirectional connections among pyramidal cells. Using numerical and analytical
methods, we investigated the effects of partially symmetric connectivity on
dynamics in networks of rate units. We considered the two dynamical regimes
exhibited by random neural networks: the weak-coupling regime, where the firing
activity decays to a single fixed point unless the network is stimulated, and
the strong-coupling or chaotic regime, characterized by internally generated
fluctuating firing rates. In the weak-coupling regime, we computed analytically
for an arbitrary degree of symmetry the auto-correlation of network activity in
presence of external noise. In the chaotic regime, we performed simulations to
determine the timescale of the intrinsic fluctuations. In both cases, symmetry
increases the characteristic asymptotic decay time of the autocorrelation
function and therefore slows down the dynamics in the network.Comment: 17 pages, 7 figure
Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient
technique to obtain high diversity and coding gain on a block-fading MIMO
channel. Its maximum-likelihood (ML) performance is computed under ideal
interleaving conditions, which enables a global optimization taking into
account channel coding. Thanks to a diversity upperbound derived from the
Singleton bound, an appropriate choice of the time dimension of the space-time
coding is possible, which maximizes diversity while minimizing complexity.
Based on the analysis, an optimized interleaver and a set of linear precoders,
called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed
precoders have good performance with respect to the state of the art and exist
for any number of transmit antennas and any time dimension. With turbo codes,
they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January
2006 - First review: June 200
Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
We study analytically the dynamics of a network of sparsely connected
inhibitory integrate-and-fire neurons in a regime where individual neurons emit
spikes irregularly and at a low rate. In the limit when the number of neurons N
tends to infinity,the network exhibits a sharp transition between a stationary
and an oscillatory global activity regime where neurons are weakly
synchronized. The activity becomes oscillatory when the inhibitory feedback is
strong enough. The period of the global oscillation is found to be mainly
controlled by synaptic times, but depends also on the characteristics of the
external input. In large but finite networks, the analysis shows that global
oscillations of finite coherence time generically exist both above and below
the critical inhibition threshold. Their characteristics are determined as
functions of systems parameters, in these two different regimes. The results
are found to be in good agreement with numerical simulations.Comment: 45 pages, 11 figures, to be published in Neural Computatio
A three-threshold learning rule approaches the maximal capacity of recurrent neural networks
Understanding the theoretical foundations of how memories are encoded and
retrieved in neural populations is a central challenge in neuroscience. A
popular theoretical scenario for modeling memory function is the attractor
neural network scenario, whose prototype is the Hopfield model. The model has a
poor storage capacity, compared with the capacity achieved with perceptron
learning algorithms. Here, by transforming the perceptron learning rule, we
present an online learning rule for a recurrent neural network that achieves
near-maximal storage capacity without an explicit supervisory error signal,
relying only upon locally accessible information. The fully-connected network
consists of excitatory binary neurons with plastic recurrent connections and
non-plastic inhibitory feedback stabilizing the network dynamics; the memory
patterns are presented online as strong afferent currents, producing a bimodal
distribution for the neuron synaptic inputs. Synapses corresponding to active
inputs are modified as a function of the value of the local fields with respect
to three thresholds. Above the highest threshold, and below the lowest
threshold, no plasticity occurs. In between these two thresholds,
potentiation/depression occurs when the local field is above/below an
intermediate threshold. We simulated and analyzed a network of binary neurons
implementing this rule and measured its storage capacity for different sizes of
the basins of attraction. The storage capacity obtained through numerical
simulations is shown to be close to the value predicted by analytical
calculations. We also measured the dependence of capacity on the strength of
external inputs. Finally, we quantified the statistics of the resulting
synaptic connectivity matrix, and found that both the fraction of zero weight
synapses and the degree of symmetry of the weight matrix increase with the
number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog
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