3,137 research outputs found
A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation
Stochastic integrate-and-fire (IF) neuron models have found widespread
applications in computational neuroscience. Here we present results on the
white-noise-driven perfect, leaky, and quadratic IF models, focusing on the
spectral statistics (power spectra, cross spectra, and coherence functions) in
different dynamical regimes (noise-induced and tonic firing regimes with low or
moderate noise). We make the models comparable by tuning parameters such that
the mean value and the coefficient of variation of the interspike interval
match for all of them. We find that, under these conditions, the power spectrum
under white-noise stimulation is often very similar while the response
characteristics, described by the cross spectrum between a fraction of the
input noise and the output spike train, can differ drastically. We also
investigate how the spike trains of two neurons of the same kind (e.g. two
leaky IF neurons) correlate if they share a common noise input. We show that,
depending on the dynamical regime, either two quadratic IF models or two leaky
IFs are more strongly correlated. Our results suggest that, when choosing among
simple IF models for network simulations, the details of the model have a
strong effect on correlation and regularity of the output.Comment: 12 page
Detecting and Estimating Signals over Noisy and Unreliable Synapses: Information-Theoretic Analysis
The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission
Are the input parameters of white-noise-driven integrate-and-fire neurons uniquely determined by rate and CV?
Integrate-and-fire (IF) neurons have found widespread applications in
computational neuroscience. Particularly important are stochastic versions of
these models where the driving consists of a synaptic input modeled as white
Gaussian noise with mean and noise intensity . Different IF models
have been proposed, the firing statistics of which depends nontrivially on the
input parameters and . In order to compare these models among each
other, one must first specify the correspondence between their parameters. This
can be done by determining which set of parameters (, ) of each model
is associated to a given set of basic firing statistics as, for instance, the
firing rate and the coefficient of variation (CV) of the interspike interval
(ISI). However, it is not clear {\em a priori} whether for a given firing rate
and CV there is only one unique choice of input parameters for each model. Here
we review the dependence of rate and CV on input parameters for the perfect,
leaky, and quadratic IF neuron models and show analytically that indeed in
these three models the firing rate and the CV uniquely determine the input
parameters
The complexity of dynamics in small neural circuits
Mean-field theory is a powerful tool for studying large neural networks.
However, when the system is composed of a few neurons, macroscopic differences
between the mean-field approximation and the real behavior of the network can
arise. Here we introduce a study of the dynamics of a small firing-rate network
with excitatory and inhibitory populations, in terms of local and global
bifurcations of the neural activity. Our approach is analytically tractable in
many respects, and sheds new light on the finite-size effects of the system. In
particular, we focus on the formation of multiple branching solutions of the
neural equations through spontaneous symmetry-breaking, since this phenomenon
increases considerably the complexity of the dynamical behavior of the network.
For these reasons, branching points may reveal important mechanisms through
which neurons interact and process information, which are not accounted for by
the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of
figures 8 and 9 fixed, results unchange
Supervised Learning in Spiking Neural Networks for Precise Temporal Encoding
Precise spike timing as a means to encode information in neural networks is
biologically supported, and is advantageous over frequency-based codes by
processing input features on a much shorter time-scale. For these reasons, much
recent attention has been focused on the development of supervised learning
rules for spiking neural networks that utilise a temporal coding scheme.
However, despite significant progress in this area, there still lack rules that
have a theoretical basis, and yet can be considered biologically relevant. Here
we examine the general conditions under which synaptic plasticity most
effectively takes place to support the supervised learning of a precise
temporal code. As part of our analysis we examine two spike-based learning
methods: one of which relies on an instantaneous error signal to modify
synaptic weights in a network (INST rule), and the other one on a filtered
error signal for smoother synaptic weight modifications (FILT rule). We test
the accuracy of the solutions provided by each rule with respect to their
temporal encoding precision, and then measure the maximum number of input
patterns they can learn to memorise using the precise timings of individual
spikes as an indication of their storage capacity. Our results demonstrate the
high performance of FILT in most cases, underpinned by the rule's
error-filtering mechanism, which is predicted to provide smooth convergence
towards a desired solution during learning. We also find FILT to be most
efficient at performing input pattern memorisations, and most noticeably when
patterns are identified using spikes with sub-millisecond temporal precision.
In comparison with existing work, we determine the performance of FILT to be
consistent with that of the highly efficient E-learning Chronotron, but with
the distinct advantage that FILT is also implementable as an online method for
increased biological realism.Comment: 26 pages, 10 figures, this version is published in PLoS ONE and
incorporates reviewer comment
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 unique method for stochastic models in computational and cognitive neuroscience
We review applications of the Fokker–Planck equation for the description of systems with event trains in computational and cognitive neuroscience. The most prominent example is the spike trains generated by integrate-and-fire neurons when driven by correlated (colored) fluctuations, by adaptation currents and/or by other neurons in a recurrent network. We discuss how for a general Gaussian colored noise and an adaptation current can be incorporated into a multidimensional Fokker–Planck equation by Markovian embedding for systems with a fire-and-reset condition and how in particular the spike-train power spectrum can be determined by this equation. We then review how this framework can be used to determine the self-consistent correlation statistics in a recurrent network in which the colored fluctuations arise from the spike trains of statistically similar neurons. We then turn to the popular drift-diffusion models for binary decisions in cognitive neuroscience and demonstrate that very similar Fokker–Planck equations (with two instead of only one threshold) can be used to study the statistics of sequences of decisions. Specifically, we present a novel two-dimensional model that includes an evidence variable and an expectancy variable that can reproduce salient features of key experiments in sequential decision making.Humboldt-Universität zu Berlin (1034)Peer Reviewe
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
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