442 research outputs found
Inference of a mesoscopic population model from population spike trains
To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single neuron scale to empirical population data. To close this gap, we propose to fit such data at a meso scale, using a mechanistic but low-dimensional and hence statistically tractable model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous `pools' of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using a model of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived, and show that both single-neuron and connectivity parameters can be recovered from simulated data. In particular, our inference method extracts posterior correlations between model parameters, which define parameter subsets able to reproduce the data. We compute the Bayesian posterior for combinations of parameters using MCMC sampling and investigate how the approximations inherent to a mesoscopic population model impact the accuracy of the inferred single-neuron parameters
Resonance between Noise and Delay
We propose here a stochastic binary element whose transition rate depends on
its state at a fixed interval in the past. With this delayed stochastic
transition this is one of the simplest dynamical models under the influence of
``noise'' and ``delay''. We demonstrate numerically and analytically that we
can observe resonant phenomena between the oscillatory behavior due to noise
and that due to delay.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett Expanded and Added
Reference
Spatial Acuity and Prey Detection in Weakly Electric Fish
It is well-known that weakly electric fish can exhibit extreme temporal acuity at the behavioral level, discriminating time intervals in the submicrosecond range. However, relatively little is known about the spatial acuity of the electrosense. Here we use a recently developed model of the electric field generated by Apteronotus leptorhynchus to study spatial acuity and small signal extraction. We show that the quality of sensory information available on the lateral body surface is highest for objects close to the fish's midbody, suggesting that spatial acuity should be highest at this location. Overall, however, this information is relatively blurry and the electrosense exhibits relatively poor acuity. Despite this apparent limitation, weakly electric fish are able to extract the minute signals generated by small prey, even in the presence of large background signals. In fact, we show that the fish's poor spatial acuity may actually enhance prey detection under some conditions. This occurs because the electric image produced by a spatially dense background is relatively “blurred” or spatially uniform. Hence, the small spatially localized prey signal “pops out” when fish motion is simulated. This shows explicitly how the back-and-forth swimming, characteristic of these fish, can be used to generate motion cues that, as in other animals, assist in the extraction of sensory information when signal-to-noise ratios are low. Our study also reveals the importance of the structure of complex electrosensory backgrounds. Whereas large-object spacing is favorable for discriminating the individual elements of a scene, small spacing can increase the fish's ability to resolve a single target object against this background
Stochastic Resonance in Nonpotential Systems
We propose a method to analytically show the possibility for the appearance
of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our
results to the FitzHugh-Nagumo model under a periodic external forcing, showing
that the model exhibits stochastic resonance. The procedure that we follow is
based on the reduction to a one-dimensional dynamics in the adiabatic limit,
and in the topology of the phase space of the systems under study. Its
application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.
A Tool to Recover Scalar Time-Delay Systems from Experimental Time Series
We propose a method that is able to analyze chaotic time series, gained from
exp erimental data. The method allows to identify scalar time-delay systems. If
the dynamics of the system under investigation is governed by a scalar
time-delay differential equation of the form ,
the delay time and the functi on can be recovered. There are no
restrictions to the dimensionality of the chaotic attractor. The method turns
out to be insensitive to noise. We successfully apply the method to various
time series taken from a computer experiment and two different electronic
oscillators
Noise and Periodic Modulations in Neural Excitable Media
We have analyzed the interplay between noise and periodic modulations in a
mean field model of a neural excitable medium. To this purpose, we have
considered two types of modulations; namely, variations of the resistance and
oscillations of the threshold. In both cases, stochastic resonance is present,
irrespective of if the system is monostable or bistable.Comment: 13 pages, RevTex, 5 PostScript figure
Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons
By varying the noise intensity, we study stochastic spiking coherence (i.e.,
collective coherence between noise-induced neural spikings) in an inhibitory
population of subthreshold neurons (which cannot fire spontaneously without
noise). This stochastic spiking coherence may be well visualized in the raster
plot of neural spikes. For a coherent case, partially-occupied "stripes"
(composed of spikes and indicating collective coherence) are formed in the
raster plot. This partial occupation occurs due to "stochastic spike skipping"
which is well shown in the multi-peaked interspike interval histogram. The main
purpose of our work is to quantitatively measure the degree of stochastic
spiking coherence seen in the raster plot. We introduce a new spike-based
coherence measure by considering the occupation pattern and the pacing
pattern of spikes in the stripes. In particular, the pacing degree between
spikes is determined in a statistical-mechanical way by quantifying the average
contribution of (microscopic) individual spikes to the (macroscopic)
ensemble-averaged global potential. This "statistical-mechanical" measure
is in contrast to the conventional measures such as the "thermodynamic" order
parameter (which concerns the time-averaged fluctuations of the macroscopic
global potential), the "microscopic" correlation-based measure (based on the
cross-correlation between the microscopic individual potentials), and the
measures of precise spike timing (based on the peri-stimulus time histogram).
In terms of , we quantitatively characterize the stochastic spiking
coherence, and find that reflects the degree of collective spiking
coherence seen in the raster plot very well. Hence, the
"statistical-mechanical" spike-based measure may be used usefully to
quantify the degree of stochastic spiking coherence in a statistical-mechanical
way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc
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