4,892 research outputs found
Stochastic mean field formulation of the dynamics of diluted neural networks
We consider pulse-coupled Leaky Integrate-and-Fire neural networks with
randomly distributed synaptic couplings. This random dilution induces
fluctuations in the evolution of the macroscopic variables and deterministic
chaos at the microscopic level. Our main aim is to mimic the effect of the
dilution as a noise source acting on the dynamics of a globally coupled
non-chaotic system. Indeed, the evolution of a diluted neural network can be
well approximated as a fully pulse coupled network, where each neuron is driven
by a mean synaptic current plus additive noise. These terms represent the
average and the fluctuations of the synaptic currents acting on the single
neurons in the diluted system. The main microscopic and macroscopic dynamical
features can be retrieved with this stochastic approximation. Furthermore, the
microscopic stability of the diluted network can be also reproduced, as
demonstrated from the almost coincidence of the measured Lyapunov exponents in
the deterministic and stochastic cases for an ample range of system sizes. Our
results strongly suggest that the fluctuations in the synaptic currents are
responsible for the emergence of chaos in this class of pulse coupled networks.Comment: 12 Pages, 4 Figure
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
Dynamic Decomposition of Spatiotemporal Neural Signals
Neural signals are characterized by rich temporal and spatiotemporal dynamics
that reflect the organization of cortical networks. Theoretical research has
shown how neural networks can operate at different dynamic ranges that
correspond to specific types of information processing. Here we present a data
analysis framework that uses a linearized model of these dynamic states in
order to decompose the measured neural signal into a series of components that
capture both rhythmic and non-rhythmic neural activity. The method is based on
stochastic differential equations and Gaussian process regression. Through
computer simulations and analysis of magnetoencephalographic data, we
demonstrate the efficacy of the method in identifying meaningful modulations of
oscillatory signals corrupted by structured temporal and spatiotemporal noise.
These results suggest that the method is particularly suitable for the analysis
and interpretation of complex temporal and spatiotemporal neural signals
Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses
Populations of uncoupled limit-cycle oscillators receiving common random
impulses show various types of phase-coherent states, which are characterized
by the distribution of phase differences between pairs of oscillators. We
develop a theory to predict the stationary distribution of pairwise phase
difference from the phase response curve, which quantitatively encapsulates the
oscillator dynamics, via averaging of the Frobenius-Perron equation describing
the impulse-driven oscillators. The validity of our theory is confirmed by
direct numerical simulations using the FitzHugh-Nagumo neural oscillator
receiving common Poisson impulses as an example
Detection of synchronization from univariate data using wavelet transform
A method is proposed for detecting from univariate data the presence of
synchronization of a self-sustained oscillator by external driving with varying
frequency. The method is based on the analysis of difference between the
oscillator instantaneous phases calculated using continuous wavelet transform
at time moments shifted by a certain constant value relative to each other. We
apply our method to a driven asymmetric van der Pol oscillator, experimental
data from a driven electronic oscillator with delayed feedback and human
heartbeat time series. In the latest case, the analysis of the heart rate
variability data reveals synchronous regimes between the respiration and slow
oscillations in blood pressure.Comment: 10 pages, 9 figure
Order parameter expansion study of synchronous firing induced by quenched noise in the active rotator model
We use a recently developed order parameter expansion method to study the
transition to synchronous firing occuring in a system of coupled active
rotators under the exclusive presence of quenched noise. The method predicts
correctly the existence of a transition from a rest state to a regime of
synchronous firing and another transition out of it as the intensity of the
quenched noise increases and leads to analytical expressions for the critical
noise intensities in the large coupling regime. It also predicts the order of
the transitions for different probability distribution functions of the
quenched variables. We use numerical simulations and finite size scaling theory
to estimate the critical exponents of the transitions and found values which
are consistent with those reported in other scalar systems in the exclusive
presence of additive static disorder
Retinal oscillations carry visual information to cortex
Thalamic relay cells fire action potentials that transmit information from
retina to cortex. The amount of information that spike trains encode is usually
estimated from the precision of spike timing with respect to the stimulus.
Sensory input, however, is only one factor that influences neural activity. For
example, intrinsic dynamics, such as oscillations of networks of neurons, also
modulate firing pattern. Here, we asked if retinal oscillations might help to
convey information to neurons downstream. Specifically, we made whole-cell
recordings from relay cells to reveal retinal inputs (EPSPs) and thalamic
outputs (spikes) and analyzed these events with information theory. Our results
show that thalamic spike trains operate as two multiplexed channels. One
channel, which occupies a low frequency band (<30 Hz), is encoded by average
firing rate with respect to the stimulus and carries information about local
changes in the image over time. The other operates in the gamma frequency band
(40-80 Hz) and is encoded by spike time relative to the retinal oscillations.
Because these oscillations involve extensive areas of the retina, it is likely
that the second channel transmits information about global features of the
visual scene. At times, the second channel conveyed even more information than
the first.Comment: 21 pages, 10 figures, submitted to Frontiers in Systems Neuroscienc
Noise-induced behaviors in neural mean field dynamics
The collective behavior of cortical neurons is strongly affected by the
presence of noise at the level of individual cells. In order to study these
phenomena in large-scale assemblies of neurons, we consider networks of
firing-rate neurons with linear intrinsic dynamics and nonlinear coupling,
belonging to a few types of cell populations and receiving noisy currents.
Asymptotic equations as the number of neurons tends to infinity (mean field
equations) are rigorously derived based on a probabilistic approach. These
equations are implicit on the probability distribution of the solutions which
generally makes their direct analysis difficult. However, in our case, the
solutions are Gaussian, and their moments satisfy a closed system of nonlinear
ordinary differential equations (ODEs), which are much easier to study than the
original stochastic network equations, and the statistics of the empirical
process uniformly converge towards the solutions of these ODEs. Based on this
description, we analytically and numerically study the influence of noise on
the collective behaviors, and compare these asymptotic regimes to simulations
of the network. We observe that the mean field equations provide an accurate
description of the solutions of the network equations for network sizes as
small as a few hundreds of neurons. In particular, we observe that the level of
noise in the system qualitatively modifies its collective behavior, producing
for instance synchronized oscillations of the whole network, desynchronization
of oscillating regimes, and stabilization or destabilization of stationary
solutions. These results shed a new light on the role of noise in shaping
collective dynamics of neurons, and gives us clues for understanding similar
phenomena observed in biological networks
Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized EMG
We investigate the relationship between the extensor electromyogram (EMG) and
tremor time series in physiological hand tremor by cross-spectral analysis.
Special attention is directed to the phase spectrum and the effects of
observational noise. We calculate the theoretical phase spectrum for a second
order linear stochastic process and compare the results to measured tremor data
recorded from subjects who did not show a synchronized EMG activity in the
corresponding extensor muscle. The results show that physiological tremor is
well described by the proposed model and that the measured EMG represents a
Newtonian force by which the muscle acts on the hand.Comment: 9 pages, 6 figures, to appear in Biological Cybernetic
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