1,137 research outputs found
Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
We demonstrate deterministic extensive chaos in the dynamics of large sparse
networks of theta neurons in the balanced state. The analysis is based on
numerically exact calculations of the full spectrum of Lyapunov exponents, the
entropy production rate and the attractor dimension. Extensive chaos is found
in inhibitory networks and becomes more intense when an excitatory population
is included. We find a strikingly high rate of entropy production that would
limit information representation in cortical spike patterns to the immediate
stimulus response.Comment: 4 pages, 4 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
Locally embedded presages of global network bursts
Spontaneous, synchronous bursting of neural population is a widely observed
phenomenon in nervous networks, which is considered important for functions and
dysfunctions of the brain. However, how the global synchrony across a large
number of neurons emerges from an initially non-bursting network state is not
fully understood. In this study, we develop a new state-space reconstruction
method combined with high-resolution recordings of cultured neurons. This
method extracts deterministic signatures of upcoming global bursts in "local"
dynamics of individual neurons during non-bursting periods. We find that local
information within a single-cell time series can compare with or even
outperform the global mean field activity for predicting future global bursts.
Moreover, the inter-cell variability in the burst predictability is found to
reflect the network structure realized in the non-bursting periods. These
findings demonstrate the deterministic mechanisms underlying the locally
concentrated early-warnings of the global state transition in self-organized
networks
Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons
We investigate the regularity of spontaneous spiking activity on Newman-Watts
small-world networks consisting of biophysically realistic Hodgkin-Huxley
neurons with a tunable intensity of intrinsic noise and fraction of blocked
voltage-gated sodium and potassium ion channels embedded in neuronal membranes.
We show that there exists an optimal fraction of shortcut links between
physically distant neurons, as well as an optimal intensity of intrinsic noise,
which warrant an optimally ordered spontaneous spiking activity. This doubly
coherence resonance-like phenomenon depends significantly, and can be
controlled via the fraction of closed sodium and potassium ion channels,
whereby the impacts can be understood via the analysis of the firing rate
function as well as the deterministic system dynamics. Potential biological
implications of our findings for information propagation across neural networks
are also discussed.Comment: 6 two-column pages, 5 figures; accepted for publication in
Europhysics Letter
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
Decorrelation of neural-network activity by inhibitory feedback
Correlations in spike-train ensembles can seriously impair the encoding of
information by their spatio-temporal structure. An inevitable source of
correlation in finite neural networks is common presynaptic input to pairs of
neurons. Recent theoretical and experimental studies demonstrate that spike
correlations in recurrent neural networks are considerably smaller than
expected based on the amount of shared presynaptic input. By means of a linear
network model and simulations of networks of leaky integrate-and-fire neurons,
we show that shared-input correlations are efficiently suppressed by inhibitory
feedback. To elucidate the effect of feedback, we compare the responses of the
intact recurrent network and systems where the statistics of the feedback
channel is perturbed. The suppression of spike-train correlations and
population-rate fluctuations by inhibitory feedback can be observed both in
purely inhibitory and in excitatory-inhibitory networks. The effect is fully
understood by a linear theory and becomes already apparent at the macroscopic
level of the population averaged activity. At the microscopic level,
shared-input correlations are suppressed by spike-train correlations: In purely
inhibitory networks, they are canceled by negative spike-train correlations. In
excitatory-inhibitory networks, spike-train correlations are typically
positive. Here, the suppression of input correlations is not a result of the
mere existence of correlations between excitatory (E) and inhibitory (I)
neurons, but a consequence of a particular structure of correlations among the
three possible pairings (EE, EI, II)
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