277 research outputs found
Scale-free avalanches in arrays of FitzHugh-Nagumo oscillators
The activity in the brain cortex remarkably shows a simultaneous presence of
robust collective oscillations and neuronal avalanches, where intermittent
bursts of pseudo-synchronous spiking are interspersed with long periods of
quiescence. The mechanisms allowing for such a coexistence are still a matter
of an intensive debate. Here, we demonstrate that avalanche activity patterns
can emerge in a rather simple model of an array of diffusively coupled neural
oscillators with multiple timescale local dynamics in vicinity of a canard
transition. The avalanches coexist with the fully synchronous state where the
units perform relaxation oscillations. We show that the mechanism behind the
avalanches is based on an inhibitory effect of interactions, which may quench
the spiking of units due to an interplay with the maximal canard. The avalanche
activity bears certain heralds of criticality, including scale-invariant
distributions of event sizes. Furthermore, the system shows an increased
sensitivity to perturbations, manifested as critical slowing down and a reduced
resilience.Comment: 9 figure
Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources
We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.Peer Reviewe
Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity
We study the storage and retrieval of phase-coded patterns as stable
dynamical attractors in recurrent neural networks, for both an analog and a
integrate-and-fire spiking model. The synaptic strength is determined by a
learning rule based on spike-time-dependent plasticity, with an asymmetric time
window depending on the relative timing between pre- and post-synaptic
activity. We store multiple patterns and study the network capacity.
For the analog model, we find that the network capacity scales linearly with
the network size, and that both capacity and the oscillation frequency of the
retrieval state depend on the asymmetry of the learning time window. In
addition to fully-connected networks, we study sparse networks, where each
neuron is connected only to a small number z << N of other neurons. Connections
can be short range, between neighboring neurons placed on a regular lattice, or
long range, between randomly chosen pairs of neurons. We find that a small
fraction of long range connections is able to amplify the capacity of the
network. This imply that a small-world-network topology is optimal, as a
compromise between the cost of long range connections and the capacity
increase.
Also in the spiking integrate and fire model the crucial result of storing
and retrieval of multiple phase-coded patterns is observed. The capacity of the
fully-connected spiking network is investigated, together with the relation
between oscillation frequency of retrieval state and window asymmetry
Metastability, Criticality and Phase Transitions in brain and its Models
This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures
Criticality and its effect on other cortical phenomena
Neuronal avalanches are a cortical phenomenon defined by bursts of neuronal firing encapsulated
by periods of quiescence. It has been found both in vivo and in vitro that neuronal avalanches
follow a power law distribution which is indicative of the system being within or near a critical
state. A system is critical if it is poised between order and disorder with the possibility of
minor event leading to a large chain reaction. This is also observed by the system exhibiting
a diverging correlation length between its components as it approaches the critical point. It
has been shown that neuronal criticality is a scale-free phenomenon observed throughout the
entire system as well as within each module of the system. At a small scale, neuronal networks
produce avalanches which conform to power law-like distributions. At a larger scale, we observe
that these systems consist of modules exhibiting long-range temporal correlations identifiable
via Detrended Fluctuation Analysis (DFA). This phenomenon is hypothesised to affect network
behaviour with regards to information processing, information storage, computational power, and
stability - The Criticality Hypothesis.
This thesis attempts to better understand critical neuronal networks and how criticality may
link with other neuronal phenomena. This work begins by investigating the interplay of network
connectivity, synaptic plasticity, and criticality. Using different network construction algorithms,
the thesis demonstrates that Hebbian learning and Spike Timing Dependent Plasticity (STDP)
robustly drive small networks towards a critical state. Moreover the thesis shows that, while
the initial distribution of synaptic weights plays a significant role in attaining criticality, the
network's topology at the modular level has little or no impact.
Using an expanded eight-module oscillatory spiking neural network the thesis then shows the
link between the different critical markers we use when attempting to observe critical behaviour
at different scales. The findings demonstrate that modules exhibiting power law-like behaviour
also demonstrate long-range temporal correlations throughout the system. Furthermore, we
show that when modules no longer exhibit power law-like behaviour we find that they become
uncorrelated or noisy. This shows a correlation between power law-like behaviour observed within
each module and the long-range temporal correlations between the modules.
The thesis concludes by demonstrating how criticality may be linked with other related phenomena,
namely metastability and dynamical complexity. Metastability is a global property of neuronal
populations that migrate between attractor-like states. Metastability can be quantified by the
variance of synchrony, a measure that has been hypothesised to capture the varying influence
neuronal populations have over one another and the system as a whole. The thesis shows
a correlation between critical behaviour and metastability where the latter is most reliably
maximised only when the former is near the critical state. This conclusion is expected as
metastability, similarly to criticality reflects the interplay between the integrating and segregating
tendencies of the system components. Agreeing with previous findings this suggests that
metastable dynamics may be another marker of critical behaviour.
A neural system is said to exhibit dynamical complexity if a balance of integrated and segregated
activity occurs within the system. A common attribute of critical systems is a balance between
excitation and inhibition. The final part of the thesis attempts to understand how criticality
may be linked with dynamical complexity. This work shows a possible connection between these
phenomena providing a foundation for further analysis. The thesis concludes with a discussion
of the significant role criticality plays in determining the behaviour of neuronal networks.Open Acces
Self-sustained irregular activity in an ensemble of neural oscillators
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the
presence of a mean-field coupling and a dispersion of their natural
frequencies. In spite of the analogies with the Kuramoto setup, a much richer
scenario is observed. The "synchronised phase", which emerges upon increasing
the coupling strength, is characterized by highly-irregular fluctuations: a
time-series analysis reveals that the dynamics of the order parameter is indeed
high-dimensional. The complex dynamics appears to be the result of the
non-perturbative action of a suitably shaped phase-response curve. Such
mechanism differs from the often invoked balance between excitation and
inhibition and might provide an alternative basis to account for the
self-sustained brain activity in the resting state. The potential interest of
this dynamical regime is further strengthened by its (microscopic) linear
stability, which makes it quite suited for computational tasks. The overall
study has been performed by combining analytical and numerical studies,
starting from the linear stability analysis of the asynchronous regime, to
include the Fourier analysis of the Kuramoto order parameter, the computation
of various types of Lyapunov exponents, and a microscopic study of the
inter-spike intervals.Comment: 11 pages, 10 figure
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