217 research outputs found
Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos
Understanding of short-term synaptic depression (STSD) and other forms of
synaptic plasticity is a topical problem in neuroscience. Here we study the
role of STSD in the formation of complex patterns of brain rhythms. We use a
cortical circuit model of neural networks composed of irregular spiking
excitatory and inhibitory neurons having type 1 and 2 excitability and
stochastic dynamics. In the model, neurons form a sparsely connected network
and their spontaneous activity is driven by random spikes representing synaptic
noise. Using simulations and analytical calculations, we found that if the STSD
is absent, the neural network shows either asynchronous behavior or regular
network oscillations depending on the noise level. In networks with STSD,
changing parameters of synaptic plasticity and the noise level, we observed
transitions to complex patters of collective activity: mixed-mode and spindle
oscillations, bursts of collective activity, and chaotic behaviour.
Interestingly, these patterns are stable in a certain range of the parameters
and separated by critical boundaries. Thus, the parameters of synaptic
plasticity can play a role of control parameters or switchers between different
network states. However, changes of the parameters caused by a disease may lead
to dramatic impairment of ongoing neural activity. We analyze the chaotic
neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I.,
2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
Critical and resonance phenomena in neural networks
Brain rhythms contribute to every aspect of brain function. Here, we study
critical and resonance phenomena that precede the emergence of brain rhythms.
Using an analytical approach and simulations of a cortical circuit model of
neural networks with stochastic neurons in the presence of noise, we show that
spontaneous appearance of network oscillations occurs as a dynamical
(non-equilibrium) phase transition at a critical point determined by the noise
level, network structure, the balance between excitatory and inhibitory
neurons, and other parameters. We find that the relaxation time of neural
activity to a steady state, response to periodic stimuli at the frequency of
the oscillations, amplitude of damped oscillations, and stochastic fluctuations
of neural activity are dramatically increased when approaching the critical
point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
Peltier effect in normal metal-insulator-heavy fermion metal junctions
A theoretical study has been undertaken of the Peltier effect in normal metal
- insulator - heavy fermion metal junctions. The results indicate that, at
temperatures below the Kondo temperature, such junctions can be used as
electronic microrefrigerators to cool the normal metal electrode and are
several times more efficient in cooling than the normal metal - heavy fermion
metal junctions.Comment: 3 pages in REVTeX, 2 figures, to be published in Appl. Phys. Lett.,
April 7, 200
A neuronal network model of interictal and recurrent ictal activity
We propose a neuronal network model which undergoes a saddle-node bifurcation
on an invariant circle as the mechanism of the transition from the interictal
to the ictal (seizure) state. In the vicinity of this transition, the model
captures important dynamical features of both interictal and ictal states. We
study the nature of interictal spikes and early warnings of the transition
predicted by this model. We further demonstrate that recurrent seizures emerge
due to the interaction between two networks.Comment: 9 pages, 7 figure
k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
We develop the theory of the k-core (bootstrap) percolation on uncorrelated
random networks with arbitrary degree distributions. We show that the k-core
percolation is an unusual, hybrid phase transition with a jump emergence of the
k-core as at a first order phase transition but also with a critical
singularity as at a continuous transition. We describe the properties of the
k-core, explain the meaning of the order parameter for the k-core percolation,
and reveal the origin of the specific critical phenomena. We demonstrate that a
so-called ``corona'' of the k-core plays a crucial role (corona is a subset of
vertices in the k-core which have exactly k neighbors in the k-core). It turns
out that the k-core percolation threshold is at the same time the percolation
threshold of finite corona clusters. The mean separation of vertices in corona
clusters plays the role of the correlation length and diverges at the critical
point. We show that a random removal of even one vertex from the k-core may
result in the collapse of a vast region of the k-core around the removed
vertex. The mean size of this region diverges at the critical point. We find an
exact mapping of the k-core percolation to a model of cooperative relaxation.
This model undergoes critical relaxation with a divergent rate at some critical
moment.Comment: 11 pages, 8 figure
Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs
We generalize the belief-propagation algorithm to sparse random networks with
arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in
these networks belongs to a given set of motifs (generalization of the
configuration model). These networks can be treated as sparse uncorrelated
hypergraphs in which hyperedges represent motifs. Here a hypergraph is a
generalization of a graph, where a hyperedge can connect any number of
vertices. These uncorrelated hypergraphs are tree-like (hypertrees), which
crucially simplify the problem and allow us to apply the belief-propagation
algorithm to these loopy networks with arbitrary motifs. As natural examples,
we consider motifs in the form of finite loops and cliques. We apply the
belief-propagation algorithm to the ferromagnetic Ising model on the resulting
random networks. We obtain an exact solution of this model on networks with
finite loops or cliques as motifs. We find an exact critical temperature of the
ferromagnetic phase transition and demonstrate that with increasing the
clustering coefficient and the loop size, the critical temperature increases
compared to ordinary tree-like complex networks. Our solution also gives the
birth point of the giant connected component in these loopy networks.Comment: 9 pages, 4 figure
Correlations in interacting systems with a network topology
We study pair correlations in cooperative systems placed on complex networks.
We show that usually in these systems, the correlations between two interacting
objects (e.g., spins), separated by a distance , decay, on average,
faster than . Here is the mean number of the
-th nearest neighbors of a vertex in a network. This behavior, in
particular, leads to a dramatic weakening of correlations between second and
more distant neighbors on networks with fat-tailed degree distributions, which
have a divergent number in the infinite network limit. In this case, only
the pair correlations between the nearest neighbors are observable. We obtain
the pair correlation function of the Ising model on a complex network and also
derive our results in the framework of a phenomenological approach.Comment: 5 page
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