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This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
We study the stability and information encoding capacity of synchronized states in a neuronal network model that represents part of thalamic circuitry. Our model neurons have a Hodgkin-Huxley-type low threshold Calcium channel, display post…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
The theta rhythm is important for many cognitive functions including spatial processing, memory encoding, and memory recall. The information processing underlying these functions is thought to rely on consistent, phase-specific spiking…
A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based…
Mathematical model of spiking neuron network (SNN) supplied by astrocytes is investigated. The astrocytes are specific type of brain cells which are not electrically excitable but inducing chemical modulations of neuronal firing. We…
We investigate the collective dynamics of bursting neurons on clustered network. The clustered network is composed of subnetworks each presenting a small-world property, and in a given subnetwork each neuron has a probability to be…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…
The critical brain hypothesis receives increasing support from recent experimental results. It postulates that the brain is at a critical point between an ordered and a chaotic regime, sometimes referred to as the "edge of chaos." Another…
The response of a neuron to synaptic input strongly depends on whether or not it has just emitted a spike. We propose a neuron model that after spike emission exhibits a partial response to residual input charges and study its collective…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
The temporal activity of many biological systems, including neural circuits, exhibits fluctuations simultaneously varying over a large range of timescales. The mechanisms leading to this temporal heterogeneity are yet unknown. Here we show…