Related papers: Average synaptic activity and neural networks topo…

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…

Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…

A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning of such hyperparameters may be difficult and, typically, based on a trial-and-error…

For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…

We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…

We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…

Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic…

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

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…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system…

We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of…

Recent advancements in measurement techniques have resulted in an increasing amount of data on neural activities recorded in parallel, revealing largely heterogeneous correlation patterns across neurons. Yet, the mechanistic origin of this…

For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…

We use mean field theory to study the response properties of a simple randomly-connected model cortical network of leaky integrate-and-fire neurons with balanced excitation and inhibition. The formulation permits arbitrary temporal…

Cortical networks exhibit synchronized activity which often occurs in spontaneous events in the form of spike avalanches. Since synchronization has been causally linked to central aspects of brain function such as selective signal…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

Neural feedback-triads consisting of two feedback loops with a non-reciprocal lateral connection from one loop to the other are ubiquitous in the brain. We show analytically that the dynamics of this network topology are determined by two…

A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on…