Related papers: General time elapsed neuron network model: well-po…

We consider the problem of inferring the functional connectivity of a large-scale computer network from sparse time series of events emitted by its nodes. We do so under the following three domain-specific constraints: (a) non-stationarity…

We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…

In this work we explore recurrent representations of leaky integrate and fire neurons operating at a timescale equal to their absolute refractory period. Our coarse time scale approximation is obtained using a probability distribution…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our…

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Many complex systems - be they financial, natural, or social - are composed of units - such as stocks, neurons, or agents - whose joint activity can be represented as a multivariate time series. An issue of both practical and theoretical…

In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…

Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…

We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant…

The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…

A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…

We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…

This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…

Understanding the inner working mechanism of deep neural networks (DNNs) is essential and important for researchers to design and improve the performance of DNNs. In this work, the entropy analysis is leveraged to study the neurons…