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Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of interference distributions in large-scale…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…
We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the…
Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…
We study the large deviations performance, i.e., the exponential decay rate of the error probability, of distributed detection algorithms over random networks. At each time step $k$ each sensor: 1) averages its decision variable with the…
Recent developments in applications of artificial neural networks with over $n=10^{14}$ parameters make it extremely important to study the large $n$ behaviour of such networks. Most works studying wide neural networks have focused on the…
We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and biased processes of breaking and recovery…
We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymptotic dynamic of the membrane potential of a spiking neuron…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
Spatial telecommunication systems have evolved along the years, leading to some concerns that telecommunication companies are facing today. The main inquietude is the ability to provide quality service to customers or users in a dense…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…