Related papers: Poisson Hypothesis for Open Networks at Low Load
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
In random access protocols, the service rate depends on the number of stations with a packet buffered for transmission. We demonstrate via numerical analysis that this state-dependent rate along with the consideration of Poisson traffic and…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Which reaction networks, when taken with mass-action kinetics, have the capacity for multiple steady states? There is no complete answer to this question, but over the last 40 years various criteria have been developed that can answer this…
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…
Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…
Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density $\rho$ and a pair of nodes separated by an Euclidean distance $x$ are directly connected with probability…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…
Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. The on-off intermittency is investigated in small-world…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…
We study the behavior of epidemic routing in a delay tolerant network as a function of node density. Focusing on the probability of successful delivery to a destination within a deadline (PS), we show that PS experiences a phase transition…