Related papers: Metastability in Loss Networks with Dynamic Altern…
We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m >> n users that try to find an acceptable resource by moving…
Various functions of a network of excitable units can be enhanced if the network is in the `critical regime', where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to…
We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…
Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation…
Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of…
By using direct numerical simulations of up to a record resolution of 512x512x32768 grid points we discover the existence of a new metastable out-of-equilibrium state in rotating turbulence. We scan the phase space by varying both the…
Strong metastability and history dependence are observed in DC and pulsed transport studies of flux-line lattices in 2H-$NbSe_{2}$, leading to the identification of two distinct states of the lattice with different spatial ordering. The…
In transportation networks, a spontaneous jamming transition is often observed, e.g in urban road networks and airport networks. Because of this instability, flow distribution is significantly imbalanced on a macroscopic level. To mitigate…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
Consider the complete graph on $n$ vertices. To each vertex assign an Ising spin that can take the values $-1$ or $+1$. Each spin $i \in [n]=\{1,2,\dots, n\}$ interacts with a magnetic field $h \in [0,\infty)$, while each pair of spins $i,j…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…
In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected…
In this paper, we present algorithms for designing networks that are robust to node failures with minimal or limited number of links. We present algorithms for both the static network setting and the dynamic network setting; setting where…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…
If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the…
Delay-capacity tradeoffs for mobile networks have been analyzed through a number of research work. However, L\'{e}vy mobility known to closely capture human movement patterns has not been adopted in such work. Understanding the…
We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by…