Related papers: Fluctuations induce transitions in frustrated spar…
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
We consider a one-dimensional fluctuating interfacial profile governed by the Edwards-Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path…
Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…
We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free…
Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, epidemiology to engineering and robotics. In the presence of noise and uncertainty, inter- actions between the individual components can…
In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic…
In nervous system information is conveyed by sequence of action potentials (spikes-trains). As MacKay and McCulloch proposed, spike-trains can be represented as bits sequences coming from Information Sources. Previously, we studied…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barab\'{a}si-Albert(BA) model, and lattice networks -- by using one parameter $\omega$; $\omega=1,0, -1$ respectively correspond…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
A dimensionless parameter $\Lambda$ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repul- sion. Structural transitions…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…