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We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are…
We consider the isotropic XY quantum spin chain in a random external field in the $z$ direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope $j^{-1/2}$. Our motivation is the study of…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…
The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
In this work, we formulate and study a data dissemination problem, which can be viewed as a generalization of the index coding problem and of the data exchange problem to networks with an arbitrary topology. We define $r$-solvable networks,…
One of the important unsolved problems in information theory is the conjecture that network coding has no rate benefit over routing in undirected unicast networks. Three known bounds on the symmetric rate in undirected unicast information…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear because they are hard to predict. For theoretical models of disease spreading, on the other hand, quantities characterizing the outbreak…
The minimal time required for a system to evolve between two different states is an important notion for developing ultra-speed quantum computer and communication channel. Here, we introduce a new metric for non-degenerate density operator…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared…
We study emergent information in populations of randomly generated networked computable systems that follow a Susceptible-Infected-Susceptible contagion (or infection) model of imitation of the fittest neighbor. These networks have a…
In this paper, we present BERN-NN as an efficient tool to perform bound propagation of Neural Networks (NNs). Bound propagation is a critical step in wide range of NN model checkers and reachability analysis tools. Given a bounded input…
The asynchronous rumor algorithm spreading propagates a piece of information, the so-called rumor, in a network. Starting with a single informed node, each node is associated with an exponential time clock with rate $1$ and calls a random…
An upper bound to the information capacity of a wavelength-division multi- plexed optical fiber communication system is derived in a model incorporating the nonlinear propagation effects of cross-phase modulation (XPM). This work is based…
Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we…