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Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic…
The study of random landscapes has long relied on counting stationary points: metastable states and the barriers between them. However, this method is useless for describing flat regions, common in constraint satisfaction problems. We…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
As an alternative view to the graph formation models in the statistical physics community, we introduce graph formation models using \textit{network formation} through selfish competition as an approach to modeling graphs with particular…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
We develop a theory of the domain patterns in systems with competing short-range attractive interactions and long range repulsive Coulomb interactions. We take an energetic approach, in which patterns are considered as critical points of a…
We consider a classical field configuration, corresponding to intersection of two domain walls in a supersymmetric model, where the field profile for two parallel walls at a finite separation is known explicitly. An approximation to the…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
Two families of denotational models have emerged from the semantic analysis of linear logic: dynamic models, typically presented as game semantics, and static models, typically based on a category of relations. In this paper we introduce a…
This paper addresses the problem of identifying the graph structure of a dynamical network using measured input/output data. This problem is known as topology identification and has received considerable attention in recent literature. Most…
This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…
Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We present a numerical analysis of local community assembly through weak migration from a regional species pool. At equilibrium, the local community consists of a subset ("clique") of species from the regional community. Our analysis…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range…
In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…
In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic…