Related papers: Durrett-Levin spatial model of allelopathy
We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the…
Robust boundary states have been the focus of much recent research, both as topologically protected states and as non-Hermitian skin states. In this work, we show that many-body effects can also induce analogs of these robust states in…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
We construct and analyse a simple {\em reduced} model to study the effects of the interplay between a density undergoing an active-to-absorbing state phase transition (AAPT) and a fluctuating environment in the form of a broken symmetry…
We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules.…
We consider a system of two PDEs arising in modeling of motility of eukariotic cells on substrates. This system consists of the Allen-Cahn equation for the scalar phase field function coupled with another vectorial parabolic equation for…
Methods are lacking to handle the problem of survival analysis in the presence of an interval-censored covariate, specifically the case in which the conditional hazard of the primary event of interest depends on the occurrence of a…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…
We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…
We derive the disorder vs. doping phase diagram of the doped Hubbard model via Dynamical Mean Field Theory combined with Typical Medium Theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven)…
In real-world settings of the Deferred Acceptance stable matching algorithm, such as the American medical residency match (NRMP), school choice programs, and various national university entrance systems, candidates need to decide which…
This paper analyzes the generalized spatially heterogeneous diffusive predator-prey model introduced by the authors in \cite{LGMH20}, whose interaction terms depend on a saturation coefficient $m(x)\gneq0$. As the amplitude of the…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality…
This paper considers a natural variant of the $d$-dimensional multitype contact process in which individuals can be fertile or sterile. Fertile individuals of type $i$ give birth to an offspring of their own type at rate $\lambda_i$, the…
Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its non-interacting counterpart. This happens when two phases that are…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
We study two famous interacting particle systems, the so-called Richardson's model and the contact process, when we add a stirring dynamics to them. We prove that they both satisfy an asymptotic shape theorem, as their analogues without…
Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections. We introduce a novel hypergraph message passing framework inspired by interacting particle systems,…