Related papers: Localization and Pattern Formation in BBGKY Hierar…
From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish…
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, characterizing spike patterns in the resulting data, and linking…
We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into stable one-dimensional lattice. This lattice, as well as other optically-bound structures, are shown to…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…
A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
Generative modeling aims at producing new datapoints whose statistical properties resemble the ones in a training dataset. In recent years, there has been a burst of machine learning techniques and settings that can achieve this goal with…
We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial…
Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…
We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. Local chemical complexity in compositionally complex alloys poses challenges for…
In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…