Related papers: Topologically-based fractional diffusion and emerg…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Temporal social networks are characterized by {heterogeneous} duration of contacts, which can either follow a power-law distribution, such as in face-to-face interactions, or a Weibull distribution, such as in mobile-phone communication.…
We investigate the effect of cooperative interactions in an ensemble of microorganisms, modelled as self-propelled disk-like and rod-like particles, in a three-dimensional turbulent flow to show flocking as an emergent phenomenon. Building…
The distribution of human linguistic groups presents a number of interesting and non-trivial patterns. The distributions of the number of speakers per language and the area each group covers follow log-normal distributions, while population…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
Interactions among neighboring birds in a flock cause an alignment of their flight directions. We show that the minimally structured (maximum entropy) model consistent with these local correlations correctly predicts the propagation of…
We study the long-time hydrodynamic behavior of systems of multi-species which arise from agent-based description of alignment dynamics. The interaction between species is governed by an array of symmetric communication kernels. We prove…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however,…
Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or…
Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We show that hydrodynamic theories of polar active matter generically possess inhomogeneous traveling solutions. We introduce a unifying dynamical-system framework to establish the shape of these intrinsically nonlinear patterns, and show…
Human populations exhibit complex behaviors---characterized by long-range correlations and surges in activity---across a range of social, political, and technological contexts. Yet it remains unclear where these collective behaviors come…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…