Related papers: Pattern formation in individual-based systems with…
Creating a quantitative theory for the cortex presents challenges and raises questions. What are the significant scales--micro, meso, or macroscopic? What are the interactions--pairwise, higher order, or mean-field? And what control…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
We study the flocking and pattern formations of active particles with a Vicsek-like model that includes a configuration dependent noise term. In particular, we couple the strength of the noise with both the local density and orientation of…
An SU(2) lattice gauge theory with two doublets of complex scalar fields is considered. All continuous symmetries are identified and, using the nonperturbative methods of lattice field theory, the phase diagram is mapped out by direct…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
Standard models of sequential adsorption are implicitly formulated in a {\em scale invariant} form, by assuming adsorption on an infinite surface, with no characteristic length scales. In real situations, however, involving complex…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the…
We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size $N$ infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of…
We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication…
Near a continuous phase transition, systems with different microscopic origins display universal dynamics if their underlying symmetries are compatible. In a thermally quenched system, the Kibble-Zurek mechanism for the creation of…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
Generic results for degenerate Chenciner (generalized Neimark-Sacker) bifurcation are obtained in the present work. The bifurcation arises in two-dimensional discrete-time systems with two independent parameters. We define in this work a…
Within the Landau-Ginzburg picture of phase transitions, scalar field theories develop phase separation because of a spontaneous symmetry-breaking mechanism. This picture works in thermodynamics but also in the dynamics of phase separation.…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
Subsequence-based time series classification algorithms provide accurate and interpretable models, but training these models is extremely computation intensive. The asymptotic time complexity of subsequence-based algorithms remains a…
We demonstrate a novel mechanism for the formation of topological defects in a first order phase transition for theories in the presence of small explicit symmetry breaking terms. We carry out numerical simulations of collisions of two…