Related papers: Effects of Biases in Domain Wall Network Evolution

Domain wall networks have attracted renewed interest, particularly in relation to the dynamics of network collapse. Accurately describing this process is challenging and typically requires large scale numerical simulations. Here we adopt a…

We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these…

Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

We develop a velocity-dependent one-scale model for the evolution of domain wall networks in flat expanding or collapsing homogeneous and isotropic universes with an arbitrary number of spatial dimensions, finding the corresponding scaling…

The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…

Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold…

The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…

I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of…

Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…

We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…

Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…

The dynamics of interacting domain walls, regarded as a system of particles which are biased to move towards their nearest neighbours and annihilate when they meet, have been studied in the recent past. We study the effect of the presence…

The dynamics of a domain wall in magnetostrictive materials is investigated. The domain wall is modeled by a d-dimensional interface moving in a d+1-dimensional environment. Long-range demagnetization effects and quenched disorder are…

Many empirical networks are intrinsically pluralistic, with interactions occurring within groups of arbitrary agents. Then the agent in the network can be influenced by types of neighbors, common examples include similarity, opposition, and…

In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…