Related papers: One-scale Model for Domain Wall Network Evolution
Since the Tor network is evolving into an infrastructure for anonymous communication, analyzing the consequences of network growth is becoming more relevant than ever. In particular, adding large amounts of resources may have unintentional…
Studies on social networks have proved that endogenous and exogenous factors influence dynamics. Two streams of modeling exist on explaining the dynamics of social networks: 1) models predicting links through network properties, and 2)…
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that…
In this note, we first derive a one-parameter family of hyperparameter scaling strategies that interpolates between the neural-tangent scaling and mean-field/maximal-update scaling. We then calculate the scalings of dynamical observables --…
We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale…
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…
A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
Recently there has been a lot of interest in monitoring and identifying changes in dynamic networks, which has led to the development of a variety of monitoring methods. Unfortunately, these methods have not been systematically compared;…
We consider a classical field configuration, corresponding to intersection of two domain walls in a supersymmetric model, where the field profile for two parallel walls at a finite separation is known explicitly. An approximation to the…
We address a simple model allowing the existence of domain walls with orientational moduli localized on them. Within this model, we discuss an analytic solution and explore it in the context of previously known results. We discuss the…
Domain wall (DW) networks have a large impact on cosmology and present interesting dynamics that can be controlled by various scaling regimes. In the first stage after spontaneous breaking of the discrete symmetry, the network is seeded…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
We study classical solutions of a particular version of the modified Skyrme model in (3+1) dimensions. The model possesses Skyrmion solutions as well as stable domain walls that connect different vacua of the theory. We show that there is…