相关论文: Laplacian networks: growth, local symmetry and sha…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
In this work, we consider a method of searching of the direction of a wireless network development (the places of new access points or base stations etc.) optimized with criteria of coverage of important territories and minimum cost of…
Borrowing from concepts in expander graphs, we study the expansion properties of real-world, complex networks (e.g. social networks, unstructured peer-to-peer or P2P networks) and the extent to which these properties can be exploited to…
Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks, consisting of multiple interacting networks. However, despite significant research in…
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of…
Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to turbulence in shear flows. We demonstrate that the addition of nonlinearity to the…
Problems of interface growth have received much attention recently Such are, for example, the duffusion limited aggregation (DLA), random sequential adsorption (RSA), Laplacian growth or flame front propagation. We will mainly pay attention…
Pattern formation, arising from systems of autonomous reaction-diffusion equations, on networks has become a common topic of study in the scientific literature. In this work we focus primarily on directed networks. Although some work prior…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…
We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at…
Spectral graph theory gives an algebraical approach to analyze the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the…
We provide a long-time existence and sub-convergence result for the elastic flow of a three network in $\mathbb{R}^{n}$ under some mild topological assumptions. The evolution is such that the sum of the elastic energies of the three curves…
The study of network structural controllability focuses on the minimum number of driver nodes needed to control a whole network. Despite intensive studies on this topic, most of them consider static networks only. It is well-known, however,…
In this paper we study the uniqueness of expanding self-similar solutions to the network flow in a fixed topological class. We prove the result via the parabolic Allen-Cahn approximation proved in \cite{triodginz}. Moreover, we prove that…
Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned…
We consider for a small parameter $\varepsilon >0$ a parabolic convection-diffusion problem with P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in a three-dimensional graph-like junction consisting of thin curvilinear cylinders…
A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…