Related papers: On a Class of Nonlocal Continuity Equations on Gra…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
In this paper, we assume that $q>0$, $p>1$ and $s\in(0,1)$ , and consider the following nonlinear fractional p-Laplacian equations on finite graphs: \begin{equation*} \left\{ \begin{array}{lll} \partial_t u^q(x,t)+(-\Delta)_p^su=0,\\[15pt]…
In this paper, we study a nonlocal variational problem which consists of minimizing in $L^2$ the sum of a quadratic data fidelity and a regularization term corresponding to the $L^p$-norm of the nonlocal gradient. In particular, we study…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an…
Suppose that $G=(V, E)$ be a locally finite and connected graph with symmetric weight and uniformly positive measure, where $V$ denotes the vertex set and $E$ denotes the edge set. We are concered with the following problem $$…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of reaction-diffusion equations.
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…