Related papers: The Total Variation Flow in Metric Graphs
In this paper we provide a full classification of complete translating graphs in $\mathbf{R}^3$. We also construct two $(n-1)$-parameter families of new examples of translating graphs in $\mathbf{R}^{n+1}$.
We study a simple stochastic differential equation driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some condition, we describe the laws of all solutions. This work is a…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…
We introduce the notion of a generalized flow on a graph with coefficients in a R-representation and show that the module of flows is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff's laws and build an exact…
Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…
We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating…
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
We developed a new approach comprised of different visualizations for the comparative spatio-temporal analysis of displacement processes in porous media. We aim to analyze and compare ensemble datasets from experiments to gain insight into…
In this note we study a large class of mean curvature type flows of graphs in product manifold $N\times R$ where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish…
We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing,…
We study convex entire graphs evolving with normal velocity equal to a positive power of the mean curvature. Under mild assumptions we prove longtime existence.
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
We construct a family of trees on which a lazy simple random walk exhibits total variation cutoff. The main idea behind the construction is that hitting times of large sets should be concentrated around their means. For this sequence of…