Related papers: Approximating Diffusion on Finite Multi-Topology S…
The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gau{\ss} hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for…
We develop a theory of ultrametric graphons as limiting objects for random networks with nested hierarchical community structure. A graphon $W:[0,1]^2\to[0,1]$ is called ultrametric if $W(x,y)=w(d(x,y))$, where $d$ is an ultrametric on…
Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit…
The development of simple and fast hypergraph spectral methods has been hindered by the lack of numerical algorithms for simulating heat diffusions and computing fundamental objects, such as Personalized PageRank vectors, over hypergraphs.…
We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…
We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the…
$p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Z\'u\~niga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the…
This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = \delta \varphi$. They…
A unifying graph theoretic framework for the modelling of metro transportation networks is proposed. This is achieved by first introducing a basic graph framework for the modelling of the London underground system from a diffusion law point…
Advanced control strategies for delivering heat to users in a district heating network have the potential to improve performance and reduce wasted energy. To enable the design of such controllers, this paper proposes an automated plant…
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical…
This paper presents a distributed algorithm on wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a linear size, lightweight, (1+\epsilon)-spanner for any given \epsilon > 0. A…
We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By…
Distribution grids represent the final tier in electric networks consisting of medium and low voltage lines that connect the distribution substations to the end-users. Traditionally, distribution networks have been operated in a radial…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…