相关论文: Using Peano Curves to Construct Laplacians on Frac…

In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and…

The graph Laplacian is an important tool in Graph Signal Processing (GSP) as its eigenvalue decomposition acts as an analogue to the Fourier transform and is known as the Graph Fourier Transform (GFT). The line graph has a GFT that is a…

In this paper, the fractal calculus of fractal sets and fractal curves are compared. The analogues of the Riemann-Liouville and the Caputo integrals and derivatives are defined for the fractal curves which are non-local derivatives. The…

The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…

We establish asymptotics of growing one dimensional self-similar fractal graphs, they are networks that allow multiple weighted edges between nodes, in terms of quantum central limit theorems for algebraic probability spaces in pure state.…

The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…

In the present paper we study approximation of discs by octagons on the pixel plane. To decide which octagon approximates better the given disc we use Jaccard's distance. The table of Jaccard's distances (calculated by a software created…

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…

This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a…

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback…

Using the spectral decomposition of the Laplace-Beltrami operator we simulate fractal surfaces as random series of eigenfunctions. This approach allows us to generate random fields over smooth manifolds of arbitrary dimension, generalizing…

In this article we provide an identification between the wavelet decompositions of certain fractal representations of $C^*-$algebras of directed graphs of M. Marcolli and A. Paolucci, and the eigenspaces of Laplacians associated to spectral…

In this paper, we analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and…

We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.

For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygon) associated with the first (non-trivial) eigenvalue. In…

We define the Ricci curvature on simplicial complexes by modifying the definition of the Ricci curvature on graphs, and we prove the upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies.…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to…

We define the distance between edges of graphs and study the coarse Ricci curvature on edges. We consider the Laplacian on edges based on the Jost-Horak's definition of the Laplacian on simplicial complexes. As one of our main results, we…