Related papers: Laplacian Fractional Revival on Graphs

Many variants of join operations of graphs have been introduced and their spectral properties have been studied extensively by many researchers. This paper mainly focuses on the Laplacian spectra of some double join operations of graphs. We…

CNN architectures have terrific recognition performance but rely on spatial pooling which makes it difficult to adapt them to tasks that require dense, pixel-accurate labeling. This paper makes two contributions: (1) We demonstrate that…

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…

Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by…

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…

Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…

We introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first $k$ Dirichlet eigenvalues of the fractional…

We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…

Our primary motivation is existence and uniqueness for the obstacle problem on graphs. That is, we look for unique solutions to the problem $Lu = \chi_{\{u>0\}}$, where $L$ is the Laplacian matrix associated to a graph, and $u$ is a…

We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…

In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in [0,1[$ and…

This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including cohomology and Hodge theory. The main feature of our approach is…

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph…

We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization,…

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…

The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…

We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…

The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…