Related papers: New High Dimensional Expanders from Covers

Powering the adjacency matrix of an expander graph results in a better expander of higher degree. In this paper we seek an analogue operation for high-dimensional expanders. We show that the naive approach to powering does not preserve…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and…

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…

We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…

In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

We present a pair of heuristic algorithms. The first is to generate a random regular graph of fixed size. The second is the introduction of the Metropolis Coupled Simulated Annealer (MCSA) for optimizing spectral gaps in fixed size regular…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…

Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…

Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological…

We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…

Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to…

We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to…

Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…

We consider the question of the largest possible combinatorial diameter among $(d-1)$-dimensional simplicial complexes on $n$ vertices, denoted $H_s(n, d)$. Using a probabilistic construction we give a new lower bound on $H_s(n, d)$ that is…