相关论文: Swap cosystolic expansion

We study the stability of covers of simplicial complexes. Given a map $f:Y\to X$ that satisfies almost all of the local conditions of being a cover, is it close to being a genuine cover of $X$? Complexes $X$ for which this holds are called…

We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building…

Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions. The classical Cheeger inequality implies that for graphs edge expansion is equivalent to…

In recent years, high dimensional expanders have been found to have a variety of applications in theoretical computer science, such as efficient CSPs approximations, improved sampling and list-decoding algorithms, and more. Within that, an…

In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes, yields for every dimension, an infinite family of…

Cosystolic expansion is a high-dimensional generalization of the Cheeger constant for simplicial complexes. Originally, this notion was motivated by the fact that it implies the topological overlapping property, but more recently it was…

Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topological expansion, but nowadays a significant part of the…

High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are…

Expander graphs have been intensively studied in the last four decades. In recent years a high dimensional theory of expanders has emerged, and several variants have been studied. Among them stand out coboundary expansion and topological…

Coboundary expansion (with $\mathbb{F}_2$ coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random complexes, property testing, and above all Gromov's topological…

We construct an explicit family of 3XOR instances which is hard for $O(\sqrt{\log n})$ levels of the Sum-of-Squares hierarchy. In contrast to earlier constructions, which involve a random component, our systems can be constructed explicitly…

We introduce the co-surface graph $\mathcal{CS}$ of a finitely generated free group $\mathbb{F}$ and use it to study the geometry of hyperbolic group extensions of $\mathbb{F}$. Among other things, we show that the Gromov boundary of the…

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…

Expander graphs have been a focus of attention in computer science in the last four decades. In recent years a high dimensional theory of expanders is emerging. There are several possible generalizations of the theory of expansion to…

We study sheaves on posets, showing that cosystolic expansion of such sheaves can be derived from local expansion conditions of the sheaf and the poset (typically a high dimensional expander). When the poset at hand is a cell complex, a…

Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…

In this paper, we further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expansion in the links imply the global expansion phenomena of…

The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, namely, $\mathbb{F}_2$. In this paper, we study Cheeger-type…

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…

Recent works have shown that expansion of pseudorandom sets is of great importance. However, all current works on pseudorandom sets are limited only to product (or approximate product) spaces, where Fourier Analysis methods could be…