Maps on random hypergraphs and random simplicial complexes
نویسندگان
چکیده
Let [Formula: see text] be a simplicial complex. In this paper, we study random sub-hypergraphs and sub-complexes of text]. By considering the minimal complex that sub-hypergraph can embedded in maximal sub-hypergraph, define some maps on space probability functions We compositions these as well their actions functions.
منابع مشابه
Exponential random simplicial complexes
Abstract Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles subject to the constraints that the expected values of a set of graph observables are equal to given values. Here we extend these maximum-entropy ensembles to random simplicial complexes, which are more adequate and versatile constructions to m...
متن کاملRandom walks on simplicial complexes and harmonics†
In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k-dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi-supervised learning problem. Specifically, we...
متن کاملOn Topological Minors in Random Simplicial Complexes
Simplicial Complexes. A (finite abstract) simplicial complex is a finite set system that is closed under taking subsets, i.e., F ⊂ H ∈ X implies F ∈ X. The sets F ∈ X are called faces of X. The dimension of a face F is dim(F ) = |F | − 1. The dimension of X is the maximal dimension of any face. A k-dimensional simplicial complex will also be called a k-complex.
متن کاملRandom Abstract Simplicial Complexes Reduction
Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network nodes without modifying neither the connectivity nor the coverage of the network. In this paper, we present a reduction algorithm that lower the number of points...
متن کاملRandom Simplicial Complexes - Around the Phase Transition
This article surveys some of the work done in recent years on random simplicial complexes. We mostly consider higher-dimensional analogs of the well known phase transition inG(n, p) theory that occurs at p = 1 n . Our main objective is to provide a more streamlined and unified perspective of some of the papers in this area.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2022
ISSN: ['1793-6527', '0218-2165']
DOI: https://doi.org/10.1142/s0218216522500158