We show that if a graph H is k-colorable, then (k−1)-branching walks on H exhibit long range action, in the sense that the position of a token at time 0 constrains the configuration of its descendents arbitrarily far into the future. This long range action property is one of several investigated herein; all are similar in some respects to chromatic number but based on viewing H as the range, in...

Let p(k) denote the partition function of k. For each k ≥ 2, we describe a list of p(k) − 1 quasirandom properties that a k-uniform hypergraph can have. Our work connects previous notions on hypergraph quasirandomness, beginning with the early work of Chung and Graham and Frankl-Rödl related to strong hypergraph regularity, the spectral approach of Friedman-Wigderson, and more recent results of...

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

Recent years have witnessed a surge of interest in hypergraph-based transductive image classification. Hypergraph-based transductive learning models the high-order relationship of samples by using a hyperedge to link multiple samples. In order to extend the high-order relationship of samples, we incorporate linear correlation of sparse representation to hypergraph learning framework to improve ...

In this work we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix vector multiplica tion Then we propose two hypergraph models which avoid all de cien cies of the graph model The proposed models reduce the decomposition problem to the well known hypergraph partitioning problem widely en countered in circuit partitioning in VLSI We have implemented fast ...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...