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 generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

Compositional reasoning aims to improve scalability of verification tools by reducing the original verification task into subproblems. The simplification is typically based on assume-guarantee reasoning principles, and requires user guidance to identify appropriate assumptions for components. In this paper, we propose a fully automated approach to compositional reasoning that consists of automa...

We say that a k-uniform hypergraph C is a Hamilton cycle of type `, for some 1 ≤ ` ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei| = `. We define a class of ( , p)-regular hypergraphs, that includes random hypergraph...

For every fixed k ≥ 3 there exists a constant ck with the following property. Let H be a kuniform, D-regular hypergraph on N vertices, in which no two edges contain more than one common vertex. If k > 3 then H contains a matching covering all vertices but at most ckND. If k = 3, then H contains a matching covering all vertices but at most c3ND lnD. This improves previous estimates and implies, ...

where n = |V |. Let G = (V,E) be a 3-regular hypergraph; i.e. E is a subset of subsets of V of size 3. We consider the space, L2(V ), of real valued functions on V with the usual inner product; let e1, . . . , en be the standard basis for L2(V ), where ei takes the value 1 on the i-th vertex of V and 0 elsewhere. It is natural to construct from G a trilinear form, that is a map from τ , mapping...

We present a unified framework on the limits of constraint satisfaction problems (CSPs) and efficient parameter testing which depends only on array exchangeability and the method of cut decomposition without recourse to the weakly regular partitions. In particular, we formulate and prove a representation theorem for compact colored r-uniform directed hypergraph (r-graph) limits, and apply this ...

We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or “first eigenvalue” for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the “second eigenvalue”...

We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3, 4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of...