Symmetricity of an optimal solution of SemiDefinite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primaldual interior-point method. Introducing some operators for rearranging elements of matrices and vectors, three types of symmetric SDPs are defined by using those operators. The symmetricity of the solution on the centra...

Abstract. Recent work on eigenvalues and eigenvectors for tensors of order m ≥ 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Axm−1 = λx subject to ‖x‖ = 1, which is closely related to optimal rank-1 approximation of a symm...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

we give a survey of recent applications of group rings to combinatorics and tocryptography, including their use in the di erential cryptanalysis of block ciphers.

a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank ...

(Abstract) In this paper, we present a method of finding symmetric items in a combinatorial item set database. The techniques for finding symmetric variables in Boolean functions have been studied for long time in the area of VLSI logic design, and the BDD (Binary Decision Diagram)-based methods are presented to solve such a problem. Recently , we have developed an efficient method for handling...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...