In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of T̂ = {y ∈ ∆m|β y ≤ 0} on the standard simplex ∆m, where each component of the vector β is -1, 0 or 1.

Co-clustering exploits co-occurrence information, from contingency tables to cluster both rows and columns simultaneously. It has been established that co-clustering produces a better clustering structure as compared to conventional methods of clustering. So far, co-clustering has only been used as a technique for producing hard clusters, which might be inadequate for applications such as docum...

We consider the problem of Graphical lasso with an additional l∞ element-wise norm constraint on the precision matrix. This problem has applications in high-dimensional covariance decomposition such as in [Janzamin and Anandkumar, 2012a]. We propose an ADMM algorithm to solve this problem. We also use a continuation strategy on the penalty parameter to have a fast implemenation of the algorithm...

Let (W,S) be an irreducible Weyl or affine Weyl group. In [18], we constructed an algorithm for finding a representative set of left cells (or an l.c.r. set for short) of W in a two-sided cell Ω. In the present paper, we introduce a new simpler algorithm for finding an l.c.r. set of W in Ω when the subset F (Ω) of Ω is known (see Algorithm 3.11). Some technical tricks are introduced by some exa...

In the current paper we are seeking P1(y), P2(y), P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that P 3 1 (y)+P 3 2 (y)+P 3 3 (y) = Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a + b + c = d, since degQ(y) = 0 case coincides with above mentioned...

Prime factor fast Fourier transform (FFT) algorithms have two important advantages: they can be simultaneously self-sorting and in-place, and they have a lower operation count than conventional FFT algorithms. The major disadvantage of the prime factor FFT has been that it was only applicable to a limited set of values of the transform length N. This paper presents a generalized prime factor FF...

A priori determination of the sex of a human individual before gestation is a desirable goal in some cases. To achieve this, it is necessary to perform the separation of sperm cells containing either X or Y chromosomes. As is well known, male sex depends on the presence of chromosome Y. Once this separation is achieved in principle, we require to determine, with a high degree of accuracy, wheth...

The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this pap...

Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which for any given m m symmetric positive semideenite matrix ^ Y either connrms that ^ Y 2 ? or returns a cut, i.e., a ...