In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, l1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed l1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine project...

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut = −(uuxxx)x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u0(x) ∈ H 1(IR), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L1-norm of the strong...

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the 1-norm minimization problem 2011 . The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving 1-norm minimization problems. Under mild conditions, we show that the proposed algorit...

We discuss geometric special cases of optimization problems on graphs where the n vertices are represented as points in IR d and where the lengths of the edges are measured according to a norm with a polyhedral unit ball. We derive algorithms whose running time is polynomial in n (and depends exponentially on the number of faces of the unit ball). We consider the maximum travelling salesman pro...

Developing a stable early warning system (EWS) model that is capable to give an accurate prediction is a challenging task. This paper introduces k-nearest neighbour (k-NN) method which never been applied in predicting currency crisis before with the aim of increasing the prediction accuracy. The proposed k-NN performance depends on the choice of a distance that is used where in our analysis; we...

We concern the problem of modifying the edge lengths of a tree in minimum total cost so that the prespecified p vertices become the p-maxian with respect to the new edge lengths. This problem is called the inverse p-maxian problem on trees. Gassner proposed efficient combinatorial alogrithm to solve the the inverse 1-maxian problem on trees in 2008. For the problem with p ≥ 2, we claim that the...

The eeciency of many algorithms in parallel processing, computational geometry, image processing, and several other elds relies on \locality-preserving" indexing schemes for meshes. We concentrate on the case where the maximum distance between two mesh nodes indexed i and j shall be a slow-growing function of ji ? jj (using the Euclidean, the maximum, and the Manhattan metric). In this respect,...

We study the zero-temperature phase diagram of Ising spin systems in two dimensions in the presence of competing interactions: long-range antiferromagnetic and nearest-neighbor ferromagnetic of strength J . We first introduce the notion of a “corner energy,” which shows, when the antiferromagnetic interaction decays faster than the fourth power of the distance, that a striped state is favored w...

In recent years, the eeect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a eeciency and/or eeectiveness perspective. Recent research results show that in high dimensional space, the ...