In this paper, we introduce a new decision problem associated with lattices, named the Exact Length Vector Problem (ELVP), and prove the NP-completeness of ELVP in the ∞ norm. Moreover, we define two variants of ELVP. The one is a binary variant of ELVP, named the Binary Exact Length Vector Problem (BELVP), and is shown to be NPcomplete in any p norm (1 ≤ p ≤ ∞). The other is a nonnegative vari...

Sign eigenvectors for a real square matrix, A, are defined to be sign vectors for which all of its elements either retain the same signs or become to their opposite signs after the linear transformation A, where a sign vector is a vector with the elements equal to either 1 or −1. Existence of sign eigenvectors for symmetric positive semi-definite matrices is investigated. It is shown that the s...

Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n2/3ǫ−4 logn) independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the d...

This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted l1 norm minimization for sparsity enhancement, this paper proposes a reweighted singular value enhancement scheme to improve tensor low tubular rank in the tensor completion process. An efficient iterative decomposition scheme based on t-SVD is proposed whic...

Sharp smoothing estimates are proven for magnetic Schrr odinger semigroups in two dimensions under the assumption that the magnetic eld is bounded below by some positive constant B 0. As a consequence the L 1 norm of the associated integral kernel is bounded by the L 1 norm of the Mehler kernel of the Schrr odinger semigroup with the constant magnetic eld B 0 .

Simulation models support managers in the solution of complex problems. International agencies recommend uncertainty and global sensitivity methods as best practice in the audit, validation and application of scientific codes. However, numerical complexity, especially in the presence of a high number of factors, induces analysts to employ less informative but numerically cheaper methods. This w...

Motion estimation and compensation are widely used in video coding. This paper presents two fast block matching algorithms for motion estimation. These algorithms use the subspace features of a block to determine the block distance. With a search block size of N×N, the proposed algorithms can achieve a computation reduction factor of N/2 while retaining close-to-optimal performance in the mean ...

This paper deals with the kth nearest rectilinear distance of two regular point patterns: square and diamond lattices. The probability density functions of the kth nearest rectilinear distance are theoretically derived for k = 1, 2, . . . , 8. Upper and lower bounds of the kth nearest distance are also derived. As an application of the kth nearest distance, we consider a facility location probl...

This paper will present the important factors influencing spectral target recognition using multispectral data and suggest a different approach to small target recognition. The methodology of directed spectral search will be offered, including the use of spectral libraries, spectral similarity scores, and ROC curve analysis. The ability to find specific small targets, such as Saddam Hussein’s y...

This paper proposes a simple spatial-temporal smoothness based method for solving dense non-rigid structure-frommotion (NRSfM). First, we revisit the temporal smoothness and demonstrate that it can be extended to dense case directly. Second, we propose to exploit the spatial smoothness by resorting to the Laplacian of the 3D non-rigid shape. Third, to handle real world noise and outliers in mea...