Modern day science presentsmany challenges to data analysts. Advances in data collection provide very large (number of observations and number of dimensions) data sets. In many areas of data analysis an informative task is to find natural separations of data into homogeneous groups, i.e. clusters. In this paper we study the asymptotic behavior of hierarchical clustering in situations where both...

In this paper the asymptotic performance of a new intuitive space-time diversity scheme is analyzed. So called boosted scheme is compatible with today’s WLAN specifications with regard to convolutional coding and bit labelling, and minimizes the number of decoding iterations, required to obtain a reasonable Bit Error Rate. Good properties of the proposed scheme are proved by high asymptotic cod...

In this article, we study the short-and long-range perturbations of periodic Schrr odinger operators. The asymptotic completeness is proved in the short-range case by referring to known results on the stationary approach and more explicitly with the time-dependent approach. In the long-range case, one is able to construct modiied wave operators. In both cases, the asymptotic observables can be ...

We derive upper and lower bounds on the isoperimetric numbers and bisection widths of a large class of regular graphs of high degree. Our methods are combinatorial and do not require a knowledge of the eigenvalue spectrum. We apply these bounds to random regular graphs of high degree and the Platonic graphs over the rings Zn. In the latter case we show that these graphs are generally nonRamanuj...

MOTIVATION Although many methods and statistical approaches have been developed for protein identification by mass spectrometry, the problem of accurate assessment of statistical significance of protein identifications remains an open question. The main issues are as follows: (i) statistical significance of inferring peptide from experimental mass spectra must be platform independent and spectr...

Background Alcohol consumption levels in Russia are among the highest in the world [1]. Fetal Alcohol Spectrum Disorders in children are completely preventable by avoiding alcohol use during pregnancy [2]; yet, substantial numbers of women around the world consume alcohol during pregnancy mostly prior to pregnancy recognition [3-5]. A U.S. prevention model, Project CHOICES, utilized a pre-conce...

Studies of the mathematical properties Regge-pole and dual amplitudes are important both for their applications in high energy phenomenology generalizations to strings, superstrings, branes, other theoretical developments. In present paper, we investigate similarities differences between two classes amplitudes: one with Mandelstam analyticity (DAMA) another logarithmic trajectories (Dual-log). ...

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann “windows” of the same length the centers of which are 2l apart, and study the asymptotic behaviour of the discrete spectrum as l → ∞. It is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single-window strip and their distances vanish exponentially in the limit l → ∞. We...

We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as w...

Using a perturbation matrix, we introduced a hyperplane used to define a generalized null-spectrum, based on both the signal and noise subspaces, while the MUSIC and Min-Norm null-spectra are defined based only on the noise subspace. With the generalized nullspectrum, we derived the upper and lower bounds of a class of the generalized null-spectrum, called the maximum and minimum null-spectra, ...