Eigenvalue distributions for some correlated complex sample covariance matrices

The distributions of the smallest and largest eigenvalues for the matrix product $Z^\dagger Z$, where $Z$ is an $n \times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m \times m$ determinants. In the case of correlation along rows, these expressions are computationally more efficient than those involving sums over partitions and Schur polynomials reported recently for the same distributions.Comment: 11 page

An Efficient Large-Area Grating Coupler for Surface Plasmon Polaritons

We report the design, fabrication and characterization of a periodic grating of shallow rectangular grooves in a metallic film with the goal of maximizing the coupling efficiency of an extended plane wave (PW) of visible or near-infrared light into a single surface plasmon polariton (SPP) mode on a flat metal surface. A PW-to-SPP power conversion factor > 45 % is demonstrated at a wavelength of 780 nm, which exceeds by an order of magnitude the experimental performance of SPP grating couplers reported to date at any wavelength. Conversion efficiency is maximized by matching the dissipative SPP losses along the grating surface to the local coupling strength. This critical coupling condition is experimentally achieved by tailoring the groove depth and width using a focused ion beam.Comment: The final publication is available at http://www.springerlink.com. http://dx.doi.org/10.1007/s11468-011-9303-

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

A natural mutation in Pisum sativum L. (pea) alters starch assembly and improves glucose homeostasis in humans

Elevated postprandial glucose (PPG) is a significant risk factor for non-communicable diseases globally. Currently, there is a limited understanding of how starch structures within a carbohydrate-rich food matrix interact with the gut luminal environment to control PPG. Here, we use pea seeds (Pisum sativum) and pea flour, derived from two near-identical pea genotypes (BC1/19RR and BC1/19rr) differing primarily in the type of starch accumulated, to explore the contribution of starch structure, food matrix and intestinal environment to PPG. Using stable isotope 13C-labelled pea seeds, coupled with synchronous gastric, duodenal and plasma sampling in vivo, we demonstrate that maintenance of cell structure and changes in starch morphology are closely related to lower glucose availability in the small intestine, resulting in acutely lower PPG and promotion of changes in the gut bacterial composition associated with long-term metabolic health improvements

А Меаsuring Method for Gyro-Free Determination of the Parameters of Moving Objects

The paper presents a new method for building measuring instruments and systems for gyro-free determination of the parameters of moving objects. To illustrate the qualities of this method, a system for measuring the roll, pitch, heel and trim of a ship has been developed on its basis. The main concept of the method is based, on one hand, on a simplified design of the base coordinate system in the main measurement channel so as to reduce the instrumental errors, and, on the other hand, on an additional measurement channel operating in parallel with the main one and whose hardware and software platform makes possible performing algorithms intended to eliminate the dynamic error in real time. In this way, as well as by using suitable adaptive algorithms in the measurement procedures, low-cost measuring systems operating with high accuracy under conditions of inertial effects and whose parameters (intensity and frequency of the maximum in the spectrum) change within a wide range can be implemented

A Model of the Dynamic Error as a Measurement Result of Instruments Defining the Parameters of Moving Objects

The present paper considers a new model for the formation of the dynamic error inertial component. It is very effective in the analysis and synthesis of measuring instruments positioned on moving objects and measuring their movement parameters. The block diagram developed within this paper is used as a basis for defining the mathematical model. The block diagram is based on the set-theoretic description of the measuring system, its input and output quantities and the process of dynamic error formation. The model reflects the specific nature of the formation of the dynamic error inertial component. In addition, the model submits to the logical interrelation and sequence of the physical processes that form it. The effectiveness, usefulness and advantages of the model proposed are rooted in the wide range of possibilities it provides in relation to the analysis and synthesis of those measuring instruments, the formulation of algorithms and optimization criteria, as well as the development of new intelligent measuring systems with improved accuracy characteristics in dynamic mode

An Algorithm for Improving the Accuracy of Systems Measuring Parameters of Moving Objects

The paper considers an algorithm for increasing the accuracy of measuring systems operating on moving objects. The algorithm is based on the Kalman filter. It aims to provide a high measurement accuracy for the whole range of change of the measured quantity and the interference effects, as well as to eliminate the influence of a number of interference sources, each of which is of secondary importance but their total impact can cause a considerable distortion of the measuring signal. The algorithm is intended for gyro-free measuring systems. It is based on a model of the moving object dynamics. The mathematical model is developed in such a way that it enables to automatically adjust the algorithm parameters depending on the current state of measurement conditions. This makes possible to develop low-cost measuring systems with a high dynamic accuracy. The presented experimental results prove effectiveness of the proposed algorithm in terms of the dynamic accuracy of measuring systems of that type

Glioblastoma Multiforme Classified As Mesenchymal Subtype

ВВЕДЕНИЕ: В качестве неблагоприятных прогностических факторов при первичных глиобластомах в последнее время обсуждаются не только клинические показатели, но и различные клеточные, генетические и иммунологические маркеры. ЦЕЛЬ: Работа ставит себе целью анализировать случай с первичной мультиформенной глиобластомой и краткой выживаемостью после оперативной интер- венции, а также и определить неблагоприятные прогностические маркеры. ПРЕДСТАВЛЕНИЕ СЛУЧАЯ: Авторы представляют случай 71-оголетнего мужчины с доказанной мультиформенной глиобластомой и постоперативной выживаемостью в 48 дней. Из-за непродолжительной выживаемости пациент не подвергнут телегамматерапии и адювантной терапии Темозоломид- ом. С помощью молекулярно- биологических и иммунологических анализов определены транскрипционные и сывороточные уровни TNF-α, IL-6, YKL-40 и CD44. Устанавливаются экстремно высокие транскрипционные уровни генов CD44, IL-6 и YKL-40, увеличенная экспрессия TNF-α, сопровожденные повышенной сывороточной концентрацией IL-6, TNF-α и YKL-40 и пониженной сывороточной концентрацией CD44. ЗАКЛЮЧЕНИЕ: Молекулярно-биологически

The Beta-Wishart Ensemble

We introduce a “Broken-Arrow” matrix model for the β-Wishart ensemble, which improves on the traditional bidiagonal model by generalizing to non-identity covariance parameters. We prove that its joint eigenvalue density involves the correct hypergeometric function of two matrix arguments, and a continuous parameter β> 0. If we choose β = 1, 2, 4, we recover the classical Wishart ensembles of general covariance over the reals, complexes, and quaternions. The derivation of the joint density requires an interesting new identity about Jack polynomials in n variables. Jack polynomials are often defined as the eigenfunctions of the Laplace-Beltrami Operator. We prove that Jack polynomials are in addition eigenfunctions of an integral operator defined as an average over a β-dependent measure on the sphere. When combined with an identity due to Stanley, 32 we derive a new definition of Jack polynomials. An efficient numerical algorithm is also presented for simulations. The algorithm makes use of secular equation software for broken arrow matrices currently unavailable in the popular technical computing languages. The simulations are matched against the cdf’s for the extreme eigenvalues. The techniques here suggest that arrow and broken arrow matrices can play an important role in theoretical and computational random matrix theory including the study of corners processes