The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

New physics contributions to A(FB)(t(t)over-bar) at the Tevatron

The Tevatron has measured a discrepancy relative to the standard model prediction in the forward-backward asymmetry in top quark pair production. This asymmetry grows with the rapidity difference of the two top quarks. It also increases with the invariant mass of the t (t) over bar pair, reaching, for high invariant masses, 3.4 standard deviations above the next-to-leading order prediction for the charge asymmetry of QCD. However, perfect agreement between experiment and the standard model was found in both total and differential cross section of top quark pair production. As this result could be a sign of new physics we have parametrized this new physics in terms of a complete set of dimension six operators involving the top quark. We have then used a Markov chain Monte Carlo approach in order to find the best set of parameters that fits the data, using all available data regarding top quark pair production at the Tevatron. We have found that just a very small number of operators are able to fit the data better than the standard model.

Influência da experiência profissional e da função visual do operador no processamento semiautomático da cintigrafia de perfusão do miocárdio: variabilidade intra e interoperador na determinação dos parâmetros quantitativos

Introdução – A cintigrafia de perfusão do miocárdio (CPM) desempenha um importante papel no diagnóstico, avaliação e seguimento de pacientes com doença arterial coronária, sendo o seu processamento realizado maioritariamente de forma semiautomática. Uma vez que o desempenho dos técnicos de medicina nuclear (TMN) pode ser afetado por fatores individuais e ambientais, diferentes profissionais que processem os mesmos dados poderão obter diferentes estimativas dos parâmetros quantitativos (PQ). Objetivo – Avaliar a influência da experiência profissional e da função visual no processamento semiautomático da CPM. Analisar a variabilidade intra e interoperador na determinação dos PQ funcionais e de perfusão. Metodologia – Selecionou-se uma amostra de 20 TMN divididos em dois grupos, de acordo com a sua experiência no software Quantitative Gated SPECTTM: Grupo A (GA) – TMN ≥600h de experiência e Grupo B (GB) – TMN sem experiência. Submeteram-se os TMN a uma avaliação ortóptica e ao processamento de 21 CPM, cinco vezes, não consecutivas. Considerou-se uma visão alterada quando pelo menos um parâmetro da função visual se encontrava anormal. Para avaliar a repetibilidade e a reprodutibilidade recorreu-se à determinação dos coeficientes de variação, %. Na comparação dos PQ entre operadores, e para a análise do desempenho entre o GA e GB, aplicou-se o Teste de Friedman e de Wilcoxon, respetivamente, considerando o processamento das mesmas CPM. Para a comparação de TMN com visão normal e alterada na determinação dos PQ utilizou-se o Teste Mann-Whitney e para avaliar a influência da visão para cada PQ recorreu-se ao coeficiente de associação ETA. Diferenças estatisticamente significativas foram assumidas ao nível de significância de 5%. Resultados e Discussão – Verificou-se uma reduzida variabilidade intra (<6,59%) e inter (<5,07%) operador. O GB demonstrou ser o mais discrepante na determinação dos PQ, sendo a parede septal (PS) o único PQ que apresentou diferenças estatisticamente significativas (zw=-2,051, p=0,040), em detrimento do GA. No que se refere à influência da função visual foram detetadas diferenças estatisticamente significativas apenas na fração de ejeção do ventrículo esquerdo (FEVE) (U=11,5, p=0,012) entre TMN com visão normal e alterada, contribuindo a visão em 33,99% para a sua variação. Denotaram-se mais diferenças nos PQ obtidos em TMN que apresentam uma maior incidência de sintomatologia ocular e uma visão binocular diminuída. A FEVE demonstrou ser o parâmetro mais consistente entre operadores (1,86%). Conclusão – A CPM apresenta-se como uma técnica repetível e reprodutível, independente do operador. Verificou-se influência da experiência profissional e da função visual no processamento semiautomático da CPM, nos PQ PS e FEVE, respetivamente.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Efficient Implementation Of A Single-Precision Floating-Point Arithmetic Unit on FPGA

This paper presents a single precision floating point arithmetic unit with support for multiplication, addition, fused multiply-add, reciprocal, square-root and inverse squareroot with high-performance and low resource usage. The design uses a piecewise 2nd order polynomial approximation to implement reciprocal, square-root and inverse square-root. The unit can be configured with any number of operations and is capable to calculate any function with a throughput of one operation per cycle. The floatingpoint multiplier of the unit is also used to implement the polynomial approximation and the fused multiply-add operation. We have compared our implementation with other state-of-the-art proposals, including the Xilinx Core-Gen operators, and conclude that the approach has a high relative performance/area efficiency. © 2014 Technical University of Munich (TUM).

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.