On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix

This paper addresses the extension of the factorisation of a Hermitian matrix by an eigenvalue decomposition (EVD) to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle. Such parahermitian matrices contain polynomials or rational functions in the complex variable z, and arise e.g. as cross spectral density matrices in broadband array problems. Specifically, conditions for the existence and uniqueness of eigenvalues and eigenvectors of a parahermitian matrix EVD are given, such that these can be represented by a power or Laurent series that is absolutely convergent, at least on the unit circle, permitting a direct realisation in the time domain. Based on an analysis on the unit circle, we prove that eigenvalues exist as unique and convergent but likely infinite-length Laurent series. The eigenvectors can have an arbitrary phase response, and are shown to exist as convergent Laurent series if eigenvalues are selected as analytic functions on the unit circle, and if the phase response is selected such that the eigenvectors are Hölder continuous with α>½ on the unit circle. In the case of a discontinuous phase response or if spectral majorisation is enforced for intersecting eigenvalues, an absolutely convergent Laurent series solution for the eigenvectors of a parahermitian EVD does not exist. We provide some examples, comment on the approximation of a parahermitian matrix EVD by Laurent polynomial factors, and compare our findings to the solutions provided by polynomial matrix EVD algorithms

Melhoramento do cafeeiro: ênfase na aplicação dos marcadores moleculares.

O melhoramento genético de plantas constitui em metodologias para a criação, seleção e fixação de plantas contendo fenótipos superiores, visando o desenvolvimento de cultivares melhoradas para as necessidades dos agricultores e consumidores. Dessa forma, o melhoramento de plantas tem sido definido como ?a ciência e a arte de modificar as plantas em benefício da sociedade? ou ?a ciência, arte e o gerenciamento dos recursos visando o aperfeiçoamento das plantas para o benefício da sociedade?. Como arte, o melhoramento depende da intuição e das experiências passadas que são únicas para cada melhorista, e como ciência, depende dos princípios da agronomia, genética e outras ciências correlatas. No entanto, a tendência é aumentar a ?ciência? e depender menos da arte para tornar o processo cada vez mais eficiente. Dessa forma, o programa de melhoramento eficiente é aquele que, além da intuição do melhorista, se baseia no amplo conhecimento da cultura, biologia da planta, genética clássica, genética de populações, biometria e genética quantitativa, citogenética, genética molecular, fisiologia da planta e processo evolutivo da cultura

Photocatalytic degradation of eleven microcystin analogues and nodularin by TiO2 coated glass microspheres

Microcystins and nodularin are toxic cyanobacterial secondary metabolites produced by cyanobacteria that pose a threat to human health in drinking water. Conventional water treatment methods often fail to remove these toxins. Advanced oxidation processes such as TiO2 photocatalysis have been shown to effectively degrade these compounds. A particular issue that has limited the widespread application of TiO2 photocatalysis for water treatment has been the separation of the nanoparticulate powder from the treated water. A novel catalyst format, TiO2 coated hollow glass spheres (Photospheres™), is far more easily separated from treated water due to its buoyancy. This paper reports the photocatalytic degradation of eleven microcystin variants and nodularin in water using Photospheres™. It was found that the Photospheres™ successfully decomposed all compounds in 5min or less. This was found to be comparable to the rate of degradation observed using a Degussa P25 material, which has been previously reported to be the most efficient TiO2 for photocatalytic degradation of microcystins in water. Furthermore, it was observed that the degree of initial catalyst adsorption of the cyanotoxins depended on the amino acid in the variable positions of the microcystin molecule. The fastest degradation (2min) was observed for the hydrophobic variants (microcystin-LY, -LW, -LF). Suitability of UV-LEDs as an alternative low energy light source was also evaluated

Caracterização molecular de mutantes de bananeira da cv. terra por meio de marcadores ISSR.

A técnica de indução de mutação por irradiação tem sido muito empregada em programas de melhoramento de plantas visando a seleção de mutantes com características agronômicas desejáveis. Os marcadores moleculares são importantes ferramentas para a detecção dos efeitos da radiação gama com precisão, uma vez que, com o advento das técnicas modernas de biologia molecular, surgiram diversos métodos de detecção de polimorfismo genético direto; ou seja, em nível de DNA. O maior interesse na aplicação dos marcadores genéticos no melhoramento vegetal é a perspectiva de estabelecer ligações entre os marcadores e os genes que controlam determinada característica (OLIVEIRA et al., 1996).pdf 159

Analysis of broadband GEVD-based blind source separation

One approach to blind source separation of instantaneously mixed, non-stationary sources involves using the generalized eigenvalue decomposition of two estimated covariance matrices. The assumption is that the source statistics change with time whilst the mixing matrix does not. A recent generalisation of this approach to convolutive mixtures was achieved by extending the generalized eigenvalue decomposition to polynomial matrices. In this paper, we present a further investigation into this broadband BSS technique. We derive some expressions for the conditions under which source separation is possible. The validity of our analysis is illustrated through some computer simulations

Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"

In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R (z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow the notation in Weiss (2018)

Iterative approximation of analytic eigenvalues of a parahermitian matrix EVD

We present an algorithm that extracts analytic eigenvalues from a parahermitian matrix. Operating in the discrete Fourier transform domain, an inner iteration re-establishes the lost association between bins via a maximum likelihood sequence detection driven by a smoothness criterion. An outer iteration continues until a desired accuracy for the approximation of the extracted eigenvalues has been achieved. The approach is compared to existing algorithms

Improved diffuse fluorescence flow cytometer prototype for high sensitivity detection of rare circulating cells in vivo

Abstract. Detection and enumeration of rare circulating cells in mice are important problems in many areas of preclinical biomedical research. Recently, we developed a new method termed “diffuse fluorescence flow cytometry” (DFFC) that uses diffuse photons to increase the blood sampling volume and sensitivity versus existing in vivo flow cytometry methods. In this work, we describe a new DFFC prototype with approximately an order-of-magnitude improvement in sensitivity compared to our previous work. This sensitivity improvement is enabled by a number of technical innovations, which include a method for the removal of motion artifacts (allowing interrogation of mouse hindlegs that was less optically attenuating versus the tail) and improved collection optics and signal preamplification. We validated our system first in limb mimicking optical flow phantoms with fluorescent microspheres and then in nude mice with fluorescently labeled mesenchymal stem cells at injected concentrations of 5×103 cells/mL. In combination, these improvements resulted in an overall cell counting sensitivity of about 1 cell/mL or better in vivo

Impact of space-time covariance estimation errors on a parahermitian matrix EVD

This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations

Recent Advances in Soil Liquefaction Engineering and Seismic Site Response Evaluation

Over the past decade, major advances have occurred in both understanding and practice with regard to engineering treatment of seismic soil liquefaction and assessment of seismic site response. Seismic soil liquefaction engineering has evolved into a sub-field in its own right, and assessment and treatment of site effects affecting seismic site response has gone from a topic of controversy to a mainstream issue addressed in most modem building codes and addressed in both research and practice. This rapid evolution in the treatment of both liquefaction and site response issues has been pushed by a confluence of lessons and data provided by a series of earthquakes over the past eleven years, as well as by the research and professional/political will engendered by these major seismic events. Although the rate of progress has been laudable, further advances are occurring, and more remains to be done. As we enter a “new millenium”, engineers are increasingly well able to deal with important aspects of these two seismic problem areas. This paper will highlight a few major recent and ongoing developments in each of these two important areas of seismic practice, and will offer insights regarding work/research in progress, as well as suggestions regarding further advances needed. The first part of the paper will address soil liquefaction, and the second portion will (briefly) address engineering assessment of seismic site response