Canonical forms for complex matrix congruence and *congruence

Canonical forms for congruence and *congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347-353], based on Sergeichuk's paper [Math. USSR, Izvestiya 31 (3) (1988) 481-501], which employed the theory of representations of quivers with involution. We use standard methods of matrix analysis to prove directly that these forms are canonical. Our proof provides explicit algorithms to compute all the blocks and parameters in the canonical forms. We use these forms to derive canonical pairs for simultaneous congruence of pairs of complex symmetric and skew-symmetric matrices as well as canonical forms for simultaneous *congruence of pairs of complex Hermitian matrices.Comment: 31 page

A regularization algorithm for matrices of bilinear and sesquilinear forms

We give an algorithm that uses only unitary transformations and for each square complex matrix constructs a *congruent matrix that is a direct sum of a nonsingular matrix and singular Jordan blocks.Comment: 18 page

Closed formula for the relative entropy of entanglement in all dimensions

The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed formula for all the entangled state for which this state is a CSS. Quite amazing, our formula holds for multipartite states in all dimensions. In addition we show that if an entangled state is full rank, then its CSS is unique. For the bipartite case of two qubits our formula reduce to the one given in Phys. Rev. A 78, 032310 (2008).Comment: 8 pages, 1 figure, significantly revised; theorem 1 is now providing necessary and sufficient conditions to determine if a state is CS

Constructed wetlands: Treatment of concentrated storm water runoff (part A)

The aim of this research was to assess the treatment efficiencies for gully pot liquor of experimental vertical- flow constructed wetland filters containing Phragmites australis (Cav.) Trin. ex Steud. (common reed) and filter media of different adsorption capacities. Six out of 12 filters received inflow water spiked with metals. For 2 years, hydrated nickel and copper nitrate were added to sieved gully pot liquor to simulate contaminated primary treated storm runoff. For those six constructed wetland filters receiving heavy metals, an obvious breakthrough of dissolved nickel was recorded after road salting during the first winter. However, a breakthrough of nickel was not observed, since the inflow pH was raised to eight after the first year of operation. High pH facilitated the formation of particulate metal compounds such as nickel hydroxide. During the second year, reduction efficiencies of heavy metal, 5-days at 20°C N-Allylthiourea biochemical oxygen demand (BOD) and suspended solids (SS) improved considerably. Concentrations of BOD were frequently �20 mg/L. However, concentrations for SS were frequently �30 mg/L. These are the two international thresholds for secondary wastewater treatment. The BOD removal increased over time due to biomass maturation, and the increase of pH. An analysis of the findings with case-based reasoning can be found in the corresponding follow-up paper (Part B)

Representations of quivers and mixed graphs

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The notion of quiver representations is extended to representations of mixed graphs, which permits one to study systems of linear mappings and bilinear or sesquilinear forms. The problem of classifying such systems is reduced to the problem of classifying systems of linear mappings

Genes involved in barley yellow dwarf virus resistance of maize

KEY MESSAGE: The results of our study suggest that genes involved in general resistance mechanisms of plants contribute to variation of BYDV resistance in maize. ABSTRACT: With increasing winter temperatures in Europe, Barley yellow dwarf virus (BYDV) is expected to become a prominent problem in maize cultivation. Breeding for resistance is the best strategy to control the disease and break the transmission cycle of the virus. The objectives of our study were (1) to determine genetic variation with respect to BYDV resistance in a broad germplasm set and (2) to identify single nucleotide polymorphism (SNP) markers linked to genes that are involved in BYDV resistance. An association mapping population with 267 genotypes representing the world’s maize gene pool was grown in the greenhouse. Plants were inoculated with BYDV-PAV using viruliferous Rhopalosiphum padi. In the association mapping population, we observed considerable genotypic variance for the trait virus extinction as measured by double antibody sandwich enzyme-linked immunosorbent assay (DAS-ELISA) and the infection rate. In a genome-wide association study, we observed three SNPs significantly [false discovery rate (FDR) = 0.05] associated with the virus extinction on chromosome 10 explaining together 25 % of the phenotypic variance and five SNPs for the infection rate on chromosomes 4 and 10 explaining together 33 % of the phenotypic variance. The SNPs significantly associated with BYDV resistance can be used in marker assisted selection and will accelerate the breeding process for the development of BYDV resistant maize genotypes. Furthermore, these SNPs were located within genes which were in other organisms described to play a role in general resistance mechanisms. This suggests that these genes contribute to variation of BYDV resistance in maize. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00122-014-2400-1) contains supplementary material, which is available to authorized users

Taking Stock of Retirement: How Workers and Employers Assess Pensions, Trust, and the Economy

This survey polls workers and employers regarding their views on corporate scandals and the collapse of Enron, the impact of these events on trust in the workplace, and policy strategies needed to increase pension and retirement security

Improved transfer of quantum information using a local memory

We demonstrate that the quantum communication between two parties can be significantly improved if the receiver is allowed to store the received signals in a quantum memory before decoding them. In the limit of an infinite memory, the transfer is perfect. We prove that this scheme allows the transfer of arbitrary multipartite states along Heisenberg chains of spin-1/2 particles with random coupling strengths.Comment: 4 pages, 1 figure; added references to homogenization and asymptotic completenes

The Disposable Worker: Living in a Job-Loss Economy

This important survey finds many U.S. workers have experienced job loss and the pinch of economic uncertainty during the 2000-2003 recession. The survey includes a large sample of workers who lost their jobs. The survey shows that many workers were laid off without any advance notice, severance pay, health care coverage, or career counseling. However, large numbers of workers believe these services and benefits are critical to their economic survival. Worker confidence in the U.S. economy and political leadership were at the lowest levels recorded in the history of the then six-year Work Trends series

Cromakalim (BRL 34915) restores in vitro the membrane potential of depolarized human skeletal muscle fibres

The purpose of the present study was to analyze the effects of cromakalim (BRL 34915), a potent drug from a new class of drugs characterized as K+ channel openers, on the electrical activity of human skeletal muscle. Therefore, intracellular recordings were used to measure the effects of cromakalim on the membrane potential and input conductance of fibres from human skeletal muscle biopsies. Cromakalim in a concentration above 1 mol/l induced an increase in membrane K+ conductance. This effect resulted in a membrane hyperpolarization. The magnitude of this polarization depended on the difference between resting and K+ equilibrium potential. The effect had a rapid onset and was quickly reversible after washing. Fibres from two patients with hyperkalaemic periodic paralysis showed an excessive membrane depolarization during and also after exposure to an slightly elevated extracellular K+ concentration. In the latter situation, cromakalim repolarized the fibres to the normal resting potential. Tolbutamide (1 mmol/l) and Ba2+ (3 mmol/l) strongly antagonized the effect of cromakalim. The data show that cromakalim hyperpolarizes depolarized human skeletal muscle fibres maintained in vitro. The underlying mechanism is probably an activation of otherwise silent, ATP-regulated K+ channels. Such an effect may be of therapeutic benefit in a situation in which a membrane depolarization causes muscle paralysis