Accurate SVDs of weakly diagonally dominant M-matrices

Summary. We present a new O(n³) algorithm which computes the SVD of a weakly diagonally dominant M-matrix to high relative accuracy. The algorithm takes as an input the offdiagonal entries of the matrix and its row sums.Mathematics Subject Classification (1991): 65F15Revised version received September 19, 2003This material is based in part upon work supported by the LLNL Memorandum Agreement No. B504962 under DOE Contract No. W-7405-ENG-48, DOE Grants No. DE-FG03-94ER25219, DE-FC03-98ER25351 and DE-FC02-01ER25478, NSF Grant No. ASC-9813362, and Cooperative Agreement No. ACI-9619020.     

q-Blossoming for analytic functions

Numerical Algorithms - We construct a q-analog of the blossom for analytic functions, the analytic q-blossom. This q-analog also extends the notion of q-blossoming from polynomials to analytic...     

On a Two-Variable Class of Bernstein–Szegő Measures

The one-variable Bernstein–Szegő theory for orthogonal polynomials on the real line is extended to a class of two-variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.      

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

New class of level statistics in correlated disordered chains

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.     

Enhanced specificity of bacterial spore identification by oxidation and mass spectrometry

Addition of an oxidizing agent (e.g., hydrogen peroxide) to intact spores selectively and completely oxidizes Met-containing biomarker proteins by formation of Met sulfoxides. This reaction increases the masses of the biomarker proteins observed in matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of Bacillus spores by Deltam = (16 x n) Da, where n is the number of Met residues in the sequence of each individual protein. The procedure is very rapid, and can be performed in situ (i.e., on the MALDI target). It confirms the identity of individual biomarkers by comparing the number of Met amino acids from the experimentally determined mass shifts with predictions for n from the tentative amino acid sequence for each protein. In turn, accurate determination of n for several biomarkers allows rapid validation of the initial spore identification by MALDI-MS.     

Observations on toxicologically relevant arsenic in urine in adult offspring of families with Balkan Endemic Nephropathy and controls by batch hydride generation atomic absorption spectrometry

The aim of this study was to develop a method for the characterization of internal exposure to arsenic, which is thought to play a role in the development of a kidney disease, known as Balkan Endemic Nephropathy, typical for a district in Bulgaria, and to investigate whether the As body burden differs in the offspring versus control individuals. For this case study, an analytical procedure for the determination of toxicologically relevant arsenic (the sum of arsenite, arsenate, monomethylarsonate, and dimethylarsinate) in urine by batch-type hydride generation atomic absorption spectrometry was developed. Optimization experiments for levelling off the sensitivity of inorganic arsenic and its mono- and dimethylated species in dilute HCl–L-cysteine medium were performed. The limit of detection for hydride forming arsenic fraction was 0.5?ng As, i.e. 0.25?µg?L^?1 in 10?mL of 1?+?4 v/v diluted urine. The relative standard deviation was typically 1.5–1.8% for aqueous solution and 2–6% for urine samples at 1.0?µg?L^?1 As. The sample throughput rate was 15?h^?1. No statistical correlation and cross-correlation between individuals case-control and sex at 95% confidence were found: controls (n?=?99), mean 3.5?±?2.1 (SD), range 0.9–10.4, median 3.0?µg?L^?1 As and cases (n?=?102), mean 3.6?±?2.2 (SD), range 0.5–11.0, median 3.2?µg?L^?1 As. On the basis of this study, arsenic can be excluded as a factor involved in BEN development.