Robust Mixing for Ab-Initio Quantum Mechanical Calculations

We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent field equations of Kohn-Sham density functional theory. The algorithm is robust, requires relatively little finetuning and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.Comment: 32 Pages, 4 figure

Simple sequence repeat variation in the Daphnia pulex genome

Background: Simple sequence repeats (SSRs) are highly variable features of all genomes. Their rapid evolution makes them useful for tracing the evolutionary history of populations and investigating patterns of selection and mutation across gnomes. The recently sequenced Daphnia pulex genome provides us with a valuable data set to study the mode and tempo of SSR evolution, without the inherent biases that accompany marker selection. Results: Here we catalogue SSR loci in the Daphnia pulex genome with repeated motif sizes of 1-100 nucleotides with a minimum of 3 perfect repeats. We then used whole genome shotgun reads to determine the average heterozygosity of each SSR type and the relationship that it has to repeat number, motif size, motif sequence, and distribution of SSR loci. We find that SSR heterozygosity is motif specific, and positively correlated with repeat number as well as motif size. For non-repeat unit polymorphisms, we identify a motif-dependent end-nucleotide polymorphism bias that may contribute to the patterns of abundance for specific homopolymers, dimers, and trimers. Our observations confirm the high frequency of multiple unit variation (multistep) at large microsatellite loci, and further show that the occurrence of multiple unit variation is dependent on both repeat number and motif size. Using the Daphnia pulex genetic map, we show a positive correlation between dimer and trimer frequency and recombination. Conclusions: This genome-wide analysis of SSR variation in Daphnia pulex indicates that several aspects of SSR variation are motif dependent and suggests that a combination of unit length variation and end repeat biased base substitution contribute to the unique spectrum of SSR repeat loci

Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of these measures and the logarithmic capacity of their support. Since our approach is based on a reversible transformation between pairs of Jacobi matrices, we also discuss its application to an inverse / approximation problem. Numerical experiments show that the proposed algorithms are stable and can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure

Phase II trial of the regulatory T cell-depleting agent, denileukin diftitox, in patients with unresectable stage IV melanoma

<p>Abstract</p> <p>Background</p> <p>We previously found that administration of an interleukin 2/diphtheria toxin conjugate (DAB/IL2; Denileukin Diftitox; ONTAK) to stage IV melanoma patients depleted CD4⁺CD25^HIFoxp3⁺regulatory T cells and expanded melanoma-specific CD8⁺T cells. The goal of this study was to assess the clinical efficacy of DAB/IL2 in an expanded cohort of stage IV melanoma patients.</p> <p>Methods</p> <p>In a single-center, phase II trial, DAB/IL2 (12 μg/kg; 4 daily doses; 21 day cycles) was administered to 60 unresectable stage IV melanoma patients and response rates were assessed using a combination of 2-[¹⁸F]-fluoro-2-deoxy-glucose (FDG)-positron emission tomography (PET) and computed tomography (CT) imaging.</p> <p>Results</p> <p>After DAB/IL2 administration, 16.7% of the 60 patients had partial responses, 5% stable disease and 15% mixed responses. Importantly, 45.5% of the chemo/immuno-naïve sub-population (11/60 patients) experienced partial responses. One year survival was markedly higher in partial responders (80 ± 11.9%) relative to patients with progressive disease (23.7 ± 6.5%; <it>p </it>value < 0.001) and 40 ± 6.2% of the total DAB/IL2-treated population were alive at 1 year.</p> <p>Conclusions</p> <p>These data support the development of multi-center, randomized trials of DAB/IL2 as a monotherapy and in combination with other immunotherapeutic agents for the treatment of stage IV melanoma.</p> <p>Trial registration</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT00299689">NCT00299689</a></p

On computing accurate singular values and eigenvalues of acyclic matrices

It is known that small relative perturbations in the entries of a bidiagonal matrix only cause small relative perturbations in its singular values, independent of the values of the matrix entries. In this paper we show that a matrix has this property if and only if its associated bipartite graph is acyclic. We also show how to compute the singular values of such a matrix to high relative accuracy. The same algorithm can compute eigenvalues of symmetric acyclic matrices with tiny component-wise relative backward error. This class includes tridragonal matfices, arrow matrices, and exponentially many othershttp://archive.org/details/oncomputingaccur00demmN

A stable variant of the secant method for solving nonlinear equations

Computer Science Departmen