Exceptional sets for Diophantine inequalities

We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c

On the Distribution of Generating Functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135518/1/blms0113.pd

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

Number fields and function fields:Coalescences, contrasts and emerging applications

The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field. Although an active area of interaction for the past half century at least, the language and techniques used in analytic number theory and in the function field setting are quite different, and this has frustrated interchanges between the two areas. This situation is currently changing, and there has been substantial progress on a number of problems stimulated by bringing together ideas from each field. We here introduce the papers published in this Theo Murphy meeting issue, where some of the recent developments are explained

Some remarks on Vinogradov's mean value theorem and Tarry's problem

Let W(k, 2) denote the, least number s for which the system of equations has a solution with . We show that for large k one has W(k, 2)≦1/2k 2 (log k +loglog k + O (1)), and moreover that when K is large, one has W(k, 2)≦1/2k(k+1)+1 for at least one value k in the interval [ K, K 3/4+ε ]. We show also that the least s for which the expected asymptotic formula holds for the number of solutions of the above system of equations, inside a box, satisfies s ≦ k 2 (log k + O (loglog k ).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41627/1/605_2005_Article_BF01320189.pd

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p -adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42604/1/10599_2004_Article_334960.pd

Unbiased taxonomic annotation of metagenomic samples

The classification of reads from a metagenomic sample using a reference taxonomy is usually based on first mapping the reads to the reference sequences and then classifying each read at a node under the lowest common ancestor of the candidate sequences in the reference taxonomy with the least classification error. However, this taxonomic annotation can be biased by an imbalanced taxonomy and also by the presence of multiple nodes in the taxonomy with the least classification error for a given read. In this article, we show that the Rand index is a better indicator of classification error than the often used area under thereceiver operating characteristic (ROC) curve andF-measure for both balanced and imbalanced reference taxonomies, and we also address the second source of bias by reducing the taxonomic annotation problem for a whole metagenomic sample to a set cover problem, for which a logarithmic approximation can be obtained in linear time and an exact solution can be obtained by integer linear programming. Experimental results with a proof-of-concept implementation of the set cover approach to taxonomic annotation in a next release of the TANGO software show that the set cover approach further reduces ambiguity in the taxonomic annotation obtained with TANGO without distorting the relative abundance profile of the metagenomic sample.Peer ReviewedPostprint (published version

Simultaneous genome sequencing of symbionts and their hosts

Second-generation sequencing has made possible the sequencing of genomes of interest for even small research groups. However, obtaining separate clean cultures and clonal or inbred samples of metazoan hosts and their bacterial symbionts is often difficult. We present a computational pipeline for separating metazoan and bacterial DNA in silico rather than at the bench. The method relies on the generation of deep coverage of all the genomes in a mixed sample using Illumina short-read sequencing technology, and using aggregate properties of the different genomes to identify read sets belonging to each. This inexpensive and rapid approach has been used to sequence several nematode genomes and their bacterial endosymbionts in the last year in our laboratory and can also be used to visualize and identify unexpected contaminants (or possible symbionts) in genomic DNA samples. We hope that this method will enable researchers studying symbiotic systems to move from gene-centric to genome-centric approaches

Structure of the first representative of Pfam family PF04016 (DUF364) reveals enolase and Rossmann-like folds that combine to form a unique active site with a possible role in heavy-metal chelation.

The crystal structure of Dhaf4260 from Desulfitobacterium hafniense DCB-2 was determined by single-wavelength anomalous diffraction (SAD) to a resolution of 2.01 Å using the semi-automated high-throughput pipeline of the Joint Center for Structural Genomics (JCSG) as part of the NIGMS Protein Structure Initiative (PSI). This protein structure is the first representative of the PF04016 (DUF364) Pfam family and reveals a novel combination of two well known domains (an enolase N-terminal-like fold followed by a Rossmann-like domain). Structural and bioinformatic analyses reveal partial similarities to Rossmann-like methyltransferases, with residues from the enolase-like fold combining to form a unique active site that is likely to be involved in the condensation or hydrolysis of molecules implicated in the synthesis of flavins, pterins or other siderophores. The genome context of Dhaf4260 and homologs additionally supports a role in heavy-metal chelation

The structure of BVU2987 from Bacteroides vulgatus reveals a superfamily of bacterial periplasmic proteins with possible inhibitory function.

Proteins that contain the DUF2874 domain constitute a new Pfam family PF11396. Members of this family have predominantly been identified in microbes found in the human gut and oral cavity. The crystal structure of one member of this family, BVU2987 from Bacteroides vulgatus, has been determined, revealing a β-lactamase inhibitor protein-like structure with a tandem repeat of domains. Sequence analysis and structural comparisons reveal that BVU2987 and other DUF2874 proteins are related to β-lactamase inhibitor protein, PepSY and SmpA_OmlA proteins and hence are likely to function as inhibitory proteins