(Total) Vector Domination for Graphs with Bounded Branchwidth

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has at least $d(v)$ neighbors in $S$. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the $k$-tuple dominating set problem (this $k$ is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respectto $k$, where $k$ is the size of solution.Comment: 16 page

Space-optimal Heavy Hitters with Strong Error Bounds

The problem of finding heavy hitters and approximating the frequencies of items is at the heart of many problems in data stream analysis. It has been observed that several proposed solutions to this problem can outperform their worst-case guarantees on real data. This leads to the question of whether some stronger bounds can be guaranteed. We answer this in the positive by showing that a class of "counter-based algorithms" (including the popular and very space-efficient FREQUENT and SPACESAVING algorithms) provide much stronger approximation guarantees than previously known. Specifically, we show that errors in the approximation of individual elements do not depend on the frequencies of the most frequent elements, but only on the frequency of the remaining "tail." This shows that counter-based methods are the most space-efficient (in fact, space-optimal) algorithms having this strong error bound. This tail guarantee allows these algorithms to solve the "sparse recovery" problem. Here, the goal is to recover a faithful representation of the vector of frequencies, f. We prove that using space O(k), the algorithms construct an approximation f* to the frequency vector f so that the L1 error ||f -- f*||[subscript 1] is close to the best possible error min[subscript f2] ||f2 -- f||[subscript 1], where f2 ranges over all vectors with at most k non-zero entries. This improves the previously best known space bound of about O(k log n) for streams without element deletions (where n is the size of the domain from which stream elements are drawn). Other consequences of the tail guarantees are results for skewed (Zipfian) data, and guarantees for accuracy of merging multiple summarized streams.David & Lucile Packard Foundation (Fellowship)Center for Massive Data Algorithmics (MADALGO)National Science Foundation (U.S.). (Grant number CCF-0728645

A Genome-Wide Association Study of Diabetic Kidney Disease in Subjects With Type 2 Diabetes

dentification of sequence variants robustly associated with predisposition to diabetic kidney disease (DKD) has the potential to provide insights into the pathophysiological mechanisms responsible. We conducted a genome-wide association study (GWAS) of DKD in type 2 diabetes (T2D) using eight complementary dichotomous and quantitative DKD phenotypes: the principal dichotomous analysis involved 5,717 T2D subjects, 3,345 with DKD. Promising association signals were evaluated in up to 26,827 subjects with T2D (12,710 with DKD). A combined T1D+T2D GWAS was performed using complementary data available for subjects with T1D, which, with replication samples, involved up to 40,340 subjects with diabetes (18,582 with DKD). Analysis of specific DKD phenotypes identified a novel signal near GABRR1 (rs9942471, P = 4.5 x 10(-8)) associated with microalbuminuria in European T2D case subjects. However, no replication of this signal was observed in Asian subjects with T2D or in the equivalent T1D analysis. There was only limited support, in this substantially enlarged analysis, for association at previously reported DKD signals, except for those at UMOD and PRKAG2, both associated with estimated glomerular filtration rate. We conclude that, despite challenges in addressing phenotypic heterogeneity, access to increased sample sizes will continue to provide more robust inference regarding risk variant discovery for DKD.Peer reviewe

Polymorphism in a T-cell receptor variable gene is associated with susceptibility to a juvenile rheumatoid arthritis subset

This report demonstrates a T-cell receptor (Tcr) restriction fragment length polymorphism, defined by a Tcrb-V6.1 gene probe and Bgl II restriction enzyme, to be absolutely correlated with allelic variation in the coding sequence of a Tcrb-V6.1 gene. A pair of non-conservative amino acid substitutions distinguish the Tcrb-V6.1 allelic variants. An association of this Tcrb-V6.1 gene allelic variant with one form of juvenile rheumatoid arthritis (JRA) was established in a cohort of 126 patients. The association was observed in patients possessing the HLA-DQA1*0101 gene. Among HLA-DQA*0101 individuals, 19 of 26 patients (73.1%) carried one particular Tcrb-V6.1 gene allele as opposed to 11 of 33 controls (33%; p<0.005). Haplotypes carrying this HLA gene have previously been shown to confer increased risk for progression of arthritis in JRA. This demonstration of a disease-associated Tcrb-V gene allelic variant has not, to our knowledge, been previously reported and supports the contribution of polymorphism in the Tcr variable region genomic repertoire to human autoimmune disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46750/1/251_2004_Article_BF00166831.pd