Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Fast Algorithms for Join Operations on Tree Decompositions

Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on graphs of bounded treewidth mostly are dynamic programming algorithms using the structure of a tree decomposition of the graph. The bottleneck in the worst-case run time of these algorithms often is the computations for the so called join nodes in the associated nice tree decomposition. In this paper, we review two different approaches that have appeared in the literature about computations for the join nodes: one using fast zeta and M\"obius transforms and one using fast Fourier transforms. We combine these approaches to obtain new, faster algorithms for a broad class of vertex subset problems known as the [\sigma,\rho]-domination problems. Our main result is that we show how to solve [\sigma,\rho]-domination problems in $O(s^{t+2} t n^2 (t\log(s)+\log(n)))$ arithmetic operations. Here, t is the treewidth, s is the (fixed) number of states required to represent partial solutions of the specific [\sigma,\rho]-domination problem, and n is the number of vertices in the graph. This reduces the polynomial factors involved compared to the previously best time bound (van Rooij, Bodlaender, Rossmanith, ESA 2009) of $O( s^{t+2} (st)^{2(s-2)} n^3 )$ arithmetic operations. In particular, this removes the dependence of the degree of the polynomial on the fixed number of states~$s$.Comment: An earlier version appeared in "Treewidth, Kernels, and Algorithms. Essays Dedicated to Hans L. Bodlaender on the Occasion of His 60th Birthday" LNCS 1216

A comprehensive 1000 Genomes-based genome-wide association meta-analysis of coronary artery disease

Existing knowledge of genetic variants affecting risk of coronary artery disease (CAD) is largely based on genome-wide association studies (GWAS) analysis of common SNPs. Leveraging phased haplotypes from the 1000 Genomes Project, we report a GWAS meta-analysis of 185 thousand CAD cases and controls, interrogating 6.7 million common (MAF>0.05) as well as 2.7 million low frequency (0.005<MAF<0.05) variants. In addition to confirmation of most known CAD loci, we identified 10 novel loci, eight additive and two recessive, that contain candidate genes that newly implicate biological processes in vessel walls. We observed intra-locus allelic heterogeneity but little evidence of low frequency variants with larger effects and no evidence of synthetic association. Our analysis provides a comprehensive survey of the fine genetic architecture of CAD showing that genetic susceptibility to this common disease is largely determined by common SNPs of small effect siz

Sarcolemma-localized nNOS is required to maintain activity after mild exercise

Many neuromuscular conditions are characterized by an exaggerated exercise- induced fatigue response that is disproportionate to activity level. This fatigue is not necessarily correlated with greater central or peripheral fatigue in patients(1), and some patients experience severe fatigue without any demonstrable somatic disease(2). Except in myopathies that are due to specific metabolic defects, the mechanism underlying this type of fatigue remains unknown(2). With no treatment available, this form of inactivity is a major determinant of disability(3). Here we show, using mouse models, that this exaggerated fatigue response is distinct from a loss in specific force production by muscle, and that sarcolemma-localized signalling by neuronal nitric oxide synthase ( nNOS) in skeletal muscle is required to maintain activity after mild exercise. We show that nNOS- null mice do not have muscle pathology and have no loss of muscle- specific force after exercise but do display this exaggerated fatigue response to mild exercise. In mouse models of nNOS mislocalization from the sarcolemma, prolonged inactivity was only relieved by pharmacologically enhancing the cGMP signal that results from muscle nNOS activation during the nitric oxide signalling response to mild exercise. Our findings suggest that the mechanism underlying the exaggerated fatigue response to mild exercise is a lack of contraction- induced signalling from sarcolemma- localized nNOS, which decreases cGMP- mediated vasomodulation in the vessels that supply active muscle after mild exercise. Sarcolemmal nNOS staining was decreased in patient biopsies from a large number of distinct myopathies, suggesting a common mechanism of fatigue. Our results suggest that patients with an exaggerated fatigue response to mild exercise would show clinical improvement in response to treatment strategies aimed at improving exercise- induced signalling.Paul D. Wellstone Muscular Dystrophy Cooperative Research Center Grant ; University of Iowa Cardiovascular Interdisciplinary Research ; National Research Service Award ; National Institute of Arthritis and Musculoskeletal and Skin Diseases ; National Institutes of Health ; Senator Paul D. Wellstone Fellowship ; Muscular Dystrophy Association Development Grant ; Howard Hughes Medical InstituteWe thank M. Anderson and M. Henry for comments, and M. M. Kilburg, K. Uppal, B. J. Steinmann and S. Watkins and members of the Campbell laboratory for scientific contributions. This work was supported in part by a Paul D. Wellstone Muscular Dystrophy Cooperative Research Center Grant. Y.M.K. was supported by grants from the University of Iowa Cardiovascular Interdisciplinary Research/ National Research Service Award (NRSA) Fellowship, from an individual NRSA Fellowship from the National Institute of Arthritis and Musculoskeletal and Skin Diseases, from the National Institutes of Health (NIH), and from a Senator Paul D. Wellstone Fellowship. E.P.R. was supported by a Muscular Dystrophy Association Development Grant. R.M.W. was supported by the NIH. K.P.C. is an investigator of the Howard Hughes Medical Institute.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62850/1/nature07414.pd

How well do blood folate concentrations predict dietary folate intakes in a sample of Canadian lactating women exposed to high levels of folate? An observational study

<p>Abstract</p> <p>Background</p> <p>In 1998, mandatory folic acid fortification of white flour and select cereal grain products was implemented in Canada with the intention to increase dietary folate intakes of reproducing women. Folic acid fortification has produced a dramatic increase in blood folate concentrations among reproductive age women, and a reduction in neural tube defect (NTD)-affected pregnancies. In response to improved blood folate concentrations, many health care professionals are asking whether a folic acid supplement is necessary for NTD prevention among women with high blood folate values, and how reliably high RBC folate concentrations predict folate intakes shown in randomized controlled trials to be protective against NTDs. The objective of this study was to determine how predictive blood folate concentrations and folate intakes are of each other in a sample of well-educated lactating Canadian women exposed to high levels of synthetic folate.</p> <p>Methods</p> <p>The relationship between blood folate concentrations and dietary folate intakes, determined by weighed food records, were assessed in a sample of predominantly university-educated lactating women (32 ± 4 yr) at 4-(n = 53) and 16-wk postpartum (n = 55).</p> <p>Results</p> <p>Median blood folate concentrations of all participants were well above plasma and RBC folate cut-off levels indicative of deficiency (6.7 and 317 nmol/L, respectively) and all, except for 2 subjects, were above the cut-off for NTD-risk reduction (>906 nmol/L). Only modest associations existed between total folate intakes and plasma (r = 0.46, <it>P </it>< 0.001) and RBC (r = 0.36, <it>P </it>< 0.01) folate concentrations at 16-wk postpartum. Plasma and RBC folate values at 16-wk postpartum correctly identified the quartile of folate intake of only 26 of 55 (47%) and 18 of 55 (33%) of subjects, respectively. The mean RBC folate concentration of women consuming 151–410 μg/d of synthetic folate (2^ndquartile of intake) did not differ from that of women consuming >410 μg/d (3^rdand 4^thquartile).</p> <p>Conclusion</p> <p>Folate intakes, estimated by food composition tables, and blood folate concentrations are not predictive of each other in Canadian lactating women exposed to high levels of folate. Synthetic intakes > 151–410 μg/d in these women produced little additional benefit in terms of maximizing RBC content. More studies are needed to examine the relationship between blood folate concentration and NTD risk. Until data from such studies are available, women planning a pregnancy should continue to consume a daily folic acid supplement of 400 μg.</p

Acute-Phase-HDL Remodeling by Heparan Sulfate Generates a Novel Lipoprotein with Exceptional Cholesterol Efflux Activity from Macrophages

During episodes of acute-inflammation high-density lipoproteins (HDL), the carrier of so-called good cholesterol, experiences a major change in apolipoprotein composition and becomes acute-phase HDL (AP-HDL). This altered, but physiologically important, HDL has an increased binding affinity for macrophages that is dependent on cell surface heparan sulfate (HS). While exploring the properties of AP-HDL∶HS interactions we discovered that HS caused significant remodeling of AP-HDL. The physical nature of this change in structure and its potential importance for cholesterol efflux from cholesterol-loaded macrophages was therefore investigated. In the presence of heparin, or HS, AP-HDL solutions at pH 5.2 became turbid within minutes. Analysis by centrifugation and gel electrophoresis indicated that AP-HDL was remodeled generating novel lipid poor particles composed only of apolipoprotein AI, which we designate β2. This remodeling is dependent on pH, glycosaminoglycan type, is promoted by Ca2+ and is independent of protease or lipase activity. Compared to HDL and AP-HDL, remodeled AP-HDL (S-HDL-SAA), containing β2 particles, demonstrated a 3-fold greater cholesterol efflux activity from cholesterol-loaded macrophage. Because the identified conditions causing this change in AP-HDL structure and function can exist physiologically at the surface of the macrophage, or in its endosomes, we postulate that AP-HDL contains latent functionalities that become apparent and active when it associates with macrophage cell surface/endosomal HS. In this way initial steps in the reverse cholesterol transport pathway are focused at sites of injury to mobilize cholesterol from macrophages that are actively participating in the phagocytosis of damaged membranes rich in cholesterol. The mechanism may also be of relevance to aspects of atherogenesis

The Crystal Structure of the Escherichia coli Autoinducer-2 Processing Protein LsrF

Many bacteria produce and respond to the quorum sensing signal autoinducer-2 (AI-2). Escherichia coli and Salmonella typhimurium are among the species with the lsr operon, an operon containing AI-2 transport and processing genes that are up regulated in response to AI-2. One of the Lsr proteins, LsrF, has been implicated in processing the phosphorylated form of AI-2. Here, we present the structure of LsrF, unliganded and in complex with two phospho-AI-2 analogues, ribose-5-phosphate and ribulose-5-phosphate. The crystal structure shows that LsrF is a decamer of (αβ)8-barrels that exhibit a previously unseen N-terminal domain swap and have high structural homology with aldolases that process phosphorylated sugars. Ligand binding sites and key catalytic residues are structurally conserved, strongly implicating LsrF as a class I aldolase

Computational Lipidology: Predicting Lipoprotein Density Profiles in Human Blood Plasma

Monitoring cholesterol levels is strongly recommended to identify patients at risk for myocardial infarction. However, clinical markers beyond “bad” and “good” cholesterol are needed to precisely predict individual lipid disorders. Our work contributes to this aim by bringing together experiment and theory. We developed a novel computer-based model of the human plasma lipoprotein metabolism in order to simulate the blood lipid levels in high resolution. Instead of focusing on a few conventionally used predefined lipoprotein density classes (LDL, HDL), we consider the entire protein and lipid composition spectrum of individual lipoprotein complexes. Subsequently, their distribution over density (which equals the lipoprotein profile) is calculated. As our main results, we (i) successfully reproduced clinically measured lipoprotein profiles of healthy subjects; (ii) assigned lipoproteins to narrow density classes, named high-resolution density sub-fractions (hrDS), revealing heterogeneous lipoprotein distributions within the major lipoprotein classes; and (iii) present model-based predictions of changes in the lipoprotein distribution elicited by disorders in underlying molecular processes. In its present state, the model offers a platform for many future applications aimed at understanding the reasons for inter-individual variability, identifying new sub-fractions of potential clinical relevance and a patient-oriented diagnosis of the potential molecular causes for individual dyslipidemia