Complexity of linear circuits and geometry

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expected to have super-linear rigidity, and (iv) prove results about the ideals and degrees of cones that are of interest in their own right.Comment: 29 pages, final version to appear in FOC

Antioxidant supplementation during early development reduces parasite load but does not affect sexual ornament expression in adult ring-necked pheasants Phasianus colchicus

ArticleCopyright © 2012 The Authors. Functional Ecology © 2012 British Ecological Society1. The ‘parasite-mediated sexual selection’ (PMSS) hypothesis predicts that exaggerated male ornamentation could provide a signal to females of a males ability to resist parasites. Empirical tests of the PMSS have been largely equivocal, however, which may be because most have not considered the role of early life-history effects. 2. Many sexually-selected traits are carotenoid-based. Allocation of dietary-derived carotenoids to sexual ornaments may trade-off with allocation to pro-inflammatory immune response and/or antioxidant functions, mediated by the oxidative status of individuals. Exposure to parasites can increase oxidative stress, so under this scenario sexually-selected traits indicate ability to resist oxidative stress rather than ability to resist parasites per se. Such life-history trade-offs, mediated by oxidative status of individuals, are particularly acute during growth and development. 3. Here we use ring-necked pheasants, Phasianus colchicus, a strongly sexually-selected species, to test whether supplementation with dietary antioxidants (vitamin E) can mitigate the effects of early exposure to parasites (the nematode, Heterakis gallinarum), via alteration of the oxidative status of individuals, and positively affect the expression of sexual ornaments at adulthood. 4. We found that vitamin E mediated the effect of early exposure to parasites on levels of oxidative damage at 8 weeks of age and reduced the parasite load of individuals at adulthood as predicted. However, the expression of sexual ornaments, immune function, and growth were unaffected by either early vitamin E supplementation or manipulation of parasite load. In contrast to the predictions of the PMSS hypothesis the intensity of sexual ornament expression was not related to either parasite load or oxidative status of individuals (current or long-term). Consequently there was no evidence that the expression of sexual ornaments provided information on the ability of males to resist infection from parasites.NERCRoyal Societ

Effect of carbohydrate feeding on the bone metabolic response to running

Bone resorption is increased after running, with no change in bone formation. Feeding during exercise might attenuate this increase, preventing associated problems for bone. This study investigated the immediate and short-term bone metabolic responses to carbohydrate (CHO) feeding during treadmill running. Ten men completed two 7-day trials, once being fed CHO (8% glucose immediately before, every 20 min during, and immediately after exercise at a rate of 0.7 g CHO·kg body mass-1·h-1) and once being fed placebo (PBO). On day 4 of each trial, participants completed a 120-min treadmill run at 70% of maximal oxygen consumption (VO2 max). Blood was taken at baseline (BASE), immediately after exercise (EE), after 60 (R1) and 120 (R2) min of recovery, and on three follow-up days (FU1-FU3). Markers of bone resorption [COOH-terminal telopeptide region of collagen type 1 (β-CTX)] and formation [NH2-terminal propeptides of procollagen type 1 (P1NP)] were measured, along with osteocalcin (OC), parathyroid hormone (PTH), albumin-adjusted calcium (ACa), phosphate, glucagon-like peptide-2 (GLP-2), interleukin-6 (IL-6), insulin, cortisol, leptin, and osteoprotogerin (OPG). Area under the curve was calculated in terms of the immediate (BASE, EE, R1, and R2) and short-term (BASE, FU1, FU2, and FU3) responses to exercise. β-CTX, P1NP, and IL-6 responses to exercise were significantly lower in the immediate postexercise period with CHO feeding compared with PBO (β-CTX: P=0.028; P1NP: P=0.021; IL-6: P=0.036), although there was no difference in the short-term response (β-CTX: P=0.856; P1NP: P=0.721; IL-6: P=0.327). No other variable was significantly affected by CHO feeding during exercise. We conclude that CHO feeding during exercise attenuated the β-CTX and P1NP responses in the hours but not days following exercise, indicating an acute effect of CHO feeding on bone turnover

Inference of haplotypic phase and missing genotypes in polyploid organisms and variable copy number genomic regions

Background: The power of haplotype-based methods for association studies, identification of regions under selection, and ancestral inference, is well-established for diploid organisms. For polyploids, however, the difficulty of determining phase has limited such approaches. Polyploidy is common in plants and is also observed in animals. Partial polyploidy is sometimes observed in humans (e.g. trisomy 21; Down's syndrome), and it arises more frequently in some human tissues. Local changes in ploidy, known as copy number variations (CNV), arise throughout the genome. Here we present a method, implemented in the software polyHap, for the inference of haplotype phase and missing observations from polyploid genotypes. PolyHap allows each individual to have a different ploidy, but ploidy cannot vary over the genomic region analysed. It employs a hidden Markov model (HMM) and a sampling algorithm to infer haplotypes jointly in multiple individuals and to obtain a measure of uncertainty in its inferences. Results: In the simulation study, we combine real haplotype data to create artificial diploid, triploid, and tetraploid genotypes, and use these to demonstrate that polyHap performs well, in terms of both switch error rate in recovering phase and imputation error rate for missing genotypes. To our knowledge, there is no comparable software for phasing a large, densely genotyped region of chromosome from triploids and tetraploids, while for diploids we found polyHap to be more accurate than fastPhase. We also compare the results of polyHap to SATlotyper on an experimentally haplotyped tetraploid dataset of 12 SNPs, and show that polyHap is more accurate. Conclusion: With the availability of large SNP data in polyploids and CNV regions, we believe that polyHap, our proposed method for inferring haplotypic phase from genotype data, will be useful in enabling researchers analysing such data to exploit the power of haplotype-based analyses

Echocardiographic assessment and percutaneous closure of multiple atrial septal defects

Atrial septal defect closure is now routinely performed using a percutaneous approach under echocardiographic guidance. Centrally located, secundum defects are ideal for device closure but there is considerable morphological variation in size and location of the defects. A small proportion of atrial septal defects may have multiple fenestrations and these are often considered unsuitable for device closure. We report three cases of multiple atrial septal defects successfully closed with two Amplatzer septal occluders

A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

Molecular hydrogen beyond the optical edge of an isolated spiral galaxy

We know little about the outermost portions of galaxies because there is little light coming from them. We do know that in many cases atomic hydrogen (HI) extends well beyond the optical radius \cite{Casertano91}. In the centers of galaxies, however, molecular hydrogen (H2) usually dominates by a large factor, raising the question of whether H2 is abundant also in the outer regions but hitherto unseen.Here we report the detection of emission from carbon monoxide (CO), the most abundant tracer of H2, beyond the optical radius of the nearby galaxy NGC 4414. The molecular clouds probably formed in the regions of relatively high HI column density and in the absence of spiral density waves. The relative strength of the lines from the two lowest rotational levels indicates that both the temperature and density of the H2 are quite low compared to conditions closer to the center. The inferred surface density of the molecular material continues the monotonic decrease from the inner regions. We conclude that while molecular clouds can form in the outer region of this galaxy, there is little mass associated with them.Comment: 3 Nature page

The changing landscape of membrane protein structural biology through developments in electron microscopy

Membrane proteins are ubiquitous in biology and are key targets for therapeutic development. Despite this, our structural understanding has lagged behind that of their soluble counterparts. This review provides an overview of this important field, focusing in particular on the recent resurgence of electron microscopy (EM) and the increasing role it has to play in the structural studies of membrane proteins, and illustrating this through several case studies. In addition we examine some of the challenges remaining in structural determination, and what steps are underway to enhance our knowledge of these enigmatic proteins

Plant communities affect arbuscular mycorrhizal fungal diversity and community composition in grassland microcosms

The diversity of arbuscular mycorrhizal (AM) fungi was investigated in an unfertilized limestone grassland soil supporting different synthesized vascular plant assemblages that had developed for 3 yr. The experimental treatments comprised: bare soil; monocultures of the nonmycotrophic sedge Carex flacca; monocultures of the mycotrophic grass Festuca ovina; and a species-rich mixture of four forbs, four grasses and four sedges. The diversity of AM fungi was analysed in roots of Plantago lanceolata bioassay seedlings using terminal-restriction fragment length polymorphism (T-RFLP). The extent of AM colonization, shoot biomass and nitrogen and phosphorus concentrations were also measured. The AM diversity was affected significantly by the floristic composition of the microcosms and shoot phosphorus concentration was positively correlated with AM diversity. The diversity of AM fungi in P. lanceolata decreased in the order: bare soil > C. flacca > 12 species > F. ovina. The unexpectedly high diversity in the bare soil and sedge monoculture likely reflects differences in the modes of colonization and sources of inoculum in these treatments compared with the assemblages containing established AM-compatible plants

Acceleration-Induced Deconfinement Transitions in de Sitter Spacetime

In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding Minkowski-space deconfinement temperature by a factor nearly equal to the dimension of the de Sitter spacetime. The behavior is qualitatively and quantitatively similar to that for confining theories defined by $S^1$ compactification of CFTs, studied recently in arXiv:1007.3996.Comment: 25 pages, 7 figure