Another extension of the disc algebra

We identify the complex plane C with the open unit disc D={z:|z|<1} by the homeomorphism z --> z/(1+|z|). This leads to a compactification $\bar{C}$ of C, homeomorphic to the closed unit disc. The Euclidean metric on the closed unit disc induces a metric d on $\bar{C}$. We identify all uniform limits of polynomials on $\bar{D}$ with respect to the metric d. The class of the above limits is an extension of the disc algebra and it is denoted by $\bar{A}(D)$. We study properties of the elements of $\bar{A}(D)$ and topological properties of the class $\bar{A}(D)$ endowed with its natural topology. The class $\bar{A}(D)$ is different and, from the geometric point of view, richer than the class $\tilde{A}(D)$ introduced in Nestoridis (2010), Arxiv:1009.5364, on the basis of the chordal metric.Comment: 14 page

Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

Introduction to G2\mathrm{G}_2 geometry

These notes give an informal and leisurely introduction to $\mathrm{G}_2$ geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in $7$ dimensions that is the pointwise model for $\mathrm{G}_2$ geometry, using the octonions. The basics of $\mathrm{G}_2$-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general $\mathrm{G}_2$-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free $\mathrm{G}_2$ manifolds are considered, and we stress the similarities and differences with Kahler and Calabi-Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free $\mathrm{G}_2$ manifolds.Comment: 37 pages. To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics". Version 2: Corrected the references. No other change

One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold.Ministerio de Economía y Competitividad MTM2015-67072-

Morphogenesis of Strongyloides stercoralis Infective Larvae Requires the DAF-16 Ortholog FKTF-1

Based on metabolic and morphological similarities between infective third-stage larvae of parasitic nematodes and dauer larvae of Caenorhabditis elegans, it is hypothesized that similar genetic mechanisms control the development of these forms. In the parasite Strongyloides stercoralis, FKTF-1 is an ortholog of DAF-16, a forkhead transcription factor that regulates dauer larval development in C. elegans. Using transgenesis, we investigated the role of FKTF-1 in S. stercoralis' infective larval development. In first-stage larvae, GFP-tagged recombinant FKTF-1b localizes to the pharynx and hypodermis, tissues remodeled in infective larvae. Activating and inactivating mutations at predicted AKT phosphorylation sites on FKTF-1b give constitutive cytoplasmic and nuclear localization of the protein, respectively, indicating that its post-translational regulation is similar to other FOXO-class transcription factors. Mutant constructs designed to interfere with endogenous FKTF-1b function altered the intestinal and pharyngeal development of the larvae and resulted in some transgenic larvae failing to arrest in the infective stage. Our findings indicate that FKTF-1b is required for proper morphogenesis of S. stercoralis infective larvae and support the overall hypothesis of similar regulation of dauer development in C. elegans and the formation of infective larvae in parasitic nematodes

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio

Strongyloides stercoralis age-1: A Potential Regulator of Infective Larval Development in a Parasitic Nematode

Infective third-stage larvae (L3i) of the human parasite Strongyloides stercoralis share many morphological, developmental, and behavioral attributes with Caenorhabditis elegans dauer larvae. The ‘dauer hypothesis’ predicts that the same molecular genetic mechanisms control both dauer larval development in C. elegans and L3i morphogenesis in S. stercoralis. In C. elegans, the phosphatidylinositol-3 (PI3) kinase catalytic subunit AGE-1 functions in the insulin/IGF-1 signaling (IIS) pathway to regulate formation of dauer larvae. Here we identify and characterize Ss-age-1, the S. stercoralis homolog of the gene encoding C. elegans AGE-1. Our analysis of the Ss-age-1 genomic region revealed three exons encoding a predicted protein of 1,209 amino acids, which clustered with C. elegans AGE-1 in phylogenetic analysis. We examined temporal patterns of expression in the S. stercoralis life cycle by reverse transcription quantitative PCR and observed low levels of Ss-age-1 transcripts in all stages. To compare anatomical patterns of expression between the two species, we used Ss-age-1 or Ce-age-1 promoter::enhanced green fluorescent protein reporter constructs expressed in transgenic animals for each species. We observed conservation of expression in amphidial neurons, which play a critical role in developmental regulation of both dauer larvae and L3i. Application of the PI3 kinase inhibitor LY294002 suppressed L3i in vitro activation in a dose-dependent fashion, with 100 µM resulting in a 90% decrease (odds ratio: 0.10, 95% confidence interval: 0.08–0.13) in the odds of resumption of feeding for treated L3i in comparison to the control. Together, these data support the hypothesis that Ss-age-1 regulates the development of S. stercoralis L3i via an IIS pathway in a manner similar to that observed in C. elegans dauer larvae. Understanding the mechanisms by which infective larvae are formed and activated may lead to novel control measures and treatments for strongyloidiasis and other soil-transmitted helminthiases

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Interleukin-32 Promotes Osteoclast Differentiation but Not Osteoclast Activation

Background: Interleukin-32 (IL-32) is a newly described cytokine produced after stimulation by IL-2 or IL-18 and IFN-γ. IL-32 has the typical properties of a pro-inflammatory mediator and although its role in rheumatoid arthritis has been recently reported its effect on the osteoclastogenesis process remains unclear. Methodology/principal findings: In the present study, we have shown that IL-32 was a potent modulator of osteoclastogenesis in vitro, whereby it promoted the differentiation of osteoclast precursors into TRAcP+ VNR+ multinucleated cells expressing specific osteoclast markers (up-regulation of NFATc1, OSCAR, Cathepsin K), but it was incapable of inducing the maturation of these multinucleated cells into bone-resorbing cells. The lack of bone resorption in IL-32-treated cultures could in part be explain by the lack of F-actin ring formation by the multinucleated cells generated. Moreover, when IL-32 was added to PBMC cultures maintained with soluble RANKL, although the number of newly generated osteoclast was increased, a significant decrease of the percentage of lacunar resorption was evident suggesting a possible inhibitory effect of this cytokine on osteoclast activation. To determine the mechanism by which IL-32 induces such response, we sought to determine the intracellular pathways activated and the release of soluble mediators in response to IL-32. Our results indicated that compared to RANKL, IL-32 induced a massive activation of ERK1/2 and Akt. Moreover, IL-32 was also capable of stimulating the release of IL-4 and IFN-γ, two known inhibitors of osteoclast formation and activation. Conclusions/significance: This is the first in vitro report on the complex role of IL-32 on osteoclast precursors. Further clarification on the exact role of IL-32 in vivo is required prior to the development of any potential therapeutic approach

The Effects of Apolipoprotein F Deficiency on High Density Lipoprotein Cholesterol Metabolism in Mice

Apolipoprotein F (apoF) is 29 kilodalton secreted sialoglycoprotein that resides on the HDL and LDL fractions of human plasma. Human ApoF is also known as Lipid Transfer Inhibitor protein (LTIP) based on its ability to inhibit cholesteryl ester transfer protein (CETP)-mediated transfer events between lipoproteins. In contrast to other apolipoproteins, ApoF is predicted to lack strong amphipathic alpha helices and its true physiological function remains unknown. We previously showed that overexpression of Apolipoprotein F in mice reduced HDL cholesterol levels by 20–25% by accelerating clearance from the circulation. In order to investigate the effect of physiological levels of ApoF expression on HDL cholesterol metabolism, we generated ApoF deficient mice. Unexpectedly, deletion of ApoF had no substantial impact on plasma lipid concentrations, HDL size, lipid or protein composition. Sex-specific differences were observed in hepatic cholesterol content as well as serum cholesterol efflux capacity. Female ApoF KO mice had increased liver cholesteryl ester content relative to wild type controls on a chow diet (KO: 3.4+/−0.9 mg/dl vs. WT: 1.2+/−0.3 mg/dl, p<0.05). No differences were observed in ABCG1-mediated cholesterol efflux capacity in either sex. Interestingly, ApoB-depleted serum from male KO mice was less effective at promoting ABCA1-mediated cholesterol efflux from J774 macrophages relative to WT controls