Rational parametrization of conchoids to algebraic curves

We study the rationality of each of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base curve and on the focus but not on the distance. As a consequence, we provide an algorithm that analyzes the rationality of all the components of the conchoid and, in the affirmative case, parametrizes them. The algorithm only uses a proper parametrization of the base curve and the focus and, hence, does not require the previous computation of the conchoid. As a corollary, we show that the conchoid to the irreducible conics, with conchoid-focus on the conic, are rational and we give parametrizations. In particular we parametrize the Limaçons of Pascal. We also parametrize the conchoids of Nicomedes. Finally, we show how to find the foci from where the conchoid is rational or with two rational components

Total Degree Formula for the Generic Offset to a Parametric Surface

We provide a resultant-based formula for the total degree w.r.t. the spatial variables of the generic offset to a parametric surface. The parametrization of the surface is not assumed to be proper.Comment: Preprint of an article to be published at the International Journal of Algebra and Computation, World Scientific Publishing, DOI:10.1142/S021819671100680

An Algebraic Analysis of Conchoids to Algebraic Curves

We study the conchoid to an algebraic affine plane curve C from the perspective of algebraic geometry, analyzing their main algebraic properties. Beside C, the notion of conchoid involves a point A in the affine plane (the focus) and a nonzero field element d (the distance).We introduce the formal definition of conchoid by means of incidence diagrams.We prove that the conchoid is a 1-dimensional algebraic set having atmost two irreducible components. Moreover, with the exception of circles centered at the focus A and taking d as its radius, all components of the corresponding conchoid have dimension 1. In addition, we introduce the notions of special and simple components of a conchoid. Furthermore we state that, with the exception of lines passing through A, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to C, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve

Characterization of Adherent Bacteroidales from Intestinal Biopsies of Children and Young Adults with Inflammatory Bowel Disease

There is extensive evidence implicating the intestinal microbiota in inflammatory bowel disease [IBD], but no microbial agent has been identified as a sole causative agent. Bacteroidales are numerically dominant intestinal organisms that associate with the mucosal surface and have properties that both positively and negatively affect the host. To determine precise numbers and species of Bacteroidales adherent to the mucosal surface in IBD patients, we performed a comprehensive culture based analysis of intestinal biopsies from pediatric Crohn's disease [CD], ulcerative colitis [UC], and control subjects. We obtained biopsies from 94 patients and used multiplex PCR or 16S rDNA sequencing of Bacteroidales isolates for species identification. Eighteen different Bacteroidales species were identified in the study group, with up to ten different species per biopsy, a number higher than demonstrated using 16S rRNA gene sequencing methods. Species diversity was decreased in IBD compared to controls and with increasingly inflamed tissue. There were significant differences in predominant Bacteroidales species between biopsies from the three groups and from inflamed and uninflamed sites. Parabacteroides distasonis significantly decreased in inflamed tissue. All 373 Bacteroidales isolates collected in this study grew with mucin as the only utilizable carbon source suggesting this is a non-pathogenic feature of this bacterial order. Bacteroides fragilis isolates with the enterotoxin gene [bft], previously associated with flares of colitis, were not found more often at inflamed colonic sites or within IBD subjects. B. fragilis isolates with the ability to synthesize the immunomodulatory polysaccharide A [PSA], previously shown to be protective in murine models of colitis, were not detected more often from healthy versus inflamed tissue

Wiskott-Aldrich syndrome protein deficiency in innate immune cells leads to mucosal immune dysregulation and colitis in mice

BACKGROUND & AIMS: Immunodeficiency and autoimmune sequelae, including colitis, develop in patients and mice deficient in Wiskott-Aldrich Syndrome protein (WASP), a hematopoietic-specific intracellular signaling molecule that regulates the actin cytoskeleton. Development of colitis in WASP-deficient mice requires lymphocytes; transfer of T cells is sufficient to induce colitis in immunodeficient mice. We investigated the interactions between innate and adaptive immune cells in mucosal regulation during development of T-cell-mediated colitis in mice with WASP-deficient cells of the innate immune system. METHODS: Naïve and/or regulatory CD4(+) T cells were transferred from 129 SvEv mice into RAG-2 deficient (RAG-2 KO) mice or mice lacking WASP and RAG-2 (WRDKO). Animals were observed for the development of colitis; effector and regulatory functions of innate immune and T cells were analyzed with in vivo and in vitro assays. RESULTS: Transfer of unfractionated CD4(+) T cells induced severe colitis in WRDKO, but not RAG-2 KO, mice. Naïve wild-type T cells had higher levels of effector activity and regulatory T cells had reduced suppressive function when transferred into WRDKO mice compared to RAG-2 KO mice. Regulatory T-cell proliferation, generation, and maintenance of FoxP3 expression were reduced in WRDKO recipients, and associated with reduced numbers of CD103(+) tolerogenic dendritic cells and levels of interleukin (IL)-10. Administration of IL-10 prevented induction of colitis following transfer of T cells into WRDKO mice. CONCLUSIONS: Defective interactions between WASP-deficient innate immune cells and normal T cells disrupt mucosal regulation, potentially by altering the functions of tolerogenic dendritic cells, production of IL-10, and homeostasis of regulatory T cells

Loss of N-WASP drives early progression in an Apc model of intestinal tumourigenesis

N‐WASP (WASL) is a widely expressed cytoskeletal signalling and scaffold protein also implicated in regulation of Wnt signalling and homeostatic maintenance of skin epithelial architecture. N‐WASP mediates invasion of cancer cells in vitro and its depletion reduces invasion and metastatic dissemination of breast cancer. Given this role in cancer invasion and universal expression in the gastrointestinal tract, we explored a role for N‐WASP in the initiation and progression of colorectal cancer. While deletion of N‐wasp is not detectably harmful in the murine intestinal tract, numbers of Paneth cells increased, indicating potential changes in the stem cell niche and migration up the crypt‐villus axis was enhanced. Loss of N‐wasp promoted adenoma formation in an adenomatous polyposis coli (Apc) deletion model of intestinal tumourigenesis. Thus, we establish a tumour suppressive role of N‐WASP in early intestinal carcinogenesis despite its later pro‐invasive role in other cancers. Our study highlights that while the actin cytoskeletal machinery promotes invasion of cancer cells, it also maintains normal epithelial tissue function and thus may have tumour suppressive roles in pre‐neoplastic tissues

Beginning with criticism: An analysis of the first four volumes of Art South Africa

Art South Africa is currently the leading, professionally published art magazine in South Africa. The magazine plays an important role in the dissemination of art discourse and art news and is the only ongoing, printed forum devoted exclusively to South African contemporary art. In this paper I will be looking at Art South Africa to describe the type of art texts it presents and the particular position it has taken in the contemporary art world of South Africa. In doing this I will be analysing the magazine to register the types of writing and other information in formats such as art news, exhibition reviews, artist bios, interviews and even advertising. This paper will also be analysing selected texts to determine the key issues that are represented and the way those issues have been represented with a critical position. Looking at Art South Africa from many angles will show that criticality is one of the magazine’s ideological aims and though the magazine’s format changes over time, it has continually sought to engage its readers in critical discourse

Fluoromycobacteriophages for rapid, specific, and sensitive antibiotic susceptibility testing of Mycobacterium tuberculosis

Rapid antibiotic susceptibility testing of Mycobacterium tuberculosis is of paramount importance as multiple- and extensively- drug resistant strains of M. tuberculosis emerge and spread. We describe here a virus-based assay in which fluoromycobacteriophages are used to deliver a GFP or ZsYellow fluorescent marker gene to M. tuberculosis, which can then be monitored by fluorescent detection approaches including fluorescent microscopy and flow cytometry. Pre-clinical evaluations show that addition of either Rifampicin or Streptomycin at the time of phage addition obliterates fluorescence in susceptible cells but not in isogenic resistant bacteria enabling drug sensitivity determination in less than 24 hours. Detection requires no substrate addition, fewer than 100 cells can be identified, and resistant bacteria can be detected within mixed populations. Fluorescence withstands fixation by paraformaldehyde providing enhanced biosafety for testing MDR-TB and XDR-TB infections. © 2009 Piuri et al

An integrated clinical program and crowdsourcing strategy for genomic sequencing and Mendelian disease gene discovery.

Despite major progress in defining the genetic basis of Mendelian disorders, the molecular etiology of many cases remains unknown. Patients with these undiagnosed disorders often have complex presentations and require treatment by multiple health care specialists. Here, we describe an integrated clinical diagnostic and research program using whole-exome and whole-genome sequencing (WES/WGS) for Mendelian disease gene discovery. This program employs specific case ascertainment parameters, a WES/WGS computational analysis pipeline that is optimized for Mendelian disease gene discovery with variant callers tuned to specific inheritance modes, an interdisciplinary crowdsourcing strategy for genomic sequence analysis, matchmaking for additional cases, and integration of the findings regarding gene causality with the clinical management plan. The interdisciplinary gene discovery team includes clinical, computational, and experimental biomedical specialists who interact to identify the genetic etiology of the disease, and when so warranted, to devise improved or novel treatments for affected patients. This program effectively integrates the clinical and research missions of an academic medical center and affords both diagnostic and therapeutic options for patients suffering from genetic disease. It may therefore be germane to other academic medical institutions engaged in implementing genomic medicine programs

ZFP36L1 negatively regulates plasmacytoid differentiation of BCL1 cells by targeting BLIMP1 mRNA

The ZFP36/Tis11 family of zinc-finger proteins regulate cellular processes by binding to adenine uridine rich elements in the 3′ untranslated regions of various mRNAs and promoting their degradation. We show here that ZFP36L1 expression is largely extinguished during the transition from B cells to plasma cells, in a reciprocal pattern to that of ZFP36 and the plasma cell transcription factor, BLIMP1. Enforced expression of ZFP36L1 in the mouse BCL1 cell line blocked cytokine-induced differentiation while shRNA-mediated knock-down enhanced differentiation. Reconstruction of regulatory networks from microarray gene expression data using the ARACNe algorithm identified candidate mRNA targets for ZFP36L1 including BLIMP1. Genes that displayed down-regulation in plasma cells were significantly over-represented (P = <0.0001) in a set of previously validated ZFP36 targets suggesting that ZFP36L1 and ZFP36 target distinct sets of mRNAs during plasmacytoid differentiation. ShRNA-mediated knock-down of ZFP36L1 in BCL1 cells led to an increase in levels of BLIMP1 mRNA and protein, but not for mRNAs of other transcription factors that regulate plasmacytoid differentiation (xbp1, irf4, bcl6). Finally, ZFP36L1 significantly reduced the activity of a BLIMP1 3′ untranslated region-driven luciferase reporter. Taken together, these findings suggest that ZFP36L1 negatively regulates plasmacytoid differentiation, at least in part, by targeting the expression of BLIMP1