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

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

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

Impairment in delay discounting in schizophrenia and schizoaffective disorder but not primary mood disorders

A measure of planning and impulse control, the delay-discounting (DD) task estimates the extent to which an individual decreases the perceived value of a reward as the reward is delayed. We examined cross-disorder performance between healthy controls (n = 88), individuals with bipolar disorder (n = 23), major depressive disorder (n = 43), and primary psychotic disorders (schizophrenia and schizoaffective disorder; n = 51) on the DD task (using a $10 delayed larger reward), as well as the interaction of DD scores with other symptom domains (cognition, psychosis, and affect). We found that individuals with schizophrenia and schizoaffective disorder display significantly greater rates of discounting compared to healthy controls, while individuals with a primary mood disorder do not differ from healthy controls after adjustment for IQ. Further, impairment in working memory is associated with higher discounting rates among individuals with schizophrenia and schizoaffective disorder, but cognitive dysfunction alone does not account for the extent of impairment in DD. Taken together, these results suggest an impaired ability to plan for the future and make adaptive decisions that are specific to individuals with psychotic disorders, and likely related to adverse functional outcomes. More generally, this work demonstrates the presence of variation in impulsivity across major psychiatric illnesses, supporting the use of a trans-diagnostic perspective

Dysfunction of the Intestinal Microbiome in Inflammatory Bowel Disease and Treatment

Background: The inflammatory bowel diseases (IBD) Crohn's disease and ulcerative colitis result from alterations in intestinal microbes and the immune system. However, the precise dysfunctions of microbial metabolism in the gastrointestinal microbiome during IBD remain unclear. We analyzed the microbiota of intestinal biopsies and stool samples from 231 IBD and healthy subjects by 16S gene pyrosequencing and followed up a subset using shotgun metagenomics. Gene and pathway composition were assessed, based on 16S data from phylogenetically-related reference genomes, and associated using sparse multivariate linear modeling with medications, environmental factors, and IBD status. Results: Firmicutes and Enterobacteriaceae abundances were associated with disease status as expected, but also with treatment and subject characteristics. Microbial function, though, was more consistently perturbed than composition, with 12% of analyzed pathways changed compared with 2% of genera. We identified major shifts in oxidative stress pathways, as well as decreased carbohydrate metabolism and amino acid biosynthesis in favor of nutrient transport and uptake. The microbiome of ileal Crohn's disease was notable for increases in virulence and secretion pathways. Conclusions: This inferred functional metagenomic information provides the first insights into community-wide microbial processes and pathways that underpin IBD pathogenesis

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

Families of twisted tensor product codes

Using geometric properties of the variety \cV_{r,t}, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of \PG(rt-1,q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.Comment: Keywords: Segre Product, Veronesean, Grassmannian, Desarguesian spread, Subgeometry, Twisted Product, Constacyclic error correcting code, Minimum weigh