Truncated Product Representations for L-Functions in the Hyperelliptic Ensemble

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordWe investigate the approximation of quadratic Dirichlet L-functions over function fields by truncations of their Euler products. We first establish representations for such L-functions as products over prime polynomials times products over their zeros. This is the hybrid formula in function fields. We then prove that partial Euler products are good approximations of an L-function away from its zeros, and that, when the length of the product tends to infinity, we recover the original L-function. We also obtain explicit expressions for the arguments of quadratic Dirichlet L-functions over function fields and for the arguments of their partial Euler products. In the second part of the paper we construct, for each quadratic Dirichlet L-function over a function field, an auxiliary function based on the approximate functional equation that equals the L-function on the critical line. We also construct a parametrized family of approximations of these auxiliary functions, prove the Riemann hypothesis holds for them, and that their zeros are related to those of the associated L-function. Finally, we estimate the counting function for the zeros of this family of approximations, show that these zeros cluster near those of the associated L-function, and that, when the parameter is not too large, almost all the zeros of the approximations are simple.JCA was partially supported by a Research in Pairs - Scheme 4 London Mathematical Society grant. SMG was supported in part by National Science Foundation Grant DMS-1200582. JPK gratefully acknowledges support under EPSRC Programme Grant EP/K034383/1 (LMF: L-Functions and Modular Forms) and a Royal Society Wolfson Research Merit Award

Using global analysis, partial specifications, and an extensible assertion language for program validation and debugging

We discuss a framework for the application of abstract interpretation as an aid during program development, rather than in the more traditional application of program optimization. Program validation and detection of errors is first performed statically by comparing (partial) specifications written in terms of assertions against information obtained from (global) static analysis of the program. The results of this process are expressed in the user assertion language. Assertions (or parts of assertions) which cannot be checked statically are translated into run-time tests. The framework allows the use of assertions to be optional. It also allows using very general properties in assertions, beyond the predefined set understandable by the static analyzer and including properties defined by user programs. We also report briefly on an implementation of the framework. The resulting tool generates and checks assertions for Prolog, CLP(R), and CHIP/CLP(fd) programs, and integrates compile-time and run-time checking in a uniform way. The tool allows using properties such as types, modes, non-failure, determinacy, and computational cost, and can treat modules separately, performing incremental analysis

Treadmill walking differently affects body composition and metabolic parameters of female rats from normal or small litters

This work assessed whether walking affects bodily development and metabolic parameters of female rats raised in small litters (three pups, group S) or control litters (nine pups, group C). After weaning, some of the rats had five sessions per week of a 30-min treadmill walking (CE and SE), while the others remained sedentary (CS and SS) until the age of 120 days. Exercise caused a reduction of body weight (CS/CE = 1.18), Lee index (CS/CE = 1.04), fasting blood glucose (CS/CE = 1.35), mesenteric (CS/CE = 1.23), and ovarian fat (CS/CE = 1.33) in CE, but only glucose was decreased in SE (SS/SE = 1.16). The diameter of adipocytes decreased to a half in the small-litter groups. Exercise increased subcutaneous (CS/CE = 0.88 and SS/SE = 0.71), but decreased retroperitoneal adipocytes (CS/CE = 1.2 and SS/SE = 1.3). Litter size reduction had little impact on females at the age of 120 days, but the light physical activity seemed insufficient to counteract all the effects of lactational overfeeding. On the other hand, pups from exercised mothers had a decrease in their biometric and glycemic indexes, demonstrating the transgenerational action of regular, although light, exercise

Nernst branes from special geometry

We construct new black brane solutions in $U(1)$ gauged ${\cal N}=2$ supergravity with a general cubic prepotential, which have entropy density $s\sim T^{1/3}$ as $T \rightarrow 0$ and thus satisfy the Nernst Law. By using the real formulation of special geometry, we are able to obtain analytical solutions in closed form as functions of two parameters, the temperature $T$ and the chemical potential $\mu$. Our solutions interpolate between hyperscaling violating Lifshitz geometries with $(z,\theta)=(0,2)$ at the horizon and $(z,\theta)=(1,-1)$ at infinity. In the zero temperature limit, where the entropy density goes to zero, we recover the extremal Nernst branes of Barisch et al, and the parameters of the near horizon geometry change to $(z,\theta)=(3,1)$.Comment: 37 pages. v2: numerical pre-factors of scalar fields q_A corrected in Section 3. No changes to conclusions. References adde

Innate immune signaling in hearts and buccal mucosa cells of patients with arrhythmogenic cardiomyopathy

Background: Nuclear factor κB (NF-κB) signaling in cardiac myocytes causes disease in a mouse model of arrhythmogenic cardiomyopathy (ACM) by mobilizing CCR2-expressing macrophages that promote myocardial injury and arrhythmias. Buccal mucosa cells exhibit pathologic features similar to those seen in cardiac myocytes in patients with ACM. Objectives: We sought to determine if persistent innate immune signaling via NF-κB occurs in cardiac myocytes in patients with ACM and if this is associated with myocardial infiltration of proinflammatory cells expressing CCR2. We also determined if buccal mucosa cells from young subjects with inherited disease alleles exhibit NF-κB signaling. Methods: We analyzed myocardium from ACM patients who died suddenly or required cardiac transplantation. We also analyzed buccal mucosa cells from young subjects with inherited disease alleles. The presence of immunoreactive signal for RelA/p65 in nuclei of cardiac myocytes and buccal cells was used as a reliable indicator of active NF-κB signaling. We also counted myocardial CCR2-expressing cells. Results: RelA/p65 signal was seen in numerous cardiac myocyte nuclei in 34 of 36 cases of ACM but not in 19 age-matched control individuals. Cells expressing CCR2 were increased in patient hearts in numbers directly correlated with the number of cardiac myocytes showing NF-κB signaling. NF-κB signaling was observed in buccal cells in young subjects with active disease. Conclusions: Patients with clinically active ACM exhibit persistent innate immune responses in cardiac myocytes and buccal mucosa cells, reflecting a local and systemic inflammatory process. Such individuals may benefit from anti-inflammatory therapy

Analysis of buccal mucosa as a prognostic tool in children with arrhythmogenic cardiomyopathy

Background The diagnosis of arrhythmogenic cardiomyopathy (ACM) is challenging especially in children at risk of adverse events. Analysis of cardiac myocyte junctional protein distribution may have diagnostic and prognostic implications, but its utility is limited by the need for a myocardial sample. We previously reported that buccal mucosa cells show junctional protein redistribution similar to that seen in cardiac myocytes of adult patients with ACM. Objectives We aimed to determine when junctional protein distribution abnormalities first occur in children with ACM variants and whether they correlate with progression of clinically apparent disease. Methods We analyzed buccal mucosa samples of children and adolescents with a family history of ACM (n = 13) and age-matched controls (n = 13). Samples were immunostained for plakoglobin, desmoplakin, plakophilin-1 and connexin43 and analyzed by confocal microscopy. All participants were swabbed at least twice with an average interval of 12–18 months between samplings. Results Junctional protein re-localization in buccal mucosa cells did not correlate with the presence of ACM-causing variants but instead occurred with clinical onset of disease. No changes in protein distribution were seen unless and until there was clinical evidence of disease. In addition, progressive shifts in the distribution of key proteins correlated with worsening of the disease phenotype. Finally, we observed restoration of junctional signal for Cx43 in patient with a favorable response to anti-arrhythmic therapy. Conclusions Due to ethical concerns about obtaining heart biopsies in children with no apparent disease, it has not been possible to analyze molecular changes in cardiac myocytes with the onset/progression of clinical disease. Using buccal smears as a surrogate for the myocardium may facilitate future studies of mechanisms and pathophysiological consequences of junctional protein redistribution in ACM. Buccal cells may also be a safe and inexpensive tool for risk stratification and potentially monitoring response to treatment in children bearing ACM variants

Increased S-nitrosylation and proteasomal degradation of caspase-3 during infection contribute to the persistence of adherent invasive escherichia coli (AIEC) in immune cells

Adherent invasive Escherichia coli (AIEC) have been implicated as a causative agent of Crohn's disease (CD) due to their isolation from the intestines of CD sufferers and their ability to persist in macrophages inducing granulomas. The rapid intracellular multiplication of AIEC sets it apart from other enteric pathogens such as Salmonella Typhimurium which after limited replication induce programmed cell death (PCD). Understanding the response of infected cells to the increased AIEC bacterial load and associated metabolic stress may offer insights into AIEC pathogenesis and its association with CD. Here we show that AIEC persistence within macrophages and dendritic cells is facilitated by increased proteasomal degradation of caspase-3. In addition S-nitrosylation of pro- and active forms of caspase-3, which can inhibit the enzymes activity, is increased in AIEC infected macrophages. This S-nitrosylated caspase-3 was seen to accumulate upon inhibition of the proteasome indicating an additional role for S-nitrosylation in inducing caspase-3 degradation in a manner independent of ubiquitination. In addition to the autophagic genetic defects that are linked to CD, this delay in apoptosis mediated in AIEC infected cells through increased degradation of caspase-3, may be an essential factor in its prolonged persistence in CD patients

Specific fatty acid intake and the risk of pancreatic cancer in Canada

The possible association of specific fatty acid (FA) intake and pancreatic cancer risk was investigated in a population-based case–control study of 462 histologically confirmed cases and 4721 frequency-matched controls in eight Canadian provinces between 1994 and 1997. Dietary intake was assessed by means of a self-administered food frequency questionnaire. Unconditional logistic regression was used to assess associations between dietary FAs and pancreatic cancer risk. After adjustment for age, province, body mass index, smoking, educational attainment, fat and total energy intake, statistically significant inverse associations were observed between pancreatic cancer risk and palmitate (odds ratios (ORs)=0.73; 95% confidence intervals (CIs) 0.56–0.96; P-trend=0.02), stearate (OR=0.70; 95% CI 0.51–0.94; P-trend=0.04), oleate (OR=0.75; 95% CI 0.55–1.02; P-trend=0.04), saturated FAs (OR=0.67; 95% CI 0.50–0.91; P-trend=0.01), and monounsaturated FAs (OR=0.72; 95% CI 0.53–0.98; P-trend=0.02), when comparing the highest quartile of intake to the lowest. Significant interactions were detected between body mass index and both saturated and monounsaturated FAs, with a markedly reduced risk associated with intake of stearate (OR=0.36; 95% CI 0.18–0.70; P-trend=0.001), oleate (OR=0.36; 95% CI 0.19–0.72; P-trend=0.002), saturated FAs (OR=0.35; 95% CI 0.18–0.67; P-trend=0.002), and monounsaturated FAs (OR=0.32; 95% CI 0.16–0.63; P-trend<0.0001) among subjects who are obese. The results suggest that substituting polyunsaturated FAs with saturated or monounsaturated FAs may reduce pancreatic cancer risk, independently of total energy intake, particularly among obese subjects