A note on the signature representations of the symmetric groups

For a partition {\lambda} and a prime p, we prove a necessary and sufficient condition for there exists a composition {\delta} such that {\delta} can be obtained from {\lambda} after rearrangement and all the partial sums of {\delta} are not divisible by p.Comment: This is a substantially revised version of previous ones. In the third section, we calculate some explicit p-Kostka number

The Implications of Ignorance for Quantum Error Correction Thresholds

Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for the likes of the Toric code require them to work well beyond this limit. We argue that without the assumption of being below the distance limit, the success of error correction is not only contingent on the noise model, but what the noise model is believed to be. Any discrepancy must adversely affect the threshold rate, and risks invalidating existing threshold theorems. We prove that for the 2D Toric code, suitable thresholds still exist by utilising a mapping to the 2D random bond Ising model.Comment: 8 pages, 2 figures. Title change enforced by journa

Generating sets of Affine groups of low genus

We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy group is a primitive affine permutation group

Evaluating the Role of the Steroid and Xenobiotic Receptor (SXR/PXR) in PCB-153 Metabolism and Protection against Associated Adverse Effects during Perinatal and Chronic Exposure in Mice.

BACKGROUND:Polychlorinated biphenyls (PCBs) are environmental toxicants; PCB exposure has been associated with adverse effects on wildlife and humans. However, the mechanisms underlying these adverse effects are not fully understood. The steroid and xenobiotic receptor [SXR; also known as the pregnane X receptor (PXR) and formally known as NR1I2] is a nuclear hormone receptor that regulates inducible metabolism of drugs and xenobiotics and is activated or inhibited by various PCB congeners. OBJECTIVES:The aim of this study was to investigate the effects of exposure to PCB-153, the most prevalent PCB congener in human tissues, on SXR knockout mice (SXRKO) and to elucidate the role of SXR in PCB-153 metabolism and promotion of its harmful effects. METHODS:Wild-type (WT) and SXRKO mice were chronically or perinatally exposed to a low dose (54μg/kg/d) of PCB-153. Blood, livers, and spleens were analyzed using transcriptome sequencing (RNA-seq) and molecular techniques to investigate the impacts of exposure on metabolism, oxidative stress, and hematological parameters. RESULTS:SXRKO mice perinatally exposed to PCB-153 displayed elevated oxidative stress, symptoms of hemolytic anemia, and premature death. Transcriptomal analysis revealed that expression of genes involved in metabolic processes was altered in SXRKO mice. Elevated levels of the PCB-153 metabolite, 3-OH-PCB-153, were found in exposed SXRKO mice compared to exposed WT mice. Blood hemoglobin (HGB) levels were lower throughout the lifespan, and the occurrence of intestinal tumors was larger in SXRKO mice chronically exposed to PCB-153 compared to vehicle and WT controls. DISCUSSION:Our results suggest that altered metabolism induced by SXR loss of function resulted in the accumulation of hydroxylated metabolites upon exposure to PCB-153, leading to oxidative stress, hemolytic anemia, and tumor development in a mouse model. These results support a major role for SXR/PXR in protection against xenobiotic-induced oxidative stress by maintaining proper metabolism in response to PCB-153 exposure. This role of SXR could be generally applicable to other environmental toxicants as well as pharmaceutical drugs. https://doi.org/10.1289/EHP6262

The pharmacokinetics of anthocyanins and their metabolites in humans

Background and Purpose: Anthocyanins are phytochemicals with reported vasoactive bioactivity. However, given their instability at neutral pH, they are presumed to undergo significant degradation and subsequent biotransformation. The aim of the present study was to establish the pharmacokinetics of the metabolites of cyanidin-3-glucoside (C3G), a widely consumed dietary phytochemical with potential cardioprotective properties. Experimental Approach: A 500 mg oral bolus dose of 6,8,10,3′,5′-13C5-C3G was fed to eight healthy male participants, followed by a 48 h collection (0, 0.5, 1, 2, 4, 6, 24, 48 h) of blood, urine and faecal samples. Samples were analysed by HPLC-ESI-MS/MS with elimination kinetics established using non-compartmental pharmacokinetic modelling. Key Results: Seventeen 13C-labelled compounds were identified in the serum, including 13C5-C3G, its degradation products, protocatechuic acid (PCA) and phloroglucinaldehyde (PGA), 13 metabolites of PCA and 1 metabolite derived from PGA. The maximal concentrations of the phenolic metabolites (Cmax) ranged from 10 to 2000 nM, between 2 and 30 h (tmax) post-consumption, with half-lives of elimination observed between 0.5 and 96 h. The major phenolic metabolites identified were hippuric acid and ferulic acid, which peaked in the serum at approximately 16 and 8 h respectively. Conclusions and Implications: Anthocyanins are metabolized to a structurally diverse range of metabolites that exhibit dynamic kinetic profiles. Understanding the elimination kinetics of these metabolites is key to the design of future studies examining their utility in dietary interventions or as therapeutics for disease risk reduction

Multilevel modelling for inference of genetic regulatory networks

Time-course experiments with microarrays are often used to study dynamic biological systems and genetic regulatory networks (GRNs) that model how genes influence each other in cell-level development of organisms. The inference for GRNs provides important insights into the fundamental biological processes such as growth and is useful in disease diagnosis and genomic drug design. Due to the experimental design, multilevel data hierarchies are often present in time-course gene expression data. Most existing methods, however, ignore the dependency of the expression measurements over time and the correlation among gene expression profiles. Such independence assumptions violate regulatory interactions and can result in overlooking certain important subject effects and lead to spurious inference for regulatory networks or mechanisms. In this paper, a multilevel mixed-effects model is adopted to incorporate data hierarchies in the analysis of time-course data, where temporal and subject effects are both assumed to be random. The method starts with the clustering of genes by fitting the mixture model within the multilevel random-effects model framework using the expectation-maximization (EM) algorithm. The network of regulatory interactions is then determined by searching for regulatory control elements (activators and inhibitors) shared by the clusters of co-expressed genes, based on a time-lagged correlation coefficients measurement. The method is applied to two real time-course datasets from the budding yeast (Saccharomyces cerevisiae) genome. It is shown that the proposed method provides clusters of cell-cycle regulated genes that are supported by existing gene function annotations, and hence enables inference on regulatory interactions for the genetic network

Regional association of pCASL-MRI with FDG-PET and PiB-PET in people at risk for autosomal dominant Alzheimer's disease.

Autosomal dominant Alzheimer's disease (ADAD) is a small subset of Alzheimer's disease that is genetically determined with 100% penetrance. It provides a valuable window into studying the course of pathologic processes that leads to dementia. Arterial spin labeling (ASL) MRI is a potential AD imaging marker that non-invasively measures cerebral perfusion. In this study, we investigated the relationship of cerebral blood flow measured by pseudo-continuous ASL (pCASL) MRI with measures of cerebral metabolism (FDG PET) and amyloid deposition (Pittsburgh Compound B (PiB) PET). Thirty-one participants at risk for ADAD (age 39 ± 13 years, 19 females) were recruited into this study, and 21 of them received both MRI and FDG and PiB PET scans. Considerable variability was observed in regional correlations between ASL-CBF and FDG across subjects. Both regional hypo-perfusion and hypo-metabolism were associated with amyloid deposition. Cross-sectional analyses of each biomarker as a function of the estimated years to expected dementia diagnosis indicated an inverse relationship of both perfusion and glucose metabolism with amyloid deposition during AD development. These findings indicate that neurovascular dysfunction is associated with amyloid pathology, and also indicate that ASL CBF may serve as a sensitive early biomarker for AD. The direct comparison among the three biomarkers provides complementary information for understanding the pathophysiological process of AD