Combinatorial proofs on the joint distribution of descents and inverse descents

Let $A_{n,i,j}$ be the number of permutations on $[n]$ with $i-1$ descents and $j-1$ inverse descents. Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial and arithmetic properties of $A_{n,i,j}$, which contain a recurrence of $A_{n,i,j}$. Using the idea of balls in boxes, Petersen gave a combinatorial interpretation for the generating function of $A_{n,i,j}$, and obtained the same recurrence of $A_{n,i,j}$ from its generating function. Subsequently, Petersen asked whether there is a visual way to understand this recurrence. In this paper, after observing the internal structures of permutation grids, we present a combinatorial proof of the recurrence of $A_{n,i,j}$. Let $I_{n,k}$ and $J_{n,k}$ count the number of involutions and fixed-point free involutions on $[n]$ with $k$ descents, respectively. With the help of generating functions, Guo and Zeng derived two recurrences of $I_{n,k}$ and $J_{2n,k}$ that play an essential role in the proof of their unimodal properties. Unexpectedly, the constructive approach to the recurrence of $A_{n,i,j}$ is found to fuel the combinatorial interpretations of these two recurrences of $I_{n,k}$ and $J_{2n,k}$

A retrospective study of HIV antiretroviral treatment persistence in a commercially insured population in the United States

This study examined factors associated with persistence (time from initiation to discontinuation of treatment) on initial antiretroviral (ARV) therapy in commercially insured HIV patients in the United States, a population not well researched. This retrospective analysis of US health insurance claims data from 1 January 2003 to 30 June 2008 included treatment-naive patients aged 18–65 years with an HIV diagnosis receiving ARV therapy consisting of at least two individual nucleoside reverse transcriptase inhibitors (NRTIs) or one fixed-dose combination NRTI, plus at least one nonnucleoside reverse transcriptase inhibitor (NNRTI) or one protease inhibitor (PI), with or without ritonavir. Descriptive statistics, Kaplan-Meier survival estimation, and Cox proportional hazards regression models were completed. Patients were considered persistent until any component of the regimen was modified or there was a gap in treatment > 90 days. A total of 2460 patients met full inclusion criteria (1388 NNRTI and 1072 PI). Mean (SD) time to discontinuation for NNRTI- vs PI-based regimens was 370 (346) vs 295 (338) days (p < 0.001). Female sex, substance use, low comorbidity score, index year before 2007, geographical region, and taking a lopinavir/ritonavir regimen predicted discontinuation. Relative to NNRTI-based regimens, PI-based regimens demonstrated a greater risk of discontinuation (hazard ratio [HR], 1.32; p <0.001). The fixed-dose efavirenz/emtricitabine/tenofovir combination yielded the lowest risk of discontinuation (HR, 0.39; p < 0.001). HIV treatment persistence was longer with NNRTI-based regimens than PI-based regimens. The fixed-dose regimen of once-daily efavirenz/emtricitabine/tenofovir had the lowest risk of discontinuation

Imaging of X-Ray-Excited Emissions from Quantum Dots and Biological Tissue in Whole Mouse

© The Author(s) 2019. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.Optical imaging in clinical and preclinical settings can provide a wealth of biological information, particularly when coupled with targetted nanoparticles, but optical scattering and absorption limit the depth and resolution in both animal and human subjects. Two new hybrid approaches are presented, using the penetrating power of X-rays to increase the depth of optical imaging. Foremost, we demonstrate the excitation by X-rays of quantum-dots (QD) emitting in the near-infrared (NIR), using a clinical X-ray system to map the distribution of QDs at depth in whole mouse. We elicit a clear, spatially-resolved NIR signal from deep organs (brain, liver and kidney) with short (1 second) exposures and tolerable radiation doses that will permit future in vivo applications. Furthermore, X-ray-excited endogenous emission is also detected from whole mouse. The use of keV X-rays to excite emission from QDs and tissue represent novel biomedical imaging technologies, and exploit emerging QDs as optical probes for spatial-temporal molecular imaging at greater depth than previously possible.Peer reviewe

Microarray blob-defect removal improves array analysis

ABSTRACT Motivation: New generation Affymetrix oligonucleotide microarrays often have blob-like image defects that will require investigators to either repeat their hybridization assays or analyze their data with the defects left in place. We investigated the effect of analyzing a spikein experiment on Affymetrix ENCODE tiling arrays in the presence of simulated blobs covering between 1 and 9% of the array area. Using two different ChIP-chip tiling array analysis programs (Affymetrix Tiling Array Software TAS and Model-based Analysis of Tiling arrays MAT), we found that even the smallest blob defects significantly decreased the sensitivity and increased the false discovery rate (FDR) of the spike-in target prediction. Results: We introduced a new software tool, the Microarray Blob Remover (MBR), which allows rapid visualization, detection, and removal of various blob defects from the .CEL files of different types of Affymetrix microarrays. It is shown that using MBR significantly improves the sensitivity and FDR of a tiling array analysis compared to leaving the affected probes in the analysis. Availability: The MBR software and the sample array .CEL files used in this paper are available at

Scope for Credit Risk Diversification

This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk

Rare germline variants in DNA repair genes and the angiogenesis pathway predispose prostate cancer patients to develop metastatic disease

Background Prostate cancer (PrCa) demonstrates a heterogeneous clinical presentation ranging from largely indolent to lethal. We sought to identify a signature of rare inherited variants that distinguishes between these two extreme phenotypes. Methods We sequenced germline whole exomes from 139 aggressive (metastatic, age of diagnosis < 60) and 141 non-aggressive (low clinical grade, age of diagnosis ≥60) PrCa cases. We conducted rare variant association analyses at gene and gene set levels using SKAT and Bayesian risk index techniques. GO term enrichment analysis was performed for genes with the highest differential burden of rare disruptive variants. Results Protein truncating variants (PTVs) in specific DNA repair genes were significantly overrepresented among patients with the aggressive phenotype, with BRCA2, ATM and NBN the most frequently mutated genes. Differential burden of rare variants was identified between metastatic and non-aggressive cases for several genes implicated in angiogenesis, conferring both deleterious and protective effects. Conclusions Inherited PTVs in several DNA repair genes distinguish aggressive from non-aggressive PrCa cases. Furthermore, inherited variants in genes with roles in angiogenesis may be potential predictors for risk of metastases. If validated in a larger dataset, these findings have potential for future clinical application

Crystal structure of rhodopsin bound to arrestin by femtosecond X-ray laser.

G-protein-coupled receptors (GPCRs) signal primarily through G proteins or arrestins. Arrestin binding to GPCRs blocks G protein interaction and redirects signalling to numerous G-protein-independent pathways. Here we report the crystal structure of a constitutively active form of human rhodopsin bound to a pre-activated form of the mouse visual arrestin, determined by serial femtosecond X-ray laser crystallography. Together with extensive biochemical and mutagenesis data, the structure reveals an overall architecture of the rhodopsin-arrestin assembly in which rhodopsin uses distinct structural elements, including transmembrane helix 7 and helix 8, to recruit arrestin. Correspondingly, arrestin adopts the pre-activated conformation, with a ∼20° rotation between the amino and carboxy domains, which opens up a cleft in arrestin to accommodate a short helix formed by the second intracellular loop of rhodopsin. This structure provides a basis for understanding GPCR-mediated arrestin-biased signalling and demonstrates the power of X-ray lasers for advancing the frontiers of structural biology

Interaction between Thymidylate Synthase and Its Cognate mRNA in Zebrafish Embryos

Thymidylate synthase (TS), which catalyzes the de novo synthesis of dUMP, is an important target for cancer therapy. In this report, the effects of 5-fluorouracil (5-FU) and ZD1694 on the regulation of TS gene expression were evaluated in zebrafish embryos. Our results revealed that the expression of TS was increased by about six-fold when embryos were treated with 1.0 µM 5-FU and there was a greater than 10-fold increase in the TS protein level after treatment with 0.4 µM ZD1694. Northern blot analysis confirmed that expression of TS mRNA was identical in treated or untreated embryos. Gel shift and immunoprecipitation assays revealed that zebrafish TS was specifically bound with its cognate mRNA in vitro and in vivo. We identified a 20 nt RNA sequence, TS:N20, localized to the 5′-UTR of TS mRNA, which corresponded to nt 13–32; TS:N20 bound to the TS protein with an affinity similar to that of the full-length TS mRNA. The MFold program predicted that TS:N20 formed a stable stem-loop structure similar to that of the cis-acting element found in human TS mRNA. Variant RNAs with either a deletion or mutation in the core motif of TS:N20 were unable to bind to the TS protein. In vitro translation experiments, using the rabbit lysate system, confirmed that zebrafish TS mRNA translation was significantly repressed when an excess amount of TS protein was included in the system. Additionally, a TS stability experiment confirmed that treatment of zebrafish embryos with 5-FU could increase the TS stability significantly, and the half life of TS protein was about 2.7 times longer than in untreated embryos. Our study revealed a structural requirement for the interaction of TS RNA with TS protein. These findings also demonstrated that the increase in TS protein induced by 5-FU occurs at the post-transcriptional level and that increased stability and translation efficiency both contributed to the increase in TS protein levels induced by TS inhibitors

Identification of COUP-TFII Orphan Nuclear Receptor as a Retinoic Acid–Activated Receptor

The chicken ovalbumin upstream promoter-transcription factors (COUP-TFI and II) make up the most conserved subfamily of nuclear receptors that play key roles in angiogenesis, neuronal development, organogenesis, cell fate determination, and metabolic homeostasis. Although the biological functions of COUP-TFs have been studied extensively, little is known of their structural features or aspects of ligand regulation. Here we report the ligand-free 1.48 Å crystal structure of the human COUP-TFII ligand-binding domain. The structure reveals an autorepressed conformation of the receptor, where helix α10 is bent into the ligand-binding pocket and the activation function-2 helix is folded into the cofactor binding site, thus preventing the recruitment of coactivators. In contrast, in multiple cell lines, COUP-TFII exhibits constitutive transcriptional activity, which can be further potentiated by nuclear receptor coactivators. Mutations designed to disrupt cofactor binding, dimerization, and ligand binding, substantially reduce the COUP-TFII transcriptional activity. Importantly, retinoid acids are able to promote COUP-TFII to recruit coactivators and activate a COUP-TF reporter construct. Although the concentration needed is higher than the physiological levels of retinoic acids, these findings demonstrate that COUP-TFII is a ligand-regulated nuclear receptor, in which ligands activate the receptor by releasing it from the autorepressed conformation