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 $J_{2n,k}$

Observation of Coalescence Process of Silver Nanospheres During Shape Transformation to Nanoprisms

In this report, we observed the growth mechanism and the shape transformation from spherical nanoparticles (diameter ~6 nm) to triangular nanoprisms (bisector length ~100 nm). We used a simple direct chemical reduction method and provided evidences for the growth of silver nanoprisms via a coalescence process. Unlike previous reports, our method does not rely upon light, heat, or strong oxidant for the shape transformation. This transformation could be launched by fine-tuning the pH value of the silver colloidal solution. Based on our extensive examination using transmission electron microscopy, we propose a non-point initiated growth mechanism, which is a combination of coalescence and dissolution–recrystallization process during the growth of silver nanoprisms

A Spatial Analysis of County-level Variation in Syphilis and Gonorrhea in Guangdong Province, China

Sexually transmitted infections (STI) have made a resurgence in many rapidly developing regions of southern China, but there is little understanding of the social changes that contribute to this spatial distribution of STI. This study examines county-level socio-demographic characteristics associated with syphilis and gonorrhea in Guangdong Province.This study uses linear regression and spatial lag regression to determine county-level (n = 97) socio-demographic characteristics associated with a greater burden of syphilis, gonorrhea, and a combined syphilis/gonorrhea index. Data were obtained from the 2005 China Population Census and published public health data. A range of socio-demographic variables including gross domestic product, the Gender Empowerment Measure, standard of living, education level, migrant population and employment are examined. Reported syphilis and gonorrhea cases are disproportionately clustered in the Pearl River Delta, the central region of Guangdong Province. A higher fraction of employed men among the adult population, higher fraction of divorced men among the adult population, and higher standard of living (based on water availability and people per room) are significantly associated with higher STI cases across all three models. Gross domestic product and gender inequality measures are not significant predictors of reported STI in these models.Although many ecological studies of STIs have found poverty to be associated with higher reported STI, this analysis found a greater number of reported syphilis cases in counties with a higher standard of living. Spatially targeted syphilis screening measures in regions with a higher standard of living may facilitate successful control efforts. This analysis also reinforces the importance of changing male sexual behaviors as part of a comprehensive response to syphilis control in China

An integrated ontology resource to explore and study host-virus relationships.

Our growing knowledge of viruses reveals how these pathogens manage to evade innate host defenses. A global scheme emerges in which many viruses usurp key cellular defense mechanisms and often inhibit the same components of antiviral signaling. To accurately describe these processes, we have generated a comprehensive dictionary for eukaryotic host-virus interactions. This controlled vocabulary has been detailed in 57 ViralZone resource web pages which contain a global description of all molecular processes. In order to annotate viral gene products with this vocabulary, an ontology has been built in a hierarchy of UniProt Knowledgebase (UniProtKB) keyword terms and corresponding Gene Ontology (GO) terms have been developed in parallel. The results are 65 UniProtKB keywords related to 57 GO terms, which have been used in 14,390 manual annotations; 908,723 automatic annotations and propagated to an estimation of 922,941 GO annotations. ViralZone pages, UniProtKB keywords and GO terms provide complementary tools to users, and the three resources have been linked to each other through host-virus vocabulary

A Biological Global Positioning System: Considerations for Tracking Stem Cell Behaviors in the Whole Body

Many recent research studies have proposed stem cell therapy as a treatment for cancer, spinal cord injuries, brain damage, cardiovascular disease, and other conditions. Some of these experimental therapies have been tested in small animals and, in rare cases, in humans. Medical researchers anticipate extensive clinical applications of stem cell therapy in the future. The lack of basic knowledge concerning basic stem cell biology-survival, migration, differentiation, integration in a real time manner when transplanted into damaged CNS remains an absolute bottleneck for attempt to design stem cell therapies for CNS diseases. A major challenge to the development of clinical applied stem cell therapy in medical practice remains the lack of efficient stem cell tracking methods. As a result, the fate of the vast majority of stem cells transplanted in the human central nervous system (CNS), particularly in the detrimental effects, remains unknown. The paucity of knowledge concerning basic stem cell biology—survival, migration, differentiation, integration in real-time when transplanted into damaged CNS remains a bottleneck in the attempt to design stem cell therapies for CNS diseases. Even though excellent histological techniques remain as the gold standard, no good in vivo techniques are currently available to assess the transplanted graft for migration, differentiation, or survival. To address these issues, herein we propose strategies to investigate the lineage fate determination of derived human embryonic stem cells (hESC) transplanted in vivo into the CNS. Here, we describe a comprehensive biological Global Positioning System (bGPS) to track transplanted stem cells. But, first, we review, four currently used standard methods for tracking stem cells in vivo: magnetic resonance imaging (MRI), bioluminescence imaging (BLI), positron emission tomography (PET) imaging and fluorescence imaging (FLI) with quantum dots. We summarize these modalities and propose criteria that can be employed to rank the practical usefulness for specific applications. Based on the results of this review, we argue that additional qualities are still needed to advance these modalities toward clinical applications. We then discuss an ideal procedure for labeling and tracking stem cells in vivo, finally, we present a novel imaging system based on our experiments

Host Responses to Intestinal Microbial Antigens in Gluten-Sensitive Mice

BACKGROUND AND AIMS: Excessive uptake of commensal bacterial antigens through a permeable intestinal barrier may influence host responses to specific antigen in a genetically predisposed host. The aim of this study was to investigate whether intestinal barrier dysfunction induced by indomethacin treatment affects the host response to intestinal microbiota in gluten-sensitized HLA-DQ8/HCD4 mice. METHODOLOGY/PRINCIPAL FINDINGS: HLA-DQ8/HCD4 mice were sensitized with gluten, and gavaged with indomethacin plus gluten. Intestinal permeability was assessed by Ussing chamber; epithelial cell (EC) ultra-structure by electron microscopy; RNA expression of genes coding for junctional proteins by Q-real-time PCR; immune response by in-vitro antigen-specific T-cell proliferation and cytokine analysis by cytometric bead array; intestinal microbiota by fluorescence in situ hybridization and analysis of systemic antibodies against intestinal microbiota by surface staining of live bacteria with serum followed by FACS analysis. Indomethacin led to a more pronounced increase in intestinal permeability in gluten-sensitized mice. These changes were accompanied by severe EC damage, decreased E-cadherin RNA level, elevated IFN-gamma in splenocyte culture supernatant, and production of significant IgM antibody against intestinal microbiota. CONCLUSION: Indomethacin potentiates barrier dysfunction and EC injury induced by gluten, affects systemic IFN-gamma production and the host response to intestinal microbiota antigens in HLA-DQ8/HCD4 mice. The results suggest that environmental factors that alter the intestinal barrier may predispose individuals to an increased susceptibility to gluten through a bystander immune activation to intestinal microbiota