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 $J_{2n,k}$

Extending political participation in China: new opportunities for citizens in the policy process

Authoritarian political systems are portrayed as offering few opportunities for citizens to participate in politics – particularly in the policy process. This paper’s contribution is to set out new mechanisms that enable Authoritarian political systems are portrayed as offering few opportunities for citizens to participate in politics – particularly in the policy process. This paper’s contribution is to set out new mechanisms that enable Chinese citizens to evaluate government performance, contribute to decision-making, shape policy agendas and feed back on implementation. Based on fieldwork in the city of Hangzhou, we argue that the local party-state orchestrates citizen participation in the policy process, but members of the public nevertheless do have influence. Political participation is widening in China, but it is still controlled. It is not yet clearly part of a process of democratization, but it does establish the principle of citizen rights to oversee the government

Obesity, diabetes, serum glucose, and risk of primary liver cancer by birth cohort, race/ethnicity, and sex: Multiphasic health checkup study

Obesity and diabetes have been associated with liver cancer. However, recent US-based studies have suggested a lack of association between obesity and liver cancer among blacks and women

Does Squamous Differentiation Portend Worse Outcomes in Urothelial Bladder Cancer?

Introduction Interest on the impact of variant histology in bladder cancer prognosis is increasing. Although squamous differentiation is the most well characterized, only recently have less common variants gained increased recognition. We assessed whether squamous differentiation conferred a worse prognosis than nonvariant urothelial bladder cancer in a contemporary cohort of patients treated with radical cystectomy given the increased awareness of other less common variants. Methods We identified patients with squamous differentiation or nonvariant histology on transurethral resection of bladder tumor and/or cystectomy pathology during a 10-year period. Disease specific and overall survival were evaluated using Kaplan-Meier methodology. Cox regression was used to assess variables associated with mortality. Results Between 2003 and 2013, 934 patients underwent cystectomy for urothelial bladder cancer. Overall 617 nonvariant and 118 squamous differentiation cases were identified, and the remainder was nonsquamous differentiation variant histology. Overall 75% of patients with squamous differentiation had muscle invasive disease at diagnosis compared with 59% of those with nonvariant histology (p=0.002). Nonorgan confined disease at cystectomy was more common in patients with squamous differentiation (57% vs 44%, p=0.009). Among cases on neoadjuvant chemotherapy 20% (9 of 45) of nonvariant and 13% (1 of 8) of squamous differentiation were pT0N0 (p=0.527). Median followup was 52 months. Adjusted for demographics, pathological stage and chemotherapy, squamous differentiation was not associated with an increased risk of disease specific (HR 1.35, 95% CI 0.90–2.04, p=0.150) or all cause mortality (HR 0.90, 95% CI 0.60–1.25, p=0.515). Conclusions In a contemporary cohort of urothelial bladder cancer with recognition and characterization of less commonly described variants, squamous differentiation is not associated with a worse disease specific and all cause mortality when compared to a pure nonvariant cohort

Application of pharmacogenomics and bioinformatics to exemplify the utility of human <i>ex vivo</i> organoculture models in the field of precision medicine

Here we describe a collaboration between industry, the National Health Service (NHS) and academia that sought to demonstrate how early understanding of both pharmacology and genomics can improve strategies for the development of precision medicines. Diseased tissue ethically acquired from patients suffering from chronic obstructive pulmonary disease (COPD), was used to investigate inter-patient variability in drug efficacy using ex vivo organocultures of fresh lung tissue as the test system. The reduction in inflammatory cytokines in the presence of various test drugs was used as the measure of drug efficacy and the individual patient responses were then matched against genotype and microRNA profiles in an attempt to identify unique predictors of drug responsiveness. Our findings suggest that genetic variation in CYP2E1 and SMAD3 genes may partly explain the observed variation in drug response

Cancer risk among 21st century blood transfusion recipients

Background: Some carcinogenic viruses are known to be transmissible by blood transfusion. Intensive viral screening of transfused blood now exists in most countries. In the UK, high-sensitivity nucleic acid amplification tests for hepatitis C virus were introduced in 1999 and it was thought that this would reduce, and possibly eliminate, transfusion-related liver cancer. We aimed to investigate cancer risk in recipients of blood transfusion in 2000 or after. Methods: A total of 1.3 million UK women recruited in 1998 on average were followed for hospital records of blood transfusion and for cancer registrations. After excluding women with cancer or precancerous conditions before or at the time of transfusion, Cox regression yielded adjusted relative risks of 11 site-specific cancers for women with compared to without prior blood transfusion. Results: During follow up, 11 274 (0.9%) women had a first recorded transfusion in 2000 or after, and 1648 (14.6%) of them were subsequently diagnosed with cancer, a mean 6.8 years after the transfusion. In the first 5 years after transfusion there were significant excesses for most site-specific cancers examined, presumably because some had preclinical cancer. However, 5 or more years (mean 8 years) after blood transfusion, there were significant excess risks only for liver cancer (adjusted relative risk = 2.63, 95%CI 1.45-4.78) and for non-Hodgkin lymphoma (adjusted relative risk = 1.74, 1.21-2.51). When analyses were restricted to those undergoing hip or knee replacement surgery, the commonest procedure associated with transfusion, these relative risks were not materially altered. Conclusions: In a large cohort of UK women, transfusions in the 21st century were associated with long-term increased risks of liver cancer and non-Hodgkin lymphoma. Some of these malignancies may have been caused by carcinogenic agents that are not currently screened for in transfused blood.The Million Women Study is funded by Medical Research Council and Cancer Research UK (Cancer Research UK: C570/ A16491, Medical Research Council: MR/K02700X/1

Genetically Determined Plasma Lipid Levels and Risk of Diabetic Retinopathy: A Mendelian Randomization Study.

Results from observational studies examining dyslipidemia as a risk factor for diabetic retinopathy (DR) have been inconsistent. We evaluated the causal relationship between plasma lipids and DR using a Mendelian randomization approach. We pooled genome-wide association studies summary statistics from 18 studies for two DR phenotypes: any DR (N = 2,969 case and 4,096 control subjects) and severe DR (N = 1,277 case and 3,980 control subjects). Previously identified lipid-associated single nucleotide polymorphisms served as instrumental variables. Meta-analysis to combine the Mendelian randomization estimates from different cohorts was conducted. There was no statistically significant change in odds ratios of having any DR or severe DR for any of the lipid fractions in the primary analysis that used single nucleotide polymorphisms that did not have a pleiotropic effect on another lipid fraction. Similarly, there was no significant association in the Caucasian and Chinese subgroup analyses. This study did not show evidence of a causal role of the four lipid fractions on DR. However, the study had limited power to detect odds ratios less than 1.23 per SD in genetically induced increase in plasma lipid levels, thus we cannot exclude that causal relationships with more modest effect sizes exist

Expression of DC-SIGN and DC-SIGNR on human sinusoidal endothelium: a role for capturing hepatitis C virus particles.

Hepatic sinusoidal endothelial cells are unique among endothelial cells in their ability to internalize and process a diverse range of antigens. DC-SIGNR, a type 2 C-type lectin expressed on liver sinusoids, has been shown to bind with high affinity to hepatitis C virus (HCV) E2 glycoprotein. DC-SIGN is a closely related homologue reported to be expressed only on dendritic cells and a subset of macrophages and has similar binding affinity to HCV E2 glycoprotein. These receptors function as adhesion and antigen presentation molecules. We report distinct patterns of DC-SIGNR and DC-SIGN expression in human liver tissue and show for the first time that both C-type lectins are expressed on sinusoidal endothelial cells. We confirmed that these receptors are functional by demonstrating their ability to bind HCV E2 glycoproteins. Although these lectins on primary sinusoidal cells support HCV E2 binding, they are unable to support HCV entry. These data support a model where DC-SIGN and DC-SIGNR on sinusoidal endothelium provide a mechanism for high affinity binding of circulating HCV within the liver sinusoids allowing subsequent transfer of the virus to underlying hepatocytes, in a manner analogous to DC-SIGN presentation of human immunodeficiency virus on dendritic cells