Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

HIV-Specific T-Cells Accumulate in the Liver in HCV/HIV Co-Infection

BACKGROUND AND AIMS: Hepatitis C Virus (HCV)-related liver disease progresses more rapidly in individuals co-infected with Human Immunodeficiency Virus-1 (HIV), although the underlying immunologic mechanisms are unknown. We examined whether HIV-specific T-cells are identified in the liver of HCV/HIV co-infected individuals and promote liver inflammation through bystander immune responses. METHODS: Ex-vivo intra-hepatic lymphocytes from HCV mono-infected and HCV/HIV co-infected individuals were assessed for immune responses to HIV and HCV antigens by polychromatic flow cytometry. RESULTS: HCV/HIV liver biopsies had similar frequencies of lymphocytes but lower percentages of CD4+ T-cells compared to HCV biopsies. In co-infection, intra-hepatic HIV-specific CD8+ and CD4+ T-cells producing IFN-gamma and TNF-alpha were detected and were comparable in frequency to those that were HCV-specific. In co-infected individuals, viral-specific CD8+ T-cells produced more of the fibrogenic cytokine, TNF-alpha. In both mono- and co-infected individuals, intra-hepatic HCV-specific T-cells were poorly functional compared to HIV-specific T-cells. In co-infection, HAART was not associated with a reconstitution of intra-hepatic CD4+ T-cells and was associated with reduction in both HIV and HCV-specific intra-hepatic cytokine responses. CONCLUSION: The accumulation of functional HIV-specific T-cells in the liver during HCV/HIV co-infection may represent a bystander role for HIV in inducing faster progression of liver disease

Generalizations of the short pulse equation

We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Research and practice for ultra-high risk for psychosis : a national survey of early intervention in psychosis services in England

Background: Evidence from meta-analyses of randomized clinical trials show interventions for young people at ultra-high risk (UHR) of developing psychosis are effective both clinically and economically. While research evidence has begun to be integrated into clinical guidelines, there is a lack of research on the implementation of these guidelines. This paper examines service provision for UHR individuals in accordance with current clinical guidelines within the National Health Service (NHS) in England. Method: A self-report online survey was completed by clinical leaders of early intervention in psychosis (EIP) teams (N = 50) within the NHS across England. Results: Of the 50 EIP teams responding (from 30 NHS trusts), 53% reported inclusion of the UHR group in their service mandate, with age range predominantly 14 to 35 years (81%) and service provided for at least 12 months (53%). Provision of services according to NICE clinical guidelines showed 50% of services offered cognitive behavioural therapy (CBT) for psychosis, and 42% offered family intervention. Contrary to guidelines, 50% of services offered antipsychotic medication. Around half of services provided training in assessment by Comprehensive Assessment of At Risk Mental States, psycho-education, CBT for psychosis, family work and treatment for anxiety and depression. Conclusions: Despite clear evidence for the benefit of early intervention in this population, current provision for UHR within EIP services in England does not match clinical guidelines. While some argue this is due to a lack of allocated funding, it is important to note the similar variable adherence to clinical guidelines in the treatment of people with established schizophrenia

Approximations to large amplitude solitary waves on nonlinear electrical lattices

In this paper we describe an approximate method to characterise solitary wave solutions of nonlinear lattice equations. It is based upon one and two point Pade approximations to a series of the real exponential travelling wave solutions of the underlying dispersive system. The theory is applied to an example of a lattice system which models an experimental nonlinear transmission line and the results obtained are consistent with numerical simulations even for relatively large amplitude solitary waves. The speed-amplitude relation is investigated and compared with that derived using quasi-continuum methods