Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-classical weights, for which the diagonal Ising correlations arise as the leading coefficient of the polynomials specialised appropriately. Here we demonstrate that the next-to-diagonal correlations of the anisotropic Ising model are evaluated as one of the elements of this isomonodromic system or essentially as the Cauchy-Hilbert transform of one of the bi-orthogonal polynomials.Comment: 11 pages, 1 figur

Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function

Immunoarchitecture of the Regenerating Rat Spleen: Effects of Partial Splenectomy and Heterotopic Autotransplantation

To investigate the microstructure of in situ (eutopic) and autotransplanted (ectopic) splenic remnants, adult Sprague-Dawley rats were studied 60 days after 1) subtotal (~80%) splenectomy, 2) total splenectomy followed by single or multiple remnant intraperitoneal autotransplantation, or 3) sham operation. Total nucleated cell counts were determined in excised splenic remnants, and immunohistochemical staining using monoclonal antibodies to rat B-and T-cell antigens was performed in serial tissue sections. Immunoarchitecture of eutopic remnants was indistinguishable from that of intact spleens and total nucleated cell counts remained proportional to weight. In contrast, ectopic remnants showed sparsity and abnormal mixing of B and T lymphocyte subpopulations with widespread loss of follicles and periarteriolar lymphoid sheaths in addition to lower density and marked reduction of total nucleated cells. These findings provide immunohistologic evidence that preservation of intact vasculature is critical to splenic architecture, which may account in part for the demonstrable functional inferiority of ectopic remnants

On equivariant characteristic ideals of real classes

Let $p$ be an odd prime, $F/{\Bbb Q}$ an abelian totally real number field, $F_\infty/F$ its cyclotomic ${\Bbb Z}_p$-extension, $G_\infty = Gal (F_\infty / {\Bbb Q}),$ ${\Bbb A} = {\Bbb Z}_p [[G_\infty]].$ We give an explicit description of the equivariant characteristic ideal of $H^2_{Iw} (F_\infty, {\Bbb Z}_p(m))$ over ${\Bbb A}$ for all odd $m \in {\Bbb Z}$ by applying M. Witte's formulation of an equivariant main conjecture (or "limit theorem") due to Burns and Greither. This could shed some light on Greenberg's conjecture on the vanishing of the $\lambda$-invariant of $F_\infty/F.

A novel approach to model 4 decades of marine chemical data

The awareness of the negative effects of chemical pollution in the sixties has led to an increased concern on the chemical status of the marine environment in the following decades. International regulation in Europe started with the Oslo and Paris convention in the seventies, later on leading to the OSPAR commission. At national level, extended research on chemical pollutants in marine sediments and marine biota was done within the “Project Mer/Projekt Zee” from 1970 to 1976. Since then, a long series of research and monitoring projects was conducted, reporting on the chemical status of the Belgian Part of the North&nbsp;Sea. &nbsp; Within the 4demon project, a major work package focused on the collection, quality control and intercalibration of more than 40 years of data on heavy metals and polychlorinated biphenyls. In this presentation, the modelling approach and results on sediment data will be&nbsp;presented. &nbsp; Within current OSPAR and MSFD monitoring on chemical pollution, variability in location, seasonality, grain size, etc. is reduced thanks to standardized OSPAR guidelines. This facilitates comparability of data within and between regions and assessments based on 5-15 year timetrends are frequently made. Within more than 40 years of pollution data, variability is much larger, and multiple issues should be tackled to intercalibrate the data: changes in sampling locations and analyses methods over time, missing essential metadata, sample analysis on different grain size fractions,… Therefore, existing time trend modelling approaches could not be applied within the 4Demon project. An alternative approach, focused on cluster analysis and different normalisation procedures was proposed. A parametric linear mixed effect model was used to integrate all data into consistent long term time lines which give a view on PCB and heavy metal pollution on a large time&nbsp;frame. &nbsp; Acknowledgement We want to thank the Belgian Science Policy Office (BELSPO) for the financial support of the 4Demon&nbsp;project.</p

Electron phonon coupling in ultrathin Pb films on Si(111): Where the heck is the energy?

In this work, we study the heat transfer from electron to phonon system within a five monolayer thin epitaxial Pb film on Si(111) upon fs-laser excitation. The response of the electron system is determined using time-resolved photoelectron spectroscopy while the lattice excitation is measured by means of the Debye-Waller effect in time-resolved reflection high-energy electron diffraction. The electrons lose their heat within 0.5 ps while the lattice temperature rises slowly in 3.5 to 8 ps, leaving a gap of 3-7 ps. We propose that the hidden energy is transiently stored in high-frequency phonon modes for which diffraction is insensitive and which are excited in 0.5 ps. Within a three-temperature model we use three heat baths, namely electrons, high-frequency and low-frequency phonon modes to simulate the observations. The excitation of low-frequency acoustic phonons, i.e., thermalization of the lattice is facilitated through anharmonic phonon-phonon interaction

Effect of human rotavirus vaccine on severe diarrhea in African infants.

BACKGROUND: Rotavirus is the most common cause of severe gastroenteritis among young children worldwide. Data are needed to assess the efficacy of the rotavirus vaccine in African children. METHODS: We conducted a randomized, placebo-controlled, multicenter trial in South Africa (3166 infants; 64.1% of the total) and Malawi (1773 infants; 35.9% of the total) to evaluate the efficacy of a live, oral rotavirus vaccine in preventing severe rotavirus gastroenteritis. Healthy infants were randomly assigned in a 1:1:1 ratio to receive two doses of vaccine (in addition to one dose of placebo) or three doses of vaccine--the pooled vaccine group--or three doses of placebo at 6, 10, and 14 weeks of age. Episodes of gastroenteritis caused by wild-type rotavirus during the first year of life were assessed through active follow-up surveillance and were graded with the use of the Vesikari scale. RESULTS: A total of 4939 infants were enrolled and randomly assigned to one of the three groups; 1647 infants received two doses of the vaccine, 1651 infants received three doses of the vaccine, and 1641 received placebo. Of the 4417 infants included in the per-protocol efficacy analysis, severe rotavirus gastroenteritis occurred in 4.9% of the infants in the placebo group and in 1.9% of those in the pooled vaccine group (vaccine efficacy, 61.2%; 95% confidence interval, 44.0 to 73.2). Vaccine efficacy was lower in Malawi than in South Africa (49.4% vs. 76.9%); however, the number of episodes of severe rotavirus gastroenteritis that were prevented was greater in Malawi than in South Africa (6.7 vs. 4.2 cases prevented per 100 infants vaccinated per year). Efficacy against all-cause severe gastroenteritis was 30.2%. At least one serious adverse event was reported in 9.7% of the infants in the pooled vaccine group and in 11.5% of the infants in the placebo group. CONCLUSIONS: Human rotavirus vaccine significantly reduced the incidence of severe rotavirus gastroenteritis among African infants during the first year of life. (ClinicalTrials.gov number, NCT00241644.

Spectral density asymptotics for Gaussian and Laguerre β\beta-ensembles in the exponentially small region

The first two terms in the large $N$ asymptotic expansion of the $\beta$ moment of the characteristic polynomial for the Gaussian and Laguerre $\beta$-ensembles are calculated. This is used to compute the asymptotic expansion of the spectral density in these ensembles, in the exponentially small region outside the leading support, up to terms $o(1)$ . The leading form of the right tail of the distribution of the largest eigenvalue is given by the density in this regime. It is demonstrated that there is a scaling from this, to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.Comment: 19 page