Topological Phenomena in the Real Periodic Sine-Gordon Theory

The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the consequences of this property. In particular this description allows to calculate the topological charge of solutions (the averaging of the $x$-derivative of the potential) and to show that the averaging of other standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure

Iso-spectral deformations of general matrix and their reductions on Lie algebras

We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we consider several reductions of the hierarchy. These include not only the integrable systems studied by Bogoyavlensky and Kostant, but also their generalizations which were not known to be integrable before. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.Comment: 25 pages, AMSLaTe

Biomarkers of oxidative and nitrosative damage in Alzheimer's disease and mild cognitive impairment

Alzheimer's disease (AD) is the most common type of dementia in the elderly. Products of oxidative and nitrosative stress (OS and NS, respectively) accumulate with aging, which is the main risk factor for AD. This provides the basis for the involvement of OS and NS in AD pathogenesis. OS and NS occur in biological systems due to the dysregulation of the redox balance, caused by a deficiency of antioxidants and/or the overproduction of free radicals. Free radical attack against lipids, proteins, sugars and nucleic acids leads to the formation of bioproducts whose detection in fluids and tissues represents the currently available method for assessing oxidative/nitrosative damage. Post-mortem and in-vivo studies have demonstrated an accumulation of products of free radical damage in the central nervous system and in the peripheral tissues of subjects with AD or mild cognitive impairment (MCI). In addition to their individual role, biomarkers for OS and NS in AD are associated with altered bioenergetics and amyloid-beta (Aβ) metabolism. In this review we discuss the main results obtained in the field of biomarkers of oxidative/nitrosative stress in AD and MCI in humans, in addition to their potential role as a tool for diagnosis, prognosis and treatment efficacy in AD. © 2009 Elsevier Ireland Ltd. All rights reserved

Econometric analysis of the link between public transport accessibility and employment

Modern transport policy analysis has ceased to be mainly about transport impacts and is now focussed on the effects of provision and policy upon the operation of the economy and society. For people on the edge of the labour market, many of whom do not have access to other forms of transport, public transport is a very important source of accessibility to jobs. This analysis addresses what we see as a key research gap in Britain - whether there is a systematic variation in the level of employment at the local level with the quality of the public transport network. To address this we apply regression analysis to explain employment as a function of accessibility and other local labour and socioeconomic variables. Our data were based on a cross-section of output areas from the English part of the 2011 Census. We found a statistically significant relationship suggesting that, all else being equal, areas with shorter public transport times were associated with higher employment levels

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

Large N expansion of the 2-matrix model

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.Comment: 41 pages, 9 figures eps

Cognitive performance in elderly patients undergoing carotid endarterectomy or carotid artery stenting: A twelve-month follow-up study

Background: It is still a matter of debate if and to what extent carotid endarterectomy (CEA) and carotid artery stenting (CAS) impair cognitive functioning in the elderly. Methods: We conducted a nonrandomized clinical trial on subjects with asymptomatic carotid artery stenosis comparing CEA (n = 28; 24 males and 4 females; 72.6 ± 5.8 years old) with CAS (n = 29; 17 males and 12 females; 75.1 ± 5.7 years old). Cognition, mood and functional status were evaluated by a broad spectrum of tests performed on the day prior to carotid reopening as well as 3 and 12 months after. Results: No significant differences in scores on cognitive tests including the Babcock story recall test and Rey's auditory verbal learning test (memory), category naming test (verbal fluency), trail-making test parts A and B (attention and executive function) and controlled oral word association test (executive functioning) were observed 3 and 12 months after carotid reopening independent of the technique used. Only scores on the copy drawing test (visuospatial and constructional abilities) slightly but significantly (p < 0.05) worsened in the CAS group 12 months after the intervention. No significant differences between the CEA and CAS groups were detected regarding mood and functional status after 3 and 12 months. Conclusions: CEA and CAS seem to be safe procedures in elderly patients in terms of cognitive, mood and functional status in the short and long term. CAS might be preferred for the shorter hospital stay, but further studies with a larger number of old and oldest old subjects with a longer follow-up are needed to better understand the cost-effectiveness of both treatments

On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian, we introduce two families of discrete matrix models constructed both with the help of the Erdos-Renyi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogs of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions in the cases of constant and vanishing edge probabilities as n tends to infinity.Comment: 34 pages, 8 figure

The influence of microstructure on the performance of white porcelain stoneware

In the last years polished white porcelain stoneware tiles, coupling the smooth and glossy surface with the increased body whiteness, get a prominent role on the market. The bright white colour is obtained by adding noteworthy quantity of opacifiers, such as zircon, corundum and spinel. To better understand the complex relationships among the microstructure and the mechanical, tribological and functional behaviour of this class of products, four polished white porcelain stoneware tiles were selected and thoroughly characterized by a wide spectrum of chemico-physical and microstructural analyses. Products exhibit excellent mechanical properties (flexural strength, Young modulus, fracture toughness) with a clear dependence of these properties on porosity and phase composition. Mullite and zircon tend to increase the mechanical performances, through a predominant mechanism of matrix reinforcement, while quartz plays an opposite role