The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in $L^{2}$ Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit

Mother-child histocompatibility and risk of rheumatoid arthritis and systemic lupus erythematosus among mothers.

The study objective was to test the hypothesis that having histocompatible children increases the risk of rheumatoid arthritis (RA) and systemic lupus erythematosus (SLE), possibly by contributing to the persistence of fetal cells acquired during pregnancy. We conducted a case control study using data from the UC San Francisco Mother Child Immunogenetic Study and studies at the Inova Translational Medicine Institute. We imputed human leukocyte antigen (HLA) alleles and minor histocompatibility antigens (mHags). We created a variable of exposure to histocompatible children. We estimated an average sequence similarity matching (SSM) score for each mother based on discordant mother-child alleles as a measure of histocompatibility. We used logistic regression models to estimate odds ratios (ORs) and 95% confidence intervals. A total of 138 RA, 117 SLE, and 913 control mothers were analyzed. Increased risk of RA was associated with having any child compatible at HLA-B (OR 1.9; 1.2-3.1), DPB1 (OR 1.8; 1.2-2.6) or DQB1 (OR 1.8; 1.2-2.7). Compatibility at mHag ZAPHIR was associated with reduced risk of SLE among mothers carrying the HLA-restriction allele B*07:02 (n = 262; OR 0.4; 0.2-0.8). Our findings support the hypothesis that mother-child histocompatibility is associated with risk of RA and SLE

Tear fluid biomarkers in ocular and systemic disease: potential use for predictive, preventive and personalised medicine

In the field of predictive, preventive and personalised medicine, researchers are keen to identify novel and reliable ways to predict and diagnose disease, as well as to monitor patient response to therapeutic agents. In the last decade alone, the sensitivity of profiling technologies has undergone huge improvements in detection sensitivity, thus allowing quantification of minute samples, for example body fluids that were previously difficult to assay. As a consequence, there has been a huge increase in tear fluid investigation, predominantly in the field of ocular surface disease. As tears are a more accessible and less complex body fluid (than serum or plasma) and sampling is much less invasive, research is starting to focus on how disease processes affect the proteomic, lipidomic and metabolomic composition of the tear film. By determining compositional changes to tear profiles, crucial pathways in disease progression may be identified, allowing for more predictive and personalised therapy of the individual. This article will provide an overview of the various putative tear fluid biomarkers that have been identified to date, ranging from ocular surface disease and retinopathies to cancer and multiple sclerosis. Putative tear fluid biomarkers of ocular disorders, as well as the more recent field of systemic disease biomarkers, will be shown

Properties of field functionals and characterization of local functionals

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincar\'e lemma and defining multi-vector fields and graded functionals within our framework.Comment: 32 pages, no figur

Abdominal pain in an adult with Type 2 diabetes: A case report

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens