Convergence of measures on compactifications of locally symmetric spaces

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S=Γ∖G/K is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when G=SL3(R) and Γ=SL3(Z)

Distributions, non-smooth manifolds, transmutations and boundary value problems

One discusses the problem of constructing the theory of pseudo differential equations on manifoldswith a non-smooth boundary.Using special factorization principle and transmutation operators we consider some general boundary value problems for elliptic pseudo-differential equations in canonical non-smooth manifold

Interpreting Meta-Analyses of Genome-Wide Association Studies

Meta-analysis is an increasingly popular tool for combining multiple genome-wide association studies in a single analysis to identify associations with small effect sizes. The effect sizes between studies in a meta-analysis may differ and these differences, or heterogeneity, can be caused by many factors. If heterogeneity is observed in the results of a meta-analysis, interpreting the cause of heterogeneity is important because the correct interpretation can lead to a better understanding of the disease and a more effective design of a replication study. However, interpreting heterogeneous results is difficult. The standard approach of examining the association p-values of the studies does not effectively predict if the effect exists in each study. In this paper, we propose a framework facilitating the interpretation of the results of a meta-analysis. Our framework is based on a new statistic representing the posterior probability that the effect exists in each study, which is estimated utilizing cross-study information. Simulations and application to the real data show that our framework can effectively segregate the studies predicted to have an effect, the studies predicted to not have an effect, and the ambiguous studies that are underpowered. In addition to helping interpretation, the new framework also allows us to develop a new association testing procedure taking into account the existence of effect

On limit behavior of a solution to boundary value problem in a plane sector

Authors study a certain boundary value problem in Sobolev-Slobodetskii spaces with integral condition in a plane excluding a ray from origin. Using auxiliary problem in outside of a convex cone and the wave factorization concept, we construct a general solution and consider transfer to limit boundary value problem. It was shown that limit boundary value problem can be solvable only if the boundary function satisfies to a certain singular functional equatio

Human Blood Vessel–Derived Endothelial Progenitors for Endothelialization of Small Diameter Vascular Prosthesis

BACKGROUND:Coronary bypass graft failure as a result of acute thrombosis and intimal hyperplasia has been the major challenge in surgical procedures involving small-diameter vascular prosthesis. Coating synthetic grafts with patients' own endothelial cells has been suggested to improve the patency rate and overall success of bypass surgeries. METHODOLOGY/PRINCIPAL FINDINGS:We isolated endothelial progenitor cells (EPCs) from leftover pieces of human saphenous vein/mammary artery. We demonstrate that EPCs can be expanded to generate millions of cells under low-density culture conditions. Exposure to high-density conditions induces differentiation to endothelial cell phenotype. EPC-derived endothelial cells show expression of CD144high, CD31, and vWF. We then assessed the ability of differentiated endothelial cells to adhere and grow on small diameter expanded polytetrafluoroethylene (ePTFE) tubings. Since ePTFE tubings are highly hydrophobic, we optimized protocols to introduce hydrophilic groups on luminal surface of ePTFE tubings. We demonstrate here a stepwise protocol that involves introduction of hydrophilic moieties and coating with defined ECM components that support adhesion of endothelial cells, but not of blood platelets. CONCLUSION/SIGNIFICANCE:Our data confirms that endothelial progenitors obtained from adult human blood vessels can be expanded in vitro under xenoprotein-free conditions, for potential use in endothelialization of small diameter ePTFE grafts. These endothelialized grafts may represent a promising treatment strategy for improving the clinical outcome of small-caliber vascular grafts in cardiac bypass surgeries

Diffraction from polygonal-conical screens, an operator approach

The aim of this work is to construct explicitly resolvent operators for a class of boundary value problems in diffraction theory. These are formulated as boundary value problems for the three-dimensional Helmholtz equation with Dirichlet or Neumann conditions on a plane screen of polynomial-conical form (including unbounded and multiply-connected screens), in weak formulation. The method is based upon operator theoretical techniques in Hilbert spaces, such as the construction of matrical coupling relations and certain orthogonal projections, which represent new techniques in this area of applications. Various cross connections are exposed, particularly considering classical Wiener-Hopf operators in So\-bo\-lev spaces as general Wiener-Hopf operators in Hilbert spaces and studying relations between the crucial operators in game. Former results are extended, particularly to multiply-connected screens

Combined deformation and solidification-driven porosity formation in aluminum alloys

In die-casting processes, the high cooling rates and pressures affect the alloy solidification and deformation behavior, and thereby impact the final mechanical properties of cast components. In this study, isothermal semi-solid compression and subsequent cooling of aluminum die-cast alloy specimens were characterized using fast synchrotron tomography. This enabled the investigation and quantification of gas and shrinkage porosity evolution during deformation and solidification. The analysis of the 4D images (3D plus time) revealed two distinct mechanisms by which porosity formed; (i) deformation-induced growth due to the enrichment of local hydrogen content by the advective hydrogen transport, as well as a pressure drop in the dilatant shear bands, and (ii) diffusion-controlled growth during the solidification. The rates of pore growth were quantified throughout the process, and a Gaussian distribution function was found to represent the variation in the pore growth rate in both regimes. Using a one-dimensional diffusion model for hydrogen pore growth, the hydrogen flux required for driving pore growth during these regimes was estimated, providing a new insight into the role of advective transport associated with the deformation in the mushy region

Psychopathological consequences related to problematic Instagram use among adolescents: the mediating role of body image dissatisfaction and moderating role of gender

In a minority of cases, problematic use of technology can negatively impact on adolescents and impair some aspects of their social, emotional, and psychological development. The purpose of the present study was to examine the direct and indirect effects of problematic Instagram use (PIU) on different psychopathological outcomes including loneliness, depression, anxiety, and social anxiety via body image dissatisfaction (BID). Additionally, moderating role of gender on the relationships among variables was investigated. A total of 491 adolescents (Mage = 15.92 years, SDage = 1.07; range = 14 to 19 years) were recruited for the study to complete a questionnaire that included the relevant assessment tools for the aforementioned variables. Mediation and moderation analyses showed that among male adolescents, PIU was directly associated with loneliness, depression, general anxiety, and social anxiety and BID partially mediated these associations. Among females, PIU was directly associated with depression and indirectly with general anxiety and social anxiety via BID. Gender significantly moderated the direct relationships of PIU with loneliness, general anxiety, and social anxiety. PIU was directly associated with loneliness, general anxiety, and social anxiety among males only, whereas among females, PIU was indirectly associated with general and social anxiety via BID but was not related to loneliness. Results of this study indicate that PIU has different negative psychological effects on male and female adolescents and that BID appears to be one explanatory factor for these impairments especially among females