Nodal domains of Maass forms I

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the $L^2$-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.Comment: To appear in GAF

Dual symmetry and the vacuum energy

In this work we present a new hidden symmetry in gravity for the scale factor in the FRW model, for $k=0$. This exact symmetry vanishes the cosmological constant. We interpret this hidden symmetry as a dual symmetry in the sense that appears in the string theory.Comment: 7 pages, no figures, work sent to Class. Quantum Gra

A comprehensive ovine model of blood transfusion

Background: The growing awareness of transfusion-associated morbidity and mortality necessitates investigations into the underlying mechanisms. Small animals have been the dominant transfusion model but have associated limitations. This study aimed to develop a comprehensive large animal (ovine) model of transfusion encompassing: blood collection, processing and storage, compatibility testing right through to post-transfusion outcomes. Materials and methods: Two units of blood were collected from each of 12 adult male Merino sheep and processed into 24 ovine-packed red blood cell (PRBC) units. Baseline haematological parameters of ovine blood and PRBC cells were analysed. Biochemical changes in ovine PRBCs were characterized during the 42-day storage period. Immunological compatibility of the blood was confirmed with sera from potential recipient sheep, using a saline and albumin agglutination cross-match. Following confirmation of compatibility, each recipient sheep (n = 12) was transfused with two units of ovine PRBC. Results: Procedures for collecting, processing, cross-matching and transfusing ovine blood were established. Although ovine red blood cells are smaller and higher in number, their mean cell haemoglobin concentration is similar to human red blood cells. Ovine PRBC showed improved storage properties in saline-adenine-glucose-mannitol (SAG-M) compared with previous human PRBC studies. Seventy-six compatibility tests were performed and 17·1% were incompatible. Only cross-match compatible ovine PRBC were transfused and no adverse reactions were observed. Conclusion: These findings demonstrate the utility of the ovine model for future blood transfusion studies and highlight the importance of compatibility testing in animal models involving homologous transfusions

Vortex Polarity Switching in Magnets with Surface Anisotropy

Vortex core reversal in magnetic particle is essentially influenced by a surface anisotropy. Under the action of a perpendicular static magnetic field the vortex core undergoes a shape deformationof pillow- or barrel-shaped type, depending on the type of the surface anisotropy. This deformation plays a key point in the switching mechanism: We predict that the vortex polarity switching is accompanied (i) by a linear singularity in case of Heisenberg magnet with bulk anisotropy only and (ii) by a point singularities in case of surface anisotropy or exchange anisotropy. We study in details the switching process using spin-lattice simulations and propose a simple analytical description using a wired core model, which provides an adequate description of the Bloch point statics, its dynamics and the Bloch point mediated switching process. Our analytical predictions are confirmed by spin-lattice simulations for Heisenberg magnet and micromagnetic simulations for nanomagnet with account of a dipolar interaction.Comment: 17 pages, 15 figure

Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $\mu$ and degree $-\frac12+i\tau$, where $\tau$ is a non-negative real parameter. Solutions of this equation are the conical functions ${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ and ${Q}^{\mu}_{-\frac12+i\tau}(x)$, $x>-1$. An algorithm for computing a numerically satisfactory pair of solutions is already available when $-1<x<1$ (see \cite{gil:2009:con}, \cite{gil:2012:cpc}).In this paper, we present a stable computational scheme for a real valued numerically satisfactory companion of the function ${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ for $x>1$, the function $\Re\left\{e^{-i\pi \mu} {{Q}}^{\mu}_{-\frac{1}{2}+i\tau}(x) \right\}$. The proposed algorithm allows the computation of the function on a large parameter domain without requiring the use of extended precision arithmetic.Comment: To be published in Numerical Algoritm

Interspecies differences in protein expression do not impact the spatiotemporal regulation of glycoprotein VI mediated activation

Background Accurate protein quantification is a vital prerequisite for generating meaningful predictions when using systems biology approaches, a method that is increasingly being used to unravel the complexities of sub cellular interactions and as part of the drug discovery process. Quantitative proteomics, flow cytometry and western blotting have been extensively used to define human platelet protein copy numbers, yet for mouse platelets, a model widely used for platelet research, evidence is largely limited to a single proteomic dataset in which the total amount of proteins were generally comparatively higher than those found in human platelets. Objectives To investigate the functional implications of discrepancies between levels of mouse and human proteins in the GPVI signalling pathway using a systems pharmacology model of GPVI Methods The protein copy number of mouse platelet receptors was determined using flow cytometry. The Virtual Platelet, a mathematical model of Glycoprotein VI (GPVI) signalling, was used to determine the consequences of protein copy number differences observed between human and mouse platelets. Results and conclusion Despite the small size of mouse platelets compared to human platelets they possessed a greater density of surface receptors alongside a higher concentration of intracellular signalling proteins. Surprisingly the predicted temporal profile of Syk activity was similar in both species with predictions supported experimentally. Super resolution microscopy demonstrates that the spatial distribution of Syk is similar between species, suggesting that the spatial distribution of receptors and signalling molecules in activated platelets, rather than their copy number, is important for signalling pathway regulation

Computation of parabolic cylinder functions having complex argument

Numerical methods for the computation of the parabolic cylinder $U(a,z)$ for real $a$ and complex $z$ are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main main methods can be complemented with Maclaurin series and a Poincar\'e asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with $5\times 10^{-13}$ relative accuracy in double precision floating point arithmetic