Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Rotating Black Holes in Metric-Affine Gravity

Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially symmetric exact solution of the vacuum field equations. This black hole solution embodies a Kerr-deSitter metric and the post-Riemannian structures of torsion and nonmetricity. The solution is characterized by mass, angular momentum, and shear charge, the latter of which is a measure for violating Lorentz invariance.Comment: 32 pages latex, 3 table

K-matrices for non-abelian quantum Hall states

Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.Comment: LaTeX, 12 page

Tunnelling rates for the nonlinear Wannier-Stark problem

We present a method to numerically compute accurate tunnelling rates for a Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii equation. Our method is based on a sophisticated real-time integration of the complex-scaled Gross-Pitaevskii equation, and it is capable of finding the stationary eigenvalues for the Wannier-Stark problem. We show that even weak nonlinearities have significant effects in the vicinity of very sensitive resonant tunnelling peaks, which occur in the rates as a function of the Stark field amplitude. The mean-field interaction induces a broadening and a shift of the peaks, and the latter is explained by analytic perturbation theory

Applying machine learning to improve simulations of a chaotic dynamical system using empirical error correction

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models still show many differences compared with observations. Machine learning has been applied to solve certain prediction problems with great success, and recently it's been proposed that this could replace the role of physically-derived dynamical weather and climate models to give better quality simulations. Here, instead, a framework using machine learning together with physically-derived models is tested, in which it is learnt how to correct the errors of the latter from timestep to timestep. This maintains the physical understanding built into the models, whilst allowing performance improvements, and also requires much simpler algorithms and less training data. This is tested in the context of simulating the chaotic Lorenz '96 system, and it is shown that the approach yields models that are stable and that give both improved skill in initialised predictions and better long-term climate statistics. Improvements in long-term statistics are smaller than for single time-step tendencies, however, indicating that it would be valuable to develop methods that target improvements on longer time scales. Future strategies for the development of this approach and possible applications to making progress on important scientific problems are discussed.Comment: 26p, 7 figures To be published in Journal of Advances in Modeling Earth System

Schottky barrier formation at the Au to rare earth doped GaN thin film interface

The Schottky barriers formed at the interface between gold and various rare earth doped GaN thin films (RE = Yb, Er, Gd) were investigated in situ using synchrotron photoemission spectroscopy. The resultant Schottky barrier heights were measured as 1.68 ± 0.1 eV (Yb:GaN), 1.64 ± 0.1 eV (Er:GaN), and 1.33 ± 0.1 eV (Gd:GaN). We find compelling evidence that thin layers of gold do not wet and uniformly cover the GaN surface, even with rare earth doping of the GaN. Furthermore, the trend of the Schottky barrier heights follows the trend of the rare earth metal work function

Cosmic Ray Protons and Magnetic Fields in Clusters of Galaxies and their Cosmological Consequences

The masses of clusters of galaxies estimated by gravitational lensing exceed in many cases the mass estimates based on hydrostatic equilibrium. This may suggest the existence of nonthermal pressure. We ask if radio galaxies can heat and support the cluster gas with injected cosmic ray protons and magnetic field densities, which are permitted by Faraday rotation and gamma ray observations of clusters of galaxies. We conclude that they are powerful enough to do this within a cluster radius of roughly 1 Mpc. If present, nonthermal pressures could lead to a revised estimate of the ratio of baryonic mass to total mass, and the apparent baryonic overdensity in clusters would disappear. In consequence, $\Omega_{\rm cold}$, the clumping part of the cosmological density $\Omega_{o}$, would be larger than $0.4\,h_{50}^{-1/2}$.Comment: Accepted by ApJ, 16 pages, LaTeX, 2 figures, epsfig.sty, aaspp4.st

Metabolic changes related to the IDH1 mutation in gliomas preserve TCA-cycle activity: An investigation at the protein level

The discovery of the IDH1 R132H (IDH1 mut) mutation in low-grade glioma and the associated change in function of the IDH1 enzyme has increased the interest in glioma metabolism. In an earlier study, we found that changes in expression of genes involved in the aerobic glycolysis and the TCA cycle are associated with IDH1 mut. Here, we apply proteomics to FFPE samples of diffuse gliomas with or without IDH1 mutations, to map changes in protein levels associated with this mutation. We observed significant changes in the enz