10,008 research outputs found

    Principal eigenvalues for k-Hessian operators by maximum principle methods

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    For fully nonlinear k-Hessian operators on bounded strictly (k - 1)-convex domains Ω of RN, a characterization of the principal eigenvalue associated to a k-convex and negative principal eigenfunction will be given as the supremum over values of a spectral parameter for which admissible viscosity supersolutions obey a minimum principle. The admissibility condition is phrased in terms of the natural closed convex cone Σk ⊂ S(N) which is an elliptic set in the sense of Krylov [23] which corresponds to using k-convex functions as admissibility constraints in the formulation of viscosity subsolutions and supersolutions. Moreover, the associated principal eigenfunction is constructed by an iterative viscosity solution technique, which exploits a compactness property which results from the establishment of a global Hölder estimate for the unique k-convex solutions of the approximating equations

    Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms

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    Hyperfine intervals in light hydrogenic atoms and ions are among the most accurately measured quantities in physics. The theory of QED corrections has recently advanced to the point that uncalculated terms for hydrogenic atoms and ions are probably smaller than 0.1 parts per million (ppm), and the experiments are even more accurate. The difference of the experiments and QED theory is interpreted as the effect on the hyperfine interaction of the (finite) nuclear charge and magnetization distributions, and this difference varies from tens to hundreds of ppm. We have calculated the dominant component of the 1s hyperfine interval for deuterium, tritium and singly ionized helium, using modern second-generation potentials to compute the nuclear component of the hyperfine splitting for the deuteron and the trinucleon systems. The calculated nuclear corrections are within 3% of the experimental values for deuterium and tritium, but are about 20% discrepant for singly ionized helium. The nuclear corrections for the trinucleon systems can be qualitatively understood by invoking SU(4) symmetry.Comment: 26 pages, 1 figure, latex - submitted to Physical Review

    Computationally efficient methods for fitting mixed models to electronic health records data

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    Motivated by two case studies using primary care records from the Clinical Practice Research Datalink, we describe statistical methods that facilitate the analysis of tall data, with very large numbers of observations. Our focus is on investigating the association between patient characteristics and an outcome of interest, while allowing for variation among general practices. We explore ways to fit mixed effects models to tall data, including predictors of interest and confounding factors as covariates, and including random intercepts to allow for heterogeneity in outcome among practices. We introduce: (1) weighted regression and (2) meta-analysis of estimated regression coefficients from each practice. Both methods reduce the size of the dataset, thus decreasing the time required for statistical analysis. We compare the methods to an existing subsampling approach. All methods give similar point estimates, and weighted regression and meta-analysis give similar standard errors for point estimates to analysis of the entire dataset, but the subsampling method gives larger standard errors. Where all data are discrete, weighted regression is equivalent to fitting the mixed model to the entire dataset. In the presence of a continuous covariate, meta-analysis is useful. Both methods are easy to implement in standard statistical softwareThe authors are grateful to the CPRD team at the University of Cambridge. In particular, we thank Carol Wilson and Anna Cassel for providing access to the case study datasets that they spent much time preparing for analysis. Kirsty Rhodes was funded by Medical Research Council Unit Programmes U105260558 and MC_UU_00002/5. Rebecca Turner and Ian White were funded by Medical Research Council Unit Programmes U105260558 and MC_UU_12023/2

    Voice Hacking: Using Smartphones to Spread Ransomware to Traditional PCs

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    This paper presents a voice hacking proof of concept that demonstrates the ability to deploy a sequence of hacks, triggered by speaking a smartphone command, to launch ransomware and other destructive attacks against vulnerable Windows computers on any wireless network the phone connects to after the voice command is issued. Specifically, a spoken, broadcast, or pre-recorded voice command directs vulnerable Android smartphones or tablets to a malicious download page that compromises the Android device and uses it as a proxy to run software designed to scan the Android device’s local area network for Windows computers vulnerable to the EternalBlue exploit, spreading a ransomware-like application to those PCs, and executing it remotely. The demonstrated proof of concept, with relevant source code included in the appendix, can be extended and adapted to allow other voice-enabled, mobile, and IoT devices to perform multi-platform attacks against traditional PCs, as well as other mobile and IoT devices, and even critical infrastructure systems. In addition to describing the proof-of-concept attack in detail, the authors propose several remedies individuals and organizations can employ to prevent such attacks

    Voice Hacking Proof of Concept: Using Smartphones to Spread Ransomware to Traditional PCs

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    This paper presents a working proof of concept that demonstrates the ability to deploy a sequence of hacks, triggered by speaking a smartphone command, to launch ransomware and other destructive attacks against vulnerable Windows computers on any wireless network the phone connects to after the voice command is issued. Specifically, a spoken, broadcast, or pre-recorded voice command directs vulnerable Android smartphones or tablets to a malicious download page that compromises the Android device and uses it as a proxy to run software designed to scan the Android device’s local area network for Windows computers vulnerable to the EternalBlue exploit, spreading a ransomware-like application to those PCs, and executing it remotely. In addition to describing the proof-of-concept attack in detail, the authors propose several remedies individuals and organizations can use to prevent such attacks

    Supercell technique for total-energy calculations of finite charged and polar systems

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    We study the behavior of total-energy supercell calculations for dipolar molecules and charged clusters. Using a cutoff Coulomb interaction within the framework of a plane-wave basis set formalism, with all other aspects of the method (pseudopotentials, basis set, exchange-correlation functional) unchanged, we are able to assess directly the interaction effects present in the supercell technique. We find that the supercell method gives structures and energies in almost total agreement with the results of calculations for finite systems, even for molecules with large dipole moments. We also show that the performance of finite-grid calculations can be improved by allowing a degree of aliasing in the Hartree energy, and by using a reciprocal space definition of the cutoff Coulomb interaction

    Finite Temperature Path Integral Method for Fermions and Bosons: a Grand Canonical Approach

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    The calculation of the density matrix for fermions and bosons in the Grand Canonical Ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It is shown that in a Path Integral Formulation fermionic density matrix can be expressed via an integration over a novel representation of the universal temperature dependent functional. While several representations for the universal functional have already been developed, they are usually presented in a form inconvenient for computer calculations. In this work we discuss a new representation for the universal functional in terms of Hankel functions which is advantageous for computational applications. Temperature scaling for the universal functional and its derivatives are also introduced thus allowing an efficient rescaling rather then recalculation of the functional at different temperatures. A simple illustration of the method of calculation of density profiles in Grand Canonical ensemble is presented using a system of noninteracting electrons in a finite confining potential.Comment: 13 pages 3 figure

    Compton Scattering by Static and Moving Media I. The Transfer Equation and Its Moments

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    Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first moments, in both the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in epsilon/m_e, T_e/m_e, and V, where epsilon is the photon energy, T_e and m_e are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second-order in V usually should be retained, because if the radiation energy density is sufficiently large compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second-order in V are at least as important as the effects described by the terms that are first-order in V, even when V is small. Our equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and the diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V^2 > 3 T_e/m_e.Comment: 31 pages, accepted for publication in The Astrophysical Journa

    Modeling and Simulation of Multi-Lane Traffic Flow

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    A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, overtaking and lane-changing maneuvers is systematically deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations contain corrections with respect to previous models. For efficient computer simulations, a reduced model delineating the coarse-grained temporal behavior is derived and applied to bottleneck situations.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm
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