Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Concepts, Developments and Advanced Applications of the PAX Toolkit

The Physics Analysis eXpert (PAX) is an open source toolkit for high energy physics analysis. The C++ class collection provided by PAX is deployed in a number of analyses with complex event topologies at Tevatron and LHC. In this article, we summarize basic concepts and class structure of the PAX kernel. We report about the most recent developments of the kernel and introduce two new PAX accessories. The PaxFactory, that provides a class collection to facilitate event hypothesis evolution, and VisualPax, a Graphical User Interface for PAX objects

The Density of States and the Spectral Shift Density of Random Schroedinger Operators

In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur

Cardiac arrest and COVID-19: inflammation, angiotensin-converting enzyme 2, and the destabilization of non-significant coronary artery disease-a case report.

The new β-coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) appears to exhibit cardiovascular pathogenicity through use of angiotensin-converting enzyme 2 (ACE2) for cell entry and the development of a major systemic inflammation. Furthermore, cardiovascular comorbidities increase susceptibility to SARS-CoV-2 infection and the development of a severe form of COronaVIrus Disease 2019 (COVID-19). We describe the case of a COVID-19 patient whose inaugural presentation was a refractory cardiac arrest secondary to the destabilization of known, non-significant coronary artery disease. Patient was supported by venoarterial extracorporeal life support. After 12 h of support, cardiac function remained stable on low vasopressor support but the patient remained in a coma and brainstem death was diagnosed. Myocardial injury is frequently seen among critically unwell COVID-19 patients and increases the risk of mortality. This case illustrates several potential mechanisms that are thought to drive the cardiac complications seen in COVID-19. We present the potential role of inflammation and ACE2 in the pathophysiology of COVID-19

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Studies of orbital parameters and pulse profile of the accreting millisecond pulsar XTE J1807-294

The accreting millisecond pulsar XTE J1807-294 was observed by XMM-Newton on March 22, 2003 after its discovery on February 21, 2003 by RXTE. The source was detected in its bright phase with an observed average count rate of 33.3 cts/s in the EPIC-pn camera in the 0.5-10 keV energy band (3.7 mCrab). Using the earlier established best-fit orbital period of 40.0741+/-0.0005 minutes from RXTE observations and considering a circular binary orbit as first approximation, we derived a value of 4.8+/-0.1 lt-ms for the projected orbital radius of the binary system and an epoch of the orbital phase of MJD 52720.67415(16). The barycentric mean spin period of the pulsar was derived as 5.2459427+/-0.0000004 ms. The pulsar's spin-pulse profile showed a prominent (1.5 ms FWHM) pulse, with energy and orbital phase dependence in the amplitude and shape. The measured pulsed fraction in four energy bands was found to be 3.1+/-0.2 % (0.5-3.0 keV), 5.4+/-0.4 % (3.0-6.0 keV), 5.1+/-0.7 % (6.0-10.0 keV) and 3.7+/-0.2 % (0.5-10.0 keV), respectively. Studies of spin-profiles with orbital phase and energy showed significant increase in its pulsed fraction during the second observed orbit of the neutron star, gradually declining in the subsequent two orbits, which was associated with sudden but marginal increase in mass accretion. From our investigations of orbital parameters and estimation of other properties of this compact binary system, we conclude that XTE J1807-294 is very likely a candidate for a millisecond radio pulsar.Comment: 4 pages, 4 figures, Accepted for publication in Astronomy and Astrophysics letter

Physics Analysis Expert PAX: First Applications

PAX (Physics Analysis Expert) is a novel, C++ based toolkit designed to assist teams in particle physics data analysis issues. The core of PAX are event interpretation containers, holding relevant information about and possible interpretations of a physics event. Providing this new level of abstraction beyond the results of the detector reconstruction programs, PAX facilitates the buildup and use of modern analysis factories. Class structure and user command syntax of PAX are set up to support expert teams as well as newcomers in preparing for the challenges expected to arise in the data analysis at future hadron colliders.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 7 pages, LaTeX, 10 eps figures. PSN THLT00