Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Time, frequency and information domain analysis of heart period and QT variability in asymptomatic long QT syndrome type 2 patients.

none8siThis study was designed to characterize in time, frequency and information domains heart period (HP) and QT interval variabilities in asymptomatic (ASYMP) long QT syndrome type 2 (LQT2) subjects. HP, approximated as the temporal distance between two consecutive R-wave peaks, and QT, approximated as the temporal distance between the R-wave peak and the T-wave offset, were automatically derived from 24h Holter recordings in 10 ASYMP LQT2 patients and 13 healthy non mutation carriers (NMC) subjects. All analyses were carried out during DAY (from 2 to 6 PM) and NIGHT (from 12 to 4 AM). Mean, variance, spectral power and complexity indices at short, medium and long time scales were assessed over HP and QT beat-to-beat series. Circadian rhythmicity was evident in both NMC and ASYMP LQT2 but ASYMP LQT2 subjects were characterized by higher HP, QT interval and HP variability during both DAY and NIGHT. In addition, multiscale complexity analysis was able to differentiate the groups by showing a higher HP complexity and a lower QT complexity at long time scales in ASYMP LQT2 during DAY. ASYMP LQT2 exhibited a different autonomic control compared to NMC and such a differentiation could be protective and assure them a lower risk profile.Bari V, 11.; Girardengo, G; Marchi, A; De Maria, B; Brink, Pa; Crotti, L; Schwartz, Pj; Porta, ABari V, 1. 1.; Girardengo, Giulia; Marchi, A; De Maria, B; Brink, Pa; Crotti, Lia; Schwartz, Peter; Porta, A

Sex-Biased Gene Flow Among Elk in the Greater Yellowstone Ecosystem

We quantified patterns of population genetic structure to help understand gene flow among elk populations across the Greater Yellowstone Ecosystem. We sequenced 596 base pairs of the mitochondrial control region of 380 elk from eight populations. Analysis revealed high mitochondrial DNA variation within populations, averaging 13.0 haplotypes with high mean gene diversity (0.85). The genetic differentiation among populations for mitochondrial DNA was relatively high (FST = 0.161; P = 0.001) compared to genetic differentiation for nuclear microsatellite data (FST = 0.002; P = 0.332), which suggested relatively low female gene flow among populations. The estimated ratio of male to female gene flow (mm/mf = 46) was among the highest we have seen reported for large mammals. Genetic distance (for mitochondrial DNA pairwise FST) was not significantly correlated with geographic (Euclidean) distance between populations (Mantel’s r = 0.274, P = 0.168). Large mitochondrial DNA genetic distances (e.g., FST . 0.2) between some of the geographically closest populations (,65 km) suggested behavioral factors and/or landscape features might shape female gene flow patterns. Given the strong sex-biased gene flow, future research and conservation efforts should consider the sexes separately when modeling corridors of gene flow or predicting spread of maternally transmitted diseases. The growing availability of genetic data to compare male vs. female gene flow provides many exciting opportunities to explore the magnitude, causes, and implications of sex-biased gene flow likely to occur in many species

The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi

Resonant Absorption as Mode Conversion?

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.Comment: 23 pages, 8 figures, 2 tables; accepted by Solar Phys (July 9 2010

Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.Comment: 12 pages, 5 figure

A Compact Beam Stop for a Rare Kaon Decay Experiment

We describe the development and testing of a novel beam stop for use in a rare kaon decay experiment at the Brookhaven AGS. The beam stop is located inside a dipole spectrometer magnet in close proximity to straw drift chambers and intercepts a high-intensity neutral hadron beam. The design process, involving both Monte Carlo simulations and beam tests of alternative beam-stop shielding arrangements, had the goal of minimizing the leakage of particles from the beam stop and the resulting hit rates in detectors, while preserving maximum acceptance for events of interest. The beam tests consisted of measurements of rates in drift chambers, scintilation counter hodoscopes, a gas threshold Cherenkov counter, and a lead glass array. Measurements were also made with a set of specialized detectors which were sensitive to low-energy neutrons, photons, and charged particles. Comparisons are made between these measurements and a detailed Monte Carlo simulation.Comment: 39 pages, 14 figures, submitted to Nuclear Instruments and Method

Collisionless hydrodynamics for 1D motion of inhomogeneous degenerate electron gases: equivalence of two recent descriptions

Recently I. Tokatly and O. Pankratov (''TP'', Phys. Rev. B 60, 15550 (1999)) used velocity moments of a semiclassical kinetic equation to derive a hydrodynamic description of electron motion in a degenerate electron gas. Independently, the present authors (Theochem 501-502, 327 (2000)) used considerations arising from the Harmonic Potential Theorem (Phys. Rev. Lett. 73, 2244 (1994)) to generate a new form of high-frequency hydrodynamics for inhomogeneous degenerate electron gases (HPT-N3 hydrodynamics). We show here that TP hydrodynamics yields HPT-N3 hydrodynamics when linearized about a Thomas-Fermi groundstate with one-dimensional spatial inhomnogeneity.Comment: 17p

Full reduction of large finite random Ising systems by RSRG

We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain the "connected" 2-spin correlation function and the "disconnected" 2-spin correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the "connected" 2-spin correlation function along one of the principal axes. (We believe this to be the first time, where the full three dimensional correlation is calculated and not just parameters like Nu or Eta.) The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.Comment: 30 pages, 17 figure

Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation

The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and the Green's-function formalisms and can therefore serve as a bridge between various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. It has the same relation to the BS equation as has the standard Bloch equation to the ordinary Schroedinger equation and can be used to generate a perturbation expansion compatible with the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic