Extension of geodesic algebras to continuous genus

Using the Penner--Fock parameterization for Teichmuller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit. The mapping class group acts naturally in the obtained representation.Comment: 16 pages, submitted to Lett.Math.Phy

Quantum geometry from 2+1 AdS quantum gravity on the torus

Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved figures and extra figures. To appear GER

Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant

We relate the geometrical and the Chern-Simons description of (2+1)-dimensional gravity for spacetimes of topology $R\times S_g$, where $S_g$ is an oriented two-surface of genus $g>1$, for Lorentzian signature and general cosmological constant and the Euclidean case with negative cosmological constant. We show how the variables parametrising the phase space in the Chern-Simons formalism are obtained from the geometrical description and how the geometrical construction of (2+1)-spacetimes via grafting along closed, simple geodesics gives rise to transformations on the phase space. We demonstrate that these transformations are generated via the Poisson bracket by one of the two canonical Wilson loop observables associated to the geodesic, while the other acts as the Hamiltonian for infinitesimal Dehn twists. For spacetimes with Lorentzian signature, we discuss the role of the cosmological constant as a deformation parameter in the geometrical and the Chern-Simons formulation of the theory. In particular, we show that the Lie algebras of the Chern-Simons gauge groups can be identified with the (2+1)-dimensional Lorentz algebra over a commutative ring, characterised by a formal parameter $\Theta_\Lambda$ whose square is minus the cosmological constant. In this framework, the Wilson loop observables that generate grafting and Dehn twists are obtained as the real and the $\Theta_\Lambda$-component of a Wilson loop observable with values in the ring, and the grafting transformations can be viewed as infinitesimal Dehn twists with the parameter $\Theta_\Lambda$.Comment: 50 pages, 6 eps figure

My Only One

Title Only with blue backgroundhttps://scholarsjunction.msstate.edu/cht-sheet-music/9319/thumbnail.jp

Grafting and Poisson structure in (2+1)-gravity with vanishing cosmological constant

We relate the geometrical construction of (2+1)-spacetimes via grafting to phase space and Poisson structure in the Chern-Simons formulation of (2+1)-dimensional gravity with vanishing cosmological constant on manifolds of topology $R\times S_g$, where $S_g$ is an orientable two-surface of genus $g>1$. We show how grafting along simple closed geodesics \lambda is implemented in the Chern-Simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on S_g. We prove that this action is generated via the Poisson bracket by a gauge invariant observable associated to the holonomy of $\lambda$. We deduce a symmetry relation between the Poisson brackets of observables associated to the Lorentz and translational components of the holonomies of general closed curves on S_g and discuss its physical interpretation. Finally, we relate the action of grafting on the phase space to the action of Dehn twists and show that grafting can be viewed as a Dehn twist with a formal parameter $\theta$ satisfying $\theta^2=0$.Comment: 43 pages, 10 .eps figures; minor modifications: 2 figures added, explanations added, typos correcte

A Current Mode Detector Array for Gamma-Ray Asymmetry Measurements

We have built a CsI(Tl) gamma-ray detector array for the NPDGamma experiment to search for a small parity-violating directional asymmetry in the angular distribution of 2.2 MeV gamma-rays from the capture of polarized cold neutrons by protons with a sensitivity of several ppb. The weak pion-nucleon coupling constant can be determined from this asymmetry. The small size of the asymmetry requires a high cold neutron flux, control of systematic errors at the ppb level, and the use of current mode gamma-ray detection with vacuum photo diodes and low-noise solid-state preamplifiers. The average detector photoelectron yield was determined to be 1300 photoelectrons per MeV. The RMS width seen in the measurement is therefore dominated by the fluctuations in the number of gamma rays absorbed in the detector (counting statistics) rather than the intrinsic detector noise. The detectors were tested for noise performance, sensitivity to magnetic fields, pedestal stability and cosmic background. False asymmetries due to gain changes and electronic pickup in the detector system were measured to be consistent with zero to an accuracy of $10^{-9}$ in a few hours. We report on the design, operating criteria, and the results of measurements performed to test the detector array.Comment: 33 pages, 20 figures, 2 table

Fecal Viral Load and Norovirus-associated Gastroenteritis

We report the median cDNA viral load of norovirus genogroup II is >100-fold higher than that of genogroup I in the fecal specimens of patients with norovirus-associated gastroenteritis. We speculate that increased cDNA viral load accounts for the higher transmissibility of genogroup II strains through the fecal-oral route

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to anotherComment: 16 pages, talk delivered at the Geilo Winter School 201

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Fecal Viral Concentration and Diarrhea in Norovirus Gastroenteritis

Fecal viral concentrations of 40 patients infected with norovirus genogroup GII.4 correlated with diarrhea duration and frequency of vomiting. Higher viral concentration and older age were independently associated with prolonged diarrhea (>4 days). These findings provide information on the pathogenesis and transmission of norovirus infections