Presentations of Noneffective Orbifolds

It is well-known that an effective orbifold M (one for which the local stabilizer groups act effectively) can be presented as a quotient of a smooth manifold P by a locally free action of a compact lie group K. We use the language of groupoids to provide a partial answer to the question of whether a noneffective orbifold can be so presented. We also note some connections to stacks and gerbes.Comment: 19 page

Fine structure of distributions and central limit theorem in diffusive billiards

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean square displacement, but changes the limiting shape of the distributions to a non-gaussian one. Using the same methods, we give numerical evidence that a non-chaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E. Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander

An Empirical Analysis of the Canadian Term Structure of Zero-Coupon Interest Rates

Zero-coupon interest rates are the fundamental building block of fixed-income mathematics, and as such have an extensive number of applications in both finance and economics. The risk-free government zero-coupon term structure is, however, not directly observable and needs to be generated from the prices of marketable, coupon-bearing bonds. The authors introduce the first public-domain database of constant-maturity zero-coupon yield curves for the Government of Canada bond market. They first outline the mechanics of the curve-fitting algorithm that underlie the model, and then perform some preliminary statistical analysis on the resulting yield curves. The full sample period extends from January 1986 to May 2003; it is broken down into two subsamples, reflecting the structural and macroeconomic changes that impacted the Canadian fixed-income markets over that time. The authors examine the evolution of a number of key interest rates and yield-curve measures over the period, perform a principal-components analysis of the common factors that have influenced yield changes over time, and compare holding-period returns over the sample for assets of various maturities.Financial markets; Interest rates; Econometric and statistical methods

A Check List of the Lepidoptera of Fulton County, Ohio With Special Reference to the Moths of Goll Woods State Nature Preserve

The results of a comprehensive 1988-1989 survey of the Lepidoptera in the 130 hectare Goll Woods State Nature Preserve in Fulton County, Ohio are presented. In addition many records of butterflies and skippers outside the confines of the Pre­ serve are presented for the first time. This is the fifth in a series of papers featuring the current status of lepidopterous fauna in Ohio\u27s recreational areas. A total of 27 species of skippers, 51 species of butterflies and 394 species of moths was identified and tabulated for the county. Three species on this list are classified as endangered, Epidemia helloides, Lithophane semiusta and Ufeus plicatus, and two are threatened, Speyeria idalia and Clossiana selene. Although locally abundant, Lithophane semiusta Grote is known to occur only at this site in Ohio. A single specimen of Ufeus plicatus was taken and is the only known specimen for the state

Occurrence of normal and anomalous diffusion in polygonal billiard channels

From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e. when no particle can travel arbitrarily far without colliding. For the infinite horizon case we present numerical tests showing that the mean squared displacement instead grows asymptotically as t log t. When the unit cell contains accessible parallel scatterers, however, we always find anomalous super-diffusion, i.e. power-law growth with an exponent larger than 1. This behavior cannot be accounted for quantitatively by a simple continuous-time random walk model. Instead, we argue that anomalous diffusion correlates with the existence of families of propagating periodic orbits. Finally we show that when a configuration with parallel scatterers is approached there is a crossover from normal to anomalous diffusion, with the diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures, additional comments. Some higher quality figures available at http://www.fis.unam.mx/~dsander

Dashboard of sentiment in Austrian social media during COVID-19

To track online emotional expressions of the Austrian population close to real-time during the COVID-19 pandemic, we build a self-updating monitor of emotion dynamics using digital traces from three different data sources. This enables decision makers and the interested public to assess issues such as the attitude towards counter-measures taken during the pandemic and the possible emergence of a (mental) health crisis early on. We use web scraping and API access to retrieve data from the news platform derstandard.at, Twitter and a chat platform for students. We document the technical details of our workflow in order to provide materials for other researchers interested in building a similar tool for different contexts. Automated text analysis allows us to highlight changes of language use during COVID-19 in comparison to a neutral baseline. We use special word clouds to visualize that overall difference. Longitudinally, our time series show spikes in anxiety that can be linked to several events and media reporting. Additionally, we find a marked decrease in anger. The changes last for remarkably long periods of time (up to 12 weeks). We discuss these and more patterns and connect them to the emergence of collective emotions. The interactive dashboard showcasing our data is available online under http://www.mpellert.at/covid19_monitor_austria/. Our work has attracted media attention and is part of an web archive of resources on COVID-19 collected by the Austrian National Library.Comment: 23 pages, 3 figures, 1 tabl