Periodic discrete conformal maps

A discrete conformal map (DCM) maps the square lattice to the Riemann sphere such that the image of every irreducible square has the same cross-ratio. This paper shows that every periodic DCM can be determined from spectral data (a hyperelliptic compact Riemann surface, called the spectral curve, equipped with some marked points). Each point of the map corresponds to a line bundle over the spectral curve so that the map corresponds to a discrete subgroup of the Jacobi variety. We derive an explicit formula for the generic maps using Riemann theta functions, describe the typical singularities and give a geometric interpretation of DCM's as a discrete version of the Schwarzian KdV equation. As such, the DCM equation is a discrete soliton equation and we describe the dressing action of a loop group on the set of DCM's. We also show that this action corresponds to a lattice of isospectral Darboux transforms for the finite gap solutions of the KdV equation.Comment: 41 pages, 10 figures, LaTeX2

First comparison of wave observations from CoMP and AIA/SDO

Waves have long been thought to contribute to the heating of the solar corona and the generation of the solar wind. Recent observations have demonstrated evidence of quasi-periodic longitudinal disturbances and ubiquitous transverse wave propagation in many different coronal environments. This paper investigates signatures of different types of oscillatory behaviour, both above the solar limb and on-disk, by comparing findings from the Coronal Multi-channel Polarimeter (CoMP) and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) for the same active region. We study both transverse and longitudinal motion by comparing and contrasting time-distance images of parallel and perpendicular cuts along/across active region fan loops. Comparisons between parallel space-time features in CoMP Doppler velocity and transverse oscillations in AIA images are made, together with space-time analysis of propagating quasi-periodic intensity features seen near the base of loops in AIA. Signatures of transverse motions are observed along the same magnetic structure using CoMP Doppler velocity (Vphase=600-750km/s, P=3-6mins) and in AIA/SDO above the limb (P=3-8mins). Quasi-periodic intensity features (Vphase=100-200km/s, P=6-11mins) also travel along the base of the same structure. On the disk, signatures of both transverse and longitudinal intensity features were observed by AIA; both show similar properties to signatures found along structures anchored in the same active region three days earlier above the limb. Correlated features are recovered by space-time analysis of neighbouring tracks over perpendicular distances of <2.6Mm.Comment: 14 pages, 14 figures, 1 tabl

Identification, Intervention and Collaboration: The Keys To Working Successfully With Mildly Handicapped Students In Rural Areas

As the nation\u27s schools are moving toward integration of mild-to-moderate handicapped students within general education classrooms, teachers must gain additional skills and expertise in both diagnosis and remediation

The U-band Galaxy Luminosity Function of Nearby Clusters

Despite the great potential of the U-band galaxy luminosity function (GLF) to constrain the history of star formation in clusters, to clarify the question of variations of the GLF across filter bands, to provide a baseline for comparisons to high-redshift studies of the cluster GLF, and to estimate the contribution of bound systems of galaxies to the extragalactic near-UV background, determinations have so far been hampered by the generally low efficiency of detectors in the U-band and by the difficulty of constructing both deep and wide surveys. In this paper, we present U-band GLFs of three nearby, rich clusters to a limit of M_U=-17.5 (M*_U+2). Our analysis is based on a combination of separate spectroscopic and R-band and U-band photometric surveys. For this purpose, we have developed a new maximum-likelihood algorithm for calculating the luminosity function that is particularly useful for reconstructing the galaxy distribution function in multi-dimensional spaces (e.g., the number of galaxies as a simultaneous function of luminosity in different filter bands, surface brightness, star formation rate, morphology, etc.), because it requires no prior assumptions as to the shape of the distribution function. The composite luminosity function can be described by a Schechter function with characteristic magnitude M*_U=-19.82+/-0.27 and faint end slope alpha_U=-1.09+/-0.18. The total U-band GLF is slightly steeper than the R-band GLF, indicating that cluster galaxies are bluer at fainter magnitudes. Quiescent galaxies dominate the cumulative U-band flux for M_U<-14. The contribution of galaxies in nearby clusters to the U-band extragalactic background is <1% Gyr^-1 for clusters of masses ~3*10^14 to 2*10^15 M_solar.Comment: 44 pages, 11 figures, accepted for publication in Ap

An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'

In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is certainly correct, we show that the conclusions drawn from that fact were unwarranted, namely that this irregularity caused such solutions not to be able to truly describe pure gravitational waves. In this article, we resolve the paradox---since such first-order solutions must always have singular lines in space for all sufficiently large values of $r$---by showing that if we perturbatively iterate the solution up to the third order in small quantities, there are acceptable regular solutions. That these solutions become flat before they become non-twisting tells us something interesting concerning the general behavior of solutions describing gravitational radiation from a bounded source.Comment: 11 pages, a plain TeX file, submitted to ``Classical and Quantum Gravity'

Large Scale Beam-beam Simulations for the CERN LHC using Distributed Computing

We report on a large scale simulation of beam-beam effects for the CERN Large Hadron Collider (LHC). The stability of particles which experience head-on and long-range beam-beam effects was investigated for different optical configurations and machine imperfections. To cover the interesting parameter space required computing resources not available at CERN. The necessary resources were available in the LHC@home project, based on the BOINC platform. At present, this project makes more than 60000 hosts available for distributed computing. We shall discuss our experience using this system during a simulation campaign of more than six months and describe the tools and procedures necessary to ensure consistent results. The results from this extended study are presented and future plans are discussed

Improvements to PLSc: Remaining problems and simple solutions

The recent article by Dijkstra and Henseler (2015b) presents a consistent partial least squares (PLSc) estimator that corrects for measurement error attenuation and provides evidence showing that, generally, PLSc performs comparably to a wide variety of more conventional estimators for structural equation models (SEM) with latent variables. However, PLSc does not adjust for other limitations of conventional PLS, namely: (1) bias in estimates of regression coefficients due to capitalization on chance; and (2) overestimation of composite reliability due to the proportionality relation between factor loadings and indicator weights. In this article, we illustrate these problems and then propose a simple solution: the use of unit-weighted composites, rather than those constructed from PLS results, combined with errors-in-variables regression (EIV) by using reliabilities obtained from factor analysis. Our simulations show that these two improvements perform as well as or better than PLSc. We also provide examples of how our proposed estimator can be easily implemented in various proprietary and open source software packages

Explanatory debugging: Supporting end-user debugging of machine-learned programs

Many machine-learning algorithms learn rules of behavior from individual end users, such as task-oriented desktop organizers and handwriting recognizers. These rules form a “program” that tells the computer what to do when future inputs arrive. Little research has explored how an end user can debug these programs when they make mistakes. We present our progress toward enabling end users to debug these learned programs via a Natural Programming methodology. We began with a formative study exploring how users reason about and correct a text-classification program. From the results, we derived and prototyped a concept based on “explanatory debugging”, then empirically evaluated it. Our results contribute methods for exposing a learned program's logic to end users and for eliciting user corrections to improve the program's predictions