A complete set of addition laws for incomplete Edwards curves

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P₁, P₂ produce the sum P₁+P₂.     

On the numerical solution of large-scale sparse discrete-time Riccati equations

We discuss the numerical solution of large-scale discrete-time algebraic Riccati equations (DAREs) as they arise, e.g., in fully discretized linear-quadratic optimal control problems for parabolic partial differential equations (PDEs). We employ variants of Newton??s method that allow to compute an approximate low-rank factor of the solution of the DARE. The principal computation in the Newton iteration is the numerical solution of a Stein (aka discrete Lyapunov) equation in each step. For this purpose, we present a low-rank Smith method as well as a low-rank alternating-direction-implicit (ADI) iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.     

On the influence of design parameters and nonlinearities in vehicle suspensions on road deformation

Among others, two main objectives of modern vehicle design are road friendliness and ride comfort. Both aspects are strongly related since the dynamical tire forces depend on the vertical acceleration of the vehicle. In order to investigate the influence of design and operation parameters, different car models are considered which move with constant velocity on a rippled road. First, a linear half car model is examined and the influence of different design parameters is discussed. Second, nonlinear suspensions with Coulomb friction due to sealings as well as with bilinear shock absorbers are taken into account. The vertical dynamics of the vehicle model and the dynamic tire forces between vehicle and road are calculated using analytical methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Missing Point Estimation for steady aerodynamic applications

Model reduction in aerodynamic applications usually makes use of Proper Orthogonal Decomposition (POD). In this work a POD-based method, called Missing Point Estimation (MPE), will be applied to steady state flows with variation of the flow parameter angle of attack. The basic idea of MPE is to select a subset of the computational grid points (control volumes) and limit the governing equations to these. Subsequently, the remaining equations are projected onto the POD subspace. This approach has the advantage that the nonlinear right hand side of the governing equations has to be evaluated only for some selected points (control volumes) which makes the MPE faster than classical Galerkin projection. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

Transient ESR nutation signals in excited aromatic triplet states

Transient ESR nutation signals following laser pulse excitation are analyzed for the case of the photoexcited triplet state of acridine in a molecular crystal matrix. Essential features, in particular the short rise-time (< 10^?7) of the signals, can be related to the inhomogeneous nature of the ESR linewidth. Applications are discussed.     

Products of Jacobians as Prym-Tyurin varieties

Let X ₁, ..., X _m denote smooth projective curves of genus g _i ≥ 2 over an algebraically closed field of characteristic 0 and let n denote any integer at least equal to . We show that the product JX ₁ × ... × JX _m of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent n ^m-1. This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.      

On numerical methods for discrete least-squares approximation by trigonometric polynomials

Fast, efficient and reliable algorithms for discrete least-squares approximation of a real-valued function given at arbitrary distinct nodes in by trigonometric polynomials are presented. The algorithms are based on schemes for the solution of inverse unitary eigenproblems and require only arithmetic operations as compared to operations needed for algorithms that ignore the structure of the problem. An algorithm which solves this problem with real-valued data and real-valued solution using only real arithmetic is given. Numerical examples are presented that show that the proposed algorithms produce consistently accurate results that are often better than those obtained by general QR decomposition methods for the least-squares problem.

     

Measuring Lineup Difficulty By Matching Distance Metrics With Subject Choices in Crowd-Sourced Data

Graphics play a crucial role in statistical analysis and data mining. Being able to quantify structure in data that is visible in plots, and how people read the structure from plots is an ongoing challenge. The lineup protocol provides a formal framework for data plots, making inference possible. The data plot is treated like a test statistic, and lineup protocol acts like a comparison with the sampling distribution of the nulls. This article describes metrics for describing structure in data plots and evaluates them in relation to the choices that human readers made during several large Amazon Turk studies using lineups. The metrics that were more specific to the plot types tended to better match subject choices, than generic metrics. The process that we followed to evaluate metrics will be useful for general development of numerically measuring structure in plots, and also in future experiments on lineups for choosing blocks of pictures. Supplementary materials for this article are available online.     

Framed! Reproducing and Revisiting 150-Year-Old Charts

The Statistical Atlases published by the Census Bureau in the late 1800s utilized a number of novel methods for displaying data. In this paper, we examine the use of framed spine and mosaic plots used in two plates of the Statistical Atlas of 1870. We use forensic statistics to recreate the data using available census information, and then use that data to create framed charts using modern plotting methods. We then examine the effectiveness of the framed charts compared to other alternatives with a user study. The data and code for this study are available online.