An exploration of CUDA and CBEA for a gravitational wave data-analysis application (Einstein@Home)

We present a detailed approach for making use of two new computer hardware architectures -- CBEA and CUDA -- for accelerating a scientific data-analysis application (Einstein@Home). Our results suggest that both the architectures suit the application quite well and the achievable performance in the same software developmental time-frame, is nearly identical.Comment: Accepted for publication in International Conference on Parallel Processing and Applied Mathematics (PPAM 2009

A Real World Example of Solving a Quadratic Equation in Movie CGI

It is important to expose students to the beauty and usefulness of mathematics. Since computer graphics are familiar to most students due to video games and movies, they make a great source for motivating topics in mathematics. This activity shows students an application of solving quadratic equations to computing the line of sight to spherical objects in computer graphics

Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences

A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. Application to the construction of short 2-radius sequences is given, with some new 2-radius sequences found through computer search.Comment: 18 pages, to appear in Mathematics of Computatio

A Tool For Teaching Spline Methods In A Computer Graphics Course

The specialized mathematics knowledge covered in a computer graphics course is usually presented to students in an abstract way. Albeit, computer graphics is an application of this (abstract) mathematics, students may find it hard to link them together. In particular one of the most difficult topics to present in a pedagogical manner to junior students in a computer graphics course is spline methods (mathematical method for data smoothing) used for curve/surface modelling. This topic involves mainly the mathematics of parametric functions, piecewise functions, derivatives, matrices, and parametric/geometric continuities. Usually a student has a vague picture of the actual output of the application of this mathematics. Many educators have experienced that students may fully understand splines application, if and when they are assigned a software project to implement splines, and this understanding could still remain vague until the very last stages of the implementation. As an alternative, static pictures may be presented in class to provide an intuitive understanding of splines. This approach is, in effect, similar to viewing a picture in a textbook. A better alternative is for the educator to demonstrate real-time spline generation, since a picture is worth ten thousand words but a moving picture (animation) is worth ten thousand static ones. This paper presents an interactive software program which is used as a tool to introduce important concepts and algorithms of spline methods to computer science and computer engineering students. The software is specially developed for educational purposes, and generates spline curves

Guest Editors' Introduction: Special Section on Computer Arithmetic

International audienceCOMPUTER arithmetic is the mother of all computer research and application topics, like mathematics (as the title of a famous book by E.T. Bell) is the queen and servant of sciences and arithmetic the queen of mathematics. The etymology itself of the word computer is intrinsically related to the concept of arithmetic and mathematics. Interesting to note is that the origin of the word computer comes from the Latin word computare, which is defined as count, evaluate, calculate the result. In all cases, the connection between computers and computer arithmetic goes beyond simple etymology reasons. Computers are designed either to perform a specific calculation or to have extensive programmability for many changing tasks. In either case, at a certain level this translates into doing computations and arithmetic evaluations

The normalized Laplacian spectrum of subdivisions of a graph

Determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated subdivisions of simple connected graphs. As an example of application of these results we find the exact values of their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.Postprint (published version

Quantum Communication

Quantum communication, and indeed quantum information in general, has changed the way we think about quantum physics. In 1984 and 1991, the first protocol for quantum cryptography and the first application of quantum non-locality, respectively, attracted a diverse field of researchers in theoretical and experimental physics, mathematics and computer science. Since then we have seen a fundamental shift in how we understand information when it is encoded in quantum systems. We review the current state of research and future directions in this new field of science with special emphasis on quantum key distribution and quantum networks.Comment: Submitted version, 8 pg (2 cols) 5 fig