Topological Data Analysis (TDA) utilizes concepts from topology to analyze data. In general, TDA considers objects similar based on a topological invariant. Topological invariants are properties of the topological space that are homeomorphic; resilient to deformation in the space. The Euler-Poincaré Characteristic is a classic topological invariant that represents the alternating sum of the vertices, edges, faces, and higherorder cells of a closed surface. Tracking the Euler characteristic over a topological filtration produces an Euler Characteristic Curve (ECC). This study introduces a computational technique to determine the ECC of $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$ data; the technique generalizes to higher dimensions. This technique separates landscapes of lowerorder homologies utilizing triangulations of the space.

In recent years k-means++ has become a popular initialization technique for improved k-means clustering. To date, most of the work done to improve its performance has involved parallelizing algorithms that are only approximations of k-means++. In this paper we present a parallelization of the exact k-means++ algorithm, with a proof of its correctness. We develop implementations for three distinct shared-memory architectures: multicore CPU, high performance GPU, and the massively multithreaded Cray XMT platform. We demonstrate the scalability of the algorithm on each platform. In addition we present a visual approach for showing which platform performed k-means++ the fastest for varying data sizes.

coaster is a project that teaches a semester-long introductory computer graphics class by means of ten programming assignments. The assignments are incremental - each one building on the previous ones - and ultimately require implementation of most of the course content in the final one: a first-person rollercoaster simulation. Briefly described, the assignments (and their course contents) are:

MOTIVATION: Liquid chromatography-mass spectrometry-based metabolomics has gained importance in the life sciences, yet it is not supported by software tools for high throughput identification of metabolites based on their fragmentation spectra. An algorithm (ISIS: in silico identification software) and its implementation are presented and show great promise in generating in silico spectra of lipids for the purpose of structural identification. Instead of using chemical reaction rate equations or rules-based fragmentation libraries, the algorithm uses machine learning to find accurate bond cleavage rates in a mass spectrometer employing collision-induced dissociation tandem mass spectrometry. RESULTS: A preliminary test of the algorithm with 45 lipids from a subset of lipid classes shows both high sensitivity and specificity.

No abstract available.

Recently, there has been considerable interest in the representation of radiance in terms of wavelet basis functions. We will present a coordinate system called Nusselt coordinates which, when combined with wavelets, considerably simplifies computation of radiative transport and surface interaction. It also provides straightforward computation of the physical quantities involved. We show how to construct a discrete representation of the radiative transport operator Τ involving inner products of smoothing functions, discuss the possible numerical integration techniques, and present an application. We also show how surface interaction can be represented as a kind of matrix product of the wavelet projections of an incident radiance and a bidirectional reflectance distribution function (BRDF).

No abstract available.

Abstract There is a need to develop shaders that not only “look good”, but are more physically plausible. From physical and geometric considerations, we review the derivation of a shading equation expressing rejected radiance in terms of incident radiance and the bidirectional reflectance distribution function (BRDF). We then examine the connection between this equation and conventional shaders used in computer graphics. Imposing the additional physical constraints of energy conservation and Helmholtz reciprocity allows us to create variations of the conventional shaders that are more physically plausible.

This paper describes a way to perform realistic three-dimensional texturing of ray-traced objects with irregular surfaces. Such texturing has teen done in the past with texture mapping, particle systems, or volumetric methods. We propose an alternative to these called a lattice. Lattices work as fast but inexact ray tracers. As long as lattices are used for small objects, though, the inexactness doesn't show on the scale of the display, and the result is acceptable. The paper shows how lattices can be integrated with a more traditional ray tracer, with several examples. Time and memory space considerations are major constraints on lattices, preventing widespread practical application at the present time. The paper discusses these limitations and how they might be reduced.