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Now showing items 1-10 of 21

#### An Octahedral Tiling on the Ideal Boundary of the Complex Hyperbolic Plane

(2006-08-02)

We present an octahedral tiling on the ideal boundary of the complex hyperbolic plane. The tiling was discovered through the use of a program we wrote called CHAT. We show visual evidence of this tiling and prove some ...

#### a survey of the attack on md5

(2006-07-31)

In Eurocrypt 2005, Wang et al. presented an exciting paper that showcased her method of breaking MD5 by attacking its collision resistance propery. However, Wang's paper does not give a thorough exposition of the attack ...

#### An Analysis of Chaum's Voter-Verifiable Election Scheme

(2005-05-03)

Chaum's Voter-Verifiable election scheme introduces a new direction for electronic voting. The scheme eliminates the need to trust any machinery or authority, and instead relies on mathematical proof to certify the ...

#### FAST TRANSFORMS BASED ON STRUCTURED MATRICES WITH APPLICATIONS TO THE FAST MULTIPOLE METHOD

(2003-12-01)

The solution of many problems in engineering and science is enabled by the availability of a fast algorithm, a significant example being the fast Fourier transform, which computes the matrix-vector product for a $N \times ...

#### On the Implementation of an Accurate and Efficient Solver for Convection-Diffusion Equations

(2003-12-03)

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow ...

#### Meshless Collocation Methods for the Numerical Solution of Elliptic Boundary Valued Problems and the Rotational Shallow Water Equations on the Sphere

(2009)

This dissertation thesis has three main goals: 1) To explore the anatomy of meshless collocation
approximation methods that have recently gained attention in the numerical analysis community; 2) Numerically demonstrate ...

#### Definable families of finite Vapnik Chervonenkis dimension

(2008-04-25)

Vapnik Chervonenkis dimension is a basic combinatorial notion with applications in machine
learning, stability theory, and statistics. We explore what effect model
theoretic structure has on the VC dimension of formulas, ...

#### Dimensionality reduction for hyperspectral data

(2008-05-09)

This thesis is about dimensionality reduction for hyperspectral data. Special emphasis is given to dimensionality reduction techniques known as kernel eigenmap methods and manifold learning algorithms. Kernel eigenmap ...

#### Entropy Stable Approximations of Nonlinear Conservation Laws and Related Fluid Equations

(2007-08-01)

We present a systematic study of novel entropy stable approximations for a variety of nonlinear conservation laws, from the scalar Burgers equation to one dimensional Navier-Stokes and two
dimensional shallow water ...

#### A Variational Shape Optimization Framework for Image Segmentation

(2006-11-15)

Image segmentation is one of the fundamental problems in image processing. The goal is to partition a given image into regions that are uniform with respect to some image features and possibly to extract the region boundaries. ...