A Compilation Strategy for Numerical Programs Based on Partial Evaluation

This work demonstrates how partial evaluation can be put to practical use in the domain of high-performance numerical computation. I have developed a technique for performing partial evaluation by using placeholders to propagate intermediate results. For an important class of numerical programs, a compiler based on this technique improves performance by an order of magnitude over conventional compilation techniques. I show that by eliminating inherently sequential data-structure references, partial evaluation exposes the low-level parallelism inherent in a computation. I have implemented several parallel scheduling and analysis programs that study the tradeoffs involved in the design of an architecture that can effectively utilize this parallelism. I present these results using the 9- body gravitational attraction problem as an example.

Multivariate Density Estimation: An SVM Approach

We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters.

Risk Bounds for Mixture Density Estimation

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

Exploiting the Parallelism Exposed by Partial Evaluation

We describe the key role played by partial evaluation in the Supercomputing Toolkit, a parallel computing system for scientific applications that effectively exploits the vast amount of parallelism exposed by partial evaluation. The Supercomputing Toolkit parallel processor and its associated partial evaluation-based compiler have been used extensively by scientists at MIT, and have made possible recent results in astrophysics showing that the motion of the planets in our solar system is chaotically unstable.

High Density Single Crystalline GaN Nanodot Arrays Fabricated Using Template-Assisted Selective Growth

High density, uniform GaN nanodot arrays with controllable size have been synthesized by using template-assisted selective growth. The GaN nanodots with average diameter 40nm, 80nm and 120nm were selectively grown by metalorganic chemical vapor deposition (MOCVD) on a nano-patterned SiO2/GaN template. The nanoporous SiO2 on GaN surface was created by inductively coupled plasma etching (ICP) using anodic aluminum oxide (AAO) template as a mask. This selective regrowth results in highly crystalline GaN nanodots confirmed by high resolution transmission electron microscopy. The narrow size distribution and uniform spatial position of the nanoscale dots offer potential advantages over self-assembled dots grown by the Stranski–Krastanow mode.