Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

A Government-Binding Based Parser for Warlpiri, a Free-Word Order Language

Free-word order languages have long posed significant problems for standard parsing algorithms. This thesis presents an implemented parser, based on Government-Binding (GB) theory, for a particular free-word order language, Warlpiri, an aboriginal language of central Australia. The words in a sentence of a free-word order language may swap about relatively freely with little effect on meaning: the permutations of a sentence mean essentially the same thing. It is assumed that this similarity in meaning is directly reflected in the syntax. The parser presented here properly processes free word order because it assigns the same syntactic structure to the permutations of a single sentence. The parser also handles fixed word order, as well as other phenomena. On the view presented here, there is no such thing as a "configurational" or "non-configurational" language. Rather, there is a spectrum of languages that are more or less ordered. The operation of this parsing system is quite different in character from that of more traditional rule-based parsing systems, e.g., context-free parsers. In this system, parsing is carried out via the construction of two different structures, one encoding precedence information and one encoding hierarchical information. This bipartite representation is the key to handling both free- and fixed-order phenomena. This thesis first presents an overview of the portion of Warlpiri that can be parsed. Following this is a description of the linguistic theory on which the parser is based. The chapter after that describes the representations and algorithms of the parser. In conclusion, the parser is compared to related work. The appendix contains a substantial list of test cases ??th grammatical and ungrammatical ??at the parser has actually processed.

Modeling Stock Order Flows and Learning Market-Making from Data

Stock markets employ specialized traders, market-makers, designed to provide liquidity and volume to the market by constantly supplying both supply and demand. In this paper, we demonstrate a novel method for modeling the market as a dynamic system and a reinforcement learning algorithm that learns profitable market-making strategies when run on this model. The sequence of buys and sells for a particular stock, the order flow, we model as an Input-Output Hidden Markov Model fit to historical data. When combined with the dynamics of the order book, this creates a highly non-linear and difficult dynamic system. Our reinforcement learning algorithm, based on likelihood ratios, is run on this partially-observable environment. We demonstrate learning results for two separate real stocks.