The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems

The Bifurcation Interpreter is a computer program that autonomously explores the steady-state orbits of one-parameter families of periodically- driven oscillators. To report its findings, the Interpreter generates schematic diagrams and English text descriptions similar to those appearing in the science and engineering research literature. Given a system of equations as input, the Interpreter uses symbolic algebra to automatically generate numerical procedures that simulate the system. The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.

Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based On P

I present a novel design methodology for the synthesis of automatic controllers, together with a computational environment---the Control Engineer's Workbench---integrating a suite of programs that automatically analyze and design controllers for high-performance, global control of nonlinear systems. This work demonstrates that difficult control synthesis tasks can be automated, using programs that actively exploit and efficiently represent knowledge of nonlinear dynamics and phase space and effectively use the representation to guide and perform the control design. The Control Engineer's Workbench combines powerful numerical and symbolic computations with artificial intelligence reasoning techniques. As a demonstration, the Workbench automatically designed a high-quality maglev controller that outperforms a previous linear design by a factor of 20.

A Dynamical Systems Model for Language Change

Formalizing linguists' intuitions of language change as a dynamical system, we quantify the time course of language change including sudden vs. gradual changes in languages. We apply the computer model to the historical loss of Verb Second from Old French to modern French, showing that otherwise adequate grammatical theories can fail our new evolutionary criterion.

The Logical Problem of Language Change

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.

Switching Between Discrete and Continuous Process Models to Predict Molecular Genetic Activity

Two kinds of process models have been used in programs that reason about change: Discrete and continuous models. We describe the design and implementation of a qualitative simulator, PEPTIDE, which uses both kinds of process models to predict the behavior of molecular energetic systems. The program uses a discrete process model to simulate both situations involving abrupt changes in quantities and the actions of small numbers of molecules. It uses a continuous process model to predict gradual changes in quantities. A novel technique, called aggregation, allows the simulator to switch between theses models through the recognition and summary of cycles. The flexibility of PEPTIDE's aggregator allows the program to detect cycles within cycles and predict the behavior of complex situations.

Modeling and Analysis of Two-Part Type Manufacturing Systems

This paper presents a model and analysis of a synchronous tandem flow line that produces different part types on unreliable machines. The machines operate according to a static priority rule, operating on the highest priority part whenever possible, and operating on lower priority parts only when unable to produce those with higher priorities. We develop a new decomposition method to analyze the behavior of the manufacturing system by decomposing the long production line into small analytically tractable components. As a first step in modeling a production line with more than one part type, we restrict ourselves to the case where there are two part types. Detailed modeling and derivations are presented with a small two-part-type production line that consists of two processing machines and two demand machines. Then, a generalized longer flow line is analyzed. Furthermore, estimates for performance measures, such as average buffer levels and production rates, are presented and compared to extensive discrete event simulation. The quantitative behavior of the two-part type processing line under different demand scenarios is also provided.