Parameter Estimation in Chaotic Systems

This report examines how to estimate the parameters of a chaotic system given noisy observations of the state behavior of the system. Investigating parameter estimation for chaotic systems is interesting because of possible applications for high-precision measurement and for use in other signal processing, communication, and control applications involving chaotic systems. In this report, we examine theoretical issues regarding parameter estimation in chaotic systems and develop an efficient algorithm to perform parameter estimation. We discover two properties that are helpful for performing parameter estimation on non-structurally stable systems. First, it turns out that most data in a time series of state observations contribute very little information about the underlying parameters of a system, while a few sections of data may be extraordinarily sensitive to parameter changes. Second, for one-parameter families of systems, we demonstrate that there is often a preferred direction in parameter space governing how easily trajectories of one system can "shadow'" trajectories of nearby systems. This asymmetry of shadowing behavior in parameter space is proved for certain families of maps of the interval. Numerical evidence indicates that similar results may be true for a wide variety of other systems. Using the two properties cited above, we devise an algorithm for performing parameter estimation. Standard parameter estimation techniques such as the extended Kalman filter perform poorly on chaotic systems because of divergence problems. The proposed algorithm achieves accuracies several orders of magnitude better than the Kalman filter and has good convergence properties for large data sets.

Generating Communications Systems Through Shared Context

In a distributed model of intelligence, peer components need to communicate with one another. I present a system which enables two agents connected by a thick twisted bundle of wires to bootstrap a simple communication system from observations of a shared environment. The agents learn a large vocabulary of symbols, as well as inflections on those symbols which allow thematic role-frames to be transmitted. Language acquisition time is rapid and linear in the number of symbols and inflections. The final communication system is robust and performance degrades gradually in the face of problems.

BioJADE: A Design and Simulation Tool for Synthetic Biological Systems

The next generations of both biological engineering and computer engineering demand that control be exerted at the molecular level. Creating, characterizing and controlling synthetic biological systems may provide us with the ability to build cells that are capable of a plethora of activities, from computation to synthesizing nanostructures. To develop these systems, we must have a set of tools not only for synthesizing systems, but also designing and simulating them. The BioJADE project provides a comprehensive, extensible design and simulation platform for synthetic biology. BioJADE is a graphical design tool built in Java, utilizing a database back end, and supports a range of simulations using an XML communication protocol. BioJADE currently supports a library of over 100 parts with which it can compile designs into actual DNA, and then generate synthesis instructions to build the physical parts. The BioJADE project contributes several tools to Synthetic Biology. BioJADE in itself is a powerful tool for synthetic biology designers. Additionally, we developed and now make use of a centralized BioBricks repository, which enables the sharing of BioBrick components between researchers, and vastly reduces the barriers to entry for aspiring Synthetic Biologists.