Taming Chaotic Circuits

Control algorithms that exploit chaotic behavior can vastly improve the performance of many practical and useful systems. The program Perfect Moment is built around a collection of such techniques. It autonomously explores a dynamical system's behavior, using rules embodying theorems and definitions from nonlinear dynamics to zero in on interesting and useful parameter ranges and state-space regions. It then constructs a reference trajectory based on that information and causes the system to follow it. This program and its results are illustrated with several examples, among them the phase-locked loop, where sections of chaotic attractors are used to increase the capture range of the circuit.

A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions

In Phys. Rev. Letters (73:2), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical fit to Zipf"s "law" cannot be used as a criterion for similarity to natural languages. Although DNA is a presumably "organized system of signs" in Mandelbrot"s (1961) sense, and observation of statistical featurs of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's "gramar" and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an M-sided die or a finite-state branching process.

Using Special-Purpose Computing to Examine Chaotic Behavior in Nonlinear Mappings

Studying chaotic behavior in nonlinear systems requires numerous computations in order to simulate the behavior of such systems. The Standard Map Machine was designed and implemented as a special computer for performing these intensive computations with high-speed and high-precision. Its impressive performance is due to its simple architecture specialized to the numerical computations required of nonlinear systems. This report discusses the design and implementation of the Standard Map Machine and its use in the study of nonlinear mappings; in particular, the study of the standard map.

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.

Retargeting of pre-set regions on chromosome for high gene expression in mammalian cells

We have developed a system to hunt and reuse special gene integration sites that allow for high and stable gene expression. A vector, named pRGFP8, was constructed. The plasmid pRGFP8 contains a reporter gene, gfp2 and two extraneous DNA fragments. The gene gfp2 makes it possible to screen the high expression regions on the chromosome. The extraneous DNA fragments can help to create the unique loci on the chromosome and increase the gene targeting frequency by increasing the homology. After transfection into Chinese hamster ovary cells (CHO) cells, the linearized pRGFP8 can integrate into the chromosome of the host cells and form the unique sites. With FACS, 90 millions transfected cells were sorted and the cells with strongest GFP expression were isolated, and then 8 stable high expression GFP CHO cell lines were selected as candidates for the new host cell. Taking the unique site created by pRGFP8 on the chromosome in the new host cells as a targeting locus, the gfp2 gene was replaced with the gene of interest, human ifngamma, by transfecting the targeting plasmid pRIH-IFN. Then using FACS, the cells with the dimmest GFP fluorescence were selected. These cells showed they had strong abilities to produce the protein of interest, IFN-gamma. During the gene targeting experiment, we found there is positive correlation between the fluorescence density of the GFP CHO host cells and the specific production rate of IFN-gamma. This result shows that the strategy in our expression system is correct: the production of the interesting protein increases with the increase fluorescence of the GFP host cells. This system, the new host cell lines and the targeting vector, can be utilized for highly expressing the gene of interest. More importantly, by using FACS, we can fully screen all the transfected cells, which can reduce the chances of losing the best cells.