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.

Variability in the Stability and Productivity of Transfected Genes in Chinese Hamster Ovary (CHO) cells

In the field of biologics production, productivity and stability of the transfected gene of interest are two very important attributes that dictate if a production process is viable. To further understand and improve these two traits, we would need to further our understanding of the factors affecting them. These would include integration site of the gene, gene copy number, cell phenotypic variation and cell environment. As these factors play different parts in the development process, they lead to variable productivity and stability of the transfected gene between clones, the well-known phenomenon of “clonal variation”. A study of this phenomenon and how the various factors contribute to it will thus shed light on strategies to improve productivity and stability in the production cell line. Of the four factors, the site of gene integration appears to be one of the most important. Hence, it is proposed that work is done on studying how different integration sites affect the productivity and stability of transfected genes in the development process. For the study to be more industrially relevant, it is proposed that the Chinese Hamster Ovary dhfr-deficient cell line, CHO-DG44, is used as the model system.