NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Mutual Information for Testing Gene-Environment Interaction

Despite current enthusiasm for investigation of gene-gene interactions and gene-environment interactions, the essential issue of how to define and detect gene-environment interactions remains unresolved. In this report, we define gene-environment interactions as a stochastic dependence in the context of the effects of the genetic and environmental risk factors on the cause of phenotypic variation among individuals. We use mutual information that is widely used in communication and complex system analysis to measure gene-environment interactions. We investigate how gene-environment interactions generate the large difference in the information measure of gene-environment interactions between the general population and a diseased population, which motives us to develop mutual information-based statistics for testing gene-environment interactions. We validated the null distribution and calculated the type 1 error rates for the mutual information-based statistics to test gene-environment interactions using extensive simulation studies. We found that the new test statistics were more powerful than the traditional logistic regression under several disease models. Finally, in order to further evaluate the performance of our new method, we applied the mutual information-based statistics to three real examples. Our results showed that P-values for the mutual information-based statistics were much smaller than that obtained by other approaches including logistic regression models.

Acetate metabolism and the control of environmental pH in Candida albicans and Saccharomyces cerevisiae

Candida albicans is the most common opportunistic fungal pathogen of humans. The balance between commensal and pathogenic C. albicans is maintained largely by phagocytes of the innate immune system. Analysis of transcriptional changes after macrophage phagocytosis indicates the C. albicans response is broadly similar to starvation, including up-regulation of alternate carbon metabolism. Systems known and suspected to be part of acetate/acetyl-CoA metabolism were also up-regulated, importantly the ACH and ACS genes, which manage acetate/acetyl-CoA interconversion, and the nine-member ATO gene family, thought to participate in transmembrane acetate transport and also linked to the process of environmental alkalinization. ^ Studies into the roles of Ach, Acs1 and Acs2 function in alternate carbon metabolism revealed a substantial role for Acs2 and lesser, but distinct roles, for Ach and Acs1. Deletion mutants were made in C. albicans and were phenotypically evaluated both in vitro and in vivo. Loss of Ach function resulted in mild growth defects on ethanol and acetate and no significant attenuation in virulence in a disseminated mouse model of infection. While loss of Acs1 did not produce any significant phenotypes, loss of Acs2 greatly impaired growth on multiple carbon sources, including glucose, ethanol and acetate. We also concluded that ACS1 and ACS2 likely comprise an essential gene pair. Expression analyses indicated that ACS2 is the predominant form under most growth conditions. ^ ATO gene function had been linked to the process of environmental alkalinization, an ammonium-mediated phenomenon described here first in C. albicans. During growth in glucose-poor, amino acid-rich conditions C. albicans can rapidly change its extracellular pH. This process was glucose-repressible and was accompanied by hyphal formation and changes in colony morphology. We showed that introduction of the ATO1G53D point mutant to C. albicans blocked alkalinization, as did over-expression of C. albicans ATO2, the only C. albicans ATO gene to lack the conserved N-terminal domain. A screen for alkalinization-deficient mutants revealed that ACH1 is essential for alkalinization. However, addition of acetate to the media restored alkalinization to the ach1 mutant. We proposed a model of ATO function in which Atos regulated the cellular co-export of ammonium and acetate. ^