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. ^

TAZ AS A REGULATOR OF MESENCHYMAL TRANSFORMATION AND CLINICAL AGGRESSIVENESS IN GLIOMAS

Glioblastoma multiforme (GBM) is an aggressive, high grade brain tumor. Microarray studies have shown a subset of GBMs with a mesenchymal gene signature. This subset is associated with poor clinical outcome and resistance to treatment. To establish the molecular drivers of this mesenchymal transition, we correlated transcription factor expression to the mesenchymal signature and identified transcriptional co-activator with PDZ-binding motif (TAZ) to be highly associated with the mesenchymal shift. High TAZ expression correlated with worse clinical outcome and higher grade. These data led to the hypothesis that TAZ is critical to the mesenchymal transition and aggressive clinical behavior seen in GBM. We investigated the expression of TAZ, its binding partner TEAD, and the mesenchymal marker FN1 in human gliomas. Western analyses demonstrated increased expression of TAZ, TEAD4, and FN1 in GBM relative to lower grade gliomas. We also identified CpG islands in the TAZ promoter that are methylated in most lower grade gliomas, but not in GBMs. TAZ-methylated glioma stem cell (GSC) lines treated with a demethylation agent showed an increase in mRNA and protein TAZ expression; therefore, methylation may be another novel way TAZ is regulated since TAZ is epigenetically silenced in tumors with a better clinical outcome. To further characterize the role of TAZ in gliomagenesis, we stably silenced or over-expressed TAZ in GSCs. Silencing of TAZ decreased invasion, self-renewal, mesenchymal protein expression, and tumor-initiating capacity. Over-expression of TAZ led to an increase in invasion, mesenchymal protein expression, mesenchymal differentiation, and tumor-initiating ability. These actions are dependent on TAZ interacting with TEAD since all these effects were abrogated with TAZ could not bind to TEAD. We also show that TAZ and TEAD directly bind to mesenchymal gene promoters. Thus, TAZ-TEAD interaction is critically important in the mesenchymal shift and in the aggressive clinical behavior of GBM. We identified TAZ as a regulator of the mesenchymal transition in gliomas. TAZ could be used as a biomarker to both estimate prognosis and stratify patients into clinically relevant subgroups. Since mesenchymal transition is correlated to tumor aggressiveness, strategies to target and inhibit TAZ-TEAD and the downstream gene targets may be warranted in alternative treatment.

Understanding and Fostering Family Resilience

This paper examines a model of resilience and provides a fictional case example from the classical musical, Fiddler on the Roof along with a discussion of how this model may be helpful in assisting families at various levels of functioning to bounce back and perhaps even experience growth through facing difficult challenges.