Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

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. ^

The transformation of a health care system: An ecology perspective

Beginning in the early 1980s, the health care system experienced momentous realignments. Fundamental changes in structures of traditional health care organizations, shifts in authority and relationships of professionals and institutions, and the increasing influence of managed care contributed to a relatively stable industry entering into a state of turbulence. The dynamics of these changes are recurring themes in the health services literature. The purpose of this dissertation was to examine the content of this literature over a defined time period and within the perspective of a theory of organizational change. ^ Using a theoretical framework based upon the organizational theory known as Organizational Ecology, secondary data from the period between 1983 and 1994 was reviewed. Analysis of the literature identified through a defined search methodology was focused upon determining the manner in which the literature characterized changes that were described. Using a model constructed from fundamentals of Organizational Ecology with which to structure an assessment of content, literature was summarized for the manner and extent of change in specific organizational forms and for the changes in emphasis by the environmental dynamics directing changes in the population of organizations. Although it was not the intent of the analysis to substantiate causal relationships between environmental resources selected as the determinants of organizational change and the observed changes in organizational forms, the structured review of content of the literature established a strong basis for inferring such a relationship. ^ The results of the integrative review of the literature and the power of the appraisal achieved through the theoretical framework constructed for the analysis indicate that there is considerable value in such an approach. An historical perspective on changes which have transformed the health care system developed within a defined organizational theory provide a unique insight into these changes and indicate the need for further development of such an analytical model. ^