Doctor of Philosophy, The Ohio State University, 2008, Physics

Ecological systems such as forest and lakes can exhibit multiple stable states, abrupt transitions and self-organization as a control parameter is varied. Understanding the dynamics of these systems and devising easily quantifiable measures with predictive capabilities using the theoretical tools of stochastic dynamics and nonequilibrium statistical physics form the focus of this thesis.We study simple ecological models with no spatial degrees of freedom, that show a catastrophic transition as a control parameter is varied and propose a novel early warning signal that exploits two ubiquitous features of ecological systems: nonlinearity and large external fluctuations. It is shown that changes in asymmetry in the distribution of time series data, quantified by changing skewness, is an early warning signal of impending regime shifts. Using simple analytical calculations, model simulations that mimic field measurements and an analysis of real data from abrupt climate change in the Sahara, we study the feasibility of skewness calculations using data available from routine monitoring. We consider a spatially explicit model of collapse of vegetation in one and two spatial dimensions. An analytical calculation based on the mean-field approximation shows that spatial variance and spatial skewness (with an appropriate sign) increase as one approaches the threshold of vegetation collapse. Our numerical calculations show that an increasing spatial variance in conjunction with a reversal in the initial changing trend of spatial skewness is a superior indicator of an impending spatial ecological regime shift when spatially explicit data are available. These results are shown to hold under several different dispersal kernels such as Gaussian, fat tailed and Cauchy. Vegetation in semi-arid regions exhibits striking spatial patterns. Theoretical models often ignore the strong fluctuations in parameters such as those arising from seasonality. We present a fully seasonal rainfall mod (open full item for complete abstract)

Committee: C Jayaprakash PhD (Committee Chair); David Stroud PhD (Committee Member); Dick Furnstahl PhD (Committee Member); Michael Poirier PhD (Committee Member) Subjects: Ecology; Physics

Doctor of Philosophy, Case Western Reserve University, 2005, Statistics

The FES Center, Cleveland, Ohio, conducts research into the use of implantable medical devices designed to expand a spinal cord injured user's workspace, and augment daily function. The research presented here is to develop and utilize statistical techniques to estimate the workspace achieved when restoring arm control. The workspace properties of interest are quantified by an experimental protocol designed to collect data to evaluate the 3-D reachable workspace and the 3-D controllable, or functional, workspace. Non-parametric and parametric strategies are developed to model the reachable workspace. Within the parametric setting superquadrics are used and confidence bounds for the shapes are presented. The controllable workspace is quantified by collecting spatial binary data, which are the success or failure of a particular task at locations within the reachable workspace. These data are modeled and checked for correspondence with the fitted model. Properties of the model are investigated. A result concerning residuals is presented, along with “jump maps”, a new technique for displaying variation across a map. In fitting models to spatial binary data, difficulties have been observed in properly capturing variance parameters from simulated datasets, when the number of binary observations is not large. Alternative algorithms and models are presented that have competing advantages. A new, promising mixture prior distribution is developed and evaluated. Finally, sequential sampling strategies for binary spatial models are developed. These competing strategies are designed to select the locations where additional observations will be sampled. In a real-time experimental setting, it is necessary to have a strategy that minimizes the amount of computation time. A new strategy is presented that minimizes the amount of computation time spent refitting the model and searching for the next point(s) to sample.

Committee: Joseph Sedransk (Advisor) Subjects: