Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Spatial and Temporal Changes in Groundwater Salinity in South Florida

A combination of statistical and interpolation methods and Geographic Information System (GIS) spatial analysis was used to evaluate the spatial and temporal changes in groundwater Cl− concentrations in Collier and Lee Counties (southwestern Florida), and Miami-Dade and Broward Counties (southeastern Florida), since 1985. In southwestern Florida, the average Cl− concentrations in the shallow wells (0–43 m) in Collier and Lee Counties increased from 132 mg L−1 in 1985 to 230 mg L−1 in 2000. The average Cl− concentrations in the deep wells (>43 m) of southwestern Florida increased from 392 mg L−1 in 1985 to 447 mg L−1 in 2000. Results also indicated a positive correlation between the mean sea level and Cl− concentrations and between the mean sea level and groundwater levels for the shallow wells. Concentrations in the Biscayne Aquifer (southeastern Florida) were significantly higher than those of southwestern Florida. The average Cl− concentrations increased from 159 mg L−1 in 1985 to 470 mg L−1 in 2010 for the shallow wells (<33 m) and from 1360 mg L−1 in 1985 to 2050 mg L−1 in 2010 for the deep wells (>33 m). In the Biscayne Aquifer, wells showed a positive or negative correlation between mean sea level and Cl− concentrations according to their location with respect to the saltwater intrusion line. Wells located inland behind canal control structures and west of the saltwater intrusion line showed negative correlation values, whereas wells located east of the saltwater intrusion line showed positive values. Overall, the results indicated that since 1985, there was a potential decline in the available freshwater resources estimated at about 12–17% of the available drinking-quality groundwater of the southeastern study area located in the Biscayne Aquifer.

Rainfall variability in the upper Napo River Basin, Ecuadorian Amazon

The purpose of this research was to investigate the influence of elevation and other terrain characteristics over the spatial and temporal distribution of rainfall. A comparative analysis was conducted between several methods of spatial interpolations using mean monthly precipitation values in order to select the best. Following those previous results it was possible to fit an Artificial Neural Network model for interpolation of monthly precipitation values for a period of 20 years, with input values such as longitude, latitude, elevation, four geomorphologic characteristics and anchored by seven weather stations, it reached a high correlation coefficient (r=0.85). This research demonstrated a strong influence of elevation and other geomorphologic variables over the spatial distribution of precipitation and the agreement that there are nonlinear relationships. This model will be used to fill gaps in time-series of monthly precipitation, and to generate maps of spatial distribution of monthly precipitation at a resolution of 1km2.

Modeling of a Heat-Induced Buckling of Plates Using the Mesh-free Method

In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.

Trends in Water Quality within the Broward County Portion of the Biscayne Aquifer

Continuous and reliable monitoring of contaminants in drinking water, which adversely affect human health, is the main goal of the Broward County Well Field Protection Program. In this study the individual monitoring station locations were used in a yearly and quarterly spatiotemporal Ordinary Kriging interpolation to create a raster network of contaminant detections. In the final analysis, the raster spatiotemporal nitrate concentration trends were overlaid with a pollution vulnerability index to determine if the concentrations are influenced by a set of independent variables. The pollution vulnerability factors are depth to water, recharge, aquifer media, soil, impact to vadose zone, and conductivity. The creation of the nitrate raster dataset had an average RMS Standardized error close to 1 at 0.98. The greatest frequency of detections and the highest concentrations are found in the months of April, May, June, July, August, and September. An average of 76.4% of the nitrate intersected with cells of the pollution vulnerability index over 100.