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. ^

Estimation of average annual daily traffic (AADT) using geographically weighted regression (GWR) method and geographic information system (GIS)

Annual average daily traffic (AADT) is important information for many transportation planning, design, operation, and maintenance activities, as well as for the allocation of highway funds. Many studies have attempted AADT estimation using factor approach, regression analysis, time series, and artificial neural networks. However, these methods are unable to account for spatially variable influence of independent variables on the dependent variable even though it is well known that to many transportation problems, including AADT estimation, spatial context is important. ^ In this study, applications of geographically weighted regression (GWR) methods to estimating AADT were investigated. The GWR based methods considered the influence of correlations among the variables over space and the spatially non-stationarity of the variables. A GWR model allows different relationships between the dependent and independent variables to exist at different points in space. In other words, model parameters vary from location to location and the locally linear regression parameters at a point are affected more by observations near that point than observations further away. ^ The study area was Broward County, Florida. Broward County lies on the Atlantic coast between Palm Beach and Miami-Dade counties. In this study, a total of 67 variables were considered as potential AADT predictors, and six variables (lanes, speed, regional accessibility, direct access, density of roadway length, and density of seasonal household) were selected to develop the models. ^ To investigate the predictive powers of various AADT predictors over the space, the statistics including local r-square, local parameter estimates, and local errors were examined and mapped. The local variations in relationships among parameters were investigated, measured, and mapped to assess the usefulness of GWR methods. ^ The results indicated that the GWR models were able to better explain the variation in the data and to predict AADT with smaller errors than the ordinary linear regression models for the same dataset. Additionally, GWR was able to model the spatial non-stationarity in the data, i.e., the spatially varying relationship between AADT and predictors, which cannot be modeled in ordinary linear regression. ^

Think before you eat: Calories and exercise equivalents presented on menus at point-of-choice

Although calorie information at the point-of-purchase at fast food restaurants is proposed as a method to decrease calorie choices and combat obesity, research results have been mixed. Much of the supportive research has weak methodology, and is limited. There is a demonstrated need to develop better techniques to assist consumers to make lower calorie food choices. Eating at fast food restaurants has been positively associated with weight gain. The current study explored the possibility of adding exercise equivalents (EE) (physical activity required to burn off the calories in the food), along with calorie information as a possible way to facilitate lower calorie choice at the point-of-choice in fast food restaurants. This three-group experimental study, in 18-34 year old, overweight and obese women, examines whether presenting caloric information in the form of EE at the point-of-choice at fast food restaurants, will lead to lower calorie food choices compared to presenting simple caloric information or no information at all. Methods. A randomized repeated measures experiment was conducted. Participants ordered a fast food meal from Burger King with menus that contained only the names of the food choices (Lunch 1). One week later (Lunch 2), study participants were given one of three menus that varied: no information, calorie information, or calorie information and EE. Study participants included 62 college aged students. Additionally, the study controlled for dietary restraint by blocking participants, before randomization, to the three groups. Results. A repeated measures analysis of variance was conducted. The study was not sufficiently powered, and while the study was designed to determine large effect sizes, a small effect size of .026, was determined. No significant differences were found in the foods ordered among the various menu conditions. Conclusion. Menu labeling alone might not be enough to reduce calories at the point-of-choice at restaurants. Additional research is necessary to determine if calorie information and EE at the point-of-choice would lead to fewer calories chosen at a meal. Studies should also look at long-term, repeated exposure to determine the effectiveness of calories and or EE at the point-of-choice at fast food restaurants.

Rigid and non-rigid point-based medical image registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Hybrid approaches to estimating freeway travel times using point traffic detector data

The accurate and reliable estimation of travel time based on point detector data is needed to support Intelligent Transportation System (ITS) applications. It has been found that the quality of travel time estimation is a function of the method used in the estimation and varies for different traffic conditions. In this study, two hybrid on-line travel time estimation models, and their corresponding off-line methods, were developed to achieve better estimation performance under various traffic conditions, including recurrent congestion and incidents. The first model combines the Mid-Point method, which is a speed-based method, with a traffic flow-based method. The second model integrates two speed-based methods: the Mid-Point method and the Minimum Speed method. In both models, the switch between travel time estimation methods is based on the congestion level and queue status automatically identified by clustering analysis. During incident conditions with rapidly changing queue lengths, shock wave analysis-based refinements are applied for on-line estimation to capture the fast queue propagation and recovery. Travel time estimates obtained from existing speed-based methods, traffic flow-based methods, and the models developed were tested using both simulation and real-world data. The results indicate that all tested methods performed at an acceptable level during periods of low congestion. However, their performances vary with an increase in congestion. Comparisons with other estimation methods also show that the developed hybrid models perform well in all cases. Further comparisons between the on-line and off-line travel time estimation methods reveal that off-line methods perform significantly better only during fast-changing congested conditions, such as during incidents. The impacts of major influential factors on the performance of travel time estimation, including data preprocessing procedures, detector errors, detector spacing, frequency of travel time updates to traveler information devices, travel time link length, and posted travel time range, were investigated in this study. The results show that these factors have more significant impacts on the estimation accuracy and reliability under congested conditions than during uncongested conditions. For the incident conditions, the estimation quality improves with the use of a short rolling period for data smoothing, more accurate detector data, and frequent travel time updates.

Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.

Think Before You Eat: Calories and Exercise Equivalents Presented on Menus at Point-of-Choice

Although calorie information at the point-of-purchase at fast food restaurants is proposed as a method to decrease calorie choices and combat obesity, research results have been mixed. Much of the supportive research has weak methodology, and is limited. There is a demonstrated need to develop better techniques to assist consumers to make lower calorie food choices. Eating at fast food restaurants has been positively associated with weight gain. The current study explored the possibility of adding exercise equivalents (EE) (physical activity required to burn off the calories in the food), along with calorie information as a possible way to facilitate lower calorie choice at the point-of-choice in fast food restaurants. This three-group experimental study, in 18-34 year old, overweight and obese women, examines whether presenting caloric information in the form of EE at the point-of-choice at fast food restaurants, will lead to lower calorie food choices compared to presenting simple caloric information or no information at all. Methods: A randomized repeated measures experiment was conducted. Participants ordered a fast food meal from Burger King with menus that contained only the names of the food choices (Lunch 1). One week later (Lunch 2), study participants were given one of three menus that varied: no information, calorie information, or calorie information and EE. Study participants included 62 college aged students. Additionally, the study controlled for dietary restraint by blocking participants, before randomization, to the three groups. Results: A repeated measures analysis of variance was conducted. The study was not sufficiently powered, and while the study was designed to determine large effect sizes, a small effect size of .026, was determined. No significant differences were found in the foods ordered among the various menu conditions. Conclusion: Menu labeling alone might not be enough to reduce calories at the point-of-choice at restaurants. Additional research is necessary to determine if calorie information and EE at the point-of-choice would lead to fewer calories chosen at a meal. Studies should also look at long-term, repeated exposure to determine the effectiveness of calories and or EE at the point-of-choice at fast food restaurants.

Rigid and Non-rigid Point-based Medical Image Registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

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.