Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. The computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions

Doctor of Philosophy

dissertationEnergy generation through combustion of hydrocarbons continues to dominate as the most common method for energy generation. In the U.S., nearly 84% of the energy consumption comes from the combustion of fossil fuels. Because of this demand, there is a continued need for improvement, enhancement, and understanding of the combustion process. As computational power increases, and our methods for modelling these complex combustion systems improve, combustion modelling has become an important tool in gaining deeper insight and understanding of these complex systems. The constant state of change in computational ability leads to a continual need for new combustion models that can take full advantage of the latest computational resources. To this end, the research presented here encompasses the development of new models which can be tailored to the available resources, allowing one to increase or decrease the amount of modelling error based on the available computational resources and desired accuracy. Principal component analysis (PCA) is used to identify the low-dimensional manifolds which exist in turbulent combustion systems. These manifolds are unique in there ability to represent a larger dimensional space with fewer components, resulting in a minimal addition of error. PCA is well-suited for the problem at hand because of its ability to allow the user to define the amount of error in approximation, depending on the resources at hand. The research presented here looks into various methods which exploit the benefits of PCA in modelling combustion systems, demonstrating several models, and providing new and interesting perspectives for the PCA-based approaches to modelling turbulent combustion

Doctor of Philosophy

dissertationEnergy generation through combustion of hydrocarbons continues to dominate as the most common method for energy generation. In the U.S., nearly 84% of the energy consumption comes from the combustion of fossil fuels. Because of this demand, there is a continued need for improvement, enhancement, and understanding of the combustion process. As computational power increases, and our methods for modelling these complex combustion systems improve, combustion modelling has become an important tool in gaining deeper insight and understanding of these complex systems. The constant state of change in computational ability leads to a continual need for new combustion models that can take full advantage of the latest computational resources. To this end, the research presented here encompasses the development of new models which can be tailored to the available resources, allowing one to increase or decrease the amount of modelling error based on the available computational resources and desired accuracy. Principal component analysis (PCA) is used to identify the low-dimensional manifolds which exist in turbulent combustion systems. These manifolds are unique in there ability to represent a larger dimensional space with fewer components, resulting in a minimal addition of error. PCA is well-suited for the problem at hand because of its ability to allow the user to define the amount of error in approximation, depending on the resources at hand. The research presented here looks into various methods which exploit the benefits of PCA in modelling combustion systems, demonstrating several models, and providing new and interesting perspectives for the PCA-based approaches to modelling turbulent combustion

Quadtree algorithms for image processing

The issue of constructing a computer-searchable image encoding algorithm for complex images and the effect of this encoded image on algorithms for image processing are considered. A regular decomposition of image (picture) area into successively smaller bounded homogeneous quadrants is defined. This hierarchical search is logarithmic, and the resulting picture representation is shown to enable rapid access of the image data to facilitate geometric image processing applications (i.e. scaling, rotation), and efficient storage. The approach is known as quadtree (Q-Tree) encoding. The applications in this thesis are primarily to grayscale pixel images as opposed to simple binary images

The Status of the Negro Industrial Worker in Houston, Texas

It has long been established in the literature of industrial science that population members occupy a specific place in human group life. This position is greatly affected by their status in the industrial pattern of society in which they move and have their being. Previous study has shown that this type of existence is not always the same in nature. Because of this type of assumption, it is possible to study the industrial status of a particular occupational group. Every individual who seeks a job is interested in two things. His first interest is in the economic returns which the job offers in the light of responsibilities and effort which it requires. His second interest is in the future it offers and the security it guarantees. The consideration of these questions depends upon the circumstances,outlook, and ambition of the potential worker. However, these interests form indexes of the individual status of individuals engaged in any type of work. Because of this theoretical possibility, this study is concerned with the following main question: What is the industrial status of Negro skilled workers in Houston, Texas? Although this question cannot be answered fully, it is believed that if specific indexes are carefully selected and treated in relation to adequate field notes, a general picture of Negro skilled workers in their socio-industrial pattern of life can be secured. In order to realize this general objective, eight main questions must be answered by the investigation; 1. How many Negroes are employed as skilled workers in Houston, Texas, and has there been an increase or decrease in the number of skilled Negro workers from 1935 to 1944? 2. What conditions have caused increases or decreases in the number of skilled Negro workers in the Houston area? 3. What are the industrial fields in which these skilled Negro workers are employed and why are they employed in these particular fields? 4. What is the average wage of skilled Negro workers in comparison with wages paid to all skilled workers in the industries of the Houston area? 5. What is the effect of special training on wages based on a comparison of averages of salaries? 6. Why is it that all employees hired to do the same type of work do not receive the same pay? 7. What is the average tenure of the skilled Negro worker? 8. What factors affect the employment of skilled Negro workers? Preliminary to any such analysis is the definition of significant terms which will be used in this problem. Therefore, we are defining status as the state or condition of a person, group or situation; it further represents one\u27s standing with relation to others. All persons having Negro blood in their veins or a descendant of the first African slaves brought to this country, as well as, individuals classified as Negroes by the management of industry will be referred to as Negroes. All persons who are skilled in the manipulation and operation of tools and machinery, possessing the technical knowledge needed for the performance of a task in industry will be referred to as skilled industrial workers. These workers represent the makers and operators of the machines used by industry. Houston, the largest city in Texas, located forty-six miles southeast of Prairie View State College, had a population of 384,518, including approximately 94,000 Negroes, in 1944.9 9Texas Almanac, 1943-1944, p. 86

Addressing The Recreation And Social Participation Gap In Children With Disabilities: Program Development Of A Recreational Summer Camp

Recreation, social participation, and leisure are important occupations of children, however, children with disabilities participate in them less frequently and more often with parents when compared to their typically developing (TD) peers (Lin, 2020; Schreuer et al., 2014; Solish et al., 2010). Therapeutic summer camps have been shown to reduce these disparities in participation while achieving positive functional gains (Flynn et al., 2019; Guest et al., 2017; Kaboski et al., 2015; Petersen et al., 2020; Sakzewski et al., 2015; Sterman et al., 2016; Walker et al., 2010; Yang et al., 2021). However, few summer camp programs are available for occupational therapy practitioners to use. The purpose of this scholarly project was to develop an all-inclusive guide to running a therapeutic summer camp and to help to mitigate the occupational imbalance that children with disabilities face. The author of the product partnered with a pediatric outpatient therapy clinic, conducted an in-depth literature review, an on-site needs assessment, and synthesized all collected data to create the current product. The final product, Hook’d on ‘Arrdenture’: A Pirate-Themed Recreation Day Camp, includes program goals, activity descriptions, staff training materials, financial considerations, marketing materials, sustainability recommendations, evaluation methods, and relevant handouts for implementation of the program. It is anticipated that the final product will aid pediatric therapy practitioners in providing supported recreation, social, and leisure participation opportunities while helping to reverse the participation gap that children with disabilities face

Cooperation and the Fate of Microbial Societies

Microorganisms have been cooperating with each other for billions of years: by sharing resources, communicating with each other, and joining together to form biofilms and other large structures. These cooperative behaviors benefit the colony as a whole; however, they may be costly to the individuals performing them. This raises the question of how such cooperation can arise from natural selection. Mathematical modeling is one important avenue for exploring this question. Evolutionary experiments are another, providing us with an opportunity to see evolutionary dynamics in action and allowing us to test predictions arising from mathematical models. A new study in this issue of PLOS Biology investigates the evolution of a cooperative resource-sharing behavior in yeast. Examining the competition between cooperating and “cheating” strains of yeast, the authors find that, depending on the initial mix of strains, this yeast society either evolves toward a stable coexistence or collapses for lack of cooperation. Using a simple mathematical model, they show how these dynamics arise from eco-evolutionary feedback, where changes in the frequencies of strains are coupled with changes in population size. This study and others illustrate the combined power of modeling and experiment to elucidate the origins of cooperation and other fundamental questions in evolutionary biology.MathematicsOrganismic and Evolutionary Biolog

Reduced-order PCA models for chemical reacting flows

pre-printOne of the most challenging aspects of turbulent combustion research is the development of reduced-order combustion models which can accurately reproduce the physics of the real system. The identification and utilization of the low dimensional manifolds in these system is paramount to understand and develop robust models which can account for turbulence-chemistry interactions. Recently, principal components analysis (PCA) has been given notable attention in its analysis of reacting systems, and its potential in reducing the number of dimensions with minimum reconstruction error. The present work provides a methodology which has the ability of exploiting the information obtained from PCA. Two formulations of the approach are shown: Manifold Generated from PCA (MG-PCA), based on a global analysis, and Manifold Generated from Local PCA (MG-L-PCA), based on performing the PCA analysis locally. The models are created using the co-variance matrix of a data-set which is representative of the system of interest. The reduced models are then used as a predictive tool for the reacting system of interest by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. The present study first looks into the optimal selection of the subset of transported variables and analyzes the effect of this selection on the approximation of the state space and chemical species source terms. Then, a demonstration of various a posteriori cases is presented

Terrorism and Boko Haram: A Reconsideration of Impacts on World Peace

While it is a fact that terrorism dates back to centuries and most of it was not studied critically, it may be considered too dangerious to assume that posture espcially in the wake of the 1990s and espcially after the September 11, 2001 attack on the World Trade Centre and the Pentagon in New York. Before then, most terrorism occurred away from the African continent and most scholars considered acts of terrorism as alien to the peoples culture, ideologies and believes. However, the wave of globalisation has berth terrorism on the African coast where countries like Somalia, Kenya and Nigeria etc have been infested and this has earned them various cliches like 'axis   of death'. In reconsiderating the impacts of Boko Haram on world peace, the study attempted a defintion of the concept of terrorism, a general overview of  terrorism around the world while zero-in on current issues of Boko Haram terrorism in Nigeria. In the final analysis, the study brings to the fore, the social/phychological, political and economic impacts of Boko Haram terrorism on world peace. It has been concluded that terrorism will continue to be a pain in the back of  world peace not only because it has proven to be a successful tool for those who believe in it but also because, belivers in acts of terror are convinced that they are tolling the paths of honor. To curb this, nations of the world must melt into bilateral and multilateral understanding and synergy against it especially now that chemical terrorism is imminent