Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Computational Analysis of Intelligent Agents: Social and Strategic Settings

The central motif of this work is prediction and optimization in presence of multiple interacting intelligent agents. We use the phrase `intelligent agents' to imply in some sense, a `bounded rationality', the exact meaning of which varies depending on the setting. Our agents may not be `rational' in the classical game theoretic sense, in that they don't always optimize a global objective. Rather, they rely on heuristics, as is natural for human agents or even software agents operating in the real-world. Within this broad framework we study the problem of influence maximization in social networks where behavior of agents is myopic, but complication stems from the structure of interaction networks. In this setting, we generalize two well-known models and give new algorithms and hardness results for our models. Then we move on to models where the agents reason strategically but are faced with considerable uncertainty. For such games, we give a new solution concept and analyze a real-world game using out techniques. Finally, the richest model we consider is that of Network Cournot Competition which deals with strategic resource allocation in hypergraphs, where agents reason strategically and their interaction is specified indirectly via player's utility functions. For this model, we give the first equilibrium computability results. In all of the above problems, we assume that payoffs for the agents are known. However, for real-world games, getting the payoffs can be quite challenging. To this end, we also study the inverse problem of inferring payoffs, given game history. We propose and evaluate a data analytic framework and we show that it is fast and performant.

INVISIBLE LABOR FOR DATA: INSTITUTIONS, INFRASTRUCTURE, AND VIRTUAL SPACE

Americans are accustomed to a wide range of data collection in their lives: census, polls, surveys, user registrations, and disclosure forms. When logging onto the Internet, users’ actions are being tracked everywhere: clicking, typing, tapping, swiping, searching, and placing orders. All of this data is stored to create data-driven profiles of each user. Social network sites, furthermore, set the voluntarily sharing of personal data as the default mode of engagement. But people’s time and energy devoted to creating this massive amount of data, on paper and online, are taken for granted. Few people would consider their time and energy spent on data production as labor. Even if some people do acknowledge their labor for data, they believe it is accessory to the activities at hand. In the face of pervasive data collection and the rising time spent on screens, why do people keep ignoring their labor for data? How has labor for data been become invisible, as something that is disregarded by many users? What does invisible labor for data imply for everyday cultural practices in the United States? Invisible Labor for Data addresses these questions. I argue that three intertwined forces contribute to framing data production as being void of labor: data production institutions throughout history, the Internet’s technological infrastructure (especially with the implementation of algorithms), and the multiplication of virtual spaces. There is a common tendency in the framework of human interactions with computers to deprive data and bodies of their materiality. My Introduction and Chapter 1 offer theoretical interventions by reinstating embodied materiality and redefining labor for data as an ongoing process. The middle Chapters present case studies explaining how labor for data is pushed to the margin of the narratives about data production. I focus on a nationwide debate in the 1960s on whether the U.S. should build a databank, contemporary Big Data practices in the data broker and the Internet industries, and the group of people who are hired to produce data for other people’s avatars in the virtual games. I conclude with a discussion on how the new development of crowdsourcing projects may usher in the new chapter in exploiting invisible and discounted labor for data.

DYNAMICS OF THE SHORT TERM AND LONG TERM AVIAN DISTRIBUTIONS IN NORTH AMERICA - THE ROLES OF VEGETATION HEIGHT HETEROGENEITY AND CLIMATIC FACTORS

Understanding how biodiversity spatially distribute over both the short term and long term, and what factors are affecting the distribution, are critical for modeling the spatial pattern of biodiversity as well as for promoting effective conservation planning and practices. This dissertation aims to examine factors that influence short-term and long-term avian distribution from the geographical sciences perspective. The research develops landscape level habitat metrics to characterize forest height heterogeneity and examines their efficacies in modelling avian richness at the continental scale. Two types of novel vegetation-height-structured habitat metrics are created based on second order texture algorithms and the concepts of patch-based habitat metrics. I correlate the height-structured metrics with the richness of different forest guilds, and also examine their efficacies in multivariate richness models. The results suggest that height heterogeneity, beyond canopy height alone, supplements habitat characterization and richness models of two forest bird guilds. The metrics and models derived in this study demonstrate practical examples of utilizing three-dimensional vegetation data for improved characterization of spatial patterns in species richness. The second and the third projects focus on analyzing centroids of avian distributions, and testing hypotheses regarding the direction and speed of these shifts. I first showcase the usefulness of centroids analysis for characterizing the distribution changes of a few case study species. Applying the centroid method on 57 permanent resident bird species, I show that multi-directional distribution shifts occurred in large number of studied species. I also demonstrate, plain birds are not shifting their distribution faster than mountain birds, contrary to the prediction based on climate change velocity hypothesis. By modelling the abundance change rate at regional level, I show that extreme climate events and precipitation measures associate closely with some of the long-term distribution shifts. This dissertation improves our understanding on bird habitat characterization for species richness modelling, and expands our knowledge on how avian populations shifted their ranges in North America responding to changing environments in the past four decades. The results provide an important scientific foundation for more accurate predictive species distribution modeling in future.

DISPATCHING AND RELOCATION OF EMERGENCY VEHICLES ON FREEWAYS: THEORIES AND APPLICATIONS

Resource allocation decisions are made to serve the current emergency without knowing which future emergency will be occurring. Different ordered combinations of emergencies result in different performance outcomes. Even though future decisions can be anticipated with scenarios, previous models follow an assumption that events over a time interval are independent. This dissertation follows an assumption that events are interdependent, because speed reduction and rubbernecking due to an initial incident provoke secondary incidents. The misconception that secondary incidents are not common has resulted in overlooking a look-ahead concept. This dissertation is a pioneer in relaxing the structural assumptions of independency during the assignment of emergency vehicles. When an emergency is detected and a request arrives, an appropriate emergency vehicle is immediately dispatched. We provide tools for quantifying impacts based on fundamentals of incident occurrences through identification, prediction, and interpretation of secondary incidents. A proposed online dispatching model minimizes the cost of moving the next emergency unit, while making the response as close to optimal as possible. Using the look-ahead concept, the online model flexibly re-computes the solution, basing future decisions on present requests. We introduce various online dispatching strategies with visualization of the algorithms, and provide insights on their differences in behavior and solution quality. The experimental evidence indicates that the algorithm works well in practice. After having served a designated request, the available and/or remaining vehicles are relocated to a new base for the next emergency. System costs will be excessive if delay regarding dispatching decisions is ignored when relocating response units. This dissertation presents an integrated method with a principle of beginning with a location phase to manage initial incidents and progressing through a dispatching phase to manage the stochastic occurrence of next incidents. Previous studies used the frequency of independent incidents and ignored scenarios in which two incidents occurred within proximal regions and intervals. The proposed analytical model relaxes the structural assumptions of Poisson process (independent increments) and incorporates evolution of primary and secondary incident probabilities over time. The mathematical model overcomes several limiting assumptions of the previous models, such as no waiting-time, returning rule to original depot, and fixed depot. The temporal locations flexible with look-ahead are compared with current practice that locates units in depots based on Poisson theory. A linearization of the formulation is presented and an efficient heuristic algorithm is implemented to deal with a large-scale problem in real-time.

AIR SIDE HEAT TRANSFER ENHANCEMENT IN HEAT EXCHANGERS UTILIZING INNOVATIVE DESIGNS AND THE ADDITIVE MANUFACTURING TECHNIQUE

Over the last decade, rapid development of additive manufacturing techniques has allowed the fabrication of innovative and complex designs. One field that can benefit from such technology is heat exchanger fabrication, as heat exchanger design has become more and more complex due to the demand for higher performance particularly on the air side of the heat exchanger. By employing the additive manufacturing, a heat exchanger design was successfully realized, which otherwise would have been very difficult to fabricate using conventional fabrication technologies. In this dissertation, additive manufacturing technique was implemented to fabricate an advanced design which focused on a combination of heat transfer surface and fluid distribution system. Although the application selected in this dissertation is focused on power plant dry cooling applications, the results of this study can directly and indirectly benefit other sectors as well, as the air-side is often the limiting side for in liquid or single phase cooling applications. Two heat exchanger designs were studied. One was an advanced metallic heat exchanger based on manifold-microchannel technology and the other was a polymer heat exchanger based on utilization of prime surface technology. Polymer heat exchangers offer several advantages over metals such as antifouling, anticorrosion, lightweight and often less expensive than comparable metallic heat exchangers. A numerical modeling and optimization were performed to calculate a design that yield an optimum performance. The optimization results show that significant performance enhancement is noted compared to the conventional heat exchangers like wavy fins and plain plate fins. Thereafter, both heat exchangers were scaled down and fabricated using additive manufacturing and experimentally tested. The manifold-micro channel design demonstrated that despite some fabrication inaccuracies, compared to a conventional wavy-fin surface, 15% - 50% increase in heat transfer coefficient was possible for the same pressure drop value. In addition, if the fabrication inaccuracy can be eliminated, an even larger performance enhancement is predicted. Since metal based additive manufacturing is still in the developmental stage, it is anticipated that with further refinement of the manufacturing process in future designs, the fabrication accuracy can be improved. For the polymer heat exchanger, by fabricating a very thin wall heat exchanger (150μm), the wall thermal resistance, which usually becomes the limiting side for polymer heat exchanger, was calculated to account for only up to 3% of the total thermal resistance. A comparison of air-side heat transfer coefficient of the polymer heat exchanger with some of the commercially available plain plate fin surface heat exchangers show that polymer heat exchanger performance is equal or superior to plain plate fin surfaces. This shows the promising potential for polymer heat exchangers to compete with conventional metallic heat exchangers when an additive manufacturing-enabled fabrication is utilized. Major contributions of this study are as follows: (1) For the first time demonstrated the potential of additive manufacturing in metal printing of heat exchangers that benefit from a sophisticated design to yield a performance substantially above the respective conventional systems. Such heat exchangers cannot be fabricated with the conventional fabrication techniques. (2) For the first time demonstrated the potential of additive manufacturing to produce polymer heat exchangers that by design minimize the role of thermal conductivity and deliver a thermal performance equal or better that their respective metallic heat exchangers. In addition of other advantages of polymer over metal like antifouling, anticorrosion, and lightweight. Details of the work are documented in respective chapters of this thesis.