A fake real projective space is a manifold homotopy equivalent to real projective space, but not diffeomorphic to it. Equivalently, it is the orbit space of a free involu- tion on a (homotopy) sphere.

In this thesis, we show that some of the fake RP6s , constructed by Hirsch and Milnor in 1963, and the analogous fake RP14s admit metrics that simutaneously have almost nonnegative sectional curvature and positive Ricci curvature. These spaces are obtained by taking the Z2 quotients of the embedded images of the standard spheres of codimension one in some of Milnor’ s exotic 7−spheres and the analogous Shimada’s exotic 15−spheres. This part of my thesis is joint work with F. Wilhelm.

Hirsch and Milnor also constructed fake RP5s using invariant subspheres of codi- mension two. Octonionically, this construction yields closed 13−manifolds, that are homotopy equivalent to RP13s. The analog to their proof that fake RP5s are not diffeomorphic to standard RP5 breaks down; since in contrast to dimension 6, there is an exotic 14−sphere. We show that some of the Hirsch-Milnor RP13s are not diffeomorphic to standard RP13s. Here we obtain a complete diffeomorphism clas- sification of the Hirsch-Milnor RP13s. This part of my thesis is joint work with C. He.

Using techniques of group diagrams we provide an elementary proof that certain 3-dimensional Brieskorn varieties are SO(2) × SO(2)−equivariantly diffeomorphic to certain Lens Spaces.

Diabetes mellitus (DM) is a metabolic disease whose prevalence has steadily risen in the United States and globally over the last three decades. In addition to its direct effects on hyperglycemia, DM has a variety of associated complications, ranging from an increased risk of cardiovascular disease to an increased risk for multiple infectious diseases. Because of these complications, DM remains a major source of disease burden in the United States and globally. Even as the prevalence of DM has risen, so too have awareness of the disease and the armamentarium of medications available for its treatment. These changes in both awareness and the ability to treat the disease have ostensibly had an impact. Rates of some of the most important complications of DM, including cerebrovascular accident (CVA) and myocardial infarction (MI) have declined in the United States while at the same time, the prevalence of DM has leveled off.

In this dissertation, I focus on three separate, but linked issues about DM. All of the work I present here was done either at the state level in California or at the level of the city of San Francisco. In chapter 1, I examine whether the decreases that have been observed for non-infectious complications of DM are also true for its infectious complications in California overall. In chapter 2, in a cohort of patients in San Francisco, I examine the potential role of medications that are frequently used to treat other conditions in persons with DM in driving the increased risk of infection in persons with DM as well as the findings I describe in chapter 1. Finally, in chapter 3, working with the same cohort studied in chapter 2, I examine the role of distance to the primary care clinic, a potentially modifiable factor, in determining diabetes control.

In chapter 1 of this dissertation, I show that in California, rates of hospitalization for infectious diseases among persons with DM have steadily increased. This result contrasts both with what has been reported for non-infectious disease complications of DM nationally as well as with my own findings for two important non-infectious disease complications of DM, CVA and MI. My results suggest that other factors beyond the level of control of DM could drive the risk of infection among persons with DM. In chapter 2, I show that while one such potential factor, collateral effects of medications used to treat other conditions (e.g. hyperlipidemia,hypertension) in persons with DM, does not appear to drive the increase risk of infection in persons with DM, two medication classes, angiotensin converting enzyme inhibitors (ACEI) and angiotensin receptor blockers (ARB) could actually reduce the risk of developing in infection. Finally, in chapter 3, I show that minimizing the distance between patients and their primary care clinics has the potential to result in a significant improvement in control of DM, as measured by the glycated hemoglobin level. Together, the three chapters of this dissertation provide a comprehensive view of DM in California as a whole and in San Francisco in particular. My findings shed new light on one of DM’s most important complications, infectious diseases, while at the same suggesting two potential methods to limit the development of these and potentially other DM-related complications.

Over the past few decades, engineering and statistical principles have played a significant role in the advancement of biology and medicine. In this dissertation, we study two problems which have applications in bioinformatics and epidemiology, respectively. We look at these problems through the lens of statistical inference, and propose exact and approximate algorithms.

The first line of work is on sequence reconstruction over deletion channels, which lies at the intersection of theoretical computer science, information theory and bioinformatics. Deletion channels have become increasingly relevant in bioinformatics to model impairments in DNA sequencing and DNA data storage. Prior works in theoretical computer science have proposed sequence alignment heuristics for deletion impairments. We take an alternate approach to this problem and propose algorithms that are rooted in statistical principles, such as maximum-likelihood decoding and maximum-aposteriori decoding. Our algorithms outperform the state-of-the-art algorithms in this space. Along the way, we also develop mathematical tools that are of general interest beyond the study of deletion channels.

The second line of work is on group testing which is related to information theory, medical testing and epidemiology. Group testing is a technique that pools together diagnostic samples from multiple individuals to identify infected individuals in a population. Such a technique potentially allows us to use fewer tests than what is required to test everyone individually. Here again, we improve upon the state-of-the-art group testing algorithms by developing a new statistical inference approach to this problem. Moreover, while traditional group testing assumes independent infections, we observe that contagious diseases like COVID-19 are governed by community spread. We show that taking into account the side information provided by the community structure may lead to significant savings – upto 60% fewer tests compared to traditional test designs in our experiments. We develop new bounds and new approaches to encoding and decoding algorithms that take into account the community structure and integrate group testing into epidemiological modeling.

Over the past century, society has been riding a wave of technology revolution empowered by Moore’s Law that has enabled trillion devices proliferating into every aspect of our daily lives. Only through innovation in material science of silicon-based transistors and manufacturing capability of advanced deposition and lithography process has made this possible. The next century is beginning to see a new emergence of “more than Moore” with devices attributing new properties such as conformability, transient/edible, self-healing, actuating motion and so much more. Similarly, these devices will be formed from union of new and old technologies, where they can be fabricated using high-throughput printing technologies for make them affordable and ubiquitous. This thesis focuses on the composition of various innovations of particle-polymer composites with additive manufacturing process such as screen-printing to design and fabricate multiple technologies such as self-propelling motors, energy harvesting, energy storage, stretchable electronics, and wearable devices. The thesis provides strategy to develop new composites for their respective technologies by sourcing the composite materials necessary to optimize the composite characteristics, which would be studied through characterization and device evaluation by varying the composite ratios. The development of new composite materials for emerging technologies is enabling a new vision of how technologies can continue to weave into every fabric of our lives.

Crowdsourcing is a powerful approach to solve some of the biggest problems today - social and scientific. To harness the potential of crowdsourcing, researchers have often relied and successfully used crowd marketplaces such as Amazon Mechanical Turk. However, in spite of a large worker base and past successes, these platforms come with their own limitations. 40% of all the tasks are spam on Mechanical Turk; and it’s also difficult to accomplish tasks which require a broader participation base, or expert knowledge. Citizen crowd, at the same time, involves distributed group of people with diverse background and skills; who might organize to accomplish tasks or solve problems without engaging with paid crowd platforms. The motivation for them lies in reasons other than micro-payments.

In this dissertation, I explore problems of varying size and duration, where mobilizing the citizen crowd can achieve worthwhile goals. To investigate the possibilities with citizen crowdsourcing, I built systems and ran initiatives that require different level of expertise. This thesis highlights three projects, ranging from seconds of micro contributions to months of highly intellectual contributions. To begin with, we built a mobile lock screen application, that supports completion of quick microtasks in short bursts of time - each time someone unlocks their phone. Next, we launched first of its kind large scale distributed and time-critical campaign in India; where we mobilized the crowd and studied aspects around team building, collaboration, incentives and communication channel; to achieve a common goal. Finally, we ran a first of its kind "research-at-scale" initiative, that explores the possibility of crowdsourcing large open ended problems - by connecting professors with students from around the world - providing access and educational value. All these initiatives have engaged thousands of people from around the world, and we can conclude that it is possible to mobilize the citizen crowd to accomplish worthy goals.

Electric Vehicle (EV) route planning is an important but hard problem, since battery capacity is limited, charging times are long, and charging stations are sparsely distributed. It is nonetheless critical to improving the time and energy efficiency of future transportation systems, and to promoting EV adoption, by reducing driver range anxiety. EV routing is usually modeled as a Shortest Feasible Path (SFP) problem, which ensures a non-negative State of Charge along the route, taking both travel time and energy consumption to be deterministic and known in advance. In practice, however, travel time and energy consumption are both stochastic variables, which can be hard to estimate accurately.

This dissertation presents a set of techniques to advance our abilities to address such stochasticity. First, we show how to accurately predict energy consumption and travel times along routes using phases, a new structuring abstraction for vehicle speed profiles. Contrary to conventional wisdom, using phases outperforms even microscopic energy estimation models. We show that using phases to generate synthetic trips preserves the real-world variance in travel times and energy consumptions of real-world trips.

Next, we show how to efficiently encapsulate the tradeoffs between travel times and robustness of feasible routes against deviations in energy consumptions using the Starting Charge Map and Buffer Map constructs. Further, we generalize the SFP problem to permit stochastic travel times and energy consumptions using two different probabilistic definitions of route feasibility. These definitions allow drivers to maintain route feasibility either in expectation, or by setting explicit lower bounds on stranding probability.

We also study how to effectively apply well-known speedup techniques, such as Contraction and Edge Hierarchies, for route planning with stochastic edge weights. We show that the choice of weight representations has a significant impact on the routing query runtimes, and introduce the tiering technique, which significantly improves query times for three different stochastic routing objectives. We evaluate all presented methods on realistic routing instances.

Lastly, we generalize the problem of identifying dwell regions for trajectory sets to that of finding shared dwell regions, and present two novel approaches to the problem. We show that our solutions outperform the state-of-the-art by nearly a factor of three.