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Some Quandaries in the Theory of Optimal Stopping
No full textThe primary objective of this dissertation is to study and derive the properties of several optimal stopping problems, and it is split into three parts.
In the first part, we use the dual perspective for optimal stopping, introduced by Davis and Karatzas, to derive pathwise conditions for commonly sought properties of a large class of optimal stopping problems, which depend on a parameter taking values in an arbitrary topological space. In particular, we show that the continuity, with respect to this parameter, of the value function, of the optimal stopping time, and of the spatial derivative of the value function, can be derived from the path properties of the reward process and its Snell envelope. Furthermore, we show that these properties imply the existence of Nash equilibria in a large class of stopping games. We provide several illustrative examples and applications. Of related, and potentially independent interest, is the continuity of solutions to stochastic differential equations with respect to a parameter other than time, and we also address this topic for one dimensional diffusions.
In the second part, we study a sequential estimation problem for an unknown reward in the presence of a random horizon. The reward takes one of two predetermined values which can be inferred from the drift of a Wiener process, which serves as a signal. The objective is to use the information in the signal to estimate the reward which is made available until a stochastic deadline that \emph{depends} on its value. The observer must therefore work quickly to determine if the reward is favorable and claim it before the deadline passes. Under general assumptions on the stochastic deadline (which may in be replaced by general discount functions), we provide a full characterization of the solution that includes an identification with the unique solution to a free-boundary problem. Our analysis derives regularity properties of the solution that imply its ``smooth fit'' with the boundary data, and we show that the free-boundary solves a particular integral equation. The continuity of the free-boundary is also established under additional structural assumptions that lead to its representation in terms of a continuous transformation of a monotone function. We provide illustrations for several examples of interest.
In the third part, we analyze a two-player, nonzero-sum Dynkin game of stopping with incomplete information. We assume that each player observes his own Brownian motion, which is not only independent of the other player's Brownian motion but also not observable by the other player. The player who stops first receives a payoff that depends on the stopping position. Under appropriate growth conditions on the reward function, we show that there are infinitely many Nash equilibria in which both players attain infinite expected payoffs. In contrast, the only equilibrium with finite expected payoffs mandates immediate stopping by at least one of the players. Our results hold in the settings of both pure and mixed strategies
Transparent Deployment of Machine Learning Models on Many-Accelerator Architectures
No full textThe growing demand for machine learning (ML) and signal processing in embedded and edge systems introduces challenges in balancing performance, energy efficiency, and software development simplicity. Heterogeneous Systems-on-Chip (SoCs), which combine general-purpose processors with specialized accelerators, offer a promising solution. However, deploying applications efficiently on such architectures requires new hardware/software co-design methodologies, integration strategies, and runtime resource management.This dissertation presents an approach that separates application logic from accelerator integration, enabling more efficient deployment of ML and signal processing workloads on many-accelerator SoCs.
To begin, I introduce ESP4ML, an open-source design flow that combines ESP, a modular SoC platform, with hls4ml, a high-level synthesis tool for generating ML accelerators. ESP4ML provides an embedded runtime software application programming interface (API) for managing accelerators dynamically within Linux. It enables data transfer between accelerators, reducing memory accesses.These features allow rapid prototyping of SoCs and are demonstrated through FPGA-based implementations executing end-to-end embedded workloads.
Following that, I analyze communication models by comparing memory-based and point-to-point (p2p) data transfer mechanisms for accelerators. Using synthetic and real-world benchmarks, such as Nightvision and Wide-Area Motion Imagery (WAMI), I show that p2p communication consistently delivers better performance and energy efficiency, particularly in multi-threaded and tile-based accelerator systems.
Next, a co-design strategy is presented that integrates the Eigen C++ linear algebra library with ESP. This enables high-level software to transparently offload computations to accelerators, achieving significant gains in both performance and energy efficiency without compromising software simplicity.
To further improve the transparency of deploying ML workloads, I introduce WOLT, a lightweight software layer that enables hardware acceleration for TensorFlow Lite (TFLite) workloads. By leveraging TFLite’s delegate interface, WOLT routes supported operations to accelerators without modifying application code. In addition, a built-in resource manager supports conflict-free, multi-tenant execution of ML applications. FPGA-based experiments on 13 workloads show that WOLT improves system performance and efficiency.
Moreover, I propose BigEnough, an approach for employing multiple accelerators of matrix-matrix multiplication tailored to different input sizes. A smart scheduler dynamically selects the best-fit accelerator at runtime, balancing computational load and maximizing energy efficiency in multi-tenant environments.
In summary, my thesis is that abstracting and separating the design of hardware and software components enables the seamless deployment of software applications, including machine learning models, onto heterogeneous many-accelerator architectures, with optimization of efficiency through a resource manager for parallel execution and streamlined accelerator invocation. I present a comprehensive and practical approach to deploying ML and signal processing workloads on heterogeneous SoCs. By combining modular hardware design, high-level software integration, and runtime efficiency, my dissertation advances embedded system design and paves the way for scalable, programmable edge computing platforms
Ginzburg–Landau Functionals and Reaction–diffusion Equations in the Large-Graph Limit
No full textGraphons are a notion of infinite graphs that are spatially continuous rather than discrete (as are the nodes of a graph). They have emerged as a mathematical formalism that attempts to preserve the essential properties of graphs as their sizes approach infinity. In this dissertation, we consider two problems on graphs, and we let the size of the graphs approach infinity. We define graphon limits of these two graph problems, and we show that the limiting problems on graphons are consistent with their graph counterparts in the sense that the solutions of the graph problems converge to the solutions of the limiting graphon problems.
In Chapters 3–6, we consider the problem of minimizing graph Ginzburg–Landau (GL) functionals. Graph GL functionals are relaxations of graph-cut functionals on graphs, and they have yielded a variety of insights in image segmentation and graph clustering. For sequences of graphs _ that converge to a limiting graphon , we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the . We also show that graphon GL functionals Γ-converge, in a sharp-interface limit, to a graphon total variation (TV) functional. Using the Γ-convergence results, we conclude that the minimizers of the Γ-converging sequences of functionals converge to the minimizers of their limiting functionals. To obtain our convergence results, we require an extension of the underlying function spaces; we discuss the need for a probabilistic interpretation (via Young measures) of the variational problems in the graphon limit.
In Chapters 7–8, we study graph RD equations, which are certain systems of differential equa-tions that are defined on the nodes of a graph. Consider a sequence of graphs that converges to a limiting graphon. We show that the solutions of the sequence of graph RD equations converge to the solution of a limiting graphon RD equation, which we define to be a continuous RD equation that has a nonlocal diffusion term. Furthermore, we show that a sequence of stochastic particle processes (that consist of a random walk and a birth-death process) on the sequence of graphs converges to the solution of the graphon RD equation.
The graphon limits of graph problems can be viewed as continuous and nonlocal counterparts of discrete graph problems, which tend to be large systems of coupled equations. Our results establish precedent and intuition for future work on graphon limits of graph problems, and they build the connection between graphon theory and nonlocal analysis
Institutions, Recognition, and Gender: Essays on Development Economics
No full textThe dissertation examines the intersection of institutional structures, social norms, and gender dynamics in developing economies through three interconnected studies. The central theme binding these papers is how formal policies and institutions intended to promote gender equality and development are mediated by social contexts, cultural beliefs, and interpersonal dynamics. Each study reveals that the effectiveness of formal interventions—whether property rights, tax enforcement, or educational access—depends critically on the underlying social structures and belief systems in which they operate.
In the first chapter, I investigate how awareness and recognition of women’s property rights affects household dynamics. Through a field experiment in rural Maharashtra, India, I find that merely documenting women’s ownership is insufficient—both spouses must recognize these rights for empowerment to occur. My intervention, which provided households with information about women’s co-ownership status and physical documentation, increased expenditure on women-specific goods by 40% and reduced men’s alcohol consumption by 33%. Effects varied significantly based on pre-existing knowledge: households with lowest initial awareness showed the strongest consumption effects, while reductions in domestic violence occurred specifically in households where wives knew about their rights but husbands did not. These findings demonstrate that changing beliefs about women’s rights is crucial for realizing the benefits of formal property ownership.
The second chapter examines how social connections to elected officials affect property tax compliance in rural India. Using a close election difference-in-discontinuities design and administrative tax data, my co-author and I find that citizens connected to local elected leaders are 20 percentage points more likely to remit taxes and remit more in tax payments. This effect is partially driven by enforcement—connected citizens face more in fines and are 32.5 percentage points more likely to be penalized. Heterogeneity analysis reveals these effects are concentrated among poorer property owners with connections to officials, suggesting that political connections can sometimes work against traditional clientelistic expectations.
In the third chapter, we investigate how educational investment in women is influenced by labor market returns. Analyzing data from India and Zambia, we test whether expanded access to secondary education produces patterns consistent with human capital accumulation or signaling theories. We find evidence of uniform increases in educational attainment, particularly in India, suggesting human capital accumulation may be the dominant mechanism. Together, these papers demonstrate that effective policy interventions must account for the complex interplay between formal institutions and informal social structures to achieve meaningful progress in gender equality and economic development
Climate Finance Vulnerability Index (CliF-VI)
No full textClimate Finance Vulnerability Index (CliF-VI) is designed to provide a comprehensive understanding of climate vulnerability for nation states in order to improve the targeting and provision of climate change adaptation financing. The CliF Vulnerability Index takes a data-informed approach, presenting both a high-level and detailed representation of a country’s climate and financial vulnerability. In addition to climate and financial vulnerability, this dashboard also provides an overview of governance considerations that may impact lending modalities or conditions
Martin Buber’s Essence of Hasidism in The Legend of the Baal-Shem and Tales of the Hasidim
No full textThe existentialist philosopher Martin Buber focuses much of his scholarly attention on revealing the spiritual core of Hasidism. While the historian Gershom Scholem criticizes Buber’s methods for their lack of historical grounding, Buber argues throughout his work that the folktales of Hasidism represent its spiritual core, despite never explicitly identifying what this spiritual essence actually is. In vaguely searching for this essence, Buber published and reinterpreted a collection of Hasidic folktales in his volume The Legend of the Baal Shem in 1907. Later, however, he backtracked, claiming to have reinterpreted these legends in a way that was unfaithful to the essence of Hasidism. In 1947, Buber published Tales of Hasidism in which he retold a number of stories he originally compiled in The Legend of the Baal Shem. Buber’s literary style differs between the two works, which raises the questions: How exactly does Buber’s interpretive style differ across the collection of stories? How does Buber reinterpret the stories differently in the two collections? And, ultimately: What is Buber’s idea of the essence of Hasidism? Using the introduction of the two collections, as well as the short stories in each collection that relate to the early life of the Baal Shem Tov, I will attempt to answer these questions, ultimately concluding that Buber’s conception of the essence of Hasidism is the sanctification of the Here and Now, the present-day world of real people
Teaching with Purpose: How Calling Buffers Burnout’s Impact on Teacher Behaviors
No full textResearch consistently demonstrates that burnout is related to more counterproductive work behaviors (CWBs) and fewer organizational citizenship behaviors (OCBs). Nonetheless, there is limited research on the relationship between calling orientation (a sense of purpose and passion for one’s work) and the behavioral outcomes of burnout, particularly within the context of teachers in the United States. The current cross-sectional study seeks to address this gap by investigating whether teachers’ sense of calling moderates the relationship between burnout and both CWBs and OCBs. A total of 108 Kindergarten to 12th grade (K-12) teachers were recruited via Prolific to participate in an online survey. Participants answered questions about their calling orientation, burnout levels, CWBs, and OCBs. We hypothesized that burnout would be positively associated with CWBs and negatively associated with OCBs, and that a strong calling orientation would buffer these relationships. The survey results supported the prediction that teachers experiencing high levels of overall burnout were more likely to engage in CWBs. Importantly, teachers with a strong sense of calling were less likely to engage in CWBs, even when experiencing reduced personal accomplishment. Contrary to expectations, overall burnout was not associated with OCBs, nor did it interact with calling orientation to predict OCBs. The findings suggest that fostering a sense of calling could help minimize CWBs and enhance teachers’ commitment to their work. Future research should explore how teacher recognition, professional development opportunities, and interventions that promote purpose or meaning can further support teacher well-being and reduce CWBs
The Tax Redistribution Gap
No full textThe tax revenue gap—the difference between how much the IRS collects in tax revenue and how much it should collect based on the text of the Internal Revenue Code—is both well-defined and well-studied. But raising revenue is just one purpose of taxation; the tax code also operates to redistribute wealth. Drawing from the tax revenue gap and redistribution literatures, this article coins a parallel concept, the tax redistribution gap, to map the extent to which the tax system falls short of its redistributive goals.
Introducing a tax redistribution gap measure challenges background assumptions in current tax discourse: first, it would call out a reliance on pre-market income as a distributive baseline, which serves to overstate the redistributive impact of the tax code; second, it would increase the profile of redistribution among policymakers and the public—understandably, measures like the tax revenue gap and tax expenditure budgets focus dialogue on tax evasion and over-spending by the government.
Ultimately, the tax redistribution gap would provide a single measure that displays how we are falling short of a key task of the state (redistribution). And by understanding and comparing the component ways our current tax systems falls short of it intended outcomes, we can better tailor redistributive policy solutions
Recentering Women in Judicial Decisions on Reproductive Practices
No full textIn the dynamic landscape of legal academia, narrative analysis emerges as an essential avenue of study. Narratives shape laws, policies, and societal norms, urging parties and observers to recognize the profound influence of stories in legal discourse. Yet, the role of storytelling, particularly within the nuanced sphere of court rulings, has been undertreated by legal scholars. This Article explores how storytelling converges with legal, ethical, and feminist perspectives in court, where narratives wield transformative power, offering a critical reading of the rhetoric and narrative structure in two court cases that address the constitutionality of restricted access to reproductive practices. The first, a ruling from the Supreme Court of Israel, Arad-Pinkas v. Committee for Approval of Embryo Carrying Agreements, establishes the eligibility of same-sex couples and single men for domestic surrogacy services after years of ineligibility. The second, Dobbs v. Jackson Women’s Health Organization, holds that the right to abortion is no longer considered a fundamental right guaranteed by the Fourteenth Amendment of the U.S. Constitution. This Article contends that the narratives underpinning legal proceedings are not mere rhetorical devices but wield ethical and practical significance, shaping society’s implicit image of women, their societal role, and the opportunities they are afforded. Through this analysis, this Article uncovers the underlying values, assumptions, and narratives that courts rely on and, perhaps more significantly, dismiss. Findings reveal tensions between women’s rights and competing interests—those of single men who rely on a woman’s body to achieve parenthood (in the Israeli case) and those of fetuses (in the Dobbs case). In both contexts, legal narratives centering these other figures are used to systematically downplay women’s interests, restrict their opportunities, and minimize their autonomy. This Article advocates for centering women in the legal narrative when discussing reproductive practices performed on women’s bodies. The failure to do so, it argues, causes far-reaching harm to women’s experiences and life opportunities. Lessons from both cases are relevant to ongoing and future advocacy fights and the women whose well-being depends on their outcomes
State Administrative Constitutionalism and Environmental Rights
No full textSince New York’s Environmental Rights Amendment took effect in 2022, judges and litigants alike have understandably struggled to make sense of it. The “Green Amendment” presents unique interpretive challenges as a state constitutional positive right that is closely related to a preexisting regulatory scheme. Thus far, Green Amendment claims have been accompanied by statutory causes of action. Consequently, courts’ early interpretations of the right have, at best, entangled—and at worst, equated—the right with adherence to existing environmental laws, especially the State Environmental Quality Review Act (SEQRA). Reviewing environmental statutory and constitutional rights claims concurrently raises questions related to state constitutional interpretation, administrative agencies’ role in constitutional interpretation, and deference. This Note seeks to propose a framework for reviewing Green Amendment claims within the existing statutory context using lessons from scholarship on state constitutionalism and administrative constitutionalism. This Note ultimately concludes that democratic proportionality review is the most appropriate way to interpret the Green Amendment as a positive state constitutional right and argues that courts can conduct this proportionality analysis by merely reviewing agencies’ mitigation findings under SEQRA using a de novo standard of review. Such an approach acknowledges that administrators engage in constitutional interpretation when implementing their statutes, but it applies the appropriate standard of review to those interpretations, since courts are the final arbiters of constitutional meaning