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Abstract This study explored how students respond to challenge when tasks become difficult and uncertain. Building on growth mindset theory and autonomy support, the research examined whether brief motivational interventions delivered immediately before a difficult task could influence persistence. University students were assigned to a growth mindset, autonomy-support, combined, or control condition before completing a task containing unsolvable questions. Results showed that participants who received either intervention persisted longer than those in the control condition, while participants who received both interventions demonstrated the greatest persistence overall. The findings suggest that persistence may be strengthened both by helping individuals view difficulty as part of growth and by creating learning environments that feel more self-endorsed and meaningful. Together, these results highlight the value of combining belief-based and context-based approaches to support motivation under challenge.

We develop the concept of, and estimation tools for, durable majority gerrymanders: electoral district maps drawn to reduce an opposing political party's probability of winning a majority in a legislative chamber. Directly interpretable, forward-looking, and motivated by the democratic principle that a party in power should have some chance of losing it, this measure provides new insights into the role of redistricting in state legislative elections. We show that, when map drawers are unconstrained, the ability to create durable majorities is so widespread that at least one party in every state can draw a map where a majority of legislative districts withstand almost any likely future electoral swing. Enacted maps are less durable, due to a combination of underlying geography, voter partisanship, and state-level guidelines. This paper provides the theoretical framework and empirical tools to understand which gerrymandered maps enable state-level majorities to emerge and to endure.

Life is full of stress-inducing activities, which have the potential to shape habitual behaviors that can increase anxiety and decrease overall well-being if not dealt with properly. While existing stress management technologies aim to mitigate these behaviors, such interventions are largely impersonal and have a high barrier to entry, offering generalized guidance and requiring users to manually trigger the intervention. This thesis presents a novel, smartwatch-based system for disrupting stress habits that automatically detects moments of physiological arousal and delivers personalized, in-the-moment reflection exercises.

A within-subjects user study examined 24 participants engaging with a prototype of this system, finding that 87.5% reported greater awareness of their stress habits after using the application. Participants also significantly preferred (p = 0.003) the automatic triggering over scheduled methods. Ultimately, this work contributes a novel integration of physiological sensing and behavior-change theory, offering insights into how wearables can support emotional regulation and habit-loop disruption within everyday routines.

Limitations to arm range of motion affects millions of individuals worldwide. Current motion tracking devices used in rehabilitation can be difficult or inconvenient to access, lowering rates of adherence. The use of a single-sensor IMU for whole-arm motion tracking has been explored through predictive modeling approaches, and has the potential for greater impact through integration with visualization platforms.

Economic mechanism design shapes our economic and social systems, silently influencing outcomes for billions worldwide—from auctions powering global online advertising to matching algorithms determining hospital placements for medical residents. Yet, despite decades of significant theoretical advances, classical economic approaches have encountered analytical bottlenecks, leaving fundamental questions unresolved. Inspired by transformative breakthroughs in the application of AI and machine learning to the natural and physical sciences, this thesis pioneers and extends Differentiable Economics, a computational framework that integrates economic theory with deep learning to systematically design optimal economic mechanisms.

Differentiable Economics reformulates economic design as an end-to-end optimization problem, representing auctions, data markets, and matching mechanisms through differentiable neural architectures. This allows previously intractable economic problems to be solved systematically and with practical computational and statistical efficiency. This thesis is organized into three main parts:

In Part 1, Auctions, I propose two neural architectures: RegretNet, a characterization-free method that flexibly addresses the design of complex multi-item auctions, and RochetNet, a characterization-based architecture that explicitly enforces incentive compatibility for single buyer settings. These architectures successfully replicate known optimal solutions, validate important conjectures, and discover entirely new  mechanisms in scenarios where analytical solutions remain elusive. Additionally, I extend the RochetNet framework to a sequential setting by developing a new reinforcement learning approach that outperforms traditional RL methods and analytical baselines.

In Part 2, Data Markets, I design neural network architectures capable of learning signaling schemes for selling information. This framework can effectively handle new economic constraints arising from obedience conditions, modeling the action that an agent will take upon receiving information, and incentive compatibility. This approach not only replicates established theoretical benchmarks but also identifies and validates novel optimal signaling strategies previously unknown in economic theory.

In Part 3, Matching Markets, I introduce permutation-equivariant convolutional neural networks alongside novel differentiable surrogate metrics for stability and incentive compatibility in the design of two-sided matching markets. This combination enables the computational exploration and characterization of previously unknown trade-offs between stability and incentive compatibility.

Taken together, these contributions highlight the potential of Differentiable Economics as a flexible and powerful methodology for economic design. This thesis takes foundational steps towards democratizing economic mechanism design, providing economists and computer scientists alike with new, accessible tools to address long-standing theoretical challenges in optimal economic design.