Computational Representations of Character Significance in Novels

Characters in novels have typically been modeled based on their presence in scenes in narrative, considering aspects like their actions, named mentions, and dialogue. This conception of character places significant emphasis on the main character who is present in the most scenes. In this work, we instead adopt a framing developed from a new literary theory proposing a six-component structural model of character. This model enables a comprehensive approach to character that accounts for the narrator-character distinction and includes a component neglected by prior methods, discussion by other characters. We compare general-purpose LLMs with task-specific transformers for operationalizing this model of character on major 19th-century British realist novels. Our methods yield both component-level and graph representations of character discussion. We then demonstrate that these representations allow us to approach literary questions at scale from a new computational lens. Specifically, we explore Woloch's classic "the one vs the many" theory of character centrality and the gendered dynamics of character discussion.

Physics-Informed Neural Solvers for Periodic Quantum Eigenproblems

This thesis presents a physics-informed machine learning framework for solving the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry, due to its distinctive band topology featuring Dirac points and its relevance to materials such as graphene. By leveraging neural networks to learn complex Bloch functions and their associated eigenvalues (energies) simultaneously, we develop a mesh-free solver enforcing the governing Schrödinger equation, Bloch periodicity, and normalization constraints through a composite loss function without supervision. The model is trained over the Brillouin zone to recover band structures and Bloch modes, with numerical validation against traditional plane-wave expansion methods. We further explore transfer learning techniques to adapt the solver from nearly-free electron potentials to strongly varying potentials, demonstrating its ability to capture changes in band structure topology. This work contributes to the growing field of physics-informed machine learning for quantum eigenproblems, providing insights into the interplay between symmetry, band structure, and neural architectures.