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Solving a continuous algebraic constraint system requires two decisions: which values satisfy the constraints, and which structural augmentation renders an unsolvable system solvable. Classical solvers answer the first well and the second…

The Non-Equilibrium Green's Function (NEGF) is the standard formalism for nano-scale electron transport. By recasting the NEGF scattering problem as a linear system of equations whose solution encodes the transmission and reflection…

LLM-based agents excel at software engineering tasks where an existing codebase provides context, but constructing a program from scratch remains fundamentally harder. Recent benchmarks such as ProgramBench quantify this gap: given only…

The Stanley--Gasharov conjecture asserts that the chromatic symmetric function of every claw-free graph is Schur-positive. Prajapati, and independently Matherne and Morales, found counterexamples, and the latter asked for an infinite family…

Consider a material point in finite dimensions moving under the influence of a potential force according to Newton's laws. Suppose the potential energy function is a generalized well, strictly convex transverse to a smooth submanifold $M$…

We study the problem of privately releasing functions, with a particular focus on curves, which are images of continuous functions on some finite interval. Many types of data exist naturally as curves, such as trajectory data or $1$D…

Materials behavior is often treated as a deterministic mapping from structure to properties, yet many important phenomena emerge from the conditional activation of multiple mechanisms across scales. This is especially evident in fatigue of…

Let $G=(V,E)$ be a possibly infinite, locally finite graph with non-negative Ollivier--Ricci curvature and degrees bounded by $d<\infty$. We prove that there exists a constant $C_d$ such that the continuous-time random walk displacement and…

We observe that the apparent inhomogeneous broadening, as measured by two-dimensional coherent spectroscopy (2DCS), of the exciton resonance in transition-metal dichalcogenide monolayers depends on the excitation strength. A key strength of…

We propose an interpretable low-rank state-space model for conditional simulation of daily regional temperature fields. The central statistical question is whether empirical orthogonal functions (EOFs) can be treated as stable large-scale…

We show that for all $k$, there exists $\varepsilon_k > 0$ such that graph $k$-coloring can be solved by a randomized algorithm with one-sided error in time $O((2-\varepsilon_k)^n)$. Prior to this work and independent concurrent work of…

We numerically study the outcome of symmetry breaking motivated by Grand Unified models. Our results show the formation of biased domain walls for a range of parameters together with magnetic monopoles. The interactions of walls and…

Min-wise hashing and its $k$-min-wise extension are fundamental tools in sampling, sketching, and similarity estimation. A standard approach to constructing such families is bounded independence. For ordinary min-wise hashing, the required…

Accurately describing a hypothetical symmetry-invariant Mott insulator presents a long-standing ing challenge in iterative quantum embedding methods. We address this issue within the ghost- Gutzwiller method, which can be solved either…

Large language model (LLM) agents are increasingly expected to assist users in completing tasks. However, existing benchmarks provide limited support for evaluating whether agents can carry out office-suite workflows at a reasonable cost.…

CT vision-language foundation models have demonstrated promising performance across downstream tasks, but are typically trained with whole-volume representations that dilute fine-grained anatomical signals. Fine-grained vision-language…

One of the central challenges in quantum error correction is determining the performance of a code in the low-error regimes needed to implement utility-scale computations. While performance at these error rates is not amenable to direct…

Accurate intraday forecasts of offshore wind are becoming increasingly important for power system operation and the integration of growing shares of offshore wind energy. Operational forecasts rely predominantly on numerical weather…

Space object tracking poses challenging estimation problems due to the significantly non-Gaussian distributions that can arise, particularly under highly nonlinear dynamics or during periods of measurement unavailability. Adaptive Gaussian…

These notes provide a self-consistent summary of the stochastic approach to anomalous diffusion based on Continuous Time Random Walks (CTRWs) and their scaling limits. An introduction to CTRWs and their relationship to the theory of…