arXiv preprints from January 1, 2026 through July 28, 2026 — 07:33:26 EST
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a new proximal ADMM algorithm and proposes two BCD methods. The first part of the research...
Molecular simulations of interfacial polar media routinely employ periodic boundary conditions parallel to the interface. We show that this lateral periodicity introduces a spatially uniform in-plane mode ($q_{\parallel}=0$) that is unscreened because every lateral replica carries identical charge fluctuations. This 2D mode reduces...
We aim to investigate the impact of image and signal properties on visual attention mechanisms during a signal detection task in digital images. The application of insight yielded from this work spans many areas of digital imaging where signal or pattern recognition is involved in complex heterogenous background. We used simulated...
Non-linear statistical inverse problems pose major challenges both for statistical analysis and computation. Likelihood-based estimators typically lead to non-convex and possibly multimodal optimization landscapes, and Markov chain Monte Carlo (MCMC) methods may mix exponentially slowly. We propose a class of computationally tractable...
Ultra-High Field MRI (UHF-MRI) is increasingly used in large-scale neuroimaging studies, yet automatic brain segmentation and cortical parcellation remain challenging due to signal inhomogeneities, heterogeneous contrasts and resolutions, and the limited availability of tools optimized for UHF data. Standard software packages such as...
We introduce an improved and fast inversion tool that is able to provide the thermodynamics of the solar atmosphere from the photosphere to the top of the chromosphere, as well as the integrated radiative losses in the chromosphere for data observed by the Interface Region Imaging Spectrograph (IRIS). This NASA mission has been...
Agglomeration refers to the process of crystal clustering due to interparticle forces. Crystal agglomeration analysis from microscopic images is challenging due to the inherent limitations of two-dimensional imaging. Overlapping crystals may appear connected even when located at different depth layers. Because optical microscopes have...
In this paper, we contribute to the Kuperberg program by giving a diagrammatic presentation of generators and relations for the affine $E_7$ unshaded subfactor planar algebra. Using this presentation, we prove that its jellyfish algorithm is a well-defined surjection onto $\mathbb{C}$. In particular, this shows that the jellyfish...
Processing in Memory (PIM) and similar terms such as Compute In Memory (CIM), Logic in Memory (LIM), In Memory Computing (IMC), and Near Memory Computing (NMC) have gained attention recently as a potentially ``revolutionary new'' technique. The truth, however, is that many examples of the technology go back over 60 years. This...
Deploying LLMs raises two coupled challenges: (1) monitoring--estimating where a model underperforms as traffic and domains drift--and (2) improvement--prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response,...
The Warmup Stable Decay (WSD) learning rate scheduler has recently become popular, largely due to its good performance and flexibility when training large language models. It remains an open question whether the remarkable performance of WSD - using a decaying learning rate for only a fraction of training compared to cosine decay - is...
Accurate prediction of solar energetic particle events is vital for safeguarding satellites, astronauts, and space-based infrastructure. Modern space weather monitoring generates massive volumes of high-frequency, multivariate time series (MVTS) data from sources such as the Geostationary perational Environmental Satellites (GOES)....
We probe the density-wave transition of the trilayer nickelate La$_4$Ni$_3$O$_{10}$ with polarization-resolved infrared spectroscopy. The low-energy electrodynamics is strongly anisotropic, with metallic in-plane and insulating out-of-plane character. In the ordered phase, the anisotropy grows more than an order of magnitude as the...
Flaky tests are a common problem in software testing. They produce inconsistent results when executed multiple times on the same code, invalidating the assumption that a test failure indicates a software defect. Recent work on LLM-based test generation has identified flakiness as a potential problem with generated tests. However, its...
Interval-censored covariates are frequently encountered in biomedical studies, particularly in time-to-event data or when measurements are subject to detection or quantification limits. Yet, the estimation of regression models with interval-censored covariates remains methodologically underdeveloped. In this article, we address the...
Open source C code underpins society's computing infrastructure. Decades of work has helped harden C code against attackers, but C projects do not consist of only C code. C projects also contain build system code for automating development tasks like compilation, testing, and packaging. These build systems are critcal to software...
In this paper we consider reduction of the stochastic Hamilton-Pontryagin principle formulated on the Pontryagin bundle of a manifold $Q$. We prove that a stochastic action invariant under the free and proper action of a Lie group $G$ drops to a reduced variational principle expressed in terms of variables of the Pontryagin bundle of...
We present a theoretical study of spin-wave scattering by a twisted domain wall (DW) in a two-dimensional ferromagnet with easy-axis anisotropy. While the twisted DW generates an effective gauge field for spin waves, leading to a deflection of their trajectories, our main focus is on a distinct effect that arises when a hard-axis...
We observe the emergence of a distinct, elasticity-driven flow state in a yield-stress fluid in the absence of inertia. Numerical simulations show that this elasto-plastic turbulent state is characterized by a broad spectrum of fluctuations in velocity and stress. Results show a non-monotonic relationship between the volume fraction...
The ubiquity of machine learning (ML) and the demand for ever-larger models bring an increase in energy consumption and environmental impact. However, little is known about the energy scaling laws in ML, and existing research focuses on training cost -- ignoring the larger cost of inference. Furthermore, tools for measuring the energy...
This work concerns the computation of ground states of two-component spin-orbit coupled Bose-Einstein condensates (SO-coupled BECs), modelled by a coupled nonlinear eigenvalue problem of Gross-Pitaevskii type. Spin-orbit coupling gives rise to fascinating phenomena, including supersolid-like phases with spatially modulated densities....
We study the Torus Puzzle, a solitaire game in which the elements of an input $m \times n$ matrix need to be rearranged into a target configuration via a sequence of unit rotations (i.e., circular shifts) of rows and/or columns. Amano et al. proposed a more permissive variant of the above puzzle, where each row and column rotation can...
Reliable clinical decision support requires medical AI agents capable of safe, multi-step reasoning over structured electronic health records (EHRs). While large language models (LLMs) show promise in healthcare, existing benchmarks inadequately assess performance on action-based tasks involving threshold evaluation, temporal...
This work introduces ABE-VVS, a framework that performs attribute based selective coordinate encryption for point cloud based volumetric video streaming, enabling lightweight yet effective digital rights management (DRM). Rather than encrypting entire point cloud frames, our approach encrypts only selected subsets of coordinates ($X,...
We study the pointwise maximal leakage (PML) envelope of the Gaussian mechanism, which characterizes the smallest information leakage bound that holds with high probability under arbitrary post-processing. For the Gaussian mechanism with a Gaussian secret, we derive a closed-form expression for the deterministic PML envelope for...