arXiv preprints from January 1, 2026 through September 23, 2026 — 00:55:24 EST
We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are typically viewed as less competitive than the Adaptive Sufficient Statistics Perturbation (AdaSSP)...
Access to reliable maternal healthcare information is a major challenge in rural India due to limited medical resources and infrastructure. With over 830 million internet users and nearly half of rural women online, digital tools offer new opportunities for health education. This study evaluates large language models (LLMs) like...
This work addresses an enumeration problem on weighted bi-colored plane trees with prescribed vertex data, with all vertices labeled distinctly. We give a bijection proof of the enumeration formula originally due to Kochetkov, hence affirmatively answer a question of Adrianov-Pakovich-Zvonkin. The argument is purely combinatorial and...
Small-scale discrepancies in the standard Lambda cold dark matter paradigm have motivated the exploration of alternative dark matter (DM) models, such as warm dark matter (WDM). We investigate the constraining power of galaxy scaling relations on cosmological, astrophysical, and WDM parameters through a joint analysis of hydrodynamic...
Type IIn supernovae (SNe IIn) are hydrogen-rich explosions embedded in dense circumstellar medium (CSM), which gives rise to their characteristic narrow hydrogen emission lines. The nature of their progenitors and pre-explosion mass loss remains, however, poorly understood. Using high-resolution Hubble Space Telescope (HST) imaging,...
We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.
We give a self-contained introduction to linear algebraic and semialgebraic groups over real closed fields, and we generalize several key results about semisimple Lie groups to algebraic and semialgebraic groups over real closed fields. We prove that a torus in a semisimple algebraic group is maximal $\mathbb{R}$-split if and only if...
Universal time-temperature scaling of conductivity spectra in disordered solids has been explained by thermally activated hopping of noninteracting particles over random energy barriers. An open problem is whether the random barrier model accounts for site energy disorder in real materials. Through mapping many-particle hopping in a...
Most numerical methods for time integration use real-valued time steps. Complex time steps, however, can provide an additional degree of freedom, as we can select the magnitude of the time step in both the real and imaginary directions. We show that specific paths in the complex time plane lead to expanded stability regions, providing...
We study density-balanced, mass-asymmetric electron-hole bilayers as a tunable platform for correlated quantum phases. With independent control of carrier density and interlayer separation, the system exhibits a rich phase diagram, including exciton condensates, Wigner crystals, and for large hole-to-electron mass ratios, an...
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with measurements of e.g. altitude, bearing, and/or range. Unlike previous tensor decomposition-based...
The equation of state (EOS) of dense matter in neutron stars (NSs) remains uncertain, particularly at supra-nuclear densities where complex nuclear interactions and the potential presence of exotic matter, like hyperons, come into play. The complex relationships existing between nuclear matter and neutron star properties are...
The rapid development of Internet of Things (IoT) technology has led to growing concerns about data security and user privacy in the interactions within distributed systems. Decentralized Applications (DApps) in distributed systems consist of on-chain and off-chain functions, where on-chain functions are smart contracts running in the...
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works connecting lattice theory, anticodes, and coding-theoretic invariants, we investigate ring-linear...
We provide a new formulation of Time-Dependent Density Functional Theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation involving a new density-to-current functional map. In the corresponding Kohn--Sham equation, the...
This paper presents a method for carrying fair comparisons of the accuracy of pose estimation using fiducial markers. These comparisons rely on large sets of high-fidelity synthetic images enabling deep exploration of the 6 degrees of freedom. A low-discrepancy sampling of the space allows to check the correlations between each degree...
We study the properties of neutron-star crust within a Bayesian framework based on a unified relativistic mean-field (RMF) description of dense matter. The analysis focuses on the posterior distributions of crust properties, constrained by nuclear experimental data, chiral effective field theory, and multimessenger neutron-star...
This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF) recently-developed for linear systems and extends it for systems with nonlinear dynamics that are...
In this paper, we construct canonical extensions of principal $\mathcal{G}^c$- (and $M^c$-)bundles on toroidal compactifications of integral canonical models of abelian-type Shimura varieties with hyperspecial levels.
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we revisit the foundations of TDDFT within a finite-dimensional setting by developing a general...
Achieving robust humanoid hiking in complex, unstructured environments requires transitioning from reactive proprioception to proactive perception. However, integrating exteroception remains a significant challenge: mapping-based methods suffer from state estimation drift; for instance, LiDAR-based methods do not handle torso jitter...
The spin-dependent thermoelectric properties of silicene nanoribbon heterostructures are investigated, in which the central conductor contains a random distribution of vacancies and is connected to two pristine leads of the same material, placed in proximity to ferromagnetic insulators. The magnetic moments of the leads are analyzed...
This thesis focuses on gravitational waves (GWs) that arise beyond linear order in cosmological perturbation theory. In recent years, scalar-induced GWs have attracted significant attention because they may serve as the observational signature of primordial black holes (PBHs) formed in the early universe. The formation of PBHs...
This paper presents a sampled-data framework for the safe navigation of controlled agents in environments cluttered with obstacles governed by uncertain linear dynamics. Collision-free motion is achieved by combining Control Barrier Function (CBF)-based safety filtering with set-valued state estimation using Constrained Convex...
In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant immaterial subset can be seen as big in contact geometric terms. This is supported by two results: one...