arXiv preprints from January 1, 2026 through September 20, 2026 — 16:00:22 EST
Common finite element discretizations for the incompressible Stokes equations with a continuous pressure approximation -- the MINI element, the Taylor--Hood element, or stabilized equal-order elements -- are not pressure-robust: the velocity error is polluted by the pressure best-approximation error, multiplied by the inverse...
Sign-based methods reduce communication costs in distributed environments, but aggregating local signs can introduce bias when data are heterogeneous. As a result, existing sign-based variance reduction methods fail to obtain the optimal convergence rates. In this paper, we solve this problem and obtain optimal rates for both...
Quantum neural networks (QNNs) are typically built from variational quantum circuits (VQCs), which are limited by local measurements. Adaptive non-local observables (ANO) address this by jointly optimizing circuit parameters and multi-qubit measurements. However, existing ANO-based VQCs learn only a single static observable that...
In this work we introduce the use of Quartic Force fields (QFF) potential expansions in the context of variational calculations. Such potentials are commonly employed in molecular Vibrational Second-Order Perturbation Theory (VPT2) studies, for which equations explicitly dependent on the QFF parameters exist. However, QFF are unbound...
Advanced lithography scanners require extreme substrate flatness in the range of nanometers to prevent focus errors. Such a flatness is challenging to reach and maintain using static substrate supports. Active correction concepts using bulk piezoelectric or linear actuators become prohibitive due to wiring and volume limitations,...
We develop and analyze a fully discrete, globally divergence-free hybridizable discontinuous Galerkin (HDG) method for a gradient-based Smagorinsky model. The method combines backward Euler time stepping, interior-penalty discretizations of molecular and nonlinear eddy diffusion, and an upwind convective flux. The discrete velocity is...
Generalist robot policies offer useful initialization, but refining compact specialists through limited physical interaction requires informative learning feedback. We present FIERCE, a generalist-initialized reinforcement learning framework centered on a unified, task-adaptive progress-failure evaluator. Its architecture shares an...
Learning generalizable robot manipulation policies requires large-scale and diverse interaction data, yet collecting real-world demonstrations remains costly and difficult to scale. Existing approaches to data collection are either dependent on specific robot hardware that limits crowdsourcing and transferability, or suffer from...
Warning: This paper contains examples of stereotypes and social bias. LLMs are increasingly used in interactive settings by the general public, making the evaluation of model behavior in multi-turn conversational scenarios important for safety, including stereotyping-related harms. However, existing multi-turn social bias evaluations...
The tree-independence number $tree\text{-}α(G)$, the induced matching treewidth $tree\text{-}μ(G)$, and the sim-width $simw(G)$ are graph parameters defined in terms of tree or branch decompositions. We establish two polynomial bounds for the tree-independence number of induced $K_{t,t}$-free graphs, one in terms of sim-width and the...
Low defect, single polarity aluminum nitride layers grown by halide vapor phase epitaxy (HVPE) methods have classically needed growth temperatures well exceeding 1100°C with many of the best results being grown in the range of 1400°C. These high temperatures have typically been required to obtain Al-polar AlN films with smooth...
YZ Cancri is an SU UMa-type dwarf nova with sparse and heterogeneous optical spectroscopy. We present a homogeneous analysis of archival outburst-related spectra and seven new low-resolution quiescent spectra. We consistently characterize the Balmer, He I, Fe II, O I, and occasional He II and Bowen features, and assess which...
Sakurai's object provides a rare opportunity to observe stellar evolution on human timescales.Since its born-again event and detection in 1996, its evolution has been extensively monitored, and recent optical spectroscopy has suggested the emergence of [WR]-type emission features. In this Letter, we present a secure spectroscopic...
Fallacy-detection benchmarks pair fallacy classes with a single "valid" or "none" class that takes everything data collection did not label as a fallacy. This construction is misleading: a classifier can learn cues that do well on this class without learning to tell a fallacy from a correct argument. We show that the low...
In this paper, we derive a new lower bound for the Hausdorff dimension of 3D Brownian cut points by proving an explicit upper bound ($<0.9999$) for $ξ_3(1,1)$, the intersection exponent for two independent Brownian motions in 3D. Consequently, the growth exponent of 3D loop-erased random walk is at least $1.0001$.
Large language models (LLMs) often suffer from capability stagnation in self-improvement training because fixed difficulty levels fail to adapt to their evolving proficiency. To address this issue, we propose STRETCH (Self-Taught Reasoning Evolution via Targeted CHallenge), a unified framework inspired by cognitive scaffolding theory....
In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a $σ_y^{(1)}σ_y^{(2)}$ interaction. By constructing an exact solution that exploits parity symmetry, and by applying...
Dual-comb technology has emerged as an essential tool for high-precision spectroscopy, real-time ranging, and high-sensitivity sensing. Integrating dual-comb sources into a single microresonator would substantially reduce pump power, footprint, system complexity, and cost, yet this remains a significant challenge. Here, we...
Emergency management assistance programs, such as relief distribution, are essential for delivering necessary supplies to affected communities. However, these programs operate in a decentralized network of local centers that face uncertain local demand and supply dynamics, resulting in inconsistent avail- ability of local services....
The main contribution of this work is to identify model parameters for an Anion Exchange Membrane (AEM) system directly from measured operational data, enabling their use in power system studies. Due to the relatively low technology readiness level (TRL) of AEM electrolysers, only limited literature reports operational parameters...
Complex networks are often compared using selected graph-theoretical measures that capture a selected set of properties with effects ranging from local to global, such as degree, clustering or betweenness centrality. Here we introduce a structural fingerprinting framework based on graphlets: small rooted subgraphs whose distributions...
Living systems compute with chemistry by mapping environmental signals onto specific internal chemical states. Despite recent advances in molecular programming, it remains unclear which physicochemical features control the computational expressivity of chemical systems. Here we inverse-design thermodynamically consistent chemical...
Let $μ$ be a finitely supported probability measure on $\mathrm{SL}_2(\mathbb{R})$ whose support generates a Zariski-dense discrete subgroup. We prove that its stationary probability measure on $\mathbb{P}^1(\mathbb{R})$ is singular with respect to the $\mathrm{SO}(2)$-invariant probability measure. The proof compares winding...
We show that for all negative $L$-space knots and framings $n\geq2g(K)$, if a certain cobordism map between cables of $K$ is non-vanishing, then the Floer lasagna module of the knot trace of $K$ with framing $-n$ is infinite dimensional. Further, for the maps on the hat flavour of link Floer homology induced by band maps,...
Let $C$ be a connected nodal curve of genus $g$ over an algebraically closed field $k$ of characteristic zero. Let \[ A(C)=\Big(J(C), {\overline{P^{g-1}_C}}, Θ(C) \Big) \] be the stable semi-abelic pair (in the sense of Alexeev) associated with its canonical compactified Jacobian $\overline{P^{g-1}_C}$ in degree $g-1$. The canonical...