arXiv preprints from January 1, 2026 through September 23, 2026 — 05:16:46 EST
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional...
This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent...
Lava worlds are rocky planets with dayside skins made molten by stellar irradiation. Tidal heating on these shortest-period planets is more than skin deep. We show how orbital eccentricities of just a few percent (within current observed bounds and maintained secularly by exterior companions) can create deep magma oceans. ``Lava tidal...
Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain systems, whose process noise, observation noise, and system states are depicted by ellipsoid sets...
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where...
This work presents a comprehensive theoretical investigation of key isomers of C2H4N2 using state-of-the-art quantum chemical methods. The objective is to characterize their molecular structures, spectroscopic constants, and electronic energies, and to elucidate plausible formation and destruction pathways, providing data critical for...
We compute explicitly the Riemannian volume, with respect to the Fubini-Study metric, of a domain bounded by a Hermitian quadric in complex projective space. The volume is a rational function of the eigenvalues of the defining quadratic form.
We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate the convergence under certain restrictions. We test our algorithms by several numerical examples.
We present a calibration-free consistency test of spatially flat $Λ$CDM based on baryon acoustic oscillation (BAO) distance measurements. The method forms ratios of BAO distances including the Hubble distance, the comoving angular diameter distance, and the volume-averaged distance, so that the sound horizon scale cancels, and then...
We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting, where each bit depends only on a single sample, and the second is a partial quantization setting, in...
Roadside billboards represent a central element of outdoor advertising, yet their presence may contribute to driver distraction and accident risk. This study introduces a fully automated pipeline for billboard detection and driver gaze duration estimation, aiming to evaluate billboard relevance without reliance on manual annotations...
Large language models (LLMs) increasingly rely on retrieving information from external corpora. This creates a new attack surface: indirect prompt injection (IPI), where hidden instructions are planted in the corpora and hijack model behavior once retrieved. Previous studies have highlighted this risk but often avoid the hardest step:...
We propose a novel digital signature cryptosystem that exploits the concept of the brute-force problem. To ensure the security of the cryptosystem, we employed several mechanisms: sharing a common secret for factorable permutations, associating permutations with the message being signed, and confirming knowledge of the shared secret...
We study the two-dimensional time-harmonic scalar transmission problem for an impedance-matched penetrable right-angle wedge: the exterior medium has wavenumber k_0 and the interior sector |theta| < pi/4 has wavenumber k_1 = nu*k_0 with nu > 1, with continuity of the total field and its normal derivative across each face. A...
In this paper, the foundations of neuromorphic computing, spiking neural networks (SNNs) and memristors, are analyzed and discussed. Neuromorphic computing is then applied to FPGA design for digital signal processing (DSP). Finite impulse response (FIR) and infinite impulse response (IIR) filters are implemented with and without...
A set $\mathcal S\subset \mathbb N$ is said to be a subset-sum-distinct or dissociated if all of its finite subsets have different sums. Alternately, an equivalent classification is if any equality of the form $$\sum_{s\in \mathcal S} \varepsilon_s \cdot s =0$$ where $\varepsilon_s \in \{-1,0,+1\}$ implies that all the...
In this paper we are interested in the stability of the $2$-rank of the class group in the cyclotomic $\mathbb{Z}_2$-extension of real biquadratic fields. In fact, we give several families of real biquadratic fields $K$ such that $ rank(A(K)) =rank(A_\infty(K))$ and $rank(A(K))\leq 3$, where $A(K)$ and $A_\infty(K)$ are the $2$-class...
We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.
Marginal effects analysis is fundamental to interpreting statistical models, yet existing implementations face computational constraints that limit analysis at scale. We introduce two Julia packages that address this gap. Margins.jl provides a clean two-function API organizing analysis around a 2-by-2 framework: evaluation context...
We propose a unified framework for not only attributing synthetic speech to its source but also for detecting speech generated by synthesizers that were not encountered during training. This requires methods that move beyond simple detection to support both detailed forensic analysis and open-set generalization. To address this, we...
We study differentiability conditions on a complex measure $ν$ at a point $x_0\in\mathbb{R}^d$, in relation with the boundary convergence at that point of the Poisson-type integral $P_tν=e^{-t\sqrt L}ν$, where $L=-Δ+|x|^2$ is the Hermite operator. In particular, we show that $x_0$ is a Lebesgue point for $ν$ iff a slightly stronger...
Concept maps have been widely utilized in education to depict knowledge structures and the interconnections between disciplinary concepts. Nonetheless, devising a computational method for automatically constructing a concept map from unstructured educational materials presents challenges due to the complexity and variability of...
We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose...
Recent advancements in vision-language-action (VLA) models have shown promise in robotic manipulation, yet they continue to struggle with long-horizon, multi-step tasks. Existing methods lack internal reasoning mechanisms that can identify task-relevant interaction cues or track progress within a subtask, leading to critical execution...
We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with nonparametric prior for the random intercepts, slopes, dynamics, and non-spherical error variances. We establish identification and consistency of the nonparametric maximum likelihood estimator (NPMLE) under general conditions, and provide...