arXiv preprints from January 1, 2026 through September 26, 2026 — 20:38:16 EST
Using a recently suggested magneto-morphological classification (MMC, Abramenko, 2021, MNRAS Vol 507) of solar active regions (ARs), we explored 3048 ARs, observed from12 May 1996 to 27 December 2021. Magnetograms were acquired with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) and with the...
One of the crucial features of optimal transport on Riemannian manifolds is the equivalence of the `static', original, formulation of the problem and of the `dynamic' one, based on the study of the continuity equation. This furnishes the key link between Wasserstein geometry and PDEs that has found so many applications in the last 20...
In this work we study some properties and applications of Nash manifolds with corners. Our first main result shows how to `build' a Nash manifold with corners ${\mathcal Q}\subset{\mathbb R}^n$ from a suitable Nash manifold $M\subset{\mathbb R}^n$ (of its same dimension), that contains ${\mathcal Q}$ as a closed subset, by folding $M$...
Developing Foundation Models for medical image analysis is essential to overcome the unique challenges of radiological tasks. The first challenges of this kind for 3D brain MRI, SSL3D and FOMO25, were held at MICCAI 2025. Our solution ranked first in tracks of both contests. It relies on a U-Net CNN architecture combined with...
A 1.5D imprecise terrain is an $x$-monotone polyline with fixed $x$-coordinates, the $y$-coordinate of each vertex is not fixed but is constrained to be in a given vertical interval. A 2.5D imprecise terrain is a triangulation with fixed $x$ and $y$-coordinates, but the $z$-coordinate of each vertex is constrained to a given vertical...
Let $T\subset{\mathbb R}^n$ be a semialgebraic set and let $μ\ge0$ be a non-negative integer. We say that $T$ is a {\em Nash $μ$-approximation target space} (or a $({\mathcal N},μ)$-${\tt ats}$ for short) if it has the following universal approximation property: {\em For each $m\in{\mathbb N}$ and each locally compact semialgebraic...
Unlabeled multigraphs have diverse applications across scientific fields, from transportation and social networks to polymer physics. In particular, multigraphs are essential for studying the relationship between the spatial organization and biological function of chromatin, which is often folded into complex polymer networks whose...
Adversarial vulnerability and lack of interpretability are critical limitations of deep neural networks, especially in safety-sensitive settings such as autonomous driving. We introduce \DesignII, a neuro-symbolic framework that integrates symbolic rule supervision into neural networks to enhance both adversarial robustness and...
A dynamical system $(X,T)$ is \emph{shift embeddable} if $(X,T)$ embeds continuously and equivariantly in the shift over $[0,1]^d$ for some finite $d$. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov's mean dimension and Lebesgue covering dimension of finite orbits are...
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to optimization, data, parameters, or learning signals can induce abrupt and irreversible collapse, undermining...
The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors contained in $U$, for any finite set $U \subseteq \R^2, \pos(U) = \R^2$. We prove that this convex hull has finitely many extreme points by providing both a vertex...
We obtain a new closed-form formula for the characteristic function of the asymmetric Student's $t$-distribution. As part of our analysis, we derive a new closed-form formula for the integral $\int_0^\infty \sin(ax)/(b^2+x^2)^n\,\mathrm{d}x$, for $a,b>0$, $n\in\mathbb{Z}^+$, expressed in terms of the exponential integral function. As...
Current RF machine-learning pipelines rely on task-specific deep networks for modulation classification and related tasks, but these models require custom architectures and labeled datasets for each problem, generalize poorly across channel conditions and SNRs, and offer little interpretability. In contrast, modern multimodal large...
Indium selenide (In2Se3), a layered chalcogenide with multiple polymorphs, is a promising material for optoelectronic and ferroelectric applications. However, achieving polymorph-pure thin films remains a major challenge due to the complex growth space. In this work, Bayesian optimization (BO) is successfully leveraged to guide the...
Long-context inference enhances the reasoning capability of Large Language Models (LLMs), but incurs significant computational overhead. Token-oriented methods, such as pruning and skipping, have shown great promise in reducing inference latency, yet still suffer from inherently insufficient structure optimization, outdated selection...
The crystal structure of Rb$_2$Ru$_2$O$_7$.H$_2$O was determined by three-dimensional electron diffraction from the individual crystallites of a solid-state powder product. Rb$_2$Ru$_2$O$_7$.H$_2$O crystallizes in space group \textit{C}2/\textit{c} ($a=7.841(3)$ Å, $b=12.500(3)$ Å, $c=8.392(2)$ Å, $β=93.57(4)^\circ$, Z=4). The...
The high-energy proton-proton collisions at the Large Hadron Collider provide the ideal conditions to study the rare processes predicted by the Standard Model (SM) such as the production of multiple electroweak bosons. These processes involve the self-interactions of the gauge bosons through triple and quartic gauge couplings (TGCs...
Let $p$ be an odd prime. We show that for sufficiently large $n$, every $2$-block of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ contains an ordinary irreducible character of degree divisible by $p$. For almost all $2$-blocks of $\mathfrak{A}_n$, we classify whether it contains a rational valued ordinary irreducible character of degree...
For a normal projective variety $X$, the $\bf Q$-factoriality defect $σ(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula of S.G. Park and M. Popa asserting that $σ(X)=h^{2n-2}(X)-h^2(X)$ by assuming only...
Condition-Based Maintenance (CBM) signifies a paradigm shift from reactive to proactive equipment management strategies in modern industrial systems. Conventional time-based maintenance schedules frequently engender superfluous expenditures and unanticipated equipment failures. In contrast, CBM utilizes real-time equipment condition...
Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference. It attributes randomness solely to the design mechanism, such as treatment assignment, survey sampling, or missingness, without imposing super-population distributional or...
We study optimal design problems for stationary diffusion involving one or more state equations and mixtures of an arbitrary number of anisotropic materials. Since such problems typically do not admit classical solutions, we adopt a homogenization-based relaxation framework. The objective considered is the maximization of a weighted...
This work presents Interactive Conversational 3D Virtual Human (ICo3D), a method for generating an interactive, conversational, and photorealistic 3D human avatar. Based on multi-view captures of a subject, we create an animatable 3D face model and a dynamic 3D body model, both rendered by splatting Gaussian primitives. Once merged...
We investigate a minimal extension of the Standard Model with a real singlet scalar and a singlet Dirac fermion acting as dark matter. Unlike a conventional singlet scalar setup, we assume that the singlet scalar does not acquire a vacuum expectation value at zero temperature. This decouples the scalar mixing angle from the...
This paper introduces OPTIMUM-DERAM, a highly consistent, scalable, secure, and decentralized shared memory solution. Traditional distributed shared memory implementations offer multi-object support by multi-threading a single object memory instance over the same set of data hosts. While theoretically sound, the amount of resources...