arXiv preprints from January 1, 2026 through September 22, 2026 — 09:33:08 EST
Let $R$ be a finite product of integral domains and $D$ be a union of prime ideals (it is possible that $R$ is just an integral domain). Let $n \geq 1$ be a positive integer. This paper introduces the $n$-total graph of a $(R, D)$. The $n$-total graph of $(R, D)$, denoted by $n-T(R)$, is an undirected simple graph with vertex set $R$,...
We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized...
Composite functions have been studied for over 40 years and appear in a wide range of optimization problems. Convex analysis of these functions focuses on (i) conditions for convexity of the function based on properties of its components, (ii) formulas for the convex conjugate of the function based on those of its components and (iii)...
We provide a closed formula for the graded Betti numbers in the linear strands of all powers of binomial edge ideals $J_G$ arising from closed graphs $G$ that do not have the complete graph $K_4$ as an induced subgraph. We show that these agree with the corresponding Betti numbers for the powers of the lexicographic initial ideal of...
Physics-aware deep learning (PADL) enables rapid prediction of complex physical systems, yet current convolutional neural network (CNN) architectures struggle with highly nonlinear flows. While scaling model size addresses complexity in broader AI, this approach yields diminishing returns for physics modeling. Drawing inspiration from...
The gauge gravitation theory in the Riemann-Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints for indefinite parameters of the theory under which solutions of isotropic cosmology describe a nonsingular accelerating Universe are given. Numerical solutions of...
We study light propagation in a medium with uniform torsion, modeled as a continuum of screw dislocations within the geometric theory of defects. By solving Maxwell's equations in covariant form, we show that torsion induces intrinsic chirality and circular birefringence: right- and left-circular polarizations acquire different...
We describe digraphs with topology which give dual representations of ortholattices. This is done via so-called dual Ploščica spaces of lattices. First, we improve the definition of Ploščica spaces from an earlier paper to give a straight and natural generalisation of the total order disconnectedness of Priestley spaces. Then we...
We consider an inverse shape problem arising in electrical impedance tomography (EIT) for nondestructive testing, in which interior defects are modeled through Robin transmission conditions. Unlike classical formulations, we impose Robin boundary conditions on both the exterior measurement surface and the interior interface, and use...
The spatial distribution of a magnetic field can be determined with micrometer resolution using widefield nitrogen vacancy (NV) center magnetic imaging. Nevertheless, reconstructing the magnetic field from the raw data can be challenging due to the degeneracy of the four possible NV axes and the tremendous amount of data. While a...
Recent recommender systems increasingly leverage embeddings from large pre-trained language models (PLMs). However, such embeddings exhibit two key limitations: (1) PLMs are not explicitly optimized to produce structured and discriminative embedding spaces, and (2) their representations remain overly generic, often failing to capture...
Out-of-distribution (OOD) detection is crucial for deploying robust and reliable machine-learning systems in open-world settings. Despite steady advances in OOD detectors, their interplay with modern training pipelines that maximize in-distribution (ID) accuracy and generalization remains under-explored. We investigate this link...
As robotics become increasingly integrated into construction workflows, their ability to interpret and respond to human behavior will be essential for enabling safe and effective collaboration. Vision-Language Models (VLMs) have emerged as a promising tool for visual understanding tasks and offer the potential to recognize human...
We show how Gravitational Path Integral formulae for various quantities that have been computed in the literature, follow from a few coarse grained hydrodynamic assumptions about the relations between space-time geometry, entropy, and fluctuations of the modular Hamiltonian of causal diamonds. These remarks have implications for the...
We investigate the long-time behavior of a $d-$dimensional supercritical branching Brownian motion with a compactly supported branching potential. It is known that, for $\mathbf{v}\in \mathbb{R}^d$, all the moments of the normalized number of particles in a bounded domain centered at $\mathbf{v} t$ converge, as $t \rightarrow \infty$,...
Lower limb exoskeletons and prostheses require precise, real time gait phase and step detections to ensure synchronized motion and user safety. Conventional methods often rely on complex force sensing hardware that introduces control latency. This paper presents a minimalist framework utilizing a single, low cost Inertial-Measurement...
Aims. By analysing the light curves of the ZZ Ceti star WD 1310+583, we aim to determine its pulsational frequencies and to give constraints on the main stellar parameters using the tools of asteroseismology. Methods. We performed the Fourier analysis of the TESS light curves of WD 1310+583 and selected the possible pulsational...
Let $H$ be a finite abelian (commutative) group of order $n \geq 2$, and $m >1$ be an integer. We define the $m$-graph of $H$, denoted by $m-G(H)$, as a simple undirected graph with vertex set $H$, and two distinct vertices, $a, b \in H$, are connected by an edge if and only if $a^m = b$ or $b^m = a$. Several results regarding the...
AI agents are increasingly the primary consumers of data, operating continuously to make concurrent, irreversible decisions. Traditional data systems designed for human analysis cycles become correctness bottlenecks under this operating regime. When multiple agents operate over shared resources, their actions interact before...
We propose a nested Wolter-I mirror design for a neutron condenser, which is based on established X-ray telescope technology. We demonstrate through simulations that it can increase the flux density at the ESS imaging instrument ODIN by up to two orders of magnitude. Experimental measurements of reflectivity and figure errors on a...
High-order Lie derivatives are essential in nonlinear systems analysis. If done symbolically, their evaluation becomes increasingly expensive as the order increases. We present a compact and efficient numerical approach for computing Lie derivatives of scalar, vector, and covector fields using the MATLAB ADTAYL package. The method...
If we consider human manipulation, it is clear that contact-rich manipulation (CRM)-the ability to use any surface of the manipulator to make contact with objects-can be far more efficient and natural than relying solely on end-effectors (i.e., fingertips). However, state-of-the-art model-based planners for CRM are still focused on...
Batch effects represent a major confounder in genomic diagnostics. In copy number variant (CNV) detection from NGS, many algorithms compare read depth between test samples and a reference sample, assuming they are process-matched. When this assumption is violated, with causes ranging from reagent lot changes to multi-site processing,...
Exciton-polaritons are light-matter hybrid quasi-particles that have emerged as a flexible platform for developing quantum technologies and engineering material properties. However, the fundamental mechanistic principles that govern their dynamics and relaxation remain elusive. In this work, we provide the microscopic mechanistic...
It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a $\mathrm{Pin}^-$ structure....