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We prove a realization theorem for stealthy point processes based on lattice induction, together with a converse in dimension one. Every probability-preserving $\mathbb R^d$-action induced from a full-rank lattice admits a generating Delone…

According to the Singer conjecture, the $L^2$-Betti numbers of a closed aspherical manifold are expected to vanish outside the middle dimension. In this paper, we study a natural analog of the Singer conjecture concerning the vanishing of…

Adapting Large Language Models (LLMs) to specialized domains often incurs an alignment tax, as fine-tuning on domain-specific tasks can cause catastrophic forgetting and substantially degrade performance on general tasks. We propose MemSFT,…

Cool plasma of coronal rain or prominences and filaments is ubiquitous in the solar corona. We explored the synthetic spectra of MgII h&k lines in detail and analyse how well a non-adiabatic magnetohydrodynamic (MHD) simulation of…

Perception tasks for autonomous vehicles need to work satisfactorily in adverse weather conditions. Due to lack of real-world weather datasets, weather simulations are a promising alternative. To ensure simulations closely mirror real-world…

For integers $n\ge s\ge2$, let $e(n,s)$ be the maximum size of a family $\mathcal F\subseteq2^{[n]}$ with no $s$ pairwise disjoint members. The problem of determining $e(n,s)$, now called the Erd\H{o}s--Kleitman problem, is closely related…

We consider the classical analytic linearization problem for vector fields on the torus $\mathbb{T}^d$ close to a constant vector field $\omega$. Our goals are twofold. First, we provide a geometric framework in which the arithmetic…

Understanding disease trajectories from longitudinal clinical data remains challenging due to complex temporal dynamics and heterogeneous patient cohorts. Here, we present a contrastive representation learning framework that models…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks. However, their reliance on computationally…

We present the first search for $B^0 \to K^0_{\rm S} \tau^+\tau^-$ decays. We look for signal decays in $B^0\bar B^0$ events produced in asymmetric-energy electron-positron collisions. This work uses samples from the Belle and Belle~II…

We investigate the nature of the $\Xi(1690)$ and $\Xi(1820)$ resonances by analyzing the recent BESIII data on $\psi(3686) \to K^-\Lambda\bar{\Xi}^+$ within a coupled-channel rescattering framework. The calculation includes the channels…

This paper presents a set-theoretic formalization of the classical usuli method of al-Sabr wa al-Taqsim (Examination and Division) for extracting legal causes ('ilal) within closed chapters of jurisprudence. A computational algorithm is…

In this paper, we establish a necessary and sufficient condition for a group action on a bifoliated plane to arise from a topological Anosov flow supported by an orientable $3$-manifold. More precisely, we show that a group action on a…

Testing query-based systems (QBSs) presents significant challenges due to the absence of ground truth for validation and the extensive time and effort required for manual testing. This paper addresses these challenges by proposing an…

This work develops well-posed homogenized strain-gradient models for linear elastostatics and elastodynamics in periodic media, with a primary focus on elastic wave propagation. Using the classical two-scale asymptotic expansion method, we…

This study develops a compartmental epidemic model for Hepatitis B virus (HBV) transmission incorporating vertical transmission, spontaneous recovery in acutely infected individuals, saturated treatment response for chronically infected…

Retrieval-augmented generation improves knowledge-intensive question answering, but indiscriminate retrieval can introduce irrelevant evidence and unnecessary computation. We investigate whether verbalized confidence from black-box language…

We develop an analytic Fourier cosine (COS) method for the valuation of compound options. By deriving closed-form expressions for the cosine coefficients at all compound stages, the proposed method eliminates the need for numerical…

Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F_q$, and let $\mathcal F\subsetneq\genfrac{[}{]}{0pt}{}{V}{k}$. The \emph{projective Ore-degree} of $\mathcal F$ is the minimum, over all $k$-subspaces…

The reactivity of lithium-metal electrolytes arises from the interplay of molecular functional groups, Li$^+$ solvation, and salt-anion participation. This interplay operates through the redistribution of electron density across donor,…