arXiv preprints from January 1, 2026 through September 30, 2026 — 03:42:03 EST
We give an overview of the construction of Borcherds algebras, particularly the Monstrous Lie algebras $\mathfrak m_g$ constructed by Carnahan, where $g$ is an element of the Monster finite simple group. When $g$ is the identity element, $\mathfrak m_g$ is the Monster Lie algebra of Borcherds. We discuss the appearance of the...
In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse problems on the whole graph is proved.
We study LTLf synthesis with multiple properties, where satisfying all properties may be impossible. Instead of enumerating subsets of properties, we compute in one fixed-point computation the relation between product-game states and the goal sets that are realizable from them, and we synthesize strategies achieving maximal realizable...
The entanglement distance of evolutionary quantum states of a two-spin system with the XXZ model has been studied. The analysis has been conducted both analytically and using quantum computing. An analytical dependence of the entanglement distance on the values of the model coupling constants and the parameters of the initial states...
Slang interpretation has been a challenging downstream task for Large Language Models (LLMs) as the expressions are inherently embedded in contextual, cultural, and linguistic frameworks. In the absence of domain-specific training data, it is difficult for LLMs to accurately interpret slang meaning based on lexical information. This...
Recent advancements in video models have shown tremendous progress, particularly in long video understanding. However, current benchmarks predominantly feature western-centric data and English as the dominant language, introducing significant biases in evaluation. To address this, we introduce MINERVA-Cultural, a challenging benchmark...
We study a one-shot joint source-channel coding setting where the source is encoded once and broadcast to $K$ decoders through independent channels. Success is predicated on at least one decoder recovering the source within a maximum distortion constraint. We find that in the one-shot regime, utilizing disjoint codebooks at each...
Interactive graph-based segmentation methods partition an image into foreground and background regions with the aid of user inputs. However, existing approaches often suffer from high computational costs, sensitivity to user interactions, and degraded performance when the foreground and background share similar color distributions. A...
Given an anisotropic integrand $F:\text{Gr}_k(\mathbb R^n)\to(0,\infty)$, we can generalize the classical isotropic area by looking at the functional $$\mathcal{F}(Σ^k):=\int_ΣF(T_xΣ)\,d\mathcal{H}^k.$$ While a monotonicity formula is not available for critical points, when $k=2$ and $n=3$ we show that the Michael-Simon inequality...
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation yields a closed form for the series. This method is used to sum several series and to solve two...
The impact of disorder on collective phenomena depends crucially on whether it is quenched or annealed. In synchronization problems, quenched disorder in higher dimensional Kuramoto models is known to produce unconventional dimensional effects, including a striking odd even dichotomy: synchronization transitions are continuous in even...
Large language models (LLMs) can increase users' perceived trust by verbalizing confidence in their outputs. However, prior work has shown that LLMs are often overconfident, making their stated confidence unreliable since it does not consistently align with factual accuracy. To better understand the sources of this verbalized...
Retrieval models are key components of Retrieval-Augmented Generation (RAG) systems, which generate search queries, process the documents returned, and generate a response. RAG systems are often dynamic and may involve multiple rounds of retrieval. While many state-of-the-art retrieval methods are available through academic IR...
Building on the well-established capacity-achieving schemes of Sun-Jafar (for replicated storage) and the closely related scheme of Banawan-Ulukus (for MDS-coded setting), a recent work by Anand et al. proposed new classes of weak private information retrieval (WPIR) schemes for the collusion-free (replication and MDS-coded) setting,...
The study is devoted to comparing the parameters of the interstellar medium of HII regions in the Kongiu and Groves catalogs for the galaxy NGC 628. The article analyzes the characteristics of star-forming regions, including a comparison of radiation fluxes in the ranges of 7.7 $μ$m and 21 $μ$m and in the H$α$, H$β$, OIII and CO...
AI agents are increasingly used in long, multi-turn workflows in both research and enterprise settings. As interactions grow, agent behavior often degrades due to loss of constraint focus, error accumulation, and memory-induced drift. This problem is especially visible in real-world deployments where context evolves, distractions are...
Adjusted similarity measures, such as Cohen's kappa for inter-rater reliability and the adjusted Rand index used to compare clustering algorithms, are a vital tool for comparing discrete labellings. These measures are intended to have the property of 0 expectation under a null distribution and maximum value 1 under maximal similarity...
We present a four-component high-resolution model of thermal dust emission for microwave and sub-mm frequencies derived from Planck HFI, WHAM and Gaia. The resulting high-resolution model derived here forms the basis for the thermal dust model employed in the Cosmoglobe DR2 reanalysis of COBE-DIRBE. The four dust components are called...
Fine-grained sparsity promises higher parametric capacity without proportional per-token compute, but often suffers from training instability, load balancing, and communication overhead. We introduce STEM (Scaling Transformers with Embedding Modules), a static, token-indexed approach that replaces the FFN up-projection with a...
The dynamic motion of topological defects in magnets induces an emergent electric field, as exemplified by the continuous flow of skyrmion vortices. However, the electrodynamics underlying this emergent field remains poorly understood. In this context, magnetic domain walls - one dimensional topological defects with two collective...
In recent years, a two-dimensional (2D) coronal seismology technique applied to spectral-imaging data from the Coronal Multi-channel Polarimeter (CoMP) and UCoMP has enabled routine measurement of the global coronal magnetic field. The technique combines coronal transverse wave phase speed from Doppler measurements with electron...
We study a variety of stochastic contact processes -- directly related to models of rumor and disease spreading -- from the viewpoint of their constants of motion, either exact or approximated. Much as in deterministic systems, constants of motion in stochastic dynamics make it possible to reduce the number of relevant variables,...
In this paper, I utilize a variant of the Selberg--Delange method to find quantitative estimates of the sums \[M_{k,ω}(x,y)=\sum_{\substack{p_{1}(n)> y\\ n\leq x} } μ(n) {ω(n)-1\choose k-1},\] where $y$ can grow with $x$ but we must have $y\leq Y_0\exp(\mathscr{p}\frac{\log x}{(\log\log (x+1))^{1+ε}})$ with $Y_0,\mathscr{p},ε>0$....
We present spatially resolved spectroscopic observations of the planetary nebula NGC 6720, the Ring Nebula, taken during the science verification phase of WEAVE, a new instrument mounted on the William Herschel Telescope on La Palma. We use the instrument's Large Integral Field Unit (LIFU) to obtain spectra of the Ring Nebula,...
We investigate the in-medium modification and dissociation of heavy quarkonium in a hot QCD medium at finite quark chemical potential and in the weak magnetic-field regime. Starting from the one-loop resummed gluon propagator in the imaginary-time formalism, and incorporating non-perturbative effects through a phenomenological...