arXiv preprints from January 1, 2026 through September 27, 2026 — 03:44:59 EST
We study the stationary sojourn time distribution in an M/G/1 queue operating under heavy traffic. It is known that the sojourn time converges to an exponential distribution in the limit. Our focus is on obtaining pre-asymptotic, higher-order approximations that go beyond the classical exponential limit. Using Stein's method, we...
Tropical algebra, including max-plus, min-plus, and related idempotent semirings, provides a unifying framework in which many optimization problems that are nonlinear in classical algebra become linear. This property makes tropical methods particularly well suited for shortest paths, scheduling, throughput analysis, and discrete event...
Routing strives to connect all the Internet, but compete: political pressure threatens routing fragmentation; architectural changes such as private clouds, carrier-grade NAT, and firewalls make connectivity conditional; and commercial disputes create partial reachability for days or years. This paper suggests *persistent, partial...
We show that the (non-Noetherian) Stanley-Reisner ring of the order complex of certain intervals in the Bruhat order on the infinite symmetric group $S_\infty$ of all auto-bijections of $\mathbb{N}$ is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. This gives an infinite-dimensional version of results due to Edelman,...
We develop an information-theoretic framework for discrete dynamics grounded in a comparison-cost functional on ratios. Given two quantities compared via their ratio \(x=a/b\), we assign a cost \(F(x)\) measuring deviation from equilibrium (\(x=1\)). Requiring coherent composition under multiplicative chaining imposes a d'Alembert...
Modern video retrieval systems are expected to handle diverse tasks ranging from corpus-level retrieval, fine-grained moment localization to flexible multimodal querying. Specialized architectures achieve strong retrieval performance by training modality-specific encoders on massive datasets, but they lack the ability to process...
In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated capacities.
Second-generation Car--Parrinello \textit{ab initio} molecular dynamics (CP2G AIMD) combines a Born--Oppenheimer-like nuclear equation of motion with a predictor-corrector propagation of the one-particle density matrix and a modified Langevin equation to ensure an accurate sampling of the Boltzmann distribution. In the CP2K...
In this paper, we introduce a simple methodology to leverage strong convexity and smoothness in order to obtain an optimal linear convergence rate for the Peaceman--Rachford splitting (PRS) scheme applied to optimization problems involving two smooth strongly convex functions. The approach consists of adding and subtracting suitable...
Bilinear Euclidean quark and gluon correlators with Wilson links have been used widely for applications of large-momentum effective field theories to computing non-perturbative collinear and soft parton physics. Due to color confinement, these correlators decay exponentially at large spatial distances, a behavior crucial for computing...
The accuracy of one-shot $G_0W_0$ and Bethe-Salpeter equation (BSE) calculations depends strongly on the underlying starting-point eigensystem, which is commonly obtained from a mean-field density-functional approximation. Range-separated hybrid (RSH) functionals provide a particularly effective starting point, however, conventional...
Let $X$ be an uncountable Polish space and let $\mathcal{H}$ be the Hindman ideal, that is, the family of all $S\subseteq ω$ which are not $IP$-sets. For each sequence $x=(x_n)_{n \in ω}$ taking values in $X$, let $Λ_{x}(FS)$ be the set of $IP$-limit points of $x$. Also, let $Λ_{x}(\mathcal{H})$ be the set of $\mathcal{H}$-limit...
Multi-domain thinking verifiers trained via Reinforcement Learning with Verifiable Rewards (RLVR) are a cornerstone of modern post-training. However, their adoption in code generation has lagged behind that of execution feedback due to the prohibitive costs of the full RLVR pipeline. In this work, we ablate three primary choices along...
In this paper, we sharpen a theorem of Artin to show that for a finite group, the dimension of the subspace of class functions spanned by the rational valued characters equals the number of conjugacy classes of cyclic subgroups.
Rutile Sn$_{1-x}$Ge$_x$O$_{2}$ alloys are promising materials for high-power electronic applications due to their dopability and tunable ultra-wide band gaps. We use first-principles density functional theory and statistical mechanics to investigate the crystallographic, electronic, and thermodynamic properties of rutile...
Precision, robustness, and efficiency are crucial aspects in the design of quantum technologies. Here, we show how genuine quantum features, together with non-Gaussianity, can be the key elements to achieve the best of these three aspects during a quantum battery-charging process. Taking inspiration from a light-matter interaction...
Topological quantum computing is expected to be less sensitive to noise because information is stored in global states rather than local features. To examine whether different device topologies show measurable differences, we study three geometries with distinct topological invariants: a Mobius strip, a loop, and a trefoil knot, which...
AI companions enable deep emotional relationships by engaging a user's sense of identity, but they also pose risks like unhealthy emotional dependence. Mitigating these risks requires first understanding the underlying process of identity construction and negotiation with AI companions. Focusing on Character.AI (C.AI), a popular AI...
Music shapes the tone of videos, yet creators often struggle to find soundtracks that match their video's mood and narrative. Recent text-to-music models let creators generate music from text prompts, but our formative study (N=8) shows creators struggle to construct diverse prompts, quickly review and compare tracks, and understand...
Modern language models like GPT-3, BERT, and LLaMA require massive training data, yet with sufficient training they reliably learn to distinguish grammatical from ungrammatical sentences. Children aged as young as 14 months already have the capacity to learn abstract grammar rules from very few exemplars, even in the presence of...
We propose a federated learning framework for the calibration of parametric insurance indices under heterogeneous renewable energy production losses. Producers locally model their losses using Tweedie generalized linear models and private data, while a common index is learned through federated optimization without sharing raw...
Given an $F$-finite regular scheme $X$ of positive characteristic and a simple normal crossing divisor $E$ on $X$, we introduce a filtration on the de Rham-Witt complex $W_mΩ^\bullet_{X\setminus E}$. When $X$ is the spectrum of a henselian discrete valuation ring $A$ with quotient field $K$, this extends the classical filtration on...
Parameter-efficient fine-tuning (PEFT) methods are widely used to adapt large language models (LLMs) to downstream tasks and are often assumed to improve factual correctness. However, how the parameter-efficient fine-tuning methods affect hallucination behavior remains insufficiently understood, especially on QA datasets. In this...
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes the dynamics of the respective wave. Different wave phenomena are thus governed by different...
We analyze daily lead-time distributions for two Airbnb demand metrics, Nights Booked (volume) and Gross Booking Value (revenue), treating each day's allocation across 0-365 days as a compositional vector. The data span 2,557 days from January 2019 through December 2025 in a large North American region. Three findings emerge. First,...