arXiv preprints from January 1, 2026 through September 24, 2026 — 02:35:50 EST
We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the mean-field consistency condition is characterized by a system of coupled forward-backward stochastic...
We investigate the redshift 1.98 galaxy cluster XLSSC 122 using the Hubble Space Telescope (HST) from the core of the cluster out to 3 Mpc, a scale equivalent to 10 times the R500 = 295 kpc radius. We present an expanded photometric and spectroscopic catalogue of the cluster, bringing the total number of spectroscopically classified...
We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+σ^2$ in the angular part, where $σ$ is the...
We prove a noncommutative analogue of Minkowski's integral inequality for commuting squares of tracial von Neumann algebras. The inequality implies a necessary condition for a quadruple of graphs to be realized as inclusion graphs of a commuting square of multi-matrix algebras. As a corollary, we obtain a unitary categorification...
Large-scale data has fuelled the success of frontier artificial intelligence (AI) models over the past decade. This expansion has relied on sustained efforts by large technology corporations to aggregate and curate internet-scale datasets. In this work, we examine the environmental, social, and economic costs of large-scale data in AI...
Recent advances, such as RegretNet, ALGnet, RegretFormer and CITransNet, use deep learning to approximate optimal multi item auctions by relaxing incentive compatibility (IC) and measuring its violation via ex post regret. However, the true accuracy of these regret estimates remains unclear. Computing exact regret is computationally...
In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied by certain Hankel and Toeplitz determinants involving I-Bessel functions, or equivalently...
News consumption on social media has become ubiquitous, yet how different forms of engagement shape psychosocial outcomes remains unclear. To address this gap, we leveraged a large-scale dataset of ~26M posts and ~45M comments on the BlueSky platform, and conducted a quasi-experimental study, matching 81,345 Treated users exposed to...
This paper introduces a self-supervised learning framework for approximating the Security-Constrained DC Optimal Power Flow (SC-DCOPF) problem using a parametric linear model. The approach preserves the physical structure of the DC-OPF while incorporating demand-dependent tunable parameters that scale transmission line limits. These...
We investigate the stability of the many-body localized phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions ($V\propto r^{-α}$). By combining exact diagonalization of static properties with Lindblad master equation simulations of open-system dynamics, we...
Radio Access Network (RAN) sharing, which often also includes spectrum sharing, is a strategic cooperative agreement among two or more mobile operators, where one operator may use another's RAN infrastructure to provide mobile services to its users. By mutually sharing physical sites, radio elements, licensed spectrum and other parts...
A ladder determinantal module is an arbitrary direct sum of ideals of maximal minors of a generic ladder matrix. In this article, we give necessary and sufficient conditions for the special fiber ring of such modules to be Gorenstein. These conditions are expressed in terms of data obtained from the underlying matrix.
We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally categorified. These transition matrices follow from their counterparts computed in this paper among...
Linguistic expressions of emotions such as depression, anxiety, and trauma-related states are pervasive in clinical notes, counseling dialogues, and online mental health communities, and accurate recognition of these emotions is essential for clinical triage, risk assessment, and timely intervention. Although large language models...
The Kepler-observed distribution of planet sizes have revealed two distinct patterns: (1) a radius valley separating super-Earths and sub-Neptunes and (2) a preference for intra-system size similarity. We present a new model for the exoplanet population observed by Kepler, which is a "hybrid" of a clustered multi-planet model in which...
Peer agents can supplement real-time collaborative learning in asynchronous online courses. Constructive Controversy (CC) theory suggests that humans deepen their understanding of a topic by confronting and resolving controversies. This study explores whether CC's benefits apply to LLM-based peer agents, focusing on the impact of...
This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the displacement and stress fields generated by a point load traveling at a constant velocity along the...
We study perfect error-correcting codes in $\mathbb{Z}^n$ for the symmetric limited-magnitude error channel, where at most $e$ coordinates of an integer vector may be altered by a value whose magnitude is at most $s$. Geometrically, such codes correspond to tilings of $\mathbb{Z}^n$ by the symmetric limited-magnitude error ball...
The reliability of data-driven applications in electric vehicle (EV) infrastructure, such as charging demand forecasting, hinges on the availability of complete, high-quality charging data. However, real-world EV datasets are often plagued by missing records, and existing imputation methods are ill-equipped for the complex, multimodal...
In this paper, we show that in Hilbert space of any finite dimension N, there are N^2 unit vectors which constitute Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM).
The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of gradient orthogonalization -- remain poorly understood, with very few works providing end-to-end...
Magnetic fields and turbulence may play a key role in the evolution of protoclusters, influencing the formation of dense cores and stars. Here, we examine the morphology of the magnetic fields in the G327.29 protocluster using both the velocity gradient technique (VGT) extracted from molecular line emissions and linear polarization in...
We investigate visual reasoning limitations of both multimodal large language models (MLLMs) and image generation models (IGMs) by creating a novel benchmark to systematically compare failure modes across image-to-text and text-to-image tasks, enabling cross-modal evaluation of visual understanding. Despite rapid growth in machine...
We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schrödinger equation (NLS) using analytical and numerical methods. Our analysis reveals both ergodic and nonergodic regimes; importantly, we find broad parameter ranges where the dynamics is...
Building upon previous research, this paper further explores the topological foundations for maintaining universal rules within ultra-large-scale societies. It finds that in small-scale societies, absolute egalitarianism and the rule of law can be compatible through peer monitoring within a fully connected network. However, in...