Tootfinder

Statistical Quantum Mechanics of the Random Permutation Sorting System (RPSS): A Self-Stabilizing True Uniform RNG
Randy Kuang
https://arxiv.org/abs/2509.10174 https://

Statistical Quantum Mechanics of the Random Permutation Sorting System (RPSS): A Self-Stabilizing True Uniform RNG
We present the Random Permutation Sorting System (RPSS), a novel framework for true uniform randomness generation grounded in statistical quantum mechanics. RPSS is built on a pair of conjugate observables, the permutation count and the elapsed sorting time, whose heavy-tailed raw distributions synchronously converge to uniformity through modular reduction. This mathematically proven convergence establishes RPSS as a True Uniform Random Number Generator (TURNG). A practical implementation, QPP-…

Structure-Aware Spectral Sparsification via Uniform Edge Sampling
Kaiwen He, Petros Drineas, Rajiv Khanna
https://arxiv.org/abs/2510.12669 https://arxiv.or…

Structure-Aware Spectral Sparsification via Uniform Edge Sampling
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges proportionally to their effective resistances, but require expensive preprocessing to estimate these resistances. We study whether uniform edge sampling-a simple, structure-agnostic strategy-can suffice for spectral clustering. Our main result shows that for graphs adm…

Cyclic universe and uniform rate inflation in loop quantum cosmology
Bikash Chandra Paul, Sahil Saini
https://arxiv.org/abs/2510.11230 https://arxiv.org/pd…

Cyclic universe and uniform rate inflation in loop quantum cosmology
We investigate uniform rate inflationary universe in the framework of Loop quantum cosmology. The potential for uniform rate inflation in a loop quantized FRW spacetime turns out to be a polymerized version of the corresponding potential in general relativity, which mimics the potentials for a polymerized scalar field and that for hybrid natural inflation (HNI). The potential leads to a cyclic universe with identical epochs separated by quantum bounces which replace the classical singularity. T…

Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint
Jonas Stapmanns, Catarina Dias, Luke Eilers, Tobias K\"uhn, Jean-Pascal Pfister
https://arxiv.org/abs/2510.12427

Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint
Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the curvature of the cost function. We find that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex and the cost const…

Rotation of crystal seed during early stages of growth reveals the anisotropy of glass matrix
R. Thapa, E. Mustermann, H. Jain, V. Dierolf, M. E. McKenzie
https://arxiv.org/abs/2510.09807

Rotation of crystal seed during early stages of growth reveals the anisotropy of glass matrix
Rotation of crystal seed during the early stages of growth in a glass matrix has been observed due to some torque, contradicting the expectations from the isotropic, uniform structure of the surrounding amorphous matrix. We establish an atomistic origin of this new phenomenon from molecular dynamics simulations using LiNbO3 and LiNbO3-SiO2 glasses as model systems. Effectively, it arises due to non-uniform forces on the seed from the surrounding glass, which appears inhomogeneous and anisotropi…

Jets at Patriots on TNF: New uniform, old rivalry, what to expect from Prime's broadcast https://www.nytimes.com/athletic/6801668/2025/11/13/jets-patriots-tnf-drake-maye-how-to-watch/

From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method
Shuchen Guo
https://arxiv.org/abs/2508.10697 https://arxiv.org/pdf/2…

From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method
We study the Kac particle model for the space-homogenous Landau equation with hard potentials. By showing a sharper Povzner-type inequality, we obtain the uniform-in-time and uniform-in-N propagation of exponential moment for the first marginal of the solution of the many-particle Liouville equation. This key property enables us to show the uniqueness of weak solutions of the corresponding infinite Landau hierarchy by coupling method. As a result, we prove the propagation of chaos for the Landa…

Low-Discrepancy Set Post-Processing via Gradient Descent
Fran\c{c}ois Cl\'ement, Linhang Huang, Woorim Lee, Cole Smidt, Braeden Sodt, Xuan Zhang
https://arxiv.org/abs/2511.10496 https://arxiv.org/pdf/2511.10496 https://arxiv.org/html/2511.10496
arXiv:2511.10496v1 Announce Type: new
Abstract: The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive, often requiring days of computation or access to GPU clusters. We show that simple gradient descent-based techniques allow for comparable results when starting with a reasonably uniform point set. Not only is this method much more efficient and accessible, but it can be applied as post-processing to any low-discrepancy set generation method for a variety of standard discrepancy measures.
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Rough isometry between Gromov hyperbolic spaces and unbounded uniformization
Vasudevarao Allu, Alan P Jose
https://arxiv.org/abs/2510.11114 https://arxiv.o…

Rough isometry between Gromov hyperbolic spaces and unbounded uniformization
In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter $ε>0$, of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently small $ε$. In this paper, we demonstrate that if two proper, roughly starlike Gromov hyperbolic spaces are roughly isometric, then the uniformity of their conformal deformations is a simultaneous property; that is, either both are uniform spaces or neither is. Our res…

Tokenization Disparities as Infrastructure Bias: How Subword Systems Create Inequities in LLM Access and Efficiency
Hailay Kidu Teklehaymanot, Wolfgang Nejdl
https://arxiv.org/abs/2510.12389

Tokenization Disparities as Infrastructure Bias: How Subword Systems Create Inequities in LLM Access and Efficiency
Tokenization disparities pose a significant barrier to achieving equitable access to artificial intelligence across linguistically diverse populations. This study conducts a large-scale cross-linguistic evaluation of tokenization efficiency in over 200 languages to systematically quantify computational inequities in large language models (LLMs). Using a standardized experimental framework, we applied consistent preprocessing and normalization protocols, followed by uniform tokenization through …

Tur\'an densities of stars in uniformly dense hypergraphs
Hao Lin, Wenling Zhou
https://arxiv.org/abs/2510.12576 https://arxiv.org/pdf/2510.12576

Turán densities of stars in uniformly dense hypergraphs
A $3$-uniform hypergraph (or $3$-graph) $H=(V,E)$ is $(d,μ, \text{dot})$-dense if for any subsets $X, Y, Z\subseteq V$, the number of triples $(x,y,z)\in X\times Y\times Y$ with $\{x,y,z\}$ being an edge of $H$ is at least $d|X||Y||Z|-μ|V|^3$. Similarly, we say that $H$ is $(d,μ, \text{dot-edge})$-dense if for any subset $X\subseteq V$ and every pair set $P\subseteq V\times V$, the number of pairs $(x,(y,z))\in X\times P$ with $\{x,y,z\}$ being an edge…

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Secret-Protected Evolution for Differentially Private Synthetic Text Generation
Tianze Wang, Zhaoyu Chen, Jian Du, Yingtai Xiao, Linjun Zhang, Qiang Yan
https://arxiv.org/abs/2510.10990

Secret-Protected Evolution for Differentially Private Synthetic Text Generation
Text data has become extremely valuable on large language models (LLMs) and even lead to general artificial intelligence (AGI). A lot of high-quality text in the real world is private and cannot be freely used due to privacy concerns. Therefore, differentially private (DP) synthetic text generation has been proposed, aiming to produce high-utility synthetic data while protecting sensitive information. However, existing DP synthetic text generation imposes uniform guarantees that often overprote…

On the $v$-adic values of G-functions I
Georgios Papas
https://arxiv.org/abs/2510.11806 https://arxiv.org/pdf/2510.11806

On the $v$-adic values of G-functions I
This is the first in a series of papers aimed at studying families of G-functions associated to $1$-parameter families of abelian schemes. In particular, the construction of relations, in both the archimedean and non-archimedean settings, at values of specific interest to problems of unlikely intersections. In this first text in this series, we record what we expect to be the theoretical foundations of this series in a uniform way. After this, we study values corresponding to ``splittings'' i…

Self-Resetting Soft Ring Enables Autonomous and Continuous Leaping under Uniform Light
Fangjie Qi, Caizhi Zhou, Haitao Qing, Haoze Sun, Jie Yin
https://arxiv.org/abs/2510.09529 …

Self-Resetting Soft Ring Enables Autonomous and Continuous Leaping under Uniform Light
Jumping is an efficient locomotion strategy to traverse cluttered, uneven, or unstable environments in nature, yet replicating continuous, autonomous leaping in soft robots remains challenging due to limited energy storage and reliance on human intervention or latches. Here, we report a millimeter-scale, self-resetting soft ring that achieves repeated vertical and stable horizontal leaps under uniform infrared illumination without external control. The ring-shaped liquid crystal elastomer body …

A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
https://arxiv.org/abs/2508.10344

A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of $\mathbb{R}^d$ (including advection equations on surfaces) by extending the error analysis of Falcone and Ferretti. A central requirement in our analysis is a remapping operator that achieves both high approximation orders and strong stability, a combination that is challenging to obtain and of independent interest. …

Fluid Antenna Enabled Direction-of-Arrival Estimation Under Time-Constrained Mobility
He Xu, Tuo Wu, Ye Tian, Kangda Zhi, Wei Liu, Baiyang Liu, Hing Cheung So, Naofal Al-Dhahir, Kin-Fai Tong, Chan-Byoung Chae, Kai-Kit Wong
https://arxiv.org/abs/2508.10820

Fluid Antenna Enabled Direction-of-Arrival Estimation Under Time-Constrained Mobility
Fluid antenna (FA) technology has emerged as a promising approach in wireless communications due to its capability of providing increased degrees of freedom (DoFs) and exceptional design flexibility. This paper addresses the challenge of direction-of-arrival (DOA) estimation for aligned received signals (ARS) and non-aligned received signals (NARS) by designing two specialized uniform FA structures under time-constrained mobility. For ARS scenarios, we propose a fully movable antenna configurat…

The 21-cm signature of X-ray heated halos around galaxies during cosmic dawn
Ka-Hou Leong, Avery Meiksin
https://arxiv.org/abs/2509.10255 https://arxiv.org…

The 21-cm signature of X-ray heated halos around galaxies during cosmic dawn
X-rays emitted by high mass X-ray binaries (HMXBs) and supernovae-driven winds in the first galaxies during Cosmic Dawn are expected to warm the intergalactic medium prior to its reionization. While most of the heating will be uniform on measurable scales, exceptionally bright sources will produce a warm ring around them with a distinctive 21-cm signature. The detection of such systems would confirm X-rays are a source of IGM heating during Cosmic Dawn and provide a test of models predicting hi…

Magnetic effects on fundamental modes in rotating neutron stars with a purely toroidal magnetic field
Anson Ka Long Yip, Tjonnie Guang Feng Li
https://arxiv.org/abs/2509.10150 h…

Magnetic effects on fundamental modes in rotating neutron stars with a purely toroidal magnetic field
Electromagnetic and gravitational-wave signals from neutron stars are shaped by rapid rotation and strong magnetic fields. Determining these properties is essential to interpret such signals, but current measurements are limited: rotation estimates rely on electromagnetic detections and assume uniform rotation, while inferring interior magnetic fields remains ambiguous due to a lack of direct observations. Measuring the excited fundamental modes of neutron stars in gravitational-wave signals of…

Stanley-Reisner ideals with linear powers
Antonino Ficarra, Somayeh Moradi
https://arxiv.org/abs/2508.10354 https://arxiv.org/pdf/2508.10354

Stanley-Reisner ideals with linear powers
Let $S = K[x_1, \dots, x_n]$ be the standard graded polynomial ring over a field $K$. In this paper, we address and completely solve two fundamental open questions in Commutative Algebra: (i) For which degrees $d$, does there exist a uniform combinatorial characterization of all squarefree monomial ideals in $S$ having $d$-linear resolutions? (ii) For which degrees $d$, does having a linear resolution coincide with having linear powers for all squarefree monomial ideals of $S$ generated in …

Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
Minju Gwak, Guijin Son, Jaehyung Kim
https://arxiv.org/abs/2510.06953 https://

Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six diffe…

Running man spreads his arms like the wings of an airplane
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Disorder to Order Transition in 1D Nonreciprocal Cahn-Hilliard Model
Navdeep Rana, Ramin Golestanian
https://arxiv.org/abs/2510.11580 https://arxiv.org/pdf…

Disorder to Order Transition in 1D Nonreciprocal Cahn-Hilliard Model
We extensively study the phenomenology of one dimensional Nonreciprocal Cahn Hilliard model for varying nonreciprocity $(α)$ and different boundary conditions. At small $α$, a perturbed uniform state evolves to a defect laden configuration that lacks global polar order. Defects are the sources and sinks of travelling waves and nonreciprocity selects defects with a unique wave number that increases monotonically with $α_c$. A critical threshold $α_c$ marks the onset of a transition to states…

Witnessing downsizing in the making: quiescent and breathing galaxies at the dawn of the Universe
Emiliano Merlin, Flaminia Fortuni, Antonello Calabr\'o, Marco Castellano, Paola Santini, Adriano Fontana, Lucas C. Kimmig, Francesco Shankar, Lorenzo Napolitano, Anton M. Koekemoer, Ray A. Lucas, Fabio Pacucci, Michael C. Cooper, Michaela Hirschmann, Pablo G. P\'erez-Gonz\'alez, Guillermo Barro, Mark Dickinson, Giovanni Gandolfi, Norman A. Grogin, Xin Wang

Witnessing downsizing in the making: quiescent and breathing galaxies at the dawn of the Universe
[Shortened for arXiv] We conduct a systematic search for $\log(M_\ast/M_\odot) \geq 9.5$ quiescent galaxies at $z > 3$ in six extragalactic deep fields observed with NIRCam, with the goal of extracting their physical and statistical features in a uniform and self-consistent manner. We exploit the ASTRODEEP-JWST photometric catalogs to single out robust candidates, including sources quenched only a few tens of Myr before the observation. We apply a SED-fitting procedure which explores three func…

Techniques of Artificial Intelligence Applied to Near-Infrared Spectra
Aminata Sow, Tidiane Diallo
https://arxiv.org/abs/2510.10638 https://arxiv.org/pdf/2…

Techniques of Artificial Intelligence Applied to Near-Infrared Spectra
This article explores the application of various artificial intelligence techniques to the analysis of near-infrared (NIR) spectra of paracetamol, within the spectral range of 900 nm to 1800 nm. The main objective is to evaluate the performance of several dimensionality reduction algorithms; namely, Principal Component Analysis (PCA), Kernel PCA (KPCA), Sparse Kernel PCA, t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP) in modeling an…

Visibility-Aware Densification for 3D Gaussian Splatting in Dynamic Urban Scenes
Yikang Zhang, Rui Fan
https://arxiv.org/abs/2510.09364 https://arxiv.org/p…

Visibility-Aware Densification for 3D Gaussian Splatting in Dynamic Urban Scenes
3D Gaussian splatting (3DGS) has demonstrated impressive performance in synthesizing high-fidelity novel views. Nonetheless, its effectiveness critically depends on the quality of the initialized point cloud. Specifically, achieving uniform and complete point coverage over the underlying scene structure requires overlapping observation frustums, an assumption that is often violated in unbounded, dynamic urban environments. Training Gaussian models with partially initialized point clouds often l…

Notes from the Physics Teaching Lab: NMR Experiments at 21 Gauss
Kenneth G. Libbrecht
https://arxiv.org/abs/2508.10738 https://arxiv.org/pdf/2508.10738

Notes from the Physics Teaching Lab: NMR Experiments at 21 Gauss
We describe a series of laboratory experiments that can be performed with the Quantum Control apparatus sold by TeachSpin, which uses pulsed NMR techniques to observe the precession of protons in a liquid water sample. With a uniform background magnetic field of 21 Gauss, the protons precess at about 90 kHz, yielding numerous relatively simple observations and measurements that are well suited to undergraduate physics teaching labs. Our goal in this paper is to document some of these experiment…

Hadamard-L\'{e}vy theorems for maps taking values in a finite dimensional space
Yacine Chitour, Zhengping Ji, Emmanuel Tr\'elat
https://arxiv.org/abs/2510.11206 https://…

Hadamard-Lévy theorems for maps taking values in a finite dimensional space
We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional Euclidean space, when its second-order differential has uniform upper and lower bounds, it has a global path-lifting property in the presence of singularities. This is then applied to the nonlinear motion planning problem, establishing in some cases the well-posedn…

New Approaches to the Fixed Point Property in L^1 Spaces
Faruk Alpay, Hamdi Alakkad
https://arxiv.org/abs/2509.10194 https://arxiv.org/pdf/2509.10194

New Approaches to the Fixed Point Property in L^1 Spaces
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that measure-compactness of a convex set is a sufficient condition. Our exposition makes all compactness and uniform integrability arguments explicit, offering a clear path from measure-theoretic compactness to weak compactness, normal structure, and ultimately fixed point…

GlyphWeaver: Unlocking Glyph Design Creativity with Uniform Glyph DSL and AI
Can Liu, Shiwei Chen, Zhibang Jiang, Yong Wang
https://arxiv.org/abs/2509.08444 https://

GlyphWeaver: Unlocking Glyph Design Creativity with Uniform Glyph DSL and AI
Expressive glyph visualizations provide a powerful and versatile means to represent complex multivariate data through compact visual encodings, but creating custom glyphs remains challenging due to the gap between design creativity and technical implementation. We present GlyphWeaver, a novel interactive system to enable an easy creation of expressive glyph visualizations. Our system comprises three key components: a glyph domain-specific language (GDSL), a GDSL operation management mechanism, …

Provable avoidance of barren plateaus for GM-QAOA
Boris Tsvelikhovskiy, Matthew Nuyten, Bojko N. Bakalov
https://arxiv.org/abs/2509.10424 https://arxiv.org…

Provable avoidance of barren plateaus for GM-QAOA
We analyze the dynamical Lie algebras (DLAs) associated with the Grover-mixer variant of the Quantum Approximate Optimization Algorithm (GM-QAOA). When the initial state is the uniform superposition of computational basis states, we show that the corresponding DLA is isomorphic to either $\mathfrak{su}_{r} \oplus \mathfrak{u}_{1}^{\oplus 2}$ or $\mathfrak{su}_{r} \oplus \mathfrak{u}_{1}$, where \(r\) denotes the number of distinct values of the objective function. We also establish an analogous…

Finding Partite Hypergraphs Efficiently
Ferran Espu\~na
https://arxiv.org/abs/2508.10641 https://arxiv.org/pdf/2508.10641

Finding Partite Hypergraphs Efficiently
We provide a deterministic polynomial-time algorithm that, for a given $k$-uniform hypergraph $H$ with $n$ vertices and edge density $d$, finds a complete $k$-partite subgraph of $H$ with parts of size at least ${c(d, k)(\log n)^{1/(k-1)}}$. This generalizes work by Mubayi and Turán on bipartite graphs. The value we obtain for the part size matches the order of magnitude guaranteed by the non-constructive proof due to Erdős and is tight up to a constant factor.

New complexity bounds for primal--dual interior-point algorithms in conic optimization
Joachim Dahl, Levent Tun\c{c}el, Lieven Vandenberghe
https://arxiv.org/abs/2509.10263 http…

New complexity bounds for primal--dual interior-point algorithms in conic optimization
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity measure for primal--dual metrics at pairs of primal and dual points. The complexity measure is defined as the largest eigenvalue of the product of the Hessians of the primal and dual barrier functions, normalized by the proximity of the points to the central path. For algorithms based on self-scaled barriers for symmetr…

Personalize Before Retrieve: LLM-based Personalized Query Expansion for User-Centric Retrieval
Yingyi Zhang, Pengyue Jia, Derong Xu, Yi Wen, Xianneng Li, Yichao Wang, Wenlin Zhang, Xiaopeng Li, Weinan Gan, Huifeng Guo, Yong Liu, Xiangyu Zhao
https://arxiv.org/abs/2510.08935

Personalize Before Retrieve: LLM-based Personalized Query Expansion for User-Centric Retrieval
Retrieval-Augmented Generation (RAG) critically depends on effective query expansion to retrieve relevant information. However, existing expansion methods adopt uniform strategies that overlook user-specific semantics, ignoring individual expression styles, preferences, and historical context. In practice, identical queries in text can express vastly different intentions across users. This representational rigidity limits the ability of current RAG systems to generalize effectively in personali…

Deterministic roughening in the dc-driven precessional regime of domain walls
E. F. Pusiol, V. Lecomte, S. Bustingorry, A. B. Kolton
https://arxiv.org/abs/2508.10859 https://

Deterministic roughening in the dc-driven precessional regime of domain walls
We numerically study the dynamics of extended domain walls in homogeneous ferromagnets driven by a uniform magnetic field at zero temperature. Using both micromagnetic Landau-Lifshitz-Gilbert simulations and a collective-coordinate model, we show that flat domain walls become linearly unstable above the Walker breakdown field and below a higher threshold, provided their length exceeds a characteristic value. This instability is captured by a quasi-universal spectral diagram, parameterized solel…

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Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
L. J. R. Bezerra Jr., W. S. Dias
https://arxiv.org/abs/2510.08781 htt…

Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schrödinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes and the influence of a refractive index detuning selectively applied along the diagonal waveguides on this transition. This detuning effectively emulates the effect…

Energy Efficiency for Massive MIMO Integrated Sensing and Communication Systems
Huy T. Nguyen, Van-Dinh Nguyen, Nhan Thanh Nguyen, Nguyen Cong Luong, Vo-Nguyen Quoc Bao, Hien Quoc Ngo, Dusit Niyato, Symeon Chatzinotas
https://arxiv.org/abs/2509.10290

Energy Efficiency for Massive MIMO Integrated Sensing and Communication Systems
This paper explores the energy efficiency (EE) of integrated sensing and communication (ISAC) systems employing massive multiple-input multiple-output (mMIMO) techniques to leverage spatial beamforming gains for both communication and sensing. We focus on an mMIMO-ISAC system operating in an orthogonal frequency-division multiplexing setting with a uniform planar array, zero-forcing downlink transmission, and mono-static radar sensing to exploit multi-carrier channel diversity. By deriving clos…

Oracle-based Uniform Sampling from Convex Bodies
Thanh Dang, Jiaming Liang
https://arxiv.org/abs/2510.02983 https://arxiv.org/pdf/2510.02983

Oracle-based Uniform Sampling from Convex Bodies
We propose new Markov chain Monte Carlo algorithms to sample a uniform distribution on a convex body $K$. Our algorithms are based on the Alternating Sampling Framework/proximal sampler, which uses Gibbs sampling on an augmented distribution and assumes access to the so-called restricted Gaussian oracle (RGO). The key contribution of this work is the efficient implementation of RGO for uniform sampling on $K$ via rejection sampling and access to either a projection oracle or a separation oracle…

Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)
Bartosz Bednarczyk, Emanuel Kiero\'nski
https://arxiv.org/abs/2509.09218 https://…

Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)
We study the Guarded Fragment with Regular Guards (RGF), which combines the expressive power of the Guarded Fragment (GF) with Propositional Dynamic Logic with Intersection and Converse (ICPDL). Our logic generalizes, in a uniform way, many previously-studied extensions of GF, including (conjunctions of) transitive or equivalence guards, transitive or equivalence closure and more. We prove 2EXPTIME-completeness of the satisfiability problem for RGF, showing that RGF is not harder than ICPDL or …

Localized states of BFSS super quantum mechanics
Oscar J. C. Dias, Jorge E. Santos
https://arxiv.org/abs/2510.07379 https://arxiv.org/pdf/2510.07379…

Localized states of BFSS super quantum mechanics
We analyze the recently discovered localized and non-uniform phases of the Banks-Fischler-Shenker-Susskind (BFSS) matrix quantum mechanics. Building on [1], we provide first-principles derivations of their properties and extend the results with new analytic and numerical insights. We show that strongly coupled BFSS dynamics emerge from a specific Carrollian transformation of 11-dimensional supergravity, which we justify in detail. In this framework, the uniform BFSS phase corresponds to a black…

Characterizing Power Spectra of Density Fluctuations in GRMHD Simulations of Black Hole Accretion Using Taylor's Frozen-in Hypothesis
Pravita Hallur, Lia Medeiros, Pierre Christian, George N. Wong
https://arxiv.org/abs/2510.09746

Characterizing Power Spectra of Density Fluctuations in GRMHD Simulations of Black Hole Accretion Using Taylor's Frozen-in Hypothesis
We characterize the spatial power spectrum of density fluctuations in magnetohydrodynamic flows in a suite of high-resolution, long-time-span general relativistic magnetohydrodynamic (GRMHD) simulations. Extracting the local spatial power spectrum in curved spacetime directly from GRMHD simulations can be challenging for several conceptual and mechanical reasons, including choices of the reference frame, the non-uniform co-ordinate grid of the outputs and limited resolution. Taylor's frozen-in …

A priori error estimates for stable generalized finite element discretization of parabolic interface optimal control problems
Xindan Zhang, Jianping Zhao, Yanren Hou
https://arxiv.org/abs/2510.12147

A priori error estimates for stable generalized finite element discretization of parabolic interface optimal control problems
In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient across the interface and the control acting on the interface. Consequently, the traditional finite element method fails to achieve optimal convergence rates when using a uniform mesh. To discretize the problem, we use fully discrete approximations based on th…

Reionization in HESTIA: Studying reionization in the LG through zoom simulations
David Attard, Luke Conaboy, Noam Libeskind, Sergey Pillipenko, Keri Dixon, Ilian T. Iliev
https://arxiv.org/abs/2509.10133

Reionization in HESTIA: Studying reionization in the LG through zoom simulations
While cosmic reionization has been broadly constrained by global observables, the interplay between internal sources (Milky Way, M31, and their satellites) and external ionization fronts remains poorly understood in a realistic Local Group (LG) context. To address this issue, we perform radiative transfer post-processing on the original HESTIA LG constrained simulation. We calibrate our source models using a uniform 1024^3 particle, dark-matter only, HESTIA simulation coupled with a subgrid col…

The most probable order of a random permutation
Adrian Beker
https://arxiv.org/abs/2510.11698 https://arxiv.org/pdf/2510.11698

The most probable order of a random permutation
Given positive integers $n$ and $m$, let $p_n(m)$ be the probability that a uniform random permutation of $[n]$ has order exactly $m$. We show that, as $n \to \infty$, the maximum of $p_n(m)$ over all $m$ is asymptotic to $1/n$, the probability of an $n$-cycle. Furthermore, for sufficiently large $n$, we show that the maximum is attained precisely if $m$ is the least positive integer divisible by all positive integers less than or equal to $n-m$. This answers a question of Acan, Burnette, Eberh…

Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
Zhao Xu
https://arxiv.org/abs/2509.05968 https://arxiv.org/pdf/250…

Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
In this paper, we study the second moment for $GL(2)\times GL(2)$ $L$-functions $L(\frac{1}{2},f\times g)$, which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either $f$ or $g$ is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both $t_f$ and $t_g$, where $t_f$, $t_g$ denote the spectral parameters of $f$, $g$. As an application, we also establish a shrinking result for QUE in the case of dihedral Ma…

On norms on Harish-Chandra modules
Joseph Bernstein, Pritam Ganguly, Bernhard Kr\"otz, Job Kuit, Eitan Sayag
https://arxiv.org/abs/2510.09370 https://…

On norms on Harish-Chandra modules
The Casselman-Wallach theorem is a foundational result in the theory of representations of real reductive groups connecting algebraic representations to topological representations. We provide a quantitative version of this theorem. For that we introduce the notion of {\it Sobolev gap} for a Harish-Chandra module. This is a new invariant whose finiteness is highly non-trivial. We determine the Sobolev gap for representations in the unitary dual of the group $\SL(2,\R)$ and establish uniform fin…

Exact solution for the current generated by dissipative master equation in single-band tight-binding systems subject to time-dependent uniform electric fields
J. M. Alendouro Pinho, B. Amorim, J. M. Viana Parente Lopes
https://arxiv.org/abs/2510.08021

Exact solution for the current generated by dissipative master equation in single-band tight-binding systems subject to time-dependent uniform electric fields
The theory of open quantum systems is one of the most essential tools for the development of quantum technologies. A particular area of interest is in the optical response of solid state systems, where dissipation is introduced phenomenologically through the relaxation time approximation and its effects are usually gauged perturbatively. Analytical exact results for driven systems under this approximation are scarce and tipically pertain only to the stationary regime. Here, we obtain the analyt…

Thinned COE random matrix models for DNA replication
Huw Day, Nina C. Snaith
https://arxiv.org/abs/2510.11748 https://arxiv.org/pdf/2510.11748

Thinned COE random matrix models for DNA replication
This paper details an observation that for more primitive organisms, such as some yeasts, the statistical distribution of the origins of replication sometimes looks remarkably like the distribution of eigenvalues from the Circular Orthogonal Ensemble (COE) of random matrices. This does not hold for more complex organisms, but a uniform thinning of the COE eigenvalues (which interpolates between the COE and uncorrelated, Poisson statistics) gives a platform to investigate characteristics of repl…

Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning
Jingyi Wu, Chao Ning, Yang Shi
https://arxiv.org/abs/2510.10214 https://

Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning
Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before sequentially incorporating them into downstream control synthesis. This segregation between ambiguity set construction and control objectives inherently introduces a structural misalignment, which undesirably leads to conservative control policies with sub-opt…

I was gonna wear an Imperial Officer's uniform this #Halloween...
...but I simply can't pretend that cosplaying in an undeniably #FASCIST uniform, is something I'd be comfortable with after 8 months of Fat Putin's dictatorial rule.
With all the suffering & hate... i…

Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads
Yuecheng Cai, Jasmin Jelovica
https://arxiv.org/abs/2510.02472 https://

Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads
Surrogate models are essential in structural analysis and optimization. We propose a heterogeneous graph representation of stiffened panels that accounts for geometrical variability, non-uniform boundary conditions, and diverse loading scenarios, using heterogeneous graph neural networks (HGNNs). The structure is partitioned into multiple structural units, such as stiffeners and the plates between them, with each unit represented by three distinct node types: geometry, boundary, and loading nod…

FLRC: Fine-grained Low-Rank Compressor for Efficient LLM Inference
Yu-Chen Lu, Chong-Yan Chen, Chi-Chih Chang, Yu-Fang Hu, Kai-Chiang Wu
https://arxiv.org/abs/2510.09332 https:/…

FLRC: Fine-grained Low-Rank Compressor for Efficient LLM Inference
Although large language models (LLM) have achieved remarkable performance, their enormous parameter counts hinder deployment on resource-constrained hardware. Low-rank compression can reduce both memory usage and computational demand, but applying a uniform compression ratio across all layers often leads to significant performance degradation, and previous methods perform poorly during decoding. To address these issues, we propose the Fine-grained Low-Rank Compressor (FLRC), which efficiently d…

Distributed Automatic Generation Control subject to Ramp-Rate-Limits: Anytime Feasibility and Uniform Network-Connectivity
Mohammadreza Doostmohammadian, Hamid R. Rabiee
https://arxiv.org/abs/2509.06588

Distributed Automatic Generation Control subject to Ramp-Rate-Limits: Anytime Feasibility and Uniform Network-Connectivity
This paper considers automatic generation control over an information-sharing network of communicating generators as a multi-agent system. The optimization solution is distributed among the agents based on information consensus algorithms, while addressing the generators' ramp-rate-limits (RRL). This is typically ignored in the existing linear/nonlinear optimization solutions but they exist in real-time power generation scenarios. Without addressing the RRL, the generators cannot follow the ass…

Optimal bidding in multiperiod day-ahead electricity markets assuming non-uniform uncertainty of clearing prices
D\'avid Csercsik, Mih\'aly Andr\'as V\'aghy
https://arxiv.org/abs/2510.07025

Optimal bidding in multiperiod day-ahead electricity markets assuming non-uniform uncertainty of clearing prices
In a recent publication, using a simple two-period model, which is already capable to capture essential non-convex multiperiod bids, Richstein et al. have shown that in the case of optimal bidding, multi-part bidding always ensures a higher expected profit for the bidder, compared to simple bidding and block-bidding. The model proposed in their analysis assumes a uniform distribution of the market-clearing prices in both periods. In this paper, we study how the conclusions of the analysis are a…

Nice day planned today although I won't have time for our usual walk.
Worked as much as I could this morning.
Now I'm just about to dress for the outside world. Uniform for these sorts of days, in this sort of weather, is jeans, t-shirt, suit jacket, runners, and some fun earrings.
Lunch with husband at Gary's at Erindale.
Then I'll bus it into Civic for ANU's First Generation Celebration event.
Then bus it back home in time for a Zoom meeting…

Man in Nazi uniform assaulted Georgia student after he was denied entry to bar, officials say (NBC News)
https://www.nbcnews.com/news/us-news/man-nazi-uniform-assaulted-georgia-student-was-denied-entry-bar-offici-rcna239893
http://www.memeorandum.com/251026/p63#a251026p63

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data
Anastasis Kratsios, Tin Sum Cheng, Daniel Roy
https://arxiv.org/abs/2509.00924

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal, as they assume noiseless data and allow network parameters to be chosen freely, independent of algorithmic realism. This paper bridges that gap by introducing an architecture-specific randomized training algorithm that constructs a uniform approximator from $…

Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains
Riku Anttila
https://arxiv.org/abs/2510.04725 https://arxiv.org/pdf/251…

Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains
We prove that sub-Gaussian heat kernel estimates are inherited from a diffusion process on the ambient space to the reflected diffusion process on a subset which is an inner uniform domain.

Full-Angle Ray Antenna Array and Omnicell Wireless Communication System
Xuancheng Zhu, Zhiwen Zhou, Yong Zeng
https://arxiv.org/abs/2509.05677 https://arxi…

Full-Angle Ray Antenna Array and Omnicell Wireless Communication System
Ray antenna array (RAA) was recently proposed as a novel multi-antenna architecture that arranges multiple massive cheap antenna elements into simple uniform linear arrays (sULAs) with different orientations. Compared with traditional architectures like hybrid analog/digital beamforming with uniform linear array (ULA) and uniform circular array (UCA), RAA has several promising advantages such as significantly reduced hardware cost, higher beamforming gains and the ability of providing uniform a…

NFL uniform schedule for Week 1: Eagles, Cowboys go with traditional look; Saints to debut new alternate

https://www.cbssports.com/nfl/news/nfl-uni

He is such an asshole

Uniform ergodicity of geodesic slice sampling
Mareike Hasenpflug
https://arxiv.org/abs/2510.06748 https://arxiv.org/pdf/2510.06748

Uniform ergodicity of geodesic slice sampling
Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for distributions with compact support that have a bounded density with respect to the Riemannian measure. The constants in our convergence bound are available explicitly, and we investigate their dependence on the hyperparameters of the geodesic slice sampler, the target d…

Dallas Cowboys' uniform combination vs Philadelphia Eagles for Week 1 https://www.si.com/nfl/cowboys/news/dallas-cowboys-uniform-combination-philadelphia-eagles-week-1-nfl-season

Controllable Domain Wall Memories with Magnetic Topological Insulator
Arifa Hoque, Sanjukta Bhanja
https://arxiv.org/abs/2510.10369 https://arxiv.org/pdf/2…

Controllable Domain Wall Memories with Magnetic Topological Insulator
Domain wall memories have undergone several changes over the years for faster shift, read, and write operations; however, fundamental issues persist due to creating pinning sites topographically along the nanowire. The deformity in notches creates non-uniform pinning strength, leading to multiple faults during shift operation. This study proposes a novel approach to address these challenges and gain greater control over domain manipulation for advanced applications in Boolean and non-Boolean pa…

New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions
Lei Zhao, Daoli Zhu, Shuzhong Zhang
https://arxiv.org/abs/2510.12105

New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions
In this paper, we study the local linear convergence behavior of proximal-gradient (PG) descent algorithm on a parameterized gap-function reformulation of a smooth but non-monotone variational inequality problem (VIP). The aim is to solve the non-monotone VI problem without assuming the existence of a Minty-type solution. We first introduce and study various error bound conditions for the gap functions in relation to the VI model. In particular, we show that uniform type error bounds imply leve…

Uniform Information Density and Syntactic Reduction: Revisiting $\textit{that}$-Mentioning in English Complement Clauses
Hailin Hao, Elsi Kaiser
https://arxiv.org/abs/2509.05254

Uniform Information Density and Syntactic Reduction: Revisiting $\textit{that}$-Mentioning in English Complement Clauses
Speakers often have multiple ways to express the same meaning. The Uniform Information Density (UID) hypothesis suggests that speakers exploit this variability to maintain a consistent rate of information transmission during language production. Building on prior work linking UID to syntactic reduction, we revisit the finding that the optional complementizer $\textit{that}$in English complement clauses is more likely to be omitted when the clause has low information density (i.e., more predicta…

Magnetically Assisted Separation of Weakly Magnetic Metal Ions in Porous Media.Part 1: Experiments
Alwell Nwachukwu, Muhammad Garba, Jamel Ali, Theo Siegrist, Munir Humayun, Hadi Mohammadigoushki
https://arxiv.org/abs/2510.09360

Magnetically Assisted Separation of Weakly Magnetic Metal Ions in Porous Media.Part 1: Experiments
We report experiments on the magnetophoresis of paramagnetic (MnCl2) and diamagnetic (ZnCl2) metal ions in porous media under the influence of a non-uniform magnetic field generated by a permanent magnet. Experiments were carried out in a range of initial ion concentrations (1-100 mM), porous media particle sizes (63 um and 500 um), and varying mixture ratios of metal ion concentrations. For single-ion magnetophoresis, paramagnetic MnCl2 migrated toward the magnet surface, with an enrichment of…

The p-adic distance of special points to subvarieties
Jos\'e Felipe Voloch
https://arxiv.org/abs/2510.08786 https://arxiv.org/pdf/2510.08786

The p-adic distance of special points to subvarieties
In a paper of Tate and the author, we conjectured a uniform bound for the p-adic distance of torsion points on a semiabelian variety, not lying in a subvariety, to that subvariety. We survey the progress made on that conjecture and on similar statements in analogous situations.

Metric uniform distribution on analytic curves
Vitaly Bergelson, Joel Moreira
https://arxiv.org/abs/2509.06909 https://arxiv.org/pdf/2509.06909

Metric uniform distribution on analytic curves
We obtain multidimensional metric uniform distribution results involving sequences in ${\mathbb R}^k$ parametrized by analytic curves. Our theorems extend the classical theorems of Weyl and Koksma in a variety of ways. One of our main results implies that for any injective sequences $a_1,\dots,a_k:{\mathbb N}\to{\mathbb Z}$ the set $$\Big\{(x_1,\dots,x_k)\in{\mathbb R}^k:\big(a_1(n)x_1,\dots,a_k(n)x_k\big)_{n\in{\mathbb N}}\text{ is uniformly distributed in }{\mathbb T}^k\Big\}$$ has full…

Performance limit of on-chip speckle spectrometers
Bhupesh Kumar, Graham D. Bruce, Luca Dal Negro, Sebastian A. Schulz
https://arxiv.org/abs/2510.09077 https://

Performance limit of on-chip speckle spectrometers
Disorder-driven, integrated speckle spectrometers offer exceptional spectral resolution within a compact design. They benefit from enhanced optical path lengths due to multiple light scattering events, however, often at the cost of low optical throughput. Here, we investigate the relationship between these two figures of merit by systematically varying the scattering strength of random-uniform disorder distributions. Furthermore, we also investigate the temperature stability of such spectromete…

Pareto-optimal Non-uniform Language Generation
Moses Charikar, Chirag Pabbaraju
https://arxiv.org/abs/2510.02795 https://arxiv.org/pdf/2510.02795

Pareto-optimal Non-uniform Language Generation
Kleinberg and Mullainathan (2024) recently proposed an interesting model for language generation in the limit: Given a countable collection of languages, and an adversary enumerating the strings of some language $L$ from the collection, the objective is to generate new strings from the target language, such that all strings generated beyond some finite time are valid. Li, Raman and Tewari (2024) and Charikar and Pabbaraju (2024) showed strong non-uniform generation guarantees in this model, giv…

Perfectly-Private Analog Secure Aggregation in Federated Learning
Delio Jaramillo-Velez, Charul Rajput, Ragnar Freij-Hollanti, Camilla Hollanti, Alexandre Graell i Amat
https://arxiv.org/abs/2509.08683

Perfectly-Private Analog Secure Aggregation in Federated Learning
In federated learning, multiple parties train models locally and share their parameters with a central server, which aggregates them to update a global model. To address the risk of exposing sensitive data through local models, secure aggregation via secure multiparty computation has been proposed to enhance privacy. At the same time, perfect privacy can only be achieved by a uniform distribution of the masked local models to be aggregated. This raises a problem when working with real valued da…

3D Moving-mesh Hydrodynamical Simulations of Wind/Jet Driven Ultraluminous X-ray Source Bubbles
Jiahui Huang, Ken Ohsuga, Hua Feng, Hui Li
https://arxiv.org/abs/2510.09066 https…

3D Moving-mesh Hydrodynamical Simulations of Wind/Jet Driven Ultraluminous X-ray Source Bubbles
We perform 3 dimensional moving-mesh hydrodynamical simulations of bubble nebulae around ultraluminous X-ray sources, using state-of-the-art software AREPO. We use a Monte-Carlo method to inject outflows with uniform mass outflow rate and momentum, in a conical funnel with a specific half opening angle. Simulation results show that the morphology of the bubble is determined by the initial momentum of the outflows, while the mechanical power of the outflows only influences the size of the bubble…

Dallas Cowboys to wear fan-favorite alternate uniform in Week 5 vs Jets https://www.si.com/nfl/cowboys/news/dallas-cowboys-fan-favorite-alternate-uniform-nfl-week-5-new-york-jets

On fundamental properties of high-order forward-backward envelope
Alireza Kabgani, Masoud Ahookhosh
https://arxiv.org/abs/2511.10421 https://arxiv.org/pdf/2511.10421 https://arxiv.org/html/2511.10421
arXiv:2511.10421v1 Announce Type: new
Abstract: This paper studies the fundamental properties of the high-order forward-backward splitting mapping (HiFBS) and its associated forward-backward envelope (HiFBE) through the lens of high-order regularization for nonconvex composite functions. Specifically, we (i) establish the boundedness and uniform boundedness of HiFBS, along with the H\"older and Lipschitz continuity of HiFBE; (ii) derive an explicit form for the subdifferentials of HiFBE; and (iii) investigate necessary and sufficient conditions for the differentiability and weak smoothness of HiFBE under suitable assumptions. By leveraging the prox-regularity of $g$ and the concept of $p$-calmness, we further demonstrate the local single-valuedness and continuity of HiFBS, which in turn guarantee the differentiability of HiFBE in neighborhoods of calm points. This paves the way for the development of gradient-based algorithms tailored to nonconvex composite optimization problems.
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Extremal constructions for apex partite hypergraphs
Qiyuan Chen, Hong Liu, Ke Ye
https://arxiv.org/abs/2510.07997 https://arxiv.org/pdf/2510.07997

Extremal constructions for apex partite hypergraphs
We establish new lower bounds for the Turán and Zarankiewicz numbers of certain apex partite hypergraphs. Given a $(d-1)$-partite $(d-1)$-uniform hypergraph $\mathcal{H}$, let $\mathcal{H}(k)$ be the $d$-partite $d$-uniform hypergraph whose $d$th part has $k$ vertices that share $\mathcal{ H}$ as a common link. We show that $ex(n,\mathcal{H}(k))=Ω_{\mathcal{ H}}(n^{d-\frac{1}{e(\mathcal{H})}})$ if $k$ is at least exponentially large in $e(\mathcal{H})$. Our bound is optimal for all Sidorenko …

Equidistribution of sequences associated with a-points of the derivatives of the Riemann zeta function
Hideki Murahara, Tomokazu Onozuka
https://arxiv.org/abs/2510.07710 https:/…

Equidistribution of sequences associated with a-points of the derivatives of the Riemann zeta function
Fujii investigated the uniform distribution of various sequences associated with the non-trivial zeros of the Riemann zeta function by evaluating certain exponential sums over these zeros. In this paper, we present analogous results for a broader class of functions, establishing the uniform distribution of sequences arising from the $a$-points of the derivatives of the Riemann zeta function.

Refine Drugs, Don't Complete Them: Uniform-Source Discrete Flows for Fragment-Based Drug Discovery
Benno Kaech, Luis Wyss, Karsten Borgwardt, Gianvito Grasso
https://arxiv.org/abs/2509.26405

Refine Drugs, Don't Complete Them: Uniform-Source Discrete Flows for Fragment-Based Drug Discovery
We introduce InVirtuoGen, a discrete flow generative model for fragmented SMILES for de novo and fragment-constrained generation, and target-property/lead optimization of small molecules. The model learns to transform a uniform source over all possible tokens into the data distribution. Unlike masked models, its training loss accounts for predictions on all sequence positions at every denoising step, shifting the generation paradigm from completion to refinement, and decoupling the number of sa…

Predicting when the Cowboys' drama with Micah Parsons might end, plus eight NFL teams just got new uniform

https://www.cbssports.com/nfl/news/predict

Dallas Cowboys to wear fan-favorite alternate uniform in Week 5 vs Jets https://www.si.com/nfl/cowboys/news/dallas-cowboys-fan-favorite-alternate-uniform-nfl-week-5-new-york-jets

Spectral extremal problems for the $(p,Q)$-spectral radius of hypergraphs
Jian Zheng, Honghai Li, Li Su
https://arxiv.org/abs/2510.02776 https://arxiv.org/…

Spectral extremal problems for the $(p,Q)$-spectral radius of hypergraphs
Let $Q$ be an $s$-vertex $r$-uniform hypergraph, and let $H$ be an $n$-vertex $r$-uniform hypergraph. Denote by $\mathcal{N}(Q,H)$ the number of isomorphic copies of $Q$ in $H$. For a hereditary family $\mathcal{P}$ of $r$-uniform hypergraphs, define $$π(Q,\mathcal{P}):=\lim\limits_{n\to \infty}\binom{n}{s}^{-1}\max\{\mathcal{N}(Q,H): H\in \mathcal{P}~~\mbox{and}~~|V(H)|=n\}.$$ For $p\geq1$, the $(p,Q)$-spectral radius of $H$ is defined as $$λ^{(p)}(Q,H):=\max_{\|\mathbf{x}\
…

Cowboys uniform schedule: What version will they wear each week of the 2025 season https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/08/28/cowboys-uniform-schedule-what-version-will-they-w…

Learning What's Missing: Attention Dispersion and EMA Stabilization in Length Generalization
P\'al Zs\'amboki, Benjamin Levi, David Ansel Josef Smith, Mitansh Kagalwala, Arlington Kell, Samuel Liechty, Cong Wang
https://arxiv.org/abs/2510.08341

Learning What's Missing: Attention Dispersion and EMA Stabilization in Length Generalization
We study length generalization in transformers through the set complement task, where a model must predict a uniform distribution over tokens absent from an input sequence -- an ability central to board-game style reasoning. Our main theoretical result establishes two statements. First, we prove tight bounds on embedding and value dimensions for single-layer attention-only transformers. Second, we show that if such a model achieves balanced logit displacement at lengths 1 and 2, then it must ge…

Parity of the partition function in quadratic progressions
Ken Ono
https://arxiv.org/abs/2509.09553 https://arxiv.org/pdf/2509.09553

Parity of the partition function in quadratic progressions
The parity of the partition function $p(n)$ remains strikingly mysterious. Beyond a handful of fragmentary results, essentially nothing is known about the distribution of parity. We prove a uniform result on quadratic progressions. If $1

Spectrum and local weak convergence of sparse random uniform hypergraphs
Kartick Adhikari, Samiron Parui
https://arxiv.org/abs/2509.05102 https://arxiv.org…

Spectrum and local weak convergence of sparse random uniform hypergraphs
The notion of local weak convergence, also known as Benjamini--Schramm convergence, was introduced by Benjamini and Schramm \cite{Benjamini-Schramm-convergence}. It is known that the local weak limit of sparse Erd\H os--Rényi graphs is the Galton--Watson measure with Poisson offspring almost surely. Recently, Adhikari, Kumar and Saha \cite{adhikari2023spectrumrandomsimplicialcomplexes} showed that the local weak limit of the line graph of sparse Linial--Meshulam complexes is the $d$-block Galt…

Uniform Tur\'an density beyond 3-graphs
Ander Lamaison
https://arxiv.org/abs/2508.20696 https://arxiv.org/pdf/2508.20696…

Uniform Turán density beyond 3-graphs
In the 1980s, Erdős and Sós first introduced an extremal problem on hypergraphs with density constraints. Given an $r$-uniform hypergraph $F$ (or $r$-graph for short), its uniform Turán density $π_u(F)$ is the smallest value of $d$ in which every hypergraph $H$ in which every linear-sized subhypergraph of $H$ has edge density at least $d$ contains $F$ as a subgraph. The first non-zero value of $π_u(F)$ was not found until 30 years later. Progress in studying the set of values of the unif…

Property O and Erd\H{o}s--Szekeres properties in linear hypergraphs
Suyun Jiang, Ander Lamaison, Minghui Ouyang
https://arxiv.org/abs/2509.08692 https://ar…

Property O and Erdős--Szekeres properties in linear hypergraphs
An oriented $k$-uniform hypergraph, or oriented $k$-graph, is said to satisfy Property O if, for every linear ordering of its vertex set, there is some edge oriented consistently with this order. The minimum number $f(k)$ of edges in a $k$-graph with Property O was first studied by Duffus, Kay, and Rödl, and later improved by Kronenberg, Kusch, Lamaison, Micek, and Tran. In particular, they established the bounds $k! + 1 \le f(k) \le \left(\lfloor\tfrac{k}{2}\rfloor+1 \right) k! - \lfloor\tfra…