arXiv preprints from January 1, 2026 through September 23, 2026 — 13:03:55 EST
Automated analyses of privacy policies enable large-scale assessments of transparency in digital ecosystems, yet existing auditing pipelines remain predominantly English-centric. This limits their ability to systematically evaluate multilingual environments, as in the European Union, where many services disclose privacy practices only...
Wireless physical neural networks (WPNNs) embed neural computation directly into analog hardware, offering lower energy consumption and latency than conventional digital implementations. In this paper, we propose a deep WPNN in which nonlinear activations are realized by a multi-hop multiple-input multiple-output (MIMO) relay network,...
With a single clear exception, every NISQ-era flagship demonstration of 'quantum advantage' has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem. Six theoretical results from 2024 through April 2026 explain the pattern: the...
Minimum-variance portfolios are well known to be highly sensitive to covariance estimation error. In this paper, we show that by imposing a block diagonal correlation structure, we can derive closed-form expressions for long-only minimum-variance portfolios that make this fragility explicit. These analytical solutions reveal that...
Let $f$ be the density of the Chernoff random variable $\mathrm{argmax}_{t\in\mathbb{R}}\{W(t)-t^2\}$, where $W$ is a two-sided Brownian motion. This note proves the conjecture of Balabdaoui and Wellner (2014) that $f$ is strongly log-concave. The proof was generated in its entirety by GPT-5.6 Sol.
We study nonlinear parabolic equations with delayed diffusion terms governed by finite signed measure kernels. The atom of the kernel at the origin is absorbed into the present-time operator, while the remaining part is treated as a residual delay kernel. Under structural assumptions on the effective present-time operators and a...
We investigate the integrality property of an arithmetic function defined on the set of odd numbers $n\geq 3$. It is constructed via Bernoulli numbers. As a result, we show that this function unifies three distinct number classes -- primes, Carmichael numbers, and Giuga numbers -- into a single integrality criterion. The article is...
Motivated by the open problem of classifying Hopf $2$-cocycles for affine algebraic reductive groups $G$ over $\mathbb{C}$, in particular by \cite[Question 7.2]{EG1} which concerns minimal Hopf $2$-cocycles, we classify (minimal) Hopf $2$-cocycles for affine algebraic reductive groups $G$ whose connected component of the identity is a...
A Schubert variety $X_0$ on a rational homogenous space $X=G/P$ is said to be homologically rigid, if any subvariety $Z$ on $X$ representing the same homology class with $X_0$ must satisfy $Z=g\cdot X_0$ for some $g\in{\rm Aut_0}(X)$. We say $X_0$ is Schur rigid, if furthermore any subvariety $Z$ on $X$ whose homology class is a...
We construct a smooth projective variety in positive characteristic whose $\mathbb{Q}_{\ell}$-coefficient etale cohomology ring is not the scalar extension of any graded $\mathbb{Q}$-algebra, providing an example of a new type of obstruction to characteristic zero liftability.
Let $G$ be a finite group, let $V$ be a finite-dimensional $G$-module over a field $k$, and let $U$ be a $G$-submodule of $V$. Wehlau conjectured that the corresponding Noether numbers satisfy $β\bigl(k[U]^G\bigr)\leq β\bigl(k[V]^G\bigr)$. We disprove this conjecture in characteristic $2$. For the dihedral group $D_8$, we construct an...
We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers. We show that in embedding dimension two, for any key, query, and value matrices,...
This paper investigates the geometry of foliations on smooth algebraic varieties over an algebraically closed field of arbitrary characteristic $p \ge 0$. We address several specific features of foliations in positive characteristic, aiming to highlight both similarities and differences with the characteristic zero case. First, we...
Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escape path for the infinite unit-strip forest and unit broadworm by Zalgaller. Earlier studies addressed these problems exclusively through geometric methods....
In this paper, we study and characterise the natural embedding of the Ree-Tits octagons. Keywords: Ree-Tits Octagon, Metasymplectic space, generalised octagon, generalised polygon
Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the...
The compressible fluid-solid interaction (FSI) with a thermomechanical phase transition is formulated at large strains within the Eulerian frame. For the deviatoric part, the Jeffreys (also called anti-Zener) rheology with an additional viscosity is adopted. The core philosophy governing the mechanical solid-liquid transition is that...
Researchers often select top-performing options or winners, based on a data-driven criterion, such as treatments, models, or model features and then report effect estimates for the selected winners. Naive post-selection estimates, however, are known to suffer from the winner's curse, producing systematically overoptimistic results. We...
We study doubly reflected backward stochastic differential equations with jumps and two completely separated right-continuous with left limits barriers in a filtration generated by an inhomogeneous Levy process. We establish existence and uniqueness results under a stochastic Lipschitz condition on the driver by means of a...
We study polynomial holomorphic $1$-forms in $\mathbb{C}^2$ that are homologically trivial along the fibers of meromorphic pencils of the form $ φ= \frac{f^p}{g^q}, $ where $f,g$ are holomorphic functions (possibly polynomials) in general position and $(p,q)=1$. We first establish a homological characterization of relative exactness:...
The theorem of Mendel and Naor (2013) associates to every compact metric probability space a large ultrametric subset carrying a probability measure controlled from above on balls by the original measure. Building on Bartal's Ramsey decompositions (2021) and the author's previous proofs of the ultrametric skeleton theorem for doubling...
We construct a vector space whose defining characteristics are rooted in univariate regular variation of random variables. Specifically, the base vector space $\mathbb{V}_b$ consists of random variables whose limiting tail probabilities, when scaled by regularly varying functions of the form $b(s)=s^αL(s)$, are finite. Defining a...
Tarski's geometry of solids reconstructs point-like objects from concentric families of spherical regions rather than taking points as primitive entities. We formalize this reconstruction in Coq within a nominal mereological framework inspired by Lesniewski. The main question is how a regional, point-free geometry can support a...
While the cosmological implications of the Swampland Conjectures are usually discussed in the context of inflationary model building, they also have implications for the violent, non-adiabatic dynamics that can follow inflation or any displacement of string moduli. We study this question through the lens of self-resonant preheating,...
Cosmic strings are not yet confirmed, topological defects formed in the early Universe. They can bend light or gravitational waves, which causes an effect similar to the gravitational lensing. Our goal is to check whether cosmic string could be detected as a lenses of gravitational waves by the Einstein Telescope (ET). To do that the...