Tootfinder

This https://arxiv.org/abs/2502.18284 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Nested Expectations with Kernel Quadrature
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then dem…

AFP: Russen nahmen im Mai viel Territorium ein
Die russischen Streitkräfte haben im Mai ihren Vormarsch in der Ukraine beschleunigen können. Dies geht aus Berechnungen der Nachrichtenagentur AFP mit Bezug auf Daten des in den USA ansässigen Instituts für Kriegsstudien (ISW) hervor. Demnach besetzte Russland im vergangenen Monat 507 Quadratkilometer. Alleine in der ostukrainischen Region Donezk sollen es fast 400 Quadratkilome…
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Ukraine-Liveblog: ++ Wadephul: Müssen Druck aufrechterhalten ++
Bundesaußenminister Wadephul hat nach einem Treffen mit US-Senator Graham eine gemeinsame harte Linie gegenüber Russlands Präsidenten Putin betont. Friedensforscher mahnen eine Verteidigungsstrategie für Europa an.

Isotopisms of quadratic quasigroups
Jack Allsop
https://arxiv.org/abs/2506.02446 https://arxiv.org/pdf/2506.02446

Isotopisms of quadratic quasigroups
A quasigroup is a pair $(Q, \cdot)$ where $Q$ is a non-empty set and $\cdot$ is a binary operation on $Q$ such that for every $(u, v) \in Q^2$ there exists a unique $(x, y) \in Q^2$ such that $u \cdot x = v = y \cdot u$. Let $q$ be an odd prime power, let $\mathbb{F}_q$ denote the finite field of order $q$, and let $\mathcal{R}_q$ denote the set of non-zero squares in $\mathbb{F}_q$. Let $\{a, b\} \subseteq \mathbb{F}_q$ be such that $\{ab, (a-1)(b-1)\} \subseteq \mathcal{R}_q$. Let $\mathcal{Q…

This https://arxiv.org/abs/2409.15683 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum DeepONet: Neural operators accelerated by quantum computing
In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as deep operator network (DeepONet), which learn mappings between infinite-dimensional function spaces, promise efficient computation of PDE solutions for a new condition in a single forward pass. However, classical DeepONet entails quadratic complexity concerni…

Nachbarin mäht schon wieder ihr Handtuch, obwohl alles dürr ist. Sie können und vor allem wollen es nicht verstehen. Alles muss ordentlich und praktisch-quadratisch sein. Nein, das ist eben nicht gut. Vielleicht auch purer Protest, weil wir die Wiese, auf die sie blicken stehen lassen. Von #MähfreierMai haben sie zwar gehört, ignorieren es aber ganz bewusst. Auch den Aufruf der Stadt

On the original Ulam's problem and its quantization
Changguang Dong, Jing Zhou
https://arxiv.org/abs/2506.01684 https://arxiv.org…

On the original Ulam's problem and its quantization
In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include …

Gaps between quadratic forms
Siddharth Iyer
https://arxiv.org/abs/2505.23428 https://arxiv.org/pdf/2505.23428

Gaps between quadratic forms
Let $\triangle$ denote the integers represented by the quadratic form $x^2+xy+y^2$ and $\square_{2}$ denote the numbers represented as a sum of two squares. For a non-zero integer $a$, let $S(\triangle,\square_{2},a)$ be the set of integers $n$ such that $n \in \triangle$, and $n + a \in \square_{2}$. We conduct a census of $S(\triangle,\square_{2},a)$ in short intervals by showing that there exists a constant $H_{a} > 0$ with \begin{align*} \# S(\triangle,\square_{2},a)\cap [x,x+H_{a}\cdot x^{…

On the quadratic 8-edge case of the Brown-Erd\H{o}s-S\'os problem
Oleg Pikhurko, Shumin Sun
https://arxiv.org/abs/2506.01739 https://

On the quadratic 8-edge case of the Brown-Erdős-Sós problem
Let $f^{(r)}(n;s,k)$ be the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no $k$ edges on at most $s$ vertices. Brown, Erdős and Sós conjectured in 1973 that the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(3)}(n;k+2,k)$ exists for all $k$. Recently, Delcourt and Postle settled the conjecture and their approach was generalised by Shangguan to every uniformity $r\ge 4$: the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(r)}(n;rk-2k+2,k)$ exists for all $r\ge 3$ and $k\ge…

This https://arxiv.org/abs/2405.19380 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Approximate Thompson Sampling for Learning Linear Quadratic Regulators with $O(\sqrt{T})$ Regret
We propose a novel Thompson sampling algorithm that learns linear quadratic regulators (LQR) with a Bayesian regret bound of $O(\sqrt{T})$. Our method leverages Langevin dynamics with a carefully designed preconditioner and incorporates a simple excitation mechanism. We show that the excitation signal drives the minimum eigenvalue of the preconditioner to grow over time, thereby accelerating the approximate posterior sampling process. Furthermore, we establish nontrivial concentration propertie…

This https://arxiv.org/abs/2502.00168 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction
Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Directly computing discriminability is often impractical, so an alternative approach is to learn features that maximize a distance or dissimilarity measure between classes. The Fisher-Rao distance is an important information geometry distance in statistical manifolds. It is induced by the Fisher information metric, a tool widely used for understanding neural r…