Tootfinder

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^{…

Linear-Quadratic Discrete-Time Dynamic Games with Unknown Dynamics
Shengyuan Huang, Xiaoguang Yang, Zhigang Cao, Wenjun Mei
https://arxiv.org/abs/2506.22073

Linear-Quadratic Discrete-Time Dynamic Games with Unknown Dynamics
Considering linear-quadratic discrete-time games with unknown input/output/state (i/o/s) dynamics and state, we provide necessary and sufficient conditions for the existence and uniqueness of feedback Nash equilibria (FNE) in the finite-horizon game, based entirely on offline input/output data. We prove that the finite-horizon unknown-dynamics game and its corresponding known-dynamics game have the same FNEs, and provide detailed relationships between their respective FNE matrices. To simplify …

Cooperative Circumnavigation for Multi-Quadrotor Systems via Onboard Sensing
Xueming Liu, Lin Li, Xiang Zhou, Qingrui Zhang, Tianjiang Hu
https://arxiv.org/abs/2506.20954

Cooperative Circumnavigation for Multi-Quadrotor Systems via Onboard Sensing
A cooperative circumnavigation framework is proposed for multi-quadrotor systems to enclose and track a moving target without reliance on external localization systems. The distinct relationships between quadrotor-quadrotor and quadrotor-target interactions are evaluated using a heterogeneous perception strategy and corresponding state estimation algorithms. A modified Kalman filter is developed to fuse visual-inertial odometry with range measurements to enhance the accuracy of inter-quadrotor …

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…

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

An Efficient Class of Bayesian Generalized Quadratic Nonlinear Dynamic Models with Application to Birth Rate Monitoring
Madelyn Clinch, Jonathan R. Bradley
https://arxiv.org/abs/2506.22188

An Efficient Class of Bayesian Generalized Quadratic Nonlinear Dynamic Models with Application to Birth Rate Monitoring
Many real-world spatio-temporal processes exhibit nonlinear dynamics that can often be described through stochastic partial differential equations. These models are flexible and scientifically motivated, however, implementing them in a fully Bayesian framework can be computationally challenging. We are motivated by birth rate data, which has important implications for public health and are known to follow nonlinear dynamics. We propose a covariance calibration strategy that specifies the covari…

Die Stadt #BadWünnenberg verlängert ihr #Förderprogramm für #Klimaschutz bis Ende 2025.
Bürgerinnen und Bürger erhalten bis zu 2.500 Euro für Maßnahmen wie

Stadt Bad Wünnenberg verlängert Förderprogramm für Klimaschutzmaßnahmen - Bad Wünnenberg
Auch im Jahr 2025 unterstützt die Stadt Bad Wünnenberg gezielt Maßnahmen zum Klimaschutz. Insgesamt stehen erneut 25.000 Euro zur Verfügung, um Bürgerinnen und Bürger zu motivieren, aktiv zur Reduzierung von Treibhausgasen und zur Anpassung an die Folgen des Klimawandels beizutragen. Die Förderrichtlinie wurde überarbeitet und inhaltlich erweitert – unter anderem wurde der Zuschuss für Gründächer und Fassadenbegrünung auf 20 Euro pro Quadratmeter erhöht.

Quasi-triangular and factorizable Poisson bialgebras
Yuanchang Lin, Dilei Lu
https://arxiv.org/abs/2506.21870 https://arxiv.org/pdf/2…

Quasi-triangular and factorizable Poisson bialgebras
In this paper, we introduce the notions of quasi-triangular and factorizable Poisson bialgebras. A factorizable Poisson bialgebra induces a factorization of the underlying Poisson algebra. We prove that the Drinfeld classical double of a Poisson bialgebra naturally admits a factorizable Poisson bialgebra structure. Furthermore, we introduce the notion of quadratic Rota-Baxter Poisson algebras and show that a quadratic Rota-Baxter Poisson algebra of zero weight induces a triangular factorizable …

Mean squares of quadratic twists of the Fourier coefficients of modular forms
Peng Gao, Yuetong Zhao
https://arxiv.org/abs/2506.22256 https://

Mean squares of quadratic twists of the Fourier coefficients of modular forms
In this paper, we evaluate asymptotically a smoothed version of the sum \[ \displaystyle \sideset{}{^*}\sum_{d \leq X} \left( \sum_{n \leq Y} λ_f(n)\Big(\frac{8d}{n}\Big)\right)^2, \] where $\Big ( \frac{8d}{\cdot}\Big )$ is the Kronecker symbol, $\sideset{}{^*}\sum$ denotes a sum over positive odd square-free integers and $λ_f(n)$ are Fourier coefficients of a given modular form $f$.

Rational connectedness for groups of proper projective similitudes
M. Archita, Karim Johannes Becher
https://arxiv.org/abs/2506.21717 https://

Rational connectedness for groups of proper projective similitudes
For a quadratic form $φ$ over a field of characteristic different from $2$, we study whether its group of proper projective similitudes ${\bf PSim}^+(φ)$ is rationally connected (i.e. $R$-trivial). We obtain new sufficient conditions in terms of structure properties of $φ$. We further provide new examples of quadratic forms $φ$ belonging to a given power of the fundamental ideal in the Witt ring and such that ${\bf PSim}^+(φ)$ is not rationally connected.