Tootfinder

Implicit Communication in Linear Quadratic Gaussian Control Systems
Gongpu Chen, Deniz Gunduz
https://arxiv.org/abs/2509.16146 https://arxiv.org/pdf/2509.1…

Implicit Communication in Linear Quadratic Gaussian Control Systems
This paper studies implicit communication in linear quadratic Gaussian control systems. We show that the control system itself can serve as an implicit communication channel, enabling the controller to transmit messages through its inputs to a receiver that observes the system state. This communication is considered implicit because (i) no explicit communication channels are needed; and (ii) information is transmitted while simultaneously fulfilling the controller's primary objective--maintaini…

An Algorithm for Computing the Exact Convex Hull in High-Dimensional Spaces
Qianwei Zhuang
https://arxiv.org/abs/2508.14407 https://arxiv.org/pdf/2508.1440…

An Algorithm for Computing the Exact Convex Hull in High-Dimensional Spaces
This study introduces a novel algorithm for computing the convex hull of a point set in high-dimensional Euclidean space. The method iteratively solves a sequence of dynamically updated quadratic programming (QP) problems for each point and leverages the solutions to provide theoretical guarantees for exact convex hull identification. Given $n$ points in an $m$-dimensional space, the algorithm achieves a best-case time complexity of $O(nm^p)$, where $p$ depends on the specific QP solver employe…

Discrete-Time LQ Stochastic Two Person Nonzero Sum Difference Games With Random Coefficients:~Closed-Loop Nash Equilibrium
Qingxin Meng, Yiwei Wu
https://arxiv.org/abs/2507.16412 …

Discrete-Time LQ Stochastic Two Person Nonzero Sum Difference Games With Random Coefficients:~Closed-Loop Nash Equilibrium
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost functionals, leading to a complex structure of fully coupled cross-coupled stochastic Riccati equations (CCREs). The key contributions lie in characterizing the equilibrium via state-feedback strategies derived by decoupling stochastic Hamiltonian systems governe…

Electron charge dynamics and charge separation: A response theory approach
Lionel Lacombe, Lucia Reining, Vitaly Gorelov
https://arxiv.org/abs/2508.14551 https://

Electron charge dynamics and charge separation: A response theory approach
This study applies response theory to investigate electron charge dynamics, with a particular focus on charge separation. We analytically assess the strengths and limitations of linear and quadratic response theories in describing charge density and current, illustrated by a model that simulates charge transfer systems. While linear response accurately captures optical properties, the quadratic response contains the minimal ingredients required to describe charge dynamics and separation. Notabl…

On Runge-Kutta convolution quadrature based fractional variational integrators
Khaled Hariz, Sina Ober-Bl\"obaum, Fernando Jimenez
https://arxiv.org/abs/2510.11082 https://…

On Runge-Kutta convolution quadrature based fractional variational integrators
Lagrangian systems subject to fractional damping can be incorporated into a variational formalism. The construction can be made by doubling the state variables and introducing fractional derivatives \cite{JiOb2}. The main objective of this paper is to use the Runge-Kutta convolution quadrature (RKCQ) method for approximating fractional derivatives, combined with higher order Galerkin methods in order to derive fractional variational integrators (FVIs). We are specially interested in the CQ base…

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen, George Em Karniadakis
https://arxiv.org/abs/2509.14198

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the residual. Different transformations correspond to distinct objective functionals: exponential weights target the minimization of uniform error, while linear weights recover the minimization of quadratic error. Within this perspective, adaptive weighting is equivalen…

Unser zweierlei Maß bei #Enteignung:
Super böse, wenn damit sichere Radwege gebaut werden. Privateigentum ist dann ein hohes Gut.
Super toll, wenn man damit auf der grünen Wiese Neubaugebiete erschließen will.
Im Ort Rastorf beschließt der Rat aus zwei lokalen Listen und CDU einstimmig bei einer Enthaltung ein Enteignungsverfahren, um ein Neubaugebiet zu erschließen, obwohl di…

Enteignung in Rastorf? „Selbst wenn ich 80.000 Euro bekäme, ich wäre nicht käuflich“
Silke Wilde soll ihr Grundstück verkaufen. Die Rastorferin besitzt 267 Quadratmeter auf dem Düsternbrook, über den die Gemeinde ein Baugebiet erschließen möchte. Doch Silke Wilde wehrt sich wie eine Löwin – auch gegen eine mögliche Enteignung.

Monte Carlo quasi-interpolation of spherical data
Zhengjie Sun, Mengyuan Lv, Xingping Sun
https://arxiv.org/abs/2510.12027 https://arxiv.org/pdf/2510.12027…

Monte Carlo quasi-interpolation of spherical data
We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte Carlo quadrature rules to construct easily computable quasi-interpolants, which provide efficient approximation to Sobolev-space functions for both clean and noisy data. To enhance the approximation power and robustness of our quasi-interpolants, we develop a…

Numerical Methods for Kernel Slicing
Nicolaj Rux, Johannes Hertrich, Sebastian Neumayer
https://arxiv.org/abs/2510.11478 https://arxiv.org/pdf/2510.11478…

Numerical Methods for Kernel Slicing
Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear complexity, provided that the kernel can be sliced and its Fourier coefficients are known. To obtain these coefficients, we view the slicing relation as an inverse problem and present two algorithms for their recovery. Extensive numerical experiments demonstrate …

Randomized flexible Krylov methods for $\ell_p$ regularization
Malena Sabat\'e Landman, Yuji Nakatsukasa
https://arxiv.org/abs/2510.11237 https://arxiv…

Randomized flexible Krylov methods for $\ell_p$ regularization
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on constructing a sequence of quadratic tangent majorants of the $\ell_2$-$\ell_1$ regularization functional (with additional smoothing to ensure differentiability at the origin), and solving them successively. Recently, flexible Krylov-Tikhonov methods have been used to …