Tootfinder

Policy-Based Trajectory Clustering in Offline Reinforcement Learning
Hao Hu, Xinqi Wang, Simon Shaolei Du
https://arxiv.org/abs/2506.09202 https://

Policy-Based Trajectory Clustering in Offline Reinforcement Learning
We introduce a novel task of clustering trajectories from offline reinforcement learning (RL) datasets, where each cluster center represents the policy that generated its trajectories. By leveraging the connection between the KL-divergence of offline trajectory distributions and a mixture of policy-induced distributions, we formulate a natural clustering objective. To solve this, we propose Policy-Guided K-means (PG-Kmeans) and Centroid-Attracted Autoencoder (CAAE). PG-Kmeans iteratively trains…

This https://arxiv.org/abs/2304.07859 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
In 1970, Schneider introduced the $m$th order difference body of a convex body, and also established the $m$th-order Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radial mean bodies, as well as prove the associated inequalities (analogues of Zhang's projection inequality, Petty's projection inequality, the Busemann-Petty centroid inequality and Busemann's random simplex inequality). We also establish a new proof of Schneider's $m$th-or…

This https://arxiv.org/abs/2412.14844 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Astrometry-Only Detection of Microlensing Events with Gaia
Astrometric microlensing events occur when a massive object passes between a distant source and the observer, causing a shift of the light centroid. The precise astrometric measurements of the Gaia mission provide an unprecedented opportunity to detect and analyze these events, revealing properties of lensing objects such as their mass and distance. We develop and test the Gaia Astrometric Microlensing Events (GAME) Filter, a software tool to identify astrometric microlensing events and derive …

Focused axisymmetric spatially chirped beams
Eric C. Nelson, Kyle J. Charbonnet, Haytham H. Effarah, Trevor Reutershan, Kyle D. Chesnut, Christopher P. J. Barty
https://arxiv.org/abs/2505.24817

Focused axisymmetric spatially chirped beams
A characterization of the focused space-time structures of radially chirped beams is provided, detailing different tunable properties such as: variable on-axis centroid velocity, symmetric pulse front tilt, transverse intensity modulations, and polarization states. While the practical generation of ideal radially chirped beams and polarizations can be problematic, it is shown that the primary characteristics of these beams can be mimicked with simple arrays of axisymmetric, 1D spatially chirped…

Generalized derivations of Complex $\omega$-Lie Superalgebras
Jia Zhou
https://arxiv.org/abs/2505.22966 https://arxiv.org/pdf/2505.22…

Generalized derivations of Complex $ω$-Lie Superalgebras
~Let $(g,~[-,-],~ω)$ be a finite-dimensional complex $ω$-Lie superalgebra. This paper explores the algbaraic structures of generalized derivation superalgebra ${\rm GDer}(g)$, compatatible generalized derivations algebra ${\rm GDer}^ω(g)$, and their subvarieties such as quasiderivation superalgebra ${\rm QDer}(g)$(${\rm QDer}^ω(g)$), centroid ${\rm Cent}(g)$ (${\rm Cent}^ω(g)$) and quasicentroid ${\rm QCent}(g)$ (${\rm QCent}^ω(g)$). We prove that ${\rm GDer}^ω(g) = {\rm QDer}^ω(g) + {\…