Tootfinder

Generalized moment maps, reduction and complex quotients
Yi Hu, Xiangsheng Wang
https://arxiv.org/abs/2508.07168 https://arxiv.org/pdf/2508.07168

Generalized moment maps, reduction and complex quotients
In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of moment maps within this broader framework. More specifically, we establish the convexity property of the generalized moment map, construct the corresponding reduction space, and analyze the Kirwan-Ness stratification. Additionally, we prove a variant of the …

Tram Positioning with Map-Enabled GNSS Data Reconciliation
Jakub Ka\v{s}par, V\'it Fanta, Vladim\'ir Havlena
https://arxiv.org/abs/2506.08032 https…

Tram Positioning with Map-Enabled GNSS Data Reconciliation
This paper presents an approach to tackle the problem of tram localization through utilizing a custom processing of Global Navigation Satellite System (GNSS) observables and the track map. The method is motivated by suboptimal performance in dense urban environments where the direct line of sight to GNSS satellites is often obscured which leads to multipath propagation of GNSS signals. The presented concept is based upon the iterated extended Kalman filter (IEKF) and has linear complexity (with…

Behaviorally Adaptive Multi-Robot Hazard Localization in Failure-Prone, Communication-Denied Environments
Alkesh K. Srivastava, Aamodh Suresh, Carlos Nieto-Granda
https://arxiv.org/abs/2508.04537

Behaviorally Adaptive Multi-Robot Hazard Localization in Failure-Prone, Communication-Denied Environments
We address the challenge of multi-robot autonomous hazard mapping in high-risk, failure-prone, communication-denied environments such as post-disaster zones, underground mines, caves, and planetary surfaces. In these missions, robots must explore and map hazards while minimizing the risk of failure due to environmental threats or hardware limitations. We introduce a behavior-adaptive, information-theoretic planning framework for multi-robot teams grounded in the concept of Behavioral Entropy (B…

Iterative Methods for the Projected Solutions of Quasi-equilibrium Problems
Didier Aussel, Jauny, Asrifa Sultana, Shivani Valecha
https://arxiv.org/abs/2506.22080

Iterative Methods for the Projected Solutions of Quasi-equilibrium Problems
Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the feasible set. This paper presents two iterative methods to determine the projected solutions for quasi-equilibrium problems (QEP). We prove the convergence of the sequence generated by iterative methods to a projected solution of the QEP under some suitable …

Learning Truthful Mechanisms without Discretization
Yunxuan Ma, Siqiang Wang, Zhijian Duan, Yukun Cheng, Xiaotie Deng
https://arxiv.org/abs/2506.22911 http…

Learning Truthful Mechanisms without Discretization
This paper introduces TEDI (Truthful, Expressive, and Dimension-Insensitive approach), a discretization-free algorithm to learn truthful and utility-maximizing mechanisms. Existing learning-based approaches often rely on discretization of outcome spaces to ensure truthfulness, which leads to inefficiency with increasing problem size. To address this limitation, we formalize the concept of pricing rules, defined as functions that map outcomes to prices. Based on this concept, we propose a novel …

Rota-Baxter operators on compact simple Lie groups and algebras
Saveliy V. Skresanov
https://arxiv.org/abs/2506.14324 https://arxiv.o…

Rota-Baxter operators on compact simple Lie groups and algebras
A Rota-Baxter operator on a Lie group $ G $ is a smooth map $ B : G \to G $ such that $ B(g)B(h) = B(gB(g)hB(g)^{-1}) $ for all $ g, h \in G $. This concept was introduced in 2021 by Guo, Lang and Sheng as a Lie group analogue of Rota-Baxter operators of weight 1 on Lie algebras. We show that the only Rota-Baxter operators on compact simple Lie groups are the trivial map and the inverse map. A similar description for Rota-Baxter operators of weight 1 on compact simple Lie algebras is provided.

Finite-time scaling on low-dimensional map bifurcations
Daniel A. Martin, Qian-Yuan Tang, Dante R. Chialvo
https://arxiv.org/abs/2505.24673 https://…

Finite-time scaling on low-dimensional map bifurcations
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in finite systems. In this work, we extend the finite-time scaling approach in several key directions. First, we present numerical results for 1D maps exhibiting period-doubling bifurcations and discontinuous transitions, analyzing selected paradigmatic examples.…

Web Diagrams of Cluster Variables for Grassmannian Gr(4,8)
Wen Ting Zhang, Rui Zhi Tang, Jin Xing Zhao
https://arxiv.org/abs/2507.18432 https://arxiv.org/p…

Web Diagrams of Cluster Variables for Grassmannian Gr(4,8)
Gaetz, Pechenik, Pfannerer, Striker, and Swanson introduced the concept of hourglass plabic graphs and provided a method for computing web diagrams and invariants corresponding to $4\times n$ Young tableaux, while Elkin, Musiker, and Wright applied Lam's method to explicitly compute the webs compatible with cluster variables in Gr(3,n) and their twists, namely, the preimages of the immanant map introduced by Fraser, Lam, and Le. In this paper, we use these two methods to compute both the web di…

Piecewise Deterministic Sampling for Constrained Distributions
Jo\"el Tatang Demano, Paul Dobson, Konstantinos Zygalakis
https://arxiv.org/abs/2508.05462 https://

Piecewise Deterministic Sampling for Constrained Distributions
In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMP) that are designed to sample from constrained probability distributions $π$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of a mirror map from convex optimisation to address sampling problems. Such samplers provides unbiased algorithms that respect the constraints and, moreover, allow for exact subsampling. We demonstrate the advantages of these algorithms on a range of c…