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 …

Bi-Equivariant Extensions Of Maps
Pavel S. Gevorgyan
https://arxiv.org/abs/2509.08616 https://arxiv.org/pdf/2509.08616

Bi-Equivariant Extensions Of Maps
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps is proven. A theorem on the bi-equivariant extension of continuous maps defined on the cross sections of a distributive binary $G$-space is also proven.

Multi-Ontology Integration with Dual-Axis Propagation for Medical Concept Representation
Mohsen Nayebi Kerdabadi, Arya Hadizadeh Moghaddam, Dongjie Wang, Zijun Yao
https://arxiv.org/abs/2508.21320

Multi-Ontology Integration with Dual-Axis Propagation for Medical Concept Representation
Medical ontology graphs map external knowledge to medical codes in electronic health records via structured relationships. By leveraging domain-approved connections (e.g., parent-child), predictive models can generate richer medical concept representations by incorporating contextual information from related concepts. However, existing literature primarily focuses on incorporating domain knowledge from a single ontology system, or from multiple ontology systems (e.g., diseases, drugs, and proce…

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…

Generative Large Language Models for Knowledge Representation: A Systematic Review of Concept Map Generation
Xiaoming Zhai
https://arxiv.org/abs/2509.14554 https://

Generative Large Language Models for Knowledge Representation: A Systematic Review of Concept Map Generation
The rise of generative large language models (LLMs) has opened new opportunities for automating knowledge representation through concept maps, a long-standing pedagogical tool valued for fostering meaningful learning and higher-order thinking. Traditional construction of concept maps is labor-intensive, requiring significant expertise and time, limiting their scalability in education. This review systematically synthesizes the emerging body of research on LLM-enabled concept map generation, foc…

Them: Cycle A-To-B, fast and efficient
Me: I reject the entire concept. The journey is the point.
#TallBike

Sheffer Polynomials and the s-ordering of Exponential Boson Operators
Robert S. Maier
https://arxiv.org/abs/2508.13094 https://arxiv.org/pdf/2508.13094

Sheffer Polynomials and the s-ordering of Exponential Boson Operators
The s-ordered form of any product of single-mode boson creation and annihilation operators, containing only a single annihilator, is computed explicitly. The s-ordering concept originated in quantum optics, and subsumes normal, symmetric (Weyl), and anti-normal ordering for any two operators satisfying a canonical commutation relation. Because the s-ordering map can be viewed as producing a function of a complex variable, its inverse is a quantization map that takes such "classical" functions t…

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…

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…

SU(4) Kondo Lattice in Semiconductor Moir\'e Materials
Sunghoon Kim
https://arxiv.org/abs/2509.18247 https://arxiv.org/pdf/2509.18247

Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
Baptiste Klein, Suzanne Aigrain, Michael Cretignier, Xavier Dumusque, Khaled Al Moulla, Jean-Fran\c{c}ois Donati, Niamh K. O'Sullivan, Haochuan Yu, Andrew Collier Cameron, Oscar Barrag\'an, Annelies Mortier, Alessandro Sozzetti
https://arxi…

Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
Doppler Imaging (DI) is a well-established technique to map a physical field at a stellar surface from a time series of high-resolution spectra. In this proof-of-concept study, we aim to show that traditional DI algorithms, originally designed for rapidly-rotating stars, have also the ability to model the activity of Sun-like stars, when observed with new-generation highly-stable spectrographs, and search for low-mass planets around them. We used DI to retrieve the relative brightness distribut…