Tootfinder

This https://arxiv.org/abs/2008.11180 has been replaced.
link: https://scholar.google.com/scholar?q=a

Weakly globular double categories and weak units
Weakly globular double categories are a model of weak $2$-categories based on the notion of weak globularity, and they are known to be suitably equivalent to Tamsamani $2$-categories. Fair $2$-categories, introduced by J. Kock, model weak $2$-categories with strictly associative compositions and weak unit laws. In this paper we establish a direct comparison between weakly globular double categories and fair $2$-categories and prove they are equivalent after localisation with respect to the $2$-…

Synthesis of Robust Optimal Strategies in Weighted Timed Games
Benjamin Monmege, Julie Parreaux, Pierre-Alain Reynier
https://arxiv.org/abs/2403.06921 http…

Synthesis of Robust Optimal Strategies in Weighted Timed Games
Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. The synthesized strategies rely on a perfect measure of time elapse, which is not realistic in practice. In order to produce strategies tolerant to timing imprecisions, we rely on a notion of robustness first introduced for timed automata. More precisely, WTGs are two-player zero-sum games played in a timed automaton equipped with integer weights in which one…

This https://arxiv.org/abs/2403.14458 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Self-distributive structures in physics
It is an important feature of our existing physical theories that observables generate one-parameter groups of transformations. In classical Hamiltonian mechanics and quantum mechanics, this is due to the fact that the observables form a Lie algebra, and it manifests itself in Noether's theorem. In this paper, we introduce Lie quandles as the minimal mathematical structure needed to express the idea that observables generate transformations. This is based on the notion of a quandle used most fa…

What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly
Tom Hanika, Tobias Hille
https://arxiv.org/abs/2404.06326 …

What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly
Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized correlation dimension. In the present work we revisit their results and contrast them with a concept based notion of intrinsic dimension (ID) recently introduced for geometric data sets. To do this, we present a novel approximation for this ID that is based on c…

This https://arxiv.org/abs/2402.16495 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Representations and cohomology of a matched pair of Lie algebras, and $L_\infty$-algebras
The notion of a matched pair of Lie algebras was introduced in the study of Lie bialgebras and Poisson-Lie groups. In this paper, we introduce representations and cohomology of a matched pair of Lie algebras. We show that there is a morphism from the cohomology of a Lie bialgebra to the cohomology of the corresponding matched pair of Lie algebras. Our cohomology is also useful to study infinitesimal deformations and abelian extensions. In the last part, we define the notion of a matched pair of…

This https://arxiv.org/abs/2002.02005 has been replaced.
link: https://scholar.google.com/scholar?q=a

On hybrid order dimension
The notion of interval order was introduced by Norbert Wiener \cite{wie} in order to clarify the relation between the notion of an instant of time and that of a period of time. This was a problem on which Bertrand Russell \cite{rus} worked at the time. Interval orders play an important role in many areas of pure and applied mathematics, graph theory, computer science and engineering. Special cases of interval order are the semiorder and linear order. All of these notions are especially importan…

This https://arxiv.org/abs/2311.18095 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On non-archimedean frames
In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that constitutes a tree to each non-archimedean frame, and then we observe that every non-archimedean frame is a quotient of the frame of opens of the tree's branch space. Moreover, we give a partial answer to when these frames are canonically isomorphic; this leads…

This https://arxiv.org/abs/2307.15075 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Manin triples associated to $n$-Lie bialgebras
In this paper, we study the Manin triples associated to $n$-Lie bialgebras. We introduce the concept of operad matrices for $n$-Lie bialgebras. In particular, by studying a special case of operad matrices, it leads to the notion of local cocycle $n$-Lie bialgebras. Furthermore, we establish a one-to-one correspondence between the double of $n$-Lie bialgebras and Manin triples of $n$-Lie algebras.

This https://arxiv.org/abs/2312.03263 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Weathering Ongoing Uncertainty: Learning and Planning in a Time-Varying Partially Observable Environment
Optimal decision-making presents a significant challenge for autonomous systems operating in uncertain, stochastic and time-varying environments. Environmental variability over time can significantly impact the system's optimal decision making strategy for mission completion. To model such environments, our work combines the previous notion of Time-Varying Markov Decision Processes (TVMDP) with partial observability and introduces Time-Varying Partially Observable Markov Decision Processes (TV-…

This https://arxiv.org/abs/2311.03647 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

An algebraic formulation of nonassociative quantum mechanics
We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop GNS construction…