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Interactions between derivatives and fixpoints have many important applications in both computer science and mathematics. In this paper, we provide a categorical framework to combine fixpoints with derivatives by studying Cartesian differential categ
Externí odkaz:
http://arxiv.org/abs/2407.12691
There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical notion of a connection on a module (and similarly, in the tangent cate
Externí odkaz:
http://arxiv.org/abs/2406.15137
Autor:
Lemay, Jean-Simon Pacaud
Cartesian differential categories provide a categorical framework for multivariable differential calculus and also the categorical semantics of the differential $\lambda$-calculus. Taylor series expansion is an important concept for both differential
Externí odkaz:
http://arxiv.org/abs/2405.19474
Autor:
Laura E. Ellestad, Larry A. Cogburn, Jean Simon, Elisabeth Le Bihan-Duval, Samuel E. Aggrey, Mardi S. Byerly, Michel J. Duclos, Tom E. Porter
Publikováno v:
BMC Genomics, Vol 20, Iss 1, Pp 1-21 (2019)
Abstract Background Though intensive genetic selection has led to extraordinary advances in growth rate and feed efficiency in production of meat-type chickens, endocrine processes controlling these traits are still poorly understood. The anterior pi
Externí odkaz:
https://doaj.org/article/81e0fa5ed6024663884c1d15ceff8b45
Drazin inverses are a fundamental algebraic structure which have been extensively deployed in semigroup theory and ring theory. Drazin inverses can also be defined for endomorphisms in any category. However, beyond a paper by Puystjens and Robinson f
Externí odkaz:
http://arxiv.org/abs/2402.18226
Publikováno v:
EPTCS 384, 2023, pp. 171-186
The notion of a Moore-Penrose inverse (M-P inverse) was introduced by Moore in 1920 and rediscovered by Penrose in 1955. The M-P inverse of a complex matrix is a special type of inverse which is unique, always exists, and can be computed using singul
Externí odkaz:
http://arxiv.org/abs/2308.16497
Autor:
Lemay, Jean-Simon Pacaud
Publikováno v:
Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:12278
Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli category of
Externí odkaz:
http://arxiv.org/abs/2308.06859
Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based learning for fun
Externí odkaz:
http://arxiv.org/abs/2308.01131
A Hopf monad, in the sense of Brugui\`eres, Lack, and Virelizier, is a special kind of monad that can be defined for any monoidal category. In this note, we study Hopf monads in the case of a category with finite biproducts, seen as a symmetric monoi
Externí odkaz:
http://arxiv.org/abs/2305.16667