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pro vyhledávání: '"Mumford, David"'
Autor:
Mumford, David
Neural nets, one of the oldest architectures for AI programming, are loosely based on biological neurons and their properties. Recent work on language applications has made the AI code closer to biological reality in several ways. This commentary exa
Externí odkaz:
http://arxiv.org/abs/2010.09101
Publikováno v:
Forum of Mathematics, Sigma 2, e19, 38 pages, 2014
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as
Externí odkaz:
http://arxiv.org/abs/1312.4995
Autor:
Michor, Peter W., Mumford, David
Publikováno v:
Annals of Global Analysis and Geometry 44, 4 (2013), 529-540
We consider the groups $\operatorname{Diff}_{\mathcal B}(\mathbb R^n)$, $\operatorname{Diff}_{H^\infty}(\mathbb R^n)$, and $\operatorname{Diff}_{\mathcal S}(\mathbb R^n)$ of smooth diffeomorphisms on $\mathbb R^n$ which differ from the identity by a
Externí odkaz:
http://arxiv.org/abs/1211.5704