3,925 research outputs found
Post-surjectivity and balancedness of cellular automata over groups
We discuss cellular automata over arbitrary finitely generated groups. We
call a cellular automaton post-surjective if for any pair of asymptotic
configurations, every pre-image of one is asymptotic to a pre-image of the
other. The well known dual concept is pre-injectivity: a cellular automaton is
pre-injective if distinct asymptotic configurations have distinct images. We
prove that pre-injective, post-surjective cellular automata are reversible.
Moreover, on sofic groups, post-surjectivity alone implies reversibility. We
also prove that reversible cellular automata over arbitrary groups are
balanced, that is, they preserve the uniform measure on the configuration
space.Comment: 16 pages, 3 figures, LaTeX "dmtcs-episciences" document class. Final
version for Discrete Mathematics and Theoretical Computer Science. Prepared
according to the editor's request
Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties
The goal of this survey is to describe some recent results concerning the L 2
extension of holomorphic sections or cohomology classes with values in vector
bundles satisfying weak semi-positivity properties. The results presented here
are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow
many techniques from the long series of papers by T. Ohsawa. The recent
achievement that we want to point out is that the surjectivity property holds
true for restriction morphisms to non necessarily reduced subvarieties,
provided these are defined as zero varieties of multiplier ideal sheaves. The
new idea involved to approach the existence problem is to make use of L 2
approximation in the Bochner-Kodaira technique. The extension results hold
under curvature conditions that look pretty optimal. However, a major unsolved
problem is to obtain natural (and hopefully best possible) L 2 estimates for
the extension in the case of non reduced subvarieties -- the case when Y has
singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292,
arXiv:1510.0523
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