8,597 research outputs found

    On the reversibility and the closed image property of linear cellular automata

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    When GG is an arbitrary group and VV is a finite-dimensional vector space, it is known that every bijective linear cellular automaton τ ⁣:VGVG\tau \colon V^G \to V^G is reversible and that the image of every linear cellular automaton τ ⁣:VGVG\tau \colon V^G \to V^G is closed in VGV^G for the prodiscrete topology. In this paper, we present a new proof of these two results which is based on the Mittag-Leffler lemma for projective sequences of sets. We also show that if GG is a non-periodic group and VV is an infinite-dimensional vector space, then there exist a linear cellular automaton τ1 ⁣:VGVG\tau_1 \colon V^G \to V^G which is bijective but not reversible and a linear cellular automaton τ2 ⁣:VGVG\tau_2 \colon V^G \to V^G whose image is not closed in VGV^G for the prodiscrete topology


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    Neuromodulation is a new promising treatment for headache disorders. It consists of peripheral nerve neurostimulation and central neurostimulation. © 2016, Touch Briefings. All rights reserved

    Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions

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    A language L over a finite alphabet is growth-sensitive (or entropy sensitive) if forbidding any set of subwords F yields a sub-language L^F whose exponential growth rate (entropy) is smaller than that of L. Let (X, E, l) be an infinite, oriented, labelled graph. Considering the graph as an (infinite) automaton, we associate with any pair of vertices x,y in X the language consisting of all words that can be read as the labels along some path from x to y. Under suitable, general assumptions we prove that these languages are growth-sensitive. This is based on using Markov chains with forbidden transitions.Comment: to appear in Theoretical Computer Science, 201

    Anabelian Intersection Theory I: The Conjecture of Bogomolov-Pop and Applications

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    We finish the proof of the conjecture of F. Bogomolov and F. Pop: Let F1F_{1} and F2F_{2} be fields finitely-generated and of transcendence degree 2\geq 2 over k1k_{1} and k2k_{2}, respectively, where k1k_{1} is either Qˉ\bar{\mathbb{Q}} or Fˉp\bar{\mathbb{F}}_{p}, and k2k_{2} is algebraically closed. We denote by GF1G_{F_1} and GF2G_{F_2} their respective absolute Galois groups. Then the canonical map \varphi_{F_{1}, F_{2}}: \Isom^i(F_1, F_2)\rightarrow \Isom^{\Out}_{\cont}(G_{F_2}, G_{F_1}) from the isomorphisms, up to Frobenius twists, of the inseparable closures of F1F_1 and F2F_2 to continuous outer isomorphisms of their Galois groups is a bijection. Thus, function fields of varieties of dimension 2\geq 2 over algebraic closures of prime fields are anabelian. We apply this to give a necessary and sufficient condition for an element of the Grothendieck-Teichm\"uller group to be an element of the absolute Galois group of Qˉ\bar{\mathbb{Q}}.Comment: 30 pages, comments welcome

    Expansive actions on uniform spaces and surjunctive maps

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    We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group Γ\Gamma and any field \K, the space of Γ\Gamma-marked groups GG such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

    Optimal Binary Locally Repairable Codes via Anticodes

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    This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes. It provides binary LRCs which attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal with respect to the Griesmer bound