8,597 research outputs found

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

When $G$ is an arbitrary group and $V$ is a finite-dimensional vector space,
it is known that every bijective linear cellular automaton $\tau \colon V^G \to
V^G$ is reversible and that the image of every linear cellular automaton $\tau
\colon V^G \to V^G$ is closed in $V^G$ 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 $G$
is a non-periodic group and $V$ is an infinite-dimensional vector space, then
there exist a linear cellular automaton $\tau_1 \colon V^G \to V^G$ which is
bijective but not reversible and a linear cellular automaton $\tau_2 \colon V^G
\to V^G$ whose image is not closed in $V^G$ for the prodiscrete topology

### Neuromodulation

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

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

We finish the proof of the conjecture of F. Bogomolov and F. Pop: Let $F_{1}$
and $F_{2}$ be fields finitely-generated and of transcendence degree $\geq 2$
over $k_{1}$ and $k_{2}$, respectively, where $k_{1}$ is either
$\bar{\mathbb{Q}}$ or $\bar{\mathbb{F}}_{p}$, and $k_{2}$ is algebraically
closed. We denote by $G_{F_1}$ and $G_{F_2}$ 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 $F_1$ and $F_2$ to
continuous outer isomorphisms of their Galois groups is a bijection. Thus,
function fields of varieties of dimension $\geq 2$ 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 $\bar{\mathbb{Q}}$.Comment: 30 pages, comments welcome

### Expansive actions on uniform spaces and surjunctive maps

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 $\Gamma$ and any field \K, the
space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is
stably finite is compact.Comment: 21 page

### Optimal Binary Locally Repairable Codes via Anticodes

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

- …