Related papers: Invariant measures for bipermutative cellular auto…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…
In this article we completely characterise constant length substitution shifts which have an almost automorphic factor, or which have a bijective substitution factor. Our approach is algebraic: we study these dynamical properties in terms…
Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively…
We consider a complete metric space $(X,d)$ and a countable number of contractive mappings on $X$, $\mathcal{F}=\{F_i:i\in\mathbb N\}$. We show the existence of a {\em smallest} invariant set (with respect to inclusion) for $\mathcal{F}$.…
If $G$ is a locally compact groupoid with a Haar system $\lambda$, then a positive definite function $p$ on $G$ has a form $p(x)=< L(x)\xi(d(x)),\xi(r(x))>$, where $L$ is a representation of $G$ on a Hilbert bundle ${\h}=(G^0,\{H_u\},\mu)$,…
For a second countable locally compact group $G$ and a closed abelian subgroup $H$, we give a range function classification of closed subspaces in $L^2(G)$ invariant under left translation by $H$. For a family $\mathscr{A} \subset L^2(G)$,…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
Gottschalk's surjunctivity conjecture for a group $G$ states that it is impossible for cellular automata (CA) over the universe $G$ with finite alphabet to produce strict embeddings of the full shift into itself. A group universe $G$…
We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts $S_\beta$. We show that any reversible CA $F:S_\beta\to S_\beta$ has an almost equicontinuous direction whenever $S_\beta$ is not sofic. This has…
Cellular automata are a famous model of computation, yet it is still a challenging task to assess the computational capacity of a given automaton; especially when it comes to showing negative results. In this paper, we focus on studying…
A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority…
This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation…
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…
Let $G$ be a subgroup of $\text{Homeo}_+(\mathbb{R})$ without crossed elements. We show the equivalence among three items: (1) existence of $G$-invariant Radon measures on $\mathbb R$; (2) existence of minimal closed subsets of $\mathbb R$;…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Let $U$ be a compact semisimple Lie group with complexification $G$ and associated Cartan involution $\Theta$. Let $\nu$ be an involutive complex Lie group automorphism of $G$ commuting with $\Theta$, and consider the associated semisimple…
Given a C*-algebra A with a semicontinuous semifinite trace tau acting on the Hilbert space H, we define the family R of bounded Riemann measurable elements w.r.t. tau as a suitable closure, a la Dedekind, of A, in analogy with one of the…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…