Marcus Pivato

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A coupled cell system is a network of dynamical systems, or ‘cells’, coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells that preserves all internal dynamics and all couplings. Symmetry can(More)
If X is a discrete abelian group and A a finite set, then a cellular automaton (CA) is a continuous map F : A −→ A that commutes with all X-shifts. If φ : A −→ R, then, for any a ∈ A, we define Σφ(a) = ∑ x∈X φ(ax) (if finite); φ is conserved by F if Σφ is constant under the action of F. We characterize such conservation laws in several ways, deriving both(More)
Let M be a monoid (e.g. N, Z, or Z), and A an abelian group. A is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A −→ A that commutes with all shift maps. Let μ be a (possibly nonstationary) probability measure on A; we develop sufficient conditions on μ and F so that the sequence {Fμ}N=1 weak*-converges to(More)
Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations (‘views’) on a family of logically interconnected propositions, or yes/no-issues. Yet, simply complying with the majority opinion in each issue often yields a logically inconsistent collection of judgements. Thus, we consider the(More)
If M is a monoid, and A is an abelian group, then A is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A −→ A that commutes with all shift maps. If F is diffusive, and μ is a harmonically mixing (HM) probability measure on A, then the sequence {Fμ}N=1 weak*-converges to the Haar measure on A, in density. Fully(More)
We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural monotonicity conditions to these auxiliary rankings. Owing to(More)
A right-sided, nearest neighbour cellular automaton (RNNCA) is a continuous transformation Φ : A−→A determined by a local rule φ : A{0,1}−→A so that, for any a ∈ A and any z ∈ Z, Φ(a)z = φ(az, az+1). We say that Φ is bipermutative if, for any choice of a ∈ A, the map A ∋ b 7→ φ(a, b) ∈ A is bijective, and also, for any choice of b ∈ A, the map A ∋ a 7→ φ(a,(More)