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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)

- Marcus Pivato
- 2010

Let A Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let σ be the shift map on A Z. A cellular automaton is a continuous, σ-commuting self-map Φ of A Z , and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset S ⊂ A Z. Suppose a ∈ A Z is S-admissible everywhere except for some small region we call a defect. It has been… (More)

Let A Z D be the Cantor space of Z D-indexed configurations in a finite alphabet A, and let σ be the Z D-action of shifts on A Z D. A cellular automaton is a continuous, σ-commuting self-map Φ of A Z D , and a Φ-invariant subshift is a closed, (Φ, σ)-invariant subset A ⊂ A Z D. Suppose a ∈ A Z D is A-admissible everywhere except for some small region we… (More)

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Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent truth-valuations ('judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. We show that, for a variety of spaces, proposi-tionwise… (More)