Cellular automata in operational probabilistic theories

The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite systems. The notion of causal influence is introduced, and its relation with the usual property of signalling is discussed. We then introduce homogeneity, namely the property of an update rule to evolve every system in the same way, and prove that systems evolving by a homogeneous rule always correspond to vertices of a Cayley graph. Next, we define the notion of locality for update rules. Cellular automata are then defined as homogeneous and local update rules. Finally, we prove a general version of the wrapping lemma, that connects CA on different Cayley graphs sharing some small-scale structure of neighbourhoods.

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Causal influence in operational probabilistic theories

Quantum ◽

10.22331/q-2021-08-03-515 ◽

2021 ◽

Vol 5 ◽

pp. 515

Author(s):

Paolo Perinotti

Keyword(s):

Quantum Theory ◽

Cellular Automata ◽

Cellular Automaton ◽

Classical Theory ◽

The Other ◽

Causal Influence ◽

Causal Networks ◽

A Cell ◽

Reversible Evolution ◽

Probabilistic Theories

We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory—where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influence on another one without signalling to it. Remarkably, the counterexample comes from classical theory, where the proposed notion of causal influence determines a redefinition of the neighbourhood of a cell in cellular automata. We stress that, according to our definition, it is impossible anyway to have causal influence in the absence of an interaction, e.g. in a Bell-like scenario. We study various conditions for causal influence, and introduce the feature that we call no interaction without disturbance, under which we prove that signalling and causal influence coincide. The proposed definition has interesting consequences on the analysis of causal networks, and leads to a revision of the notion of neighbourhood for classical cellular automata, clarifying a puzzle regarding their quantisation that apparently makes the neighbourhood larger than the original one.

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Small Scale Structure in the Earth's Ionosphere. Theory and Numerical Simulation.

10.21236/ada130462 ◽

1983 ◽

Author(s):

S. T. Zalesak

Keyword(s):

Numerical Simulation ◽

Scale Structure ◽

Small Scale ◽

Small Scale Structure

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A Search for Very Compact Structure in 17 OH Masers

Symposium - International Astronomical Union ◽

10.1017/s0074180900134618 ◽

1988 ◽

Vol 129 ◽

pp. 255-256

Author(s):

A. J. Kemball ◽

P. J. Diamond ◽

F. Mantovani

Keyword(s):

Galactic Disk ◽

Hii Regions ◽

Scale Structure ◽

Small Scale ◽

Compact Structure ◽

Small Scale Structure ◽

Interstellar Scattering

The apparent spot sizes of OH masers appear to be significantly broadened when seen through the inner galaxy or large extents of the galactic disk (Burke 1968). Bowers et al (1980) found evidence of small-scale structure (≲ 50 mas) in OH sources at distances of less than 5 kpc but this was characteristically absent in very distant sources (≳ 8kpc) at galactic longitudes 1 ≲ 40°. This result is typically explained in terms of interstellar scattering (ISS) by intervening diffuse HII regions.

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