Journal ArticleDOI
Statistical mechanics of cellular automata
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Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.Abstract:
Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 1.69. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.read more
Citations
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Journal ArticleDOI
Distribution of the sum-of-digits function of random integers: A survey
TL;DR: Four different approaches are used: a classical probability approach, Stein's method, an analytic approach and a new approach based on Krawtchouk polynomials and the Parseval identity to derive asymptotic approximations to the total variation distance.
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Reconfigurable readback-signal generator based on a field-programmable gate array
TL;DR: A readback-signal generator to provide noise-corrupted signals to a read channel simulator in a Xilinx Virtex-E field-programmable gate array (FPGA) device that uses embedded nonuniform random number generators to simulate the random characteristics of various disturbances in the read/write process.
Journal ArticleDOI
Correlated electrons in coupled quantum dots and related phenomena
TL;DR: In this paper, three topics related to correlated electrons in coupled quantum dots are discussed, including electron tunneling through a Hubbard gap induced by an increase in the density of electrons in a quantum-dot chain under an overall confining potential.
Book ChapterDOI
Quantum Cellular Automata
TL;DR: This paper presents a meta-simulation of the QMA complexity class Quantum Merlin–Arthur, the class of decision problems such that a “yes” answer can be verified by a 1-message quantum interactive proof (verifiable in BQP).
Book ChapterDOI
The Complexity of Small Universal Turing Machines
Damien Woods,Turlough Neary +1 more
TL;DR: This work surveys some work concerned with small universal Turing machines, cellular automata, and other simple models of computation and finds that Rule 110, a well-known elementary cellular automaton, is also efficiently universal.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Journal ArticleDOI
The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Journal ArticleDOI
On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
Journal ArticleDOI
Metabolic stability and epigenesis in randomly constructed genetic nets
TL;DR: The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”.
Journal ArticleDOI
Diffusion-limited aggregation, a kinetic critical phenomenon
Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth