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Some Results on Invertible Cellular Automata
"... We address certain questions concerning invertible cellular automata, and we present new results in this area. Specifically, we explicitly construct a cellular automaton in a class (residual class) previously known not to be empty only via a nonconstructive existence proof. This class contains cell ..."
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We address certain questions concerning invertible cellular automata, and we present new results in this area. Specifically, we explicitly construct a cellular automaton in a class (residual class) previously known not to be empty only via a nonconstructive existence proof. This class contains
SOME ERGODIC PROPERTIES OF INVERTIBLE CELLULAR AUTOMATA
, 902
"... Abstract. In this paper we consider invertible onedimensional linear cellular automata (CA hereafter) defined on a finite alphabet of cardinality pk, i.e. the maps Tf[l,r] : ZZ pk → ZZ pk which are given by Tf[l,r](x) = (yn) ∞ n=− ∞ , yn = f(xn+l,..., xn+r) = rP λixn+i(mod p i=l k), x = (xn) ∞ ..."
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Abstract. In this paper we consider invertible onedimensional linear cellular automata (CA hereafter) defined on a finite alphabet of cardinality pk, i.e. the maps Tf[l,r] : ZZ pk → ZZ pk which are given by Tf[l,r](x) = (yn) ∞ n=− ∞ , yn = f(xn+l,..., xn+r) = rP λixn+i(mod p i=l k), x = (xn
Metabolic stability and epigenesis in randomly connected nets
 Journal of Theoretical Biology
, 1969
"... “The world is either the effect of cause or chance. If the latter, it is a world for all that, that is to say, it is a regular and beautiful structure.” Marcus Aurelius Protoorganisms probably were randomly aggregated nets of chemical reactions. The hypothesis that contemporary organisms are also r ..."
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Cited by 637 (4 self)
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randomly constructed molecular automata is examined by modeling the gene as a binary (onoff) device and studying the behavior of large, randomly constructed nets of these binary “genes”. The results suggest that, if each “gene ” is directly affected by two or three other “genes”, then such random nets
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
Genetic Programming
, 1997
"... Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring ..."
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Cited by 1051 (12 self)
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Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover (sexual recombination) and mutation. John Holland's pioneering Adaptation in Natural and Artificial Systems (1975) described how an analog of the evolutionary process can be applied to solving mathematical problems and engineering optimization problems using what is now called the genetic algorithm (GA). The genetic algorithm attempts to find a good (or best) solution to the problem by genetically breeding a population of individuals over a series of generations. In the genetic algorithm, each individual in the population represents a candidate solut
Particle swarm optimization
, 1995
"... eberhart @ engr.iupui.edu A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications ..."
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Cited by 3535 (22 self)
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eberhart @ engr.iupui.edu A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described, 1
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development of much of theoretical computer science, was the distinction between computable and ...
An Essay Concerning Human Understanding
, 1921
"... God, having designed man for a sociable creature, made him not only with an inclination and under a necessity to have fellowship with those of his own kind, but furnished him also with language, which was to be the great instrument and common tie of society. ..."
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Cited by 790 (2 self)
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God, having designed man for a sociable creature, made him not only with an inclination and under a necessity to have fellowship with those of his own kind, but furnished him also with language, which was to be the great instrument and common tie of society.
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