Wolfram, S.: Statistical mechanics of cellular automata. Reviews of Modern Physics 55 (1983) 601--644 Home/Search Document Not in Database Summary Related Articles Check |
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Algebraic Properties of the Block Transformation on Cellular.. - Moore, Drisko (1995) (Correct)
....additional requirement that a = e makes this true. We next show some examples of r = 1 CAs whose blocked forms have twosided identities, but which are not special medial; so in fact the underlying rule depends on all its inputs and G 6= G . A non permutive example is elementary rule 218 [8], whose rule table is 000 001 010 011 100 101 110 111 0 1 0 1 1 0 1 1 which can also be written f(a i Gamma1 ; a i ; a i 1 ) ae (a i Gamma1 a i 1 ) mod 2 if a i = 0 max(a i Gamma1 ; a i 1 ) if a i = 1 After blocking to r = 1=2, G is 00 01 10 11 00 00 01 10 11 01 01 00 11 11 10 10 ....
....can define an algebra on the leftmost and rightmost inputs; by lemma 1, this algebra must have an identity. In this case, the algebra is (a b) mod 2 or max(a; b) both of which have identity 0, depending on a i . If we switch these two so that f(1; 0; 1) 1 and f(1; 1; 1) 0, we get rule 122 [8]. 8 To get a permutive example (in which G is a quasigroup) we need four states. This is because there is only one loop of size 3 with a given identity, namely 0 1 2 1 2 0 2 0 1 while for n = 4 there are four: 0 1 2 3 1 0 3 2 2 3 0 1 = Z 2 ; 1 0 3 2 2 3 1 0 3 2 0 1 1 2 3 0 2 ....
S. Wolfram, "Statistical Mechanics of Cellular Automata." Reviews of Modern Physics 55 (1983) 601-644. 10
Non-Abelian Cellular Automata - Moore (1995) (1 citation) (Correct)
....in polylogarithmic parallel time, i.e. P = NC. This would be as surprising as, say, if it turned out that P = NP. The CAs that can be predicted in polylogarithmic parallel time, then, seem to occupy a middle position between CAs that are easily predictable, such as elementary rules 90 and 150 [6] that are just addition mod 2, and computationally universal CAs that probably have to be simulated explicitly. In [1] we term these CAs quasi linear; non linear, but relatively easy to predict. 2 Preliminaries An algebra (A; Delta) is a function from A Theta A to A, written a Delta b or ....
S. Wolfram, "Statistical Mechanics of Cellular Automata." Reviews of Modern Physics 55 (1983) 601-644.
A Random Walk in Statistical Physics - Svenson (Correct)
....#S i S j ; 1.6) where R ij is the distance between spins i and j and k F is the Fermi wavevector. For more information, see [25] and [26] Spin models can also be used without an implied hamiltonian. An example of such models are cellular automata; these have been extensively studied by Wolfram [27] and others and are also useful in computing science. These models have explicit dynamical rules that determine how the spins should change in time. In a cellular automaton, the value of a spin S i in the next time step is determined by some function (generally deterministic and the same for all ....
S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (1983), no. 3, 601.
Lineage and Induction in the Development of Evolved.. - van Remortel.. (2002) (1 citation) (Correct)
....the focal cell. The transition rule can be shared ( uniform CAs) or di erent for every cell ( non uniform CAs) CAs change cell states using the mechanism of induction. CAs have been used in a wide range of scienti c research topics such as self replication[Lan84] dynamics of complex systems[Wol83,WL92], etc. More complex computational models have been proposed that exhibit both lineage and interaction. An example particularly well suited in the scope of this paper are Cell Systems , which describe development of planar multi cellular shapes [LF95,Fra96] In general these models often aim at ....
S. Wolfram. Statistical mechanics of cellular automata. Rev. Modern Physics, 55:601-644, 1983.
A Reconfigurable FPGA-Based Readback Signal Generator For.. - Jinghuan Chen Jaekyun (2002) (Correct)
.... when the Boolean functions are carefully selected and after the LHCA evolves for a number of initialization clock cycles, such a register array will output an m sequence that has the same period as that of an LFSR [7] The Boolean functions are called computation rules and categorized by Wolfram [11]. One of the setups that can generate m sequences is a careful mix (hybrid) of two Boolean functions, Rule 90 and Rule 150, in the calculation of register contents [7] Rule 90 and Rule 150 are defined as follows: and a i (t) where a i (t) is the content of register i at time t.Howto ....
S. Wolfram, "Statistical mechanics of cellular automata", Reviews of Modern Physics, vol.55, no.3, pp.601-44, July 1983.
A Reconfigurable FPGA-Based Readback Signal Generator For.. - Jinghuan Chen Jaekyun (Correct)
.... when the Boolean functions are carefully selected and after the LHCA evolves for a number of initialization clock cycles, such a register array will output an m sequence that has the same period as that of an LFSR [7] The Boolean functions are called computation rules and categorized by Wolfram [11] One of the setups that can generate m sequences is a careful mix (hybrid) of two Boolean functions, Rule 90 and Rule i50, in the calculation of register contents [7] Rule 90 and Rule 150 are defined as follows: Rule 90: a(t 1) a x(t) a, l (t) 5) and Rule S0: l) Z Z (e) where a (t) ....
.... I Symbol [ Value Pulse look up table size N 16 ISI lenh I 6 Symbol period T 8 NLTS eT 2 Signal to noise ratio SNR 10 dB Percentage of TN in total noise 90 Percentage of jitter in TN PJP 75 LHCA length lc 244 Site spacing parameter V 1 Quantization levels q 64 Uniform RN width n 11 OT ratios r and r 0.9 and 0.1 1 for pos. pulses Head nonlinearity HNL 0.9 for neg. pulses 353 0.5 o 0.5 1 o 200 400 6oo 800 1 ooo Figure 8: Generated readback signal The total area consumption of the implementaion with all modules (bitstream 0) is 99 of 12288 slices. This extreme ....
S. Wolfram, "Statistical mechanics of cellular automata", Reviews of Modern Physics, vol.55, no.3, pp.601-44, July 1983.
On Bots and Bacteria: Ontology Independent Embodiment - Quick, Dautenhahn.. (1999) (1 citation) (Correct)
.... ontological status (cf. 30] Boolean Networks, a close relative of CA, have previously been used to explore the general phenomenon of stability in genetic networks [31, 32] and more recently to model genetic activation networks [33] Whilst CA have traditionally been studied as closed systems [34], providing for their embodiment requires features analogous to sensory and effector surfaces, as a basis for a mutually perturbatory relationship with an environment (Fig. 1) S S TEM ORGANISM I Cellular Automata I ENVIRONMENT Fig. 1. CA based System embodied in an environment via sensory ....
Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55 (1983) 601- 644
Complexity as Fitness for Evolved Cellular Automata.. - Ward, Blank, Rolniak.. (Correct)
....rates of successful classi cation ( 90 ) 1 INTRODUCTION This paper investigates state changes of onedimensional, binary, cellular automata (CA) through time and space during attempts to solve the densityclassi cation task. CAs are viewed as models of dynamical systems and computation [10] [11], 4] The state of each cell may then change over time. The frequency of state changes and the spatial distribution of the state changes may re ect complex behavior by the CA [12] 6] Our study looks at these state changes in CAs updated by rules evolved by a genetic algorithm (GA) for good ....
....in the tness function for evolving update rules and its e ect on evolution time. 1.1 BACKGROUND Cellular automata are arrays, or lattices, of cells. Each cell may be in a nite number of states. At discrete time steps, the states of the cells are changed according to update rules [10] [11]. The solution of the densityclassi cation task may be viewed as nontrivial computation that requires a CA to determine the majority state in its initial con guration (IC) and update itself within a given number of time steps to achieve the majority state in every cell [9] Figure 1 shows a ....
S. Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55:601-644, 1983.
Additive Cellular Automata and Volume Growth - Ward (Correct)
....particular class of dynamical system studied by von Neumann [24] as a primitive model for self reproduction. Since then they have been widely studied in a variety of contexts in physics, biology and computer science. A detailed discussion with extensive references may be found in Wolfram s paper [31]. The state space of a cellular automaton is particularly simple: it consists in one dimension of a one dimensional array with values taken from a fixed finite alphabet, and their evolution in time is determined by a finite or local rule. Nonetheless, the global dynamical behaviour of time ....
S. Wolfram. Statistical mechanics of cellular automata. Rev. Modern Physics 55, 601--644 (1983). 29
Algebraic Construction of a New Class of.. - van Schyndel.. (1999) (1 citation) (Correct)
....and Wolfgang and Delp et al. [30] use this approach. Perfect Arrays. Searching manually for these 2D arrays with perfect auto correlations is comprehensive but it becomes impractical for arrays with more than about 40 binary elements, unless local rules can be introduced (Mertens [18] Wolfram [31]) An exhaustive search for such arrays is prohibitive. Searching for arrays with higher alphabets would be more difficult. Baumert [2] describes a generation method of perfect arrays using difference sets. The set of perfect arrays for a given size is often unique or small and their ....
S. Wolfram, "Statistical Mechanics of Cellular Automata", Reviews of Modern Physics, Vol 55.No.3, July 1983. pp. 601-643.
Exploiting the Selfish Gene Algorithm for Evolving.. - Corno, Reorda, Squillero (2000) (Correct)
....are analyzed in [9] Clans were introduced in [10] as an extension to the algorithm for dealing with more complex fitness landscapes. 2. 2 Cellular Automata Cellular Automata (CA) are finite state machines defined as uniform arrays of cells, sometimes named sites, in a n dimensional space [21]. A CA evolves in discrete steps with the next value of one cell determined by its value and that of a set of cells called the neighbor cells. The function used to compute the value of a cell is called the cell rule. When different cells implement different rules, the CA is hybrid (HCA) ....
S. Wolfram, "Statistical Mechanics of Cellular Automata," Rev. Mod. Phys. 55, 1983, pp. 601-644
Computing Shifts in 90/150 Cellular Automata Sequences - Sarkar (2001) (Correct)
....will be interested in CA with maximum period and hence in light of Theorem 3.1, we will henceforth assume l i = u j = 1 for all 2 i n and 1 j n 1. Then the matrix M becomes a tridiagonal matrix with both the lower and upper sub diagonal equal to 1. If q = 2, such a CA is called a 90 150 CA [9]. Following this convention we will call such a CA a 90 150 CA, even if q 2. Interestingly, for 90 150 CA and q = 2, the set of strings a 1 : a n which makes the matrix M non singular turns out to be a regular set. See [7] for a proof of this fact and also an exact enumeration of the set ....
S. Wolfram. Statistical Mechanics of cellular automata. Rev. Modern Physics 55, 601-644 (1983). 11
P-completeness of cellular automaton Rule 110 - Neary, Woods (2006) (Correct)
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Wolfram, S.: Statistical mechanics of cellular automata. Reviews of Modern Physics 55 (1983) 601--644
Design and Analysis of a Robust and Ecient - Block Cipher Using (2005) (Correct)
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S. Wolfram, \Statistical mechanics of cellular automata," Rev. Mod. Phys., vol. 55, no. 3, pp. 601-644, July 1983. 14
Cellular Associative Neural Networks for Pattern Recognition - Orovas (1999) (Correct)
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S. Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3):601--643, Jul 1983.
Reconfigurable Readback-Signal Generator Based on a.. - Jinghuan Chen Jaekyun (Correct)
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S. Wolfram, "Statistical mechanics of cellular automata," Rev. Mod. Phys., vol. 55, pp. 601--644, July 1983.
Ballistic Annihilation And - Deterministic Surface Growth (Correct)
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S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 1983, Vol. 55, 601. 24 FIGURE CAPTIONS
Quantifying Self-Organization in Cyclic Cellular Automata - Cosma Rohilla Shalizi (Correct)
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S. Wolfram, "Statistical mechanics of cellular automata," Reviews of Modern Physics 55, pp. 601--644, 1983. Reprinted in [35].
Unknown - Filename Algebraic Tex (Correct)
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Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601 (1983).
On Cellular Automaton Approaches to Modeling Biological.. - Alber, Kiskowski.. (2002) (1 citation) (Correct)
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S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), pp. 601--604.
The Classical Lattice-Gas Method - Yepez (1999) (Correct)
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Stephen Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3):601--644, 1983.
How Neutral Networks Influence Evolvability - Ebner, Shackleton, Shipman (2001) (Correct)
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S. Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3):601-644, July 1983.
Lattice-Gas Dynamics, Volume I - Viscous Fluids - Yepez (1995) (6 citations) (Correct)
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Stephen Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3):601--644, 1983.
Quasi-Linear Cellular Automata - Cristopher Moore Santa (1997) (2 citations) (Correct)
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S. Wolfram, "Statistical Mechanics of Cellular Automata." Reviews of Modern Physics 55 (1983) 601-644.
Cellular Automata Methods in Mathematical Physics - Smith (1994) (4 citations) (Correct)
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Steven Wolfram. Statistical mechanics of cellular automata. Reviews of Modern Physics, 55:601--644, 1983.
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