164,794 research outputs found
A Family of Controllable Cellular Automata for Pseudorandom Number Generation
In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) ─ CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG
Robustness of One-Dimensional Photonic Bandgaps Under Random Variations of Geometrical Parameters
The supercell method is used to study the variation of the photonic bandgaps
in one-dimensional photonic crystals under random perturbations to thicknesses
of the layers. The results of both plane wave and analytical band structure and
density of states calculations are presented along with the transmission
cofficient as the level of randomness and the supercell size is increased. It
is found that higher bandgaps disappear first as the randomness is gradually
increased. The lowest bandgap is found to persist up to a randomness level of
55 percent.Comment: Submitted to Physical Review B on April 8 200
Structure and Randomness of Continuous-Time Discrete-Event Processes
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic
process' intrinsic randomness; the statistical complexity gives the cost of
predicting the process. We calculate, for the first time, the entropy rate and
statistical complexity of stochastic processes generated by finite unifilar
hidden semi-Markov models---memoryful, state-dependent versions of renewal
processes. Calculating these quantities requires introducing novel mathematical
objects ({\epsilon}-machines of hidden semi-Markov processes) and new
information-theoretic methods to stochastic processes.Comment: 10 pages, 2 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/ctdep.ht
Randomness and collectivity in nuclear structure: Three theoretical puzzles
We show and interpret three examples of nontrivial results obtained in
numerical simulations of many-body systems: exponential convergence of
low-lying energy eigenvalues in the process of progressive truncation of huge
shell-model matrices, apparently ordered spectra generated by random
interactions, and regular behavior of complex many-body energies in a system
with single-particle orbitals in continuum. The possible practical applications
and new approaches are suggested.Comment: 12 pages, 4 figure
Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems
We study the effect of randomness and anisotropy on Turing patterns in
reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of
pattern formation is considered. The cases we study are: (i)randomness in the
underlying lattice structure, (ii)the case in which there is a probablity p
that at a lattice site both reaction and diffusion occur, otherwise there is
only diffusion and lastly, the effect of (iii) anisotropic and (iv) random
diffusion coefficients on the formation of Turing patterns. The general
conclusion is that the Turing mechanism of pattern formation is fairly robust
in the presence of randomness and anisotropy.Comment: 11 pages LaTeX, 14 postscript figures, accepted in Phys. Rev.
Pseudorandom number generation based on controllable cellular automata
A novel Cellular Automata (CA) Controllable CA (CCA) is proposed in this paper. Further, CCA are applied in Pseudorandom Number Generation. Randomness test results on CCA Pseudorandom Number Generators (PRNGs) show that they are better than 1-d CA PRNGs and can be comparable to 2-d ones. But they do not lose the structure simplicity of 1-d CA. Further, we develop several different types of CCA PRNGs. Based on the comparison of the randomness of different CCA PRNGs, we find that their properties are decided by the actions of the controllable cells and their neighbors. These novel CCA may be applied in other applications where structure non-uniformity or asymmetry is desired
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
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