Two Cellular Automata for the 3x+1 Map
Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1 map), are introduced. These Cellular Automata allow to test efficiently the Collatz conjecture for very large numbers.
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On Reversible Cellular Automata with Triplet Local Rules
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d reversible cellular automata with triplet local rules.
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Discrete Physics: a new way to look at cryptography
This paper shows that Physics is very close to the substitution-diffusion paradigm of symmetric ciphers. Based on this analogy, we propose a new cryptographic algorithm. Statistical Physics gives design principles to devise fast, scalable and secure encryption systems. In particular, increasing space dimension and considering larger data blocks improve both speed and security, allowing us to reach high throughput (larger than 10Gb/s on dedicated HW). The physical approach enlarges the way to look at cryptography and is expected to bring new tools and concepts to better understand and quantify security aspects.
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Spatial correlations in SIR epidemic models
We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial correlations, in an attempt to produce correlation curves similar to those reported recently for real epidemiological data. We find that introduction of a long-range interaction destroys spatial correlations very easily if neighbourhood sizes are homogeneous. For inhomogeneous neighbourhoods, very strong long-range coupling is required to achieve a similar effect.
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Statistical and Dynamical Measures of Simple Irreversible Processes
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random number generator) or a deterministic process (e.g. a chaotic map). We compare the time series obtained from the above implementations of the model by use of statistical methods (such as Detrended Fluctuation Analysis). The conclusion is that using statistical methods the two versions of the model are indistinguishable. The advantage of this observation is that we may calculate the Lyapunov exponent for the model. As a result we obtain an equation relating the DFA exponents (a statistical measure) with the Lyapunov exponent for such models. On the other hand, typical statistical properties can also be calculated, as for example the diffusion coefficient for a particle, which movement is defined by the above model.
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Quantifying Self-Organization in Cyclic Cellular Automata
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information theory that let us calculate the dynamical information content of spatial random processes. This complexity measure allows us to quantitatively determine the rate of self-organization of these cellular automata, and establish the relationship between parameter values and self-organization in CCA. The method is very general and can easily be applied to other cellular automata or even digitized experimental data.
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Metamimetic Games : Modeling Metadynamics in Social Cognition
Imitation is fundamental in the understanding of social system dynamics. But the diversity of imitation rules employed by modelers proves that the modeling of mimetic processes cannot avoid the traditional problem of endogenization of all the choices, including the one of the mimetic rules. Starting from the remark that human reflexive capacities are the ground for a new class of mimetic rules, I propose a formal framework, metamimetic games, that enable to endogenize the distribution of imitation rules while being human specific. The corresponding concepts of equilibrium - counterfactually stable state - and attractor are introduced. Finally, I give an interpretation of social differentiation in terms of cultural co-evolution among a set of possible motivations, which departs from the traditional view of optimization indexed to criteria that exist prior to the activity of agents.
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A Systems-Based Approach to Multiscale Computation: Equation-Free Detection of Coarse-Grained Bifurcations
We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of experiments, data analysis, estimation, identification and feedback). As our illustrative example, we choose a specific numerical task (the detection of stability boundaries in parameter space) for stochastic models of two simplified heterogeneous catalytic reaction mechanisms. In the equation-free framework the stochastic simulator is treated as an experiment (albeit a computational one). Short bursts of fine scale simulation (short computational experiments) are designed, executed, and their results processed and fed back to the process, in integrated protocols aimed at performing the particular coarse-grained task (the detection of a macroscopic instability). Two distinct approaches are presented; one is a direct translation of our previous protocol for adaptive detection of instabilities in laboratory experiments (Rico-Martinez et al., 2003); the second approach is motivated from numerical bifurcation algorithms for critical point detection. A comparison of the two approaches brings forth a key feature of equation-free computation: computational experiments can be easily initialized at will, in contrast to laboratory ones.
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Opinion formation and phase transitions in a probabilistic cellular automaton with two absorbing states
We discuss the process of opinion formation in a completely homogeneous, democratic population using a class of probabilistic cellular automata models with two absorbing states. Each individual can have one of two opinions that can change according to that of his neighbors. It is dominated by an overwhelming majority and can disagree against a marginal one. We present the phase diagram in the mean field approximation and from numerical experiments for the simplest nontrivial case. For arbitrarily large neighborhoods we discuss the mean field results for a non-conformist society, where each individual adheres to the overwhelming majority of its neighbors and choses an opposite opinion in other cases. Mean field results and preliminary lattice simulations with long-range connections among individuals show the presence of coherent temporal oscillations of the population.
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Chaos in a simple cellular automata model of a uniform society
In this work we study the collective behaviors arising in a model of a simplified homogeneous society. Each agent is modeled as a binary ``perceptron'', receiving neighbors' opinions as inputs and outputting one of two possible opinions, according to the conformist attitude and to the external pressure of mass media. For a neighborhood size greater than three, the system shows a very complex phase diagram, including a disordered phase and chaotic behavior. We present analytic calculations, mean fields approximation and numeric simulations for different values of the parameters.
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The Role of Redundancy in the Robustness of Random Boolean Networks
Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in "rugged" fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean networks (RBNs), being general models, can be used to explore theories of how evolution can take place in rugged landscapes; or even change the landscapes. In this paper, we study the effect that redundant nodes have on the robustness of RBNs. Using computer simulations, we have found that the addition of redundant nodes to RBNs increases their robustness. We conjecture that redundancy is a way of "smoothening" fitness landscapes. Therefore, redundancy can facilitate evolutionary searches. However, too much redundancy could reduce the rate of adaptation of an evolutionary process. Our results also provide supporting evidence in favour of Kauffman's conjecture (Kauffman, 2000, p.195).
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Dynamics of coupled Josephson junctions under the influence of applied fields
We investigate the effect of the phase difference of applied fields on the dynamics of mutually coupled Josephson junction. The system desynchronizes for any value of applied phase difference and the dynamics even changes from chaotic to periodic motion for some values of applied phase difference. We report that by keeping the value of phase difference as $π$, the system continues to be in periodic motion for a wide range of system parameter values which might be of great practical applications.
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Self-synchronization of Cellular Automata: an attempt to control patterns
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules with complex behavior a dynamic competition among all the possible stable patterns is established and no stationary regime is reached. For the particular rule coded by the decimal number 18, a self-synchronization phenomenon can be obtained, even when strong modifications to the synchronization method are applied.
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Symmetry pattern transition in cellular automata with complex behavior
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex symmetrical patterns by stochastically coupling a proportion $p$ of pairs of sites located at equal distance from the center of the lattice. A nontrivial critical value of $p$ must be surpassed in order to obtain symmetrical patterns during the evolution. This strategy is able to classify the cellular automata rules -with complex behavior- between those that support time-dependent symmetric patterns and those which do not support such kind of patterns.
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On Engineering and Emergence
The engineering and design of self-organizing systems with emergent properties is a long-standing problem in the field of complex and distributed systems, for example in the engineering of self-organizing Multi-Agent Systems. The problem of combining engineering with emergence - to find a simple rule for a complex pattern - equals the problem of science in general. Therefore the answers are similar, and the scientific method is the general solution to the problem of engineering complex systems.
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Modelling of radiation defects evolution in regular structures by the cellular automata method
The results of modeling of radiation defects formation and evolution on the surface and in the volume of a crystal are presented in this article. Statistical properties are calculated for the investigated system. It is revealed that defects structure is a multifractal and system entropy decreases, while observing self-organization of the physical system.
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Cellular Automata under the influence of noise
Noise in the local transition function is compared to fluctuations in the updating times of the cells. Obtained results are shown to be quite different in both cases. In this extended abstract we briefly explain the problem and present results obtained and comment them.
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A mesoscopic approach for multi-phase flows in nano-corrugated channels
An approach based on a lattice version of the Boltzmann kinetic equation for describing multi-phase flows in nano- and micro-corrugated devices is proposed. We specialize it to describe the wetting/dewetting transition of fluids in presence of nanoscopic grooves etched on the boundaries. This approach permits to retain the essential supra-molecular details of fluid-solid interactions without surrendering -actually boosting- the computational efficiency of continuum methods. The mesoscopic method is first validated quantitatively against Molecular Dynamics (MD) results of Cottin-Bizonne et al. [Nature Mater. 2, 237 (2003)] and then applied to more complex situations which are hardly accessible to MD simulations. The resulting analysis confirms that surface roughness and capillary effects may conspire to promote a counter-intuitive but significant reduction of the flow drag with substantial enhancement in the mass flow rates and slip-lengths in the micrometric range for highly hydrophobic surfaces.
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