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At least 73 records · Page 4Linked to original sources
arXiv2009

Boundary effects on energy dissipation in a cellular automaton model

In this paper, we numerically study energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Numerical results show that there is a nonvanishing energy dissipation rate Ed, and no true free-flow phase exists in the deterministic and nondeterministic NaSch models with OBC. In the deterministic case, there is a critical value of the extinction rate $β{cd}$ below which Ed increases with increasing $β$, but above which Ed abruptly decreases in the case of the speed limit vmax>2. However, when vmax<3, no discontiguous change in Ed occurs. In the nondeterministic case, the dissipated energy has two different contributions: one coming from the randomization, and one from the interactions, which is the only reason for dissipating energy in the deterministic case. The relative contributions of the two dissipation mechanisms are presented in the stochastic NaSch model with OBC. Energy dissipation rate Ed is directly related to traffic phase. Theoretical analyses give an agreement with numerical results in three phases (low-density, high-density and maximum current phase) for the case vmax=1.

physics.soc-ph↗
arXiv2009

Damage Spreading in Spatial and Small-world Random Boolean Networks

The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ($\bar{K} \ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\bar{K}$, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

cond-mat.dis-nn↗
arXiv2009

Modeling self-organizing traffic lights with elementary cellular automata

There have been several highway traffic models proposed based on cellular automata. The simplest one is elementary cellular automaton rule 184. We extend this model to city traffic with cellular automata coupled at intersections using only rules 184, 252, and 136. The simplicity of the model offers a clear understanding of the main properties of city traffic and its phase transitions. We use the proposed model to compare two methods for coordinating traffic lights: a green-wave method that tries to optimize phases according to expected flows and a self-organizing method that adapts to the current traffic conditions. The self-organizing method delivers considerable improvements over the green-wave method. For low densities, the self-organizing method promotes the formation and coordination of platoons that flow freely in four directions, i.e. with a maximum velocity and no stops. For medium densities, the method allows a constant usage of the intersections, exploiting their maximum flux capacity. For high densities, the method prevents gridlocks and promotes the formation and coordination of "free-spaces" that flow in the opposite direction of traffic.

nlin.CG↗
arXiv2009

Wave propagation in filamental cellular automata

Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising cooperative behaviour these can induce in terms of waves of cellular state changes along a filament of cells. We discover what the minimum requirements are, in terms of numbers of states and the range of communication between automata, to observe this for individual filaments. We also discover that populations of growing filaments may have useful features that the individual filament does not have, and we give the results of numerical simulations.

cs.FL↗
arXiv2009

Zeno Squeezing of Cellular Automata

We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets consist of a potentially infinite sequence of coupled transitions with ever increasing firing rates. Both models are capable of hypercomputations and can, for instance, ``solve'' the halting problem for Turing machines. We survey the main definitions and propositions and add new results regarding the indeterminism of self-similar cellular automata.

physics.gen-ph↗
arXiv2009

A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization

Through an extension of the ultradiscretization for the optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently proposed by Takahashi and Matsukidaira. A phase transition from free to jam phases as well as the existence of multiple metastable states are observed in numerically obtained fundamental diagrams for cellular automata (CA), which are special cases of the ultradiscrete limit of the hybrid model.

nlin.CG↗
arXiv2011

Compression-based investigation of the dynamical properties of cellular automata and other systems

A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A compression based method to estimate a characteristic exponent to detect phase transitions and measure the resiliency or sensitivity of a system to its initial conditions is also proposed. A conjecture regarding the capability of a system to reach computational universality related to the values of this phase transition coefficient is formulated. These ideas constitute a compression-based framework for investigating the dynamical properties of cellular automata and other systems.

cs.CC↗
arXiv2009

From Newton to Cellular Automata

I outline a possible logical path from the formulation of physics of classical mechanics to "abstract" systems like cellular automata. The goal of this article is that of illustrating why physicists often study extremely simplified models, instead of just numerically integrating the fundamental equations of physics. This exposition is obviously only partial and based on my expertise and my interests.

physics.pop-ph↗
arXiv2009

Xampling: Analog to Digital at Sub-Nyquist Rates

We present a sub-Nyquist analog-to-digital converter of wideband inputs. Our circuit realizes the recently proposed modulated wideband converter, which is a flexible platform for sampling signals according to their actual bandwidth occupation. The theoretical work enables, for example, a sub-Nyquist wideband receiver, which has no prior information on the transmitter carrier positions. Our design supports input signals with 2 GHz Nyquist rate and 120 MHz spectrum occupancy, with arbitrary transmission frequencies. The sampling rate is as low as 280 MHz. To the best of our knowledge, this is the first reported wideband hardware for sub-Nyquist conversion. Furthermore, the modular design is proven to compete with state-of-the-art Nyquist ADCs in terms of resolution bits and full-scale range. We describe the various circuit design considerations, with an emphasis on the nonordinary challenges the converter introduces: mixing a signal with a multiple set of sinusoids, rather than a single local oscillator, and generation of highly-transient periodic waveforms, with transient intervals on the order of the Nyquist rate. A series of hardware experiments validates the design and demonstrate sub-Nyquist sampling.

nlin.CG↗
arXiv2011

Ultimate Traces of Cellular Automata

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.

cs.FL↗
arXiv2010

Lattice Gas Automata Simulation of 2D site-percolation diffusion: Configuration dependence of the theoretically expected crossover of diffusion regime

Theoretical analysis of random walk on percolation lattices has predicted that, at the occupied site concentrations of above the threshold value, a characteristic crossover between an initial sub-diffusion to a final classical diffusion behavior should occur. In this study, we have employed the lattice gas automata model to simulate random walk over a square 2D site-percolation lattice. Quite good result was obtained for the critical exponent of diffusion coefficient. The random walker was found to obey the anomalous sub-diffusion regime, with the exponent decreasing when the occupied site concentration decreases. The expected crossover between diffusion regimes was observed in a configuration-dependent manner, but the averaging over the ensemble of lattice configurations removed any manifestation of such crossovers. This may have been originated from the removal of short-scale inhomogeneities in percolation lattices occurring after ensemble averaging.

nlin.CG↗
arXiv2010

Cellular Automation of Galactic Habitable Zone

We present a preliminary results of our Galactic Habitable Zone (GHZ) 2D probabilistic cellular automata models. The relevant time-scales (emergence of life, it's diversification and evolution influenced with the global risk function) are modeled as the probability matrix elements and are chosen in accordance with the Copernican principle to be well-represented by the data inferred from the Earth's fossil record. With Fermi's paradox as a main boundary condition the resulting histories of astrobiological landscape are discussed.

astro-ph.GA↗
arXiv2010

Cellular Automata, PDEs, and Pattern Formation

State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.

nlin.CG↗
arXiv2010

Emergence from Symmetry: A New Type of Cellular Automata

In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, this model also hints its capability of universal computation.

nlin.CG↗
arXiv2010

Cellular Automata Networks

A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new type of cellular automata networks uses local rules with a fraction of long-range shortcuts derived from the properties of small-world networks. Simulations show that the self-organized criticality emerges naturally in the system for a given probability of shortcuts and transition occurs as the probability increases to some critical value indicating the small-world behaviour of the complex automata networks. Pattern formation of cellular automata networks and the comparison with equation-based reaction-diffusion systems are also discussed

nlin.CG↗
arXiv2010

Characterization of Multispecies Living Ecosystems With Cellular Automata

A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the evolving multispecies living ecosystems. Numerical experiments show that a small perturbation or extinction event may affect many other species in the ecosystem in an avalanche manner. Both the avalanches and the extinction arising from these changes follow a power law, reflecting that the multispecies living ecosytems have the characteristics of self-organized criticality.

nlin.CG↗
arXiv2010

The dynamics of the HIV infection: a time-delay differential equation approach

In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that stress the immune system throughout the successive activation of new responses to new undetectable strains, the delay term describes the time interval necessary to mount new specific immune responses. This single term increases the number of possible solutions and changes the phase space dynamics if compared to the model without time delay. We observe very slow transits near the unstable fixed point, corresponding to a healthy state, and long time decay to the stable fixed point that corresponds to the infected state. In contrast to the results obtained for models using regular ODE, which only allow for partial descriptions of the course of the infection, our model describes the entire course of infection observed in infected patients: the primary infection, the latency period and the onset of acquired immunodeficiency syndrome (AIDS). The model also describes other scenarios, such as the very fast progression to the disease and the less common outcome in which, although the patient is exposed to HIV, he/she does not develop the disease.

physics.bio-ph↗