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At least 811 records · Page 45Linked to original sources
arXiv2003

Towards a Noether-like conservation law theorem for one dimensional reversible cellular automata

Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the results of Takesue and Hattori (1992) on the space of additive conservation laws in one dimensional cellular automata. In reversible automata, we show that conservation laws correspond to the null spaces of certain well-structured matrices. It is shown that a class of conservation laws exist that correspond to the maximal congruences of index 2. In all examples investigated, this is all the conservation laws. Thus we conjecture that there is an equality here, corresponding to a Noether--like theorem.

nlin.CG↗
arXiv2004

Updating Schemes in Random Boolean Networks: Do They Really Matter?

In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also report that all updating schemes yield very similar critical stability values, meaning that the "edge of chaos" does not depend much on the updating scheme. After discussion, we conclude that synchonous RBNs are justifiable theoretical models of biological networks.

nlin.AO↗
arXiv2004

An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by ``the behavior of CA is robust to asynchronism'' using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.

nlin.CG↗
arXiv2004

On Markovian behaviour of $p$-adic random dynamical systems

We study Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random dynamical system. Under which conditions do the orbits under such a random dynamical system form Markov chains? It is necessary that the mappings are Markov dependent. We show, however, that this is in general not sufficient. In fact, in many cases we have to require that the mappings are independent. Moreover we investigate some geometric and algebraic properties for $p-$adic monomial mappings as well as for the $p-$adic power function which are essential to the formation of attractors. $p$-adic random dynamical systems can be useful in so called $p$-adic quantum phytsics as well as in some cognitive models.

nlin.CG↗
arXiv2004

Spontaneous Emergence of Complex Optimal Networks through Evolutionary Adaptation

An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Here we present a theory of self-organization by evolutionary adaptation in which we show how the structure and organization of a network is related to the survival, or in general the performance, objectives of the system. We propose that a complex system optimizes its network structure in order to maximize its overall survival fitness which is composed of short-term and long-term survival components. These in turn depend on three critical measures of the network, namely, efficiency, robustness and cost, and the environmental selection pressure. Using a graph theoretical case study, we show that when efficiency is paramount the "Star" topology emerges and when robustness is important the "Circle" topology is found. When efficiency and robustness requirements are both important to varying degrees, other classes of networks such as the "Hub" emerge. Our assumptions and results are consistent with observations across a wide variety of applications.

nlin.AO↗
arXiv2004

Epidemiology Through Cellular Automata: Case of Study Avian Influenza in Indonesia

This paper performs the utilization of cellular automata computational analysis as the dynamic model of spatial epidemiology. Here, explored elementary aspects of cellular automata and its application in analyzing contagious disease, in this case avian influenza disease in Indonesia. Computational model is built and map-based simulation is performed using several simplified data of such transportation through sea in Indonesia, and its accordance with poultries in Indonesia, with initial condition of notified avian influenza infected area in Indonesia. The initial places are Pekalongan, West Java, East Java, and several regions in Sumatera. The result of simulation is showing the spreading-rate of influenza and in simple way and describing possible preventive action through isolation of infected areas as a major step of preventing pandemic.

nlin.CG↗
arXiv2004

Advancing density waves and phase transitions in a velocity dependent randomization traffic cellular automaton

Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium.

nlin.CG↗
arXiv2004

Introduction to Random Boolean Networks

The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study their generic properties. Like this, RBNs have been used for exploring the configurations where life could emerge. The fact that RBNs are a generalization of cellular automata makes their research a very important topic. The tutorial, intended for a broad audience, presents the state of the art in RBNs, spanning over several lines of research carried out by different groups. We focus on research done within artificial life, as we cannot exhaust the abundant research done over the decades related to RBNs.

nlin.AO↗
arXiv2004

A model for urban growth processes with continuum state cellular automata and related differential equations

A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into account migration processes from and towards the external world. The transport network is considered through an integration index describing the capability of the network to interconnect the different parts of the city. The time evolution is given by Poisson distributed stochastic jumps affecting the dynamical variables, with intensities depending on the configuration of the system in a suitable set of neighbourhoods. The intensities of the Poisson processes are given in term of a set of potentials evaluated applying fuzzy logic to a practical method frequently used in Switzerland to evaluate the attractiveness of a terrain for different land uses and the related rents. The use of a continuum state space enables one to write a system of differential equations for the time evolution of the CA and thus to study the system from a dynamical systems theory perspective. This makes it possible, in particular, to look systematically for bifurcations and phase transitions in CA based models of urban systems.

nlin.CG↗
arXiv2004

Dynamic Domains Networks

We present a model for the description of the evolution of contacts among individuals in a network. At each time step each individual is associated with a domain or neighborhood of fully connected agents.The dynamics of this changing neighborhood will later be translated into a situation where the links between individuals are also dynamic. A characterization in terms of the parameters that govern the evolution of the network and a comparison to previous work on Small World networks is presented as well.

nlin.CG↗
arXiv2004

Size-Distribution Scaling in Clusters of Allelomimetic Agents

The allelomimesis clustering model is based on only two parameters: a local parameter $α$ that represents the probability of nearest-neighbor copying and a global parameter $p$ that represents the fraction of unresponsive agents. The model results into the formation of clusters of agents, the sizes of which obey a distribution that is determined by the values of $α$ and $p$. Several experimental data are fitted by tuning the two parameters. In particular, the significance of the value of $α$ that corresponds to an experimental data is discussed and is justified according to behavioral context. Recommendations for possible extensions of the model are also enumerated.

nlin.AO↗
arXiv2004

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.

nlin.CG↗
arXiv2004

An Equation-Free Approach to Nonlinear Control: Coarse Feedback Linearization With Pole-Placement

We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the solution of a functional equation involving the macroscopic (coarse-grained) system model. In the absence of such a closed-form model, short, appropriately initialized bursts of microscopic simulation are designed and performed, and their results used to estimate on demand the quantities required for the numerical solution of the (explicitly unavailable) functional equation. Our illustrative example is a kinetic Monte Carlo realization of a simplified heterogeneous catalytic reaction scheme

nlin.CG↗
arXiv2004

Randomness Evaluation and Hardware Implementation of Nonadditive CA-Based Stream Cipher

We shall review the cellular automaton(CA)-based pseudorandom-number generators (PRNGs), and show that one of these PRNGs can generate high-quality random numbers which can pass all of the statistical tests provided by the National Institute of Standards and Technology (NIST). A CA is suitable for hardware implementation. We demonstrate that the CA-based stream cipher, which is implemented in the field-programmable gate arrays (FPGA), has a high encryption speed in a real-time video encryption and decryption system.

nlin.CD↗
arXiv2005

Second order additive invariants in elementary cellular automata

We investigate second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singularities. At the singularity, the current decays to its equilibrium value as a power law $t^α$, and the value of the exponent $α$ obtained from numerical simulations is very close to -1/2. This is in agreements with values previously reported for number-conserving rules, and leads to a conjecture that regardless of the order of the invariant, exponent $α$ seems to have a universal value of 1/2.

nlin.CG↗