Self‐organizing traffic lights at multiple‐street intersections

The elementary cellular automaton following rule 184 can mimic particles flowing in one direction at a constant speed. Therefore, this automaton can model highway traffic qualitatively. In a recent paper, we have incorporated intersections regulated by traffic lights to this model using exclusively elementary cellular automata. In such a paper, however, we only explored a rectangular grid. We now extend our model to more complex scenarios using an hexagonal grid. This extension shows first that our model can readily incorporate multiple‐way intersections and hence simulate complex scenarios. In addition, the current extension allows us to study and evaluate the behavior of two different kinds of traffic‐light controller for a grid of six‐way streets allowing for either two‐ or three‐street intersections: a traffic light that tries to adapt to the amount of traffic (which results in self‐organizing traffic lights) and a system of synchronized traffic lights with coordinated rigid periods (sometimes called the “green‐wave” method). We observe a tradeoff between system capacity and topological complexity. The green‐wave method is unable to cope with the complexity of a higher‐capacity scenario, while the self‐organizing method is scalable, adapting to the complexity of a scenario and exploiting its maximum capacity. Additionally, in this article, we propose a benchmark, independent of methods and models, to measure the performance of a traffic‐light controller comparing it against a theoretical optimum. © 2011 Wiley Periodicals, Inc. Complexity, 2012     

Application of averaging techniques to traffic flow theory

Real traffic data are very versatile and are hard to explain with the so‐called standard fundamental diagram. A simple microscopic model can show that the heterogeneity of traffic results in a reduced mean flow and that the reduction is proportional to the density variance. Standard averaging techniques allow us to evaluate this reduction without having to describe the complex microscopic interactions. Using a second equation for the variance results in a two‐dimensional hyperbolic system that can be put in conservative form. The Riemann problem is completely solved in the case of a parabolic fundamental diagram, and the solutions are compared with the famous second‐order Aw–Rascle–Zhang model in a simulation of lane reduction. Adding a diffusion term results in entropy production, and the diffusive model is studied as well. Finally, a numerical scheme is used and converges to the analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Self‐dual and self‐petrie‐dual regular maps

Regular maps are cellular decompositions of surfaces with the “highest level of symmetry”, not necessarily orientation‐preserving. Such maps can be identified with three‐generator presentations of groups G of the form G = 〈a, b, c|a² = b² = c² = (ab)^k = (bc)^m = (ca)² = … = 1〉; the positive integers k and m are the face length and the vertex degree of the map. A regular map (G;a, b, c) is self‐dual if the assignment b?b, c?a and a?c extends to an automorphism of G, and self‐Petrie‐dual if G admits an automorphism fixing b and c and interchanging a with ca. In this note we show that for infinitely many numbers k there exist finite, self‐dual and self‐Petrie‐dual regular maps of vertex degree and face length equal to k. We also prove that no such map with odd vertex degree is a normal Cayley map. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:152‐159, 2012     

Modelling traffic flow with a time‐dependent fundamental diagram

We model traffic flow with a time‐dependent fundamental diagram. A time‐dependent fundamental diagram arises naturally from various factors such as weather conditions, traffic jam or modern traffic congestion managements, etc. The model is derived from a car‐following model which takes into account the situation changes over the time elapsed time. It is a system of non‐concave hyperbolic conservation laws with time‐dependent flux and the sources. The global existence and uniqueness of the solution to the Cauchy problem is established under the condition that the variation in time of the fundamental diagram is bounded. The zero relaxation limit of the solutions is found to be the unique entropy solution of the equilibrium equation. Copyright © 2004 John Wiley & Sons, Ltd.     

On a generalized dimension of self‐affine fractals

For a d ×d expanding matrix A, we de.ne a pseudo‐norm w (x) in terms of A and use this pseudo‐norm (instead of the Euclidean norm) to define the Hausdorff measure and the Hausdorff dimension dim^w _H E for subsets E in R ^d . We show that this new approach gives convenient estimations to the classical Hausdorff dimension dim^w _H E, and in the case that the eigenvalues of A have the same modulus, then dim^w _H E and dim_H E coincide. This setup is particularly useful to study self‐affine sets T generated by ?j (x) = A^–1(x +dj), dj ∈ R ^d , j = 1, …, N. We use it to investigate the fractality of T for the case that {?j }^N _{j =1} satisfying the open set condition as well as the cases without the open set condition. We extend some well‐known results in the self‐similar sets to the self‐af.ne sets. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Life‐like self‐reproducers

In order to understand the interplay among information, genetic instructions, and phenotypic variations, self‐reproducers discovered in two‐dimensional cellular automata are considered as proto‐organisms, which undergo to mutations as they were in a real environmental situation. We realized a computational model through which we have been able to discover the genetic map of the self‐reproducers and the networks they use. Identifying in these maps sets of different functional genes, we found that mutations in the genetic sequences could affect both external shapes and behavior of the self‐reproducers, thus realizing different life‐like strategies in the evolution process. The results highlight that some strategies evolution uses in selecting organisms that are fitting with changing environmental situations maintain the self‐reproducing function, whereas other variations create new self‐reproducers. These self‐reproducers in turn realize different genetic networks, which can be very different from the basic ancestors pools. The mutations that are disruptive bring self‐reproducers to disappear, while other proto‐organisms are generated. © 2004 Wiley Periodicals, Inc. Complexity 9: 38–55, 2004     

Decomposition of integral self‐affine multi‐tiles

In contrast to the situation with self‐affine tiles, the representation of self‐affine multi‐tiles may not be unique (for a fixed dilation matrix). Let be an integral self‐affine multi‐tile associated with an integral, expansive matrix B and let K tile by translates of . In this work, we propose a stepwise method to decompose K into measure disjoint pieces  satisfying in such a way that the collection of sets forms an integral self‐affine collection associated with the matrix B and this with a minimum number of pieces . When used on a given measurable subset K which tiles by translates of , this decomposition terminates after finitely many steps if and only if the set K is an integral self‐affine multi‐tile. Furthermore, we show that the minimal decomposition we provide is unique.     

Transitive tournaments and self‐complementary graphs

A simple proof is given for a result of Sali and Simonyi on self‐complementary graphs. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 111–112, 2001     

The self‐organization of genomes

Menzerath‐Altmann law is a general law of human language stating, for instance, that the longer a word, the shorter its syllables. With the metaphor that genomes are words and chromosomes are syllables, we examine if genomes also obey the law. We find that longer genomes tend to be made of smaller chromosomes in organisms from three different kingdoms: fungi, plants, and animals. Our findings suggest that genomes self‐organize under principles similar to those of human language. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Nonextensive model of self‐organizing systems

The article concerns the new nonextensive model of self‐organizing systems and consists of two interrelated parts. The first one presents a new nonextensive model of interaction between elements of systems. The second one concerns the relationship between microscopic and macroscopic processes in complex systems. It is shown that nonextensivity and self‐organization of systems is a result of mismatch between its elements. © 2013 Wiley Periodicals, Inc. Complexity 18: 28–36, 2013     

Fractality and self‐organization in the orthodox iconography

The authors consider the Orthodox iconography of Byzantine style aimed at examining the existence of complex behavior and fractal patterns. It has been demonstrated that fractality in icons is manifested as two types—descending and ascending, where the former one corresponds to the apparent information and the latter one to the hidden causal information defining the spatiality of icon. Self‐organization, recognized as the increase of the causal information in temporal domain, corresponds to contextualization of the observer's personage position. The results presented in the forms of plots and tables confirm the adequacy of the model being the completion of visual perception. © 2015 Wiley Periodicals, Inc. Complexity 21: 55–68, 2016     

Using self‐dissimilarity to quantify complexity

For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self‐dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self‐dissimilarity. This signature can, if desired, incorporate a novel information‐theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self‐dissimilarity can be measured for many kinds of real‐world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self‐dissimilarity of a system does not require one to already have a model of the system. These facts may allow self‐dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self‐dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self‐dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007     

Average distances between points in graph‐directed self‐similar fractals

We study several distinct notions of average distances between points belonging to graph‐directed self‐similar subsets of . In particular, we compute the average distance with respect to graph‐directed self‐similar measures, and with respect to the normalised Hausdorff measure. As an application of our main results, we compute the average distance between two points belonging to the Drobot–Turner set with respect to the normalised Hausdorff measure, i.e. we compute where s denotes the Hausdorff dimension of and is the s‐dimensional Hausdorff measure; here the Drobot–Turner set (introduced by Drobot & Turner in 1989) is defined as follows, namely, for positive integers N and m and a positive real number c, the Drobot–Turner set is the set of those real numbers for which any m consecutive base N digits in the N‐ary expansion of x sum up to at least c. For example, if , and , then our results show that where is the unique positive real number such that .     

Constructing regular self‐complementary uniform hypergraphs

In this article, we examine the possible orders of t‐subset‐regular self‐complementary k‐uniform hypergraphs, which form examples of large sets of two isomorphic t‐designs. We reformulate Khosrovshahi and Tayfeh–Rezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank k, and these conditions simplify to a more transparent relation between the order n and rank k in the case where k is a sum of consecutive powers of 2. Moreover, we present new constructions for 1‐subset‐regular self‐complementary uniform hypergraphs, and prove that these necessary conditions are sufficient for all k, in the case where t = 1. © 2011 Wiley Periodicals, Inc. J Combin Designs 19: 439‐454, 2011     

Pseudo‐random properties of self‐complementary symmetric graphs

There are some results in the literature showing that Paley graphs behave in many ways like random graphs G(n, 1/2). In this paper, we extend these results to the other family of self‐complementary symmetric graphs. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 310–316, 2004     

Signal‐regulated systems and networks

The article presents the use of signal regulatory networks (SRNs), a biologically inspired model based on gene regulatory networks. SRNs are a way of understanding a class of self‐organizing IT systems, signal‐regulated systems (SRSs). This article builds on the theory of SRSs and introduces some formalisms to clarify the discussion. An exemplar SRS that can be evaluated using SRNs is presented. Finally, an implementation of an adaptive and robust solution, built on a theory of SRSs and analyzed as a SRN, is shown to be plausible. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Structural and functional growth in self‐reproducing cellular automata

In this article, we analyze the dynamics of change in two‐dimensional self‐reproducers, identifying the processes that drive their evolution. We show that changes in self‐reproducers structure and behavior depend on their genetic memory. This consists of distinct yet interlinked components determining their form and function. In some cases these components degrade gracefully, changing only slightly; in others the changes destroy the original structure and function of the self‐reproducer. We sketch these processes at the genotype and the phenotype level—showing that they follow distinct trajectories within mutation space and quantifying the degree of change produced by different trajectories. We show that changes in structure and behavior depend on the interplay between the genotype and the phenotype. This determines universal structures, from which it is possible to construct a great number of self‐reproducing systems, as we observe in biology. Creative processes of change produce divergent and/or convergent methods for the generation of self‐reproducers. Divergence involves the creation of completely new information convergence involves local change and specialization of the structures concerned. © 2006 Wiley Periodicals, Inc. Complexity 11: 12–29, 2006     

H‐self‐adjoint matrices. Application to radiosity

In computer graphics, in the radiosity context, a linear system Φx=b must be solved and there exists a diagonal positive matrix H such that H Φ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive‐definite matrix H. We shall prove that these matrices are self‐adjoint with respect to a particular innerproduct defined on ?ⁿ. As a result, like Hermitian matrices, they have real eigenvalues and they are diagonalizable. We shall also show how to extend the Courant–Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem. Copyright © 2002 John Wiley & Sons, Ltd.     

Non‐Cayley‐isomorphic self‐complementary circulant graphs

Non‐CI self‐complementary circulant graphs of prime‐squared order are constructed and enumerated. It is shown that for prime p, there exists a self‐complementary circulant graph of order p² not Cayley isomorphic to its complement if and only if p ≡ 1 (mod 8). Such graphs are also enumerated. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 128–141, 2000     

Emergence of self‐similar tree network organization

The self‐similar tree topology in open dissipative systems is formed as a result of self‐organization and found in various examples, such as river networks, blood vessels, vascular organizations in plants, and even lightning. It is generally assumed that the tree organization is a result of a dynamic process that minimizes the dissipation of energy. Here, we argue that inherent randomness is a sufficient condition for the generation of tree patterns under evolutionary dynamics and the decrease of energy expenditure is not the cause but a consequent signature. © 2008 Wiley Periodicals, Inc. Complexity, 13: 30–37, 2008