Multiway Sequential Cellular Automata

Managing risk is important to any E-commerce merchant. Various machine learning (ML) models combined with a rule set as the decision layer is a common practice to manage the risks. Unlike the ML models that can be automatically refreshed periodically based on new risk patterns, rules are generally static and rely on manual updates. To tackle that, this paper presents a data-driven and automated rule optimization method that generates multiple Pareto-optimal rule sets representing different trade-offs between business objectives. This enables business owners to make informed decisions when choosing between optimized rule sets for changing business needs and risks. Furthermore, manual work in rule management is greatly reduced. For scalability this method leverages Apache Spark and runs either on a single host or in a distributed environment in the cloud. This allows us to perform the optimization in a distributed fashion using millions of transactions, hundreds of variables and hundreds of rules during the training. The proposed method is general but we used it for optimizing real-world E-commerce (Amazon) risk rule sets. It could also be used in other fields such as finance and medicine.

We propose a competition-based knowledge integration approach to effectively integrate multiple rule sets into a centralized knowledge base. The proposed approach consists of two phases: knowledge encoding and knowledge integrating. In the encoding phase, each rule in the rule set is first encoded as a rule bit-string. The combined bit strings from multiple rule sets thus form an initial knowledge population. In the knowledge integration phase, a genetic algorithm generates an optimal or nearly optimal rule set from these initial rule sets. Experiments on diagnosing brain tumors were made to compare the accuracy of a rule set generated by the proposed approach with that of the initial rule sets derived from different groups of experts or induced by various machine learning techniques. Results show that the rule set derived by the proposed approach is much more accurate than each initial rule set on its own.

Parallel implementation of cellular automata (CA) model of heterogeneous catalysis classical reaction, namely carbon monoxide oxidation (CO) reaction over platinum surface is presented. Catalytic reactions when being far from equilibrium may be accompanied by such critical phenomena as oscillations, kinetic phase transitions and chaos. Besides fundamental interest studying of basic kinetic laws of physicochemical processes on metals of platinum group has the important practical application. These reactions are used for environmental cleaning of exhaust from CO. The asynchronous cellular automata being sometimes referred to as Monte-Carlo method are the most suitable for describing of complex behavior of nonlinear catalytic systems. CA simulation of heterogeneous catalysis reactions requires to solve problems of very large size, therefore it is necessary to use efficient algorithms of parallelization. For the asynchronous CA of efficient parallel implementation is stiff problem. Therefore to solve this problem the asynchronous CA is transformed in block-synchronous CA. The block-synchronous mode of CA operation decreases the stochasticity of the process. Therefore it is necessary to check, whether block-synchronous CA conserves asynchronous CA evolution. This is done by comparative analysis of simulation characteristics such as probability distribution of reagents concentrations mathematical expectation and dispersion of concentrations and bifurcation diagrams of oxidation reaction obtained by CA simulation with asynchronous and block-synchronous operation modes. Obtained characteristics coincidence of asynchronous and block-synchronous CA evolutions is shown. In addition, comparison asynchronous and block-synchronous CA evolutions for models “ZGB” and “naive diffusion” are performed. Consequently, conclusion about acceptable accuracy of approximation of asynchronous mode to block-synchronous one for the class “reaction – diffusion” models is made. Parallel implementation of block-synchronous CA algorithm results and estimations of its efficiency are presented.

This special issue contains a selection of papers presented at the ‘‘Third International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models’’ (ACA 2014), held as a satellite workshop of the 11th International Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six papers were selected and, after an additional review process, five of them have been included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2014 conference. The ACA workshop is devoted to the theme of asynchrony, a hot topic, inside Cellular Automata and other Discrete Models as, for instance, Boolean Networks. Cellular Automata are a well-known formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step by means of a same rule. Recent trends consider the modeling of asynchronous systems based on local and possibly non-uniform interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata and Discrete Models. Typical, but not exclusive, topics of the workshop are dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, and models of real phenomena. The paper ‘‘Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata’’ by Henryk Fukś and Nazim Fates considers aasynchronous elementary cellular automata, that is elementary cellular automata in which each cell independently updates with probability a. By means of an extension of the mean-field approximation technique, the authors study the phase transitions in such automata, i.e., the changes of the dynamical behavior which may occur when the parameter a varies. In the paper ‘‘Supercritical probabilistic cellular automata: How effective is the synchronous updating?’’, PierreYves Louis deals with the issue of quantifying the effectiveness of the parallel updating in probabilistic cellular automata, i.e., cellular automata where the local rule is defined by means of a probability. Two interesting classes of probabilistic cellular automata are considered. An analysis of simulation is presented and shows that the behavior of these classes is nearly asynchronous when transition phase phenomena occur. Boolean Networks model the dynamical interaction of components which take a binary state. They have been & Alberto Dennunzio dennunzio@disco.unimib.it

Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies by D. Floreano and C. Mattiussi This is a book that bridges biological systems and computer science. For digital-based researchers, having this book which details the biological components of natural life and seamlessly integrates that knowledge into our digital realm is an essential asset. Each chapter is systematically introduces the reader to a biological system while easing them into the its computational counterpart. There are seven chapters covering evolution, cellular, neural, developmental, immune, behavioral, and collective systems. Chapter 1 introduces the fundamental concept of computational evolution as related to biological systems. This chapter starts with the basic concepts of evolutionary theory and progresses, covering everything from fitness functions to analog circuits. The following chapter presents the next logical step upwards in biology, cellular structures and systems. Again introducing the basics of life and progressing towards cellular automata. Chapter 3 covers Neural Networks by introducing the Biological Nervous System, then the Artificial Neural Network. The core concepts to Neural Networks are detailed in a systematic and common-sense manner, introducing unsupervised learning, supervised learning, and reinforce learning, then progressing onto neural hardware and hybrid systems. In Chapter 4, the authors detail developmental systems, explaining how nature utilizes the cellular structures to how engineers can mimic nature. This theme of progression from biological introduction to digital computation is reproduced as a single voice through out each chapter. The fundamentals of Bio-Inspired Artificial Intelligence are well demonstrated, allowing for a novice researcher in this area to develop the necessary skills and have a firm grasp on this topic. Once the reader has a solid grasp of the building blocks of life, the authors present chapters related to larger systems. Of particular interest to my research is the chapter on Immune Systems. This chapter provides a fundamental understanding of the Human Immune System, detailing the finer points of immunological cellular structures, while introducing a slightly more than generalized immune response concept. After a lengthy introduction of human immunology, we are introduced to the core of Artificial Immune Systems, the Negative Selection Algorithm and Clonal Selection Algorithm. Each one of these algorithms is covered enough so that the reader is capable of understanding each respective algorithms strengths and limitations. For new researchers to Artificial Immune Systems, days of reading journal articles is summarized in these sections, allowing for intelligent and efficient decision making in choosing your next step of research. Chapter 6 and 7 provides the audience with behavior systems and collective systems, respectively. The behavioral systems covered in this book relate to aspects of AI, robots, and some machine learning. Once behavior is understood, collective and cooperative systems are covered. Optimization techniques of particle swarms, ant colonies, and topics derived for robotics are detailed and well explained. While this is not a textbook, is does cover the fundamental concepts required to research Bio-Inspired Artificial Intelligence. For myself, the quality of this book can simply be noted by the publishers, MIT Press. Many of the best books I have encountered in my studies have been published by MIT, and here is another. Floreano and Mattiussi have not let me down in their quality, albeit I do have some complaints. First, while the topics cover a solid breadth, the depth on detailing the computation side is limited. I would like to have seen either more depth in each chapter or a broader look at each chapters algorithms, but the book falls somewhere in the middle. My current research involves Danger Signals and their relationship to preventing Epidemic Attacks, so I would have like to seen more detail about Polly Matzinger's Danger Theory rather than one short paragraph saying that it is not universally accepted. While Immunologists may debate Danger Theory, novel algorithms have been developed off of the concept of Danger Theory and deserve a place in this book. Yet to counter my own argument, the authors do finish off each chapter with a Suggested Readings section outlining a series of excellent supplement papers to the chapters topics that would eventually lead the reader to these novel topics. Overall, if you are interested in this field, buy this book. You can find it online at MIT Press for a discounted price. This book will make an excellent addition to any computer researchers library. Anthony Kulis, Department of Computer Science, Southern Illinois University

Cellular automata (CA) is a well-known computation method introduced by John von Neumann and Stanislaw Ulam in the 1940s. Since then, it has been studied in various fields such as computer science, biology, physics, chemistry, and art. The Classic CA algorithm is a calculation of a grid of cells' binary states based on neighboring cells and a set of rules. With the variation of these parameters, the CA algorithm has evolved into alternative versions such as 3D CA, Multiple neighborhood CA, Multiple rules CA, and Stochastic CA (Url-1). As a rule-based generative algorithm, CA has been used as a bottom-up design approach in the architectural design process in the search for form (Frazer,1995; Dinçer et al., 2014), in simulating the displacement of individuals in space, and in revealing complex relations at the urban scale (Güzelci, 2013). There are implementations of CA tools in 3D design software for designers as additional scripts or plug-ins. However, these often have limited ability to create customized CA algorithms by the designer. This study aims to create a customizable framework for 3D CA algorithms to be used in 3D form explorations by designers. Grasshopper3D, which is a visual scripting environment in Rhinoceros 3D, is used to implement the framework. The main difference between this work and the current Grasshopper3D plug-ins for CA simulation is the customizability and the real-time control of the framework. The parameters that allow the CA algorithm to be customized are; the initial state of the 3D grid, neighborhood conditions, cell states and rules. CA algorithms are created for each customizable parameter using the framework. Those algorithms are evaluated based on the ability to generate form. A voxel-based approach is used to generate geometry from the points created by the 3D cellular automata. In future, forms generated using this framework can be used as a form generating tool for digital environments.

Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs. In particular, we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time O(1.7159^n), of split graphs in time O(1.3803^n), and of AT-free, strongly chordal, and distance-hereditary graphs in time O^*(3^{n/3}), where n is the number of vertices of the input graph. Our algorithms imply corresponding upper bounds for the number of minimal connected dominating sets for these graph classes.

Cellular automata (CA) are a research subject of plethora of works. CA are applied in many areas of natural science and suitable for modeling of difference processes, phenomenon (Belousov-Zhabotinskiy’s Reaction [2], the turbulence [3], epidemic spread [4], population dynamic [5], electoral pro-cesses [6], etc.). The 30th rule of Wolfram’s Code [1] is widely spread in computer sciences for creating of pseudorandom sequences of integers. As known, the CA is a dynamic system. Usually CA set by logical op-erations, set of rules. It is quite cumbersome for program realization and impact on debugging time. The easier way is creation of the algorithm by analytic representation and don’t use enormous amount of loops. Object of this work is representation of CA as a system of difference equations. It allows us to generalize CA, thus we could model it in spaces of any dimensions and it cells could take an arbitrary finite or infinite num-ber of states. Further we would apply famous control methods of dynamical systems using the information ofprevious states of the system. Besides, this approach helps us to consider CA wider and find new features of these systems, regular structures, periodic structures or structures that are close to periodic ones. In this work we use the superposition of linear and nonlinear maps that calls as Diffusion and Reaction according-ly. This approach is applied on CA that work as Wolfram Code [1] respectively. Examples of suggested ap-proach applying are illustrated in the last section. All in all we have represented CA in form of a system of difference equations. In further study it would allow to research phenomenon connected with CA construc-tion or we could control CA due to method represented in [7, 8].

This volume contains five papers presented during two workshops, ‘‘First International Workshop on Asynchronous Cellular Automata’’ (ACA 2010) and ‘‘Fifth International Workshop on Natural Computing’’ (IWNC 2010), held at the 9th International Conference on Cellular Automata for Research and Industry (ACRI 2010) in Ascoli Piceno (Italy) in the period September 21–24th, 2010. The ACA workshop is devoted to the theme of asynchrony inside Cellular Automata. Cellular Automata are a wellknown formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step. Recent trends consider the modeling of asynchronous systems based on local interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata. The IWNC workshop is concerned with theoretical as well as experimental studies of nature-inspired paradigms of computations. More precisely, the scientific field of Natural Computing encompasses theoretical and experimental investigations of nature-inspired principles of information processing, novel and emerging paradigms of computation and computing architectures, and case studies of simulated or real-world computing devices implemented in biological, social, chemical, engineering, and physical systems. Typical, but not exclusive, topics of the two workshops are: various aspects of asynchronous cellular automata (dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, models of real phenomena) and nature-inspired computation and communication (DNA computation, cellular automata, physics of computation, computation in living cells, nanocomputing, evolutionary computing, artificial chemistry, neural computation). After an additional review process, three papers from the ACA workshop and two from the IWNC workshop were selected and included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2010 conference. The paper by L. Manzoni is about the dynamical behavior of asynchronous cellular automata. The classical cellular automata properties are adapted to the synchronous case and related results are shown. In their paper, S. Bandini et al. give an analysis of different update schemes for asynchronous cellular automata and discuss the respective effects by means of the class of 1D cellular automata. L. Vanneschi et al. deal with genetic algorithms to evolve asynchronous cellular automata and focus on learning robustness with respect to the synchronous case. In the article by J. B. Yune`s it is shown how universal computations can be achieved on one-dimensional cellular automata and a universal brick used in grids is given—it allows to obtain intrinsic universal cellular automata. The article by Sahu et al. discusses a molecular cellular automaton recently introduced by the authors and shows novel features that have never been proposed in conventional CA models. We would like to warmly thank all referees for their valuable contributions. We also want to thank Professor Grzegorz Rozenberg for offering us the opportunity to publish this special issue in Natural Computing.

We consider asynchronous one-dimensional cellular automata (CA). It is shown that there is one with von Neumann neighborhood of radius 1 which can simulate each asynchronous one-dimensional cellular automaton. Analogous constructions are described for ?-asynchronous CA (where each cell independently enters a new state with probability ?, and for "neighborhood independent" asynchronous CA (where never two cells are updated simultaneously if one is in the neighborhood of the other). This also gives rise to a construction for so-called fully asynchronous CA (where in each step exactly one cell is updated).

In recent computer science research highly robust and scalable sets that are composed of autonomous individuals have become more and more important. The online partitioning problem (OPP) deals with the distribution of huge sets of agents onto different targets in consideration of several objectives. The agents can only interact locally and there is no central instance or global knowledge. In this paper we work on this problem field by modifying ideas from the area of cellular automata (CA). We expand the well known majority/density classification task for one-dimensional CAs to two-dimensional CAs. The transition rules for the CA are learned by using a genetic algorithm (GA). Each individual in the GA is a set of transition rules with additional distance information. This approach shows very good behaviour compared to other strategies for the OPP and is very fast once an appropriate set of rules is learned by the GA

Running a cellular automaton (CA) on a rectangular lattice is a time-honored method for studying artificial life on a digital computer. Commonly, the researcher wishes to investigate some specific or general mode of behavior, say, the ability of a coherent pattern of points to glide within the lattice, or to generate copies of itself. This technique has a problem: how to design the transitions table-the set of distinct rules that specify the next content of a cell from its current content and that of its near neighbors. Often the table is painstakingly designed manually, rule by rule. The problem is exacerbated by the potentially vast number of individual rules that need be specified to cover all combinations of center and neighbors when there are several symbols in the alphabet of the CA. In this article a method is presented to have the set of rules evolve automatically while running the CA. The transition table is initially empty, with rules being added as the need arises. A novel principle drives the evolution: maximum economy of means-maximizing the reuse of rules introduced on previous cycles. This method may not be a panacea applicable to all CA studies. Nevertheless, it is sufficiently potent to evolve sets of rules and associated patterns of points that glide (periodically regenerate themselves at another location) and to generate gliding "children" that then "mate" by collision.

This paper proposes a variation of two-dimensional (2-D) cellular automata (CA) by adopting a simpler structure than the normal 2-D CA and a unique neighborship characteristic-asymmetric neighborship. The randomness of 2-D CA based on asymmetric neighborship is discussed and compared with one-dimensional (1-D) and 2-D CA. The results show that they are better than 1-D CA and could compete with conventional 2-D CA under certain array setting, output method, and transition rule. Furthermore, the structures of 2-D CA based on asymmetric neighborship were evolved using some multiobjective genetic algorithm. The evolved 2-D CA could pass DIEHARD tests with only 50 cells, which is less than the minimal number of cells (i.e., 55 cells) needed for neighbor-changing 1-D CA to pass DIEHARD. In addition, a refinement procedure to reduce the cost of 2-D CA based on asymmetric neighborship is discussed. The minimal number of cells found is 48 cells for it to pass DIEHARD. The structure of this 48-cell 2-D CA is identical to that of the evolved 10 * 5 2-D CA, except that 2 horizontal cells in the evolved 10 * 5 2-D CA are removed.

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

Let be a class of graphs with a membership test, , and let be the class of graphs in of path‐width at most . We present an interactive framework that finds an unavoidable set for , which is a set of graphs such that any graph in contains an isomorphic copy of a graph in . At the core of our framework is an algorithm that verifies whether a set of graphs is, indeed, unavoidable for . While obstruction sets are well‐studied, so far there is no general theory or algorithm for finding unavoidable sets. In general, it is undecidable whether a finite set of graphs is unavoidable for a given graph class. However, we give a criterion for termination: our algorithm terminates whenever is locally checkable of bounded maximum degree and is a finite set of connected graphs. For example, ‐regular graphs, ‐colourable graphs, and ‐free graphs are locally checkable classes. We put special emphasis on the case that is the class of cubic graphs and tailor the algorithm to this case. In particular, we introduce the new concept of high‐degree‐first path‐decompositions, which enables highly efficient pruning techniques. We exploit our framework to prove a new lower bound on the path‐width of cubic graphs. Moreover, we determine the extremal girth values of cubic graphs of path‐width for all and all smallest graphs which take on these extremal girth values. Further, we present a new constructive characterisation of the extremal cubic graphs of path‐width 3 and girth 4.