Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Cellular automata and dynamical systems

In this thesis we investigate the theoretical nature of the mathematical structures termed cellular automata. Chapter 1: Reviews the origin and history of cellular automata in order to place the current work into context. Chapter 2: Develops a cellular automata framework which contains the main aspects of cellular automata structure which have appeared in the literature. We present a scheme for specifying the cellular automata rules for this general model and present six examples of cellular automata within the model. Chapter 3: Here we develop a statistical mechanical model of cellular automata behaviour. We consider the relationship between variations within the model and their relationship to dynamical systems. We obtain results on the variance of the state changes, scaling of the cellular automata lattice, the equivalence of noise, spatial mixing of the lattice states and entropy, synchronous and asynchronous cellular automata and the equivalence of the rule probability and the time step of a discrete approximation to a dynamical system. Chapter 4: This contains an empirical comparison of cellular automata within our general framework and the statistical mechanical model. We obtain results on the transition from limit cycle to limit point behaviour as the rule probabilities are decreased. We also discuss failures of the statistical mechanical model due to failure of the assumptions behind it. Chapter 5: Here a practical application of the preceding work to population genetics is presented. We study this in the context of some established population models and show it may be most useful in the field of epidemiology. Further generalisations of the statistical mechanical and cellular automata models allow the modelling of more complex population models and mobile populations of organisms. Chapter 6: Reviews the results obtained in the context of the open questions introduced in Chapter 1. We also consider further questions this work raises and make some general comments on how these may apply to related fields

Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

On the development of slime mould morphological, intracellular and heterotic computing devices

The use of live biological substrates in the fabrication of unconventional computing (UC) devices is steadily transcending the barriers between science fiction and reality, but efforts in this direction are impeded by ethical considerations, the field’s restrictively broad multidisciplinarity and our incomplete knowledge of fundamental biological processes. As such, very few functional prototypes of biological UC devices have been produced to date. This thesis aims to demonstrate the computational polymorphism and polyfunctionality of a chosen biological substrate — slime mould Physarum polycephalum, an arguably ‘simple’ single-celled organism — and how these properties can be harnessed to create laboratory experimental prototypes of functionally-useful biological UC prototypes. Computing devices utilising live slime mould as their key constituent element can be developed into a) heterotic, or hybrid devices, which are based on electrical recognition of slime mould behaviour via machine-organism interfaces, b) whole-organism-scale morphological processors, whose output is the organism’s morphological adaptation to environmental stimuli (input) and c) intracellular processors wherein data are represented by energetic signalling events mediated by the cytoskeleton, a nano-scale protein network. It is demonstrated that each category of device is capable of implementing logic and furthermore, specific applications for each class may be engineered, such as image processing applications for morphological processors and biosensors in the case of heterotic devices. The results presented are supported by a range of computer modelling experiments using cellular automata and multi-agent modelling. We conclude that P. polycephalum is a polymorphic UC substrate insofar as it can process multimodal sensory input and polyfunctional in its demonstrable ability to undertake a variety of computing problems. Furthermore, our results are highly applicable to the study of other living UC substrates and will inform future work in UC, biosensing, and biomedicine

Integrated information theory in complex neural systems

This thesis concerns Integrated Information Theory (IIT), a branch of information theory aimed at providing a fundamental theory of consciousness. At its core, lie two powerful intuitions: • That a system that is somehow more than the sum of its parts has non-zero integrated information, Φ; and • That a system with non-zero integrated information is conscious. The audacity of IIT’s claims about consciousness has (understandably) sparked vigorous criticism, and experimental evidence for IIT as a theory of consciousness remains scarce and indirect. Nevertheless, I argue that IIT still has merits as a theory of informational complexity within complexity science, leaving aside all claims about consciousness. In my work I follow this broad line of reasoning: showcasing applications where IIT yields rich analyses of complex systems, while critically examining its merits and limitations as a theory of consciousness. This thesis is divided in three parts. First, I describe three example applications of IIT to complex systems from the computational neuroscience literature (coupled oscillators, spiking neurons, and cellular automata), and develop novel Φ estimators to extend IIT’s range of applicability. Second, I show two important limitations of current IIT: that its axiomatic foundation is not specific enough to determine a unique measure of integrated information; and that available measures do not behave as predicted by the theory when applied to neurophysiological data. Finally, I present new theoretical developments aimed at alleviating some of IIT’s flaws. These are based on the concepts of partial information decomposition and lead to a unification of both theories, Integrated Information Decomposition, or ΦID. The thesis concludes with two experimental studies on M/EEG data, showing that a much simpler informational theory of consciousness – the entropic brain hypothesis – can yield valuable insight without the mathematical challenges brought by IIT.Open Acces

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

A Language-centered Approach to support environmental modeling with Cellular Automata

Die Anwendung von Methodiken und Technologien aus dem Bereich der Softwaretechnik auf den Bereich der Umweltmodellierung ist eine gemeinhin akzeptierte Vorgehensweise. Im Rahmen der "modellgetriebenen Entwicklung"(MDE, model-driven engineering) werden Technologien entwickelt, die darauf abzielen, Softwaresysteme vorwiegend auf Basis von im Vergleich zu Programmquelltexten relativ abstrakten Modellen zu entwickeln. Ein wesentlicher Bestandteil von MDE sind Techniken zur effizienten Entwicklung von "domänenspezifischen Sprachen"( DSL, domain-specific language), die auf Sprachmetamodellen beruhen. Die vorliegende Arbeit zeigt, wie modellgetriebene Entwicklung, und insbesondere die metamodellbasierte Beschreibung von DSLs, darüber hinaus Aspekte der Pragmatik unterstützen kann, deren Relevanz im erkenntnistheoretischen und kognitiven Hintergrund wissenschaftlichen Forschens begründet wird. Hierzu wird vor dem Hintergrund der Erkenntnisse des "modellbasierten Forschens"(model-based science und model-based reasoning) gezeigt, wie insbesondere durch Metamodelle beschriebene DSLs Möglichkeiten bieten, entsprechende pragmatische Aspekte besonders zu berücksichtigen, indem sie als Werkzeug zur Erkenntnisgewinnung aufgefasst werden. Dies ist v.a. im Kontext großer Unsicherheiten, wie sie für weite Teile der Umweltmodellierung charakterisierend sind, von grundsätzlicher Bedeutung. Die Formulierung eines sprachzentrierten Ansatzes (LCA, language-centered approach) für die Werkzeugunterstützung konkretisiert die genannten Aspekte und bildet die Basis für eine beispielhafte Implementierung eines Werkzeuges mit einer DSL für die Beschreibung von Zellulären Automaten (ZA) für die Umweltmodellierung. Anwendungsfälle belegen die Verwendbarkeit von ECAL und der entsprechenden metamodellbasierten Werkzeugimplementierung.The application of methods and technologies of software engineering to environmental modeling and simulation (EMS) is common, since both areas share basic issues of software development and digital simulation. Recent developments within the context of "Model-driven Engineering" (MDE) aim at supporting the development of software systems at the base of relatively abstract models as opposed to programming language code. A basic ingredient of MDE is the development of methods that allow the efficient development of "domain-specific languages" (DSL), in particular at the base of language metamodels. This thesis shows how MDE and language metamodeling in particular, may support pragmatic aspects that reflect epistemic and cognitive aspects of scientific investigations. For this, DSLs and language metamodeling in particular are set into the context of "model-based science" and "model-based reasoning". It is shown that the specific properties of metamodel-based DSLs may be used to support those properties, in particular transparency, which are of particular relevance against the background of uncertainty, that is a characterizing property of EMS. The findings are the base for the formulation of an corresponding specific metamodel- based approach for the provision of modeling tools for EMS (Language-centered Approach, LCA), which has been implemented (modeling tool ECA-EMS), including a new DSL for CA modeling for EMS (ECAL). At the base of this implementation, the applicability of this approach is shown

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time