Network decontamination is a well known mobile agent problem with many applications. We assume that all nodes of a network are contaminated (e.g., by a virus) and a set of agents is deployed to decontaminate them. An agent passing by a node decontaminates it, however a decontaminated node can be recontaminated if any of its neighbours is contaminated. In the vast literature a variety of models are considered and different assumptions are made on the power of the agents. In this thesis we study variation of the decontamination problem in mesh and tori topologies, under the assumption that when a node is decontaminated, it is immune to recontamination for a predefined amount of time t (called immunity time). After the immunity time is elapsed, recontamination can occur. We focus on three different models: mobile agents (MA), cellular automata (CA), and mobile cellular automata (MCA). The first two models are commonly studied and employed in several other contexts, the third model is introduced in this thesis for the first time. In each model we study the temporal decontamination problem (adapted to the particular setting) under a variety of assumptions on the capabilities of the decontaminating elements (agents for MA and MCA, decontaminating cells for CA). Some of the parameters we consider in this study are: visibility of the active elements, their ability to make copies of themselves, their ability to communicate, and the possibility to remember their past actions (memory). We describe several solutions in the various scenarios and we analyze their complexity. Efficiency is evaluated slightly differently in each model, but essentially the effort is in the minimization of the number of simultaneous decontaminating elements active in the system while performing the decontamination with a given immunity time.

Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.

Wireless sensor networks have been used in different applications due to the advancement of sensor technology. These uses also have raised different optimization issues. Most of the algorithms proposed as solutions to the various optimization problems are either centralized or distributed which are not ideal for these real life applications. Very few strictly local algorithms for wireless sensor networks exist in the literature. In this thesis, we consider some of these optimization problems of sensor networks, for example, sleep-wake scheduling, mobile dispersion, mobile object monitoring, and gathering problems. We also consider the depth adjustment problem of underwater sensor networks. We design cellular automaton based local algorithms for these problems. The cellular automaton is a bioinspired model used to model different physical systems including wireless sensor networks. One of the main advantages of using cellular automaton based algorithms is that they need very little local information to compute a solution. We perform different simulations and analysis and find that our algorithms are efficient in practice. / Thesis (Ph.D, Computing) -- Queen's University, 2012-11-25 13:37:36.854

Cellular automata (CA) are discrete dynamical systems comprised of a lattice of finite-state cells. At each time step, each cell updates its state as a function of the previous state of itself and its neighbours. Fuzzy cellular automata (FCA) are a real-valued extension of Boolean cellular automata which "fuzzifies" Boolean logic in the transition function using real values between zero and one (inclusive). To date, FCA have only been studied in disjunctive normal form (DNF). In this thesis, we study FCA in conjunctive normal form (CNF). We classify FCA in CNF both analytically and empirically. We compare these classes to their DNF counterparts. We prove that certain FCA exhibit chaos in CNF, in contrast to the periodic behaviours of DNF FCA. We also briefly explore five different forms of fuzzy logic, and suggest further study. In support of this research, we introduce novel methods of simulating and visualizing FCA.

Cellular automata (CA) are discrete dynamical systems comprised of a lattice of finite-state cells. At each time step, each cell updates its state as a function of the previous state of itself and its neighbours. Fuzzy cellular automata (FCA) are a real-valued extension of Boolean cellular automata which "fuzzifies" Boolean logic in the transition function using real values between zero and one (inclusive). To date, FCA have only been studied in disjunctive normal form (DNF). In this thesis, we study FCA in conjunctive normal form (CNF). We classify FCA in CNF both analytically and empirically. We compare these classes to their DNF counterparts. We prove that certain FCA exhibit chaos in CNF, in contrast to the periodic behaviours of DNF FCA. We also briefly explore five different forms of fuzzy logic, and suggest further study. In support of this research, we introduce novel methods of simulating and visualizing FCA.

Cellular automata (CA) are discrete dynamical systems comprised of a lattice of finite-state cells. At each time step, each cell updates its state as a function of the previous state of itself and its neighbours. Fuzzy cellular automata (FCA) are a real-valued extension of Boolean cellular automata which "fuzzifies" Boolean logic in the transition function using real values between zero and one (inclusive). To date, FCA have only been studied in disjunctive normal form (DNF). In this thesis, we study FCA in conjunctive normal form (CNF). We classify FCA in CNF both analytically and empirically. We compare these classes to their DNF counterparts. We prove that certain FCA exhibit chaos in CNF, in contrast to the periodic behaviours of DNF FCA. We also briefly explore five different forms of fuzzy logic, and suggest further study. In support of this research, we introduce novel methods of simulating and visualizing FCA.

Thesis (M.Eng.(Mechanical Engineering)--University of Pretoria, 2001. / Summaries in Afrikaans and English. Includes bibliographical references.

Master of Science / Department of Computer Science / Daniel Andresen / Modern techniques for simulating granular matter can produce excellent quality simulations, but usually involve a great enough performance cost to render them ineffective for real time applications. This leaves something to be desired for low-cost systems and interactive simulations which are more forgiving to inaccurate simulations, but much more strict in regards to the performance of the simulation itself. What follows is a proposal for a method of simulating granular matter that could potentially support millions of particles and several types for each particle while maintaining acceptable frame rates on consumer level hardware. By leveraging the power of consumer level graphics cards, effective data representation, and a model built around Cellular Automata a simulation can be run in real time.

Cellular automata (CA) are discrete dynamical systems comprised of a lattice of finite-state cells. At each time step, each cell updates its state as a function of the previous state of itself and its neighbours. Fuzzy cellular automata (FCA) are a real-valued extension of Boolean cellular automata which "fuzzifies" Boolean logic in the transition function using real values between zero and one (inclusive). To date, FCA have only been studied in disjunctive normal form (DNF). In this thesis, we study FCA in conjunctive normal form (CNF). We classify FCA in CNF both analytically and empirically. We compare these classes to their DNF counterparts. We prove that certain FCA exhibit chaos in CNF, in contrast to the periodic behaviours of DNF FCA. We also briefly explore five different forms of fuzzy logic, and suggest further study. In support of this research, we introduce novel methods of simulating and visualizing FCA.

Multigrid acceleration is typically used for the iterative solution of partial differential equations in physics and engineering. A typical multigrid implementation uses a base discretization method, such as finite elements or finite differences, and a set of successively coarser grids that is used for accelerating the convergence of the iterative solution on the base grid. The presented thesis extends the use of multigrid acceleration to the design optimization of a sample structural system and demonstrates it within the context of the recently introduced Cellular Automata paradigm for design optimization. Within the design context, the multigrid scheme is not only used for accelerating the analysis iterations, but is also used to help refine the design across multiple grid levels to accelerate the design convergence. A comparison of computational efficiencies achieved by different multigrid implementations, including the multigrid accelerated nested design iteration scheme, is presented. The method is described in its generic form which can be applicable not only to the Cellular Automata paradigm but also to more general finite element analysis based design schemes as well. / Master of Science