- Bernard De Baets, Ghent University, Belgium.
- Bastien Chopard, University of Geneva, Switzerland.
- Laurent Lefèvre, Grenoble INP ESISAR, Valence, France.
- Anna Lawniczak, Guelph University, Canada.
Bernard De BaetsKERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics Ghent University, Coupure links 653, 9000 Gent, Belgium Talk title: New directions in the classification and identification of cellular automataAbstractCatalyzed by the emergence of modern computers, cellular automata (CAs) became a full-fledged research domain in the eighties of the previous century. The relevant literature is of a dichotomous nature in the sense that studies either focus on the spatio-temporal dynamics that is evolved by CAs, while others merely use the CA paradigm to build a model for a given biological, natural or physical process. It goes without saying that a profound understanding of CA dynamics is a prerequisite for building realistic, identifiable CA-based models, though this is not straightforward due the fact that a CA is discrete in all its senses. In an attempt to quantify CA behaviour in a meaningful and reproducible way, several so-called behavioural measures have been proposed during the last two decades. Here, we show how Lyapunov exponents and Boolean derivatives can be used to get a complete picture of CA dynamics in the sense that they not only make it possible to unravel the nature of a given CA, but also allow for assessing the effect of changing model design parameters on the CA behavior. Finally, we introduce the so-called Lyapunov profile of a CA, which may be understood as the counterpart of the Lyapunov spectrum of a smooth dynamical system. These profiles capture the spreading properties of a set of defects, as well as the exponential accumulation rates of defects within this set. In a second part, we focus on 1D CAs and the space-time diagrams they evolve. We present a novel approach to the automated classification of 1D CAs according to Wolfram's classification scheme by relying on texture features grasping the diagrams' nature, followed by nearest neighbor classification. Finally, we consider the identification of 1D CAs in the context of spatially and/or temporally incomplete space-time diagrams. We formulate the identification problem as an optimization problem and present a genetic algorithm variant with individuals of variable length, corresponding to different neighborhood radii. Connections between the dynamical properties of CAs and the performance of the algorithm are explored. Bastien ChopardScientific and Parallel Computing Group, CUI. University of Geneva, 7 route de Drize, 1227 Carouge, Switzerland. Talk title: Discrete numerical methods for biomedical applicationsAbstractNumerical modeling and simulations are becoming a central approach to better understand physiological processes involving several scales and the interaction of different physical, biological or chemical phenomena. Numerical models such as lattice Boltzmann models coupled with discrete/continuous a Lagrangian descriptions of particles offer a powerful and flexible method to describe and simulate such processes. In this presentation, we will present such an approach for the case of thrombosis in cerebral aneurysms and for the description of platelet adhesion and aggregations. Anna T. LawniczakDepartment of Mathematics and Statistics University of Guelph Talk title: Cognitive Agents Learning to Cross a Cellular Automaton Based HighwayAbstractResearch in swarm robotics has shown that, for carrying out some tasks (e.g., target or source search, task allocation, exploration, mapping, cooperative transportation, unmanned aerial vehicle (UAV) controlling, post-disaster relief), it may be more efficient, reliable and economical to employ a large number (hundreds or thousands) of very simple robots than to employ a small number of sophisticated ones. For the development of swarms of autonomous robots, which may require them to learn how to accomplish some tasks in unknown dynamically changing environments, it is important to study the process of learning through observation and repetition. Since individual robots in a swarm are usually architecturally minimal with limited computational capabilities, it is important that, in a swarm of robots, the implemented learning algorithms are not computationally demanding. In the microscopic modeling of swarm of robots, individual robots may be identified as cognitive agents capable of performing cognitive acts; i.e. a sequence of the following activities: (1) “Perceiving” information in both the environment and that which is provided by other agents (2) “Reasoning” about this information using existing knowledge; (3) “Judging” the obtained information using existing knowledge; (4) “Responding” to other cognitive agents or to the external environment, as it may be required; (5) “Learning”; i.e. changing (and hopefully augmenting) the existing knowledge if the newly acquired information allows it. In this talk a simple example of a minimal cognitive agent that could be used as a virtual experimental platform to explore agent ability to learn will be identified and discussed. We will discuss the model of cognitive agents learning to cross a CA based highway. As the emphasis is on minimal storage and logical primitives, the formal methods of computational intelligence and established algorithms such as reinforcement learning algorithms are not used in this example. Instead, inspired by “biomimicry”, simple learning algorithm based on an “observational social learning” principle, i.e. each agent learns from observing the outcomes of the behaviours of other agents, is designed and its performance is investigated. We discuss the effects of the agents’ different decision-making cognitive processes, the effects of the agents’ knowledge base accumulation through observation and repetition and the effects of other model parameters on the agents’ success of learning to cross a CA based highway. Laurent LefèvreLaboratory of Conception and Integration of Systems - LCIS ESISAR - Valence, France Talk title: Some control problems for distributed parameter systemsAbstractModern control theory emerged in the late 50’s and since then successfully addressed many theoretical and application problems related with the online observation and control of finite dimensional dynamical systems. Later on, from the late 60’s, some system theorist (mainly applied mathematicians) were getting involved in the analysis and control of spatially distributed dynamical systems, also termed as distributed parameters or infinite dimensional systems, whose dynamics is usually described with sets state partial differential equations. From then, many problems were solved, especially those related to classical control problems for linear distributed parameter systems. However very challenging questions arise specifically for spatially distributed systems. In this talk we will review briefly the traditional settings for distributed parameters control systems and some important questions related to the control and observation of these systems. Then we will present some control problems related to the spatial distribution of these systems for which cellular automata like approaches could be relevant. |