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Projects

Bernard De Baets (Faculty of Bioscience Engineering, Department of Applied Mathematics, Biometrics and Process Control Ghent University, Gent, Belgium) bernard.debaets >at> ugent.be

**Description:** A cellular automaton (CA), originally conceived by John von Neumann in the first half of the previous century, is a spatio-temporal model discrete in all its senses, i.e. space is represented by an infinite lattice of cells, updates occur only at discrete time steps and the states can only take a finite number of values. Increasingly, CA based models are used as an alternative to the models based upon a set of (partial) differential equations (PDE), since they do not suffer from the drawbacks that are typical of PDE based models. Fundamental research on CA aims at unraveling the complex dynamical properties of these intrinsically simple CA; as well as at the identification of CA that are capable of exhibiting a given spatio-temporal behaviour.

In the framework of this PhD project, several bio-inspired optimization techniques, such as genetic algorithms and genetic programming, will be employed to identify elementary CA that are capable of generating given spatio-temporal patterns. Whereas the former technique has been found to perform moderately, the possibilities of the latter have only been touched upon, though this approach seems promising for finding the Boolean function governing a CA’s dynamics.

*Research goals.*By carrying out the research actions that are needed in the framework of this PhD project, the future PhD student will:

- get acquainted with CA and related spatio-temporal modeling paradigms,
- gain insight into cutting edge optimization techniques,
- be able to implement them correctly, and adapt them if necessary, in order to check their performance for identifying CA capable of reproducing given spatio-temporal patterns, and
- balance their usability and applicability.

In order to ensure connection with the already performed research on CA at the Research Unit Knowledge-based Systems (

www.kermit.ugent.be), Department of Applied Mathematics, Biometrics and Process Control, Ghent University, the implementations must be done within the mathematical-technical platform Mathematica. Besides, massive calculations can be performed on a Blade computing cluster consisting of 72 cores.