Symbiose Project Team - INRIA/Irisa © 2007 - 2008

Written by Anne SIEGEL   

Hints on research activities

My research program is to identify and take benefit of properties of dynamical systems in several domains of mathematics, computer sciences and biology where dynamics appears, even if somehow hidden. My work consists in identifying questions related to systems trajectories, then making use of the properties of these trajectories together with algorithmic computations in order to answer to questions in the domain where the dynamics was exhibited.

In theoretical computer science, this approach allowed characterizing some properties of expansions of real number in non-integer basis (beta-numeration and Dumont-Thomas substitution system). This also allowed us to propose a strategy of generation for discrete plane. Underlying dynamics are additions modulo 1 (toral additions) and fractal geometry.

In bioinformatics, I am first working on biological network construction, inducing a strong reflexion on representation abstractions. I also have conducted works on a constraint-based formalism in order to perform confrontations between large-scale data from molecular biology (transcriptomic, chip-chip, CGH) and knowledge models. Our methodology allows us to introduce dynamical (actually steady states comparisons) in data analysis, by mimic automatic reasoning over variational data.

Main results can be summarized as
  • Constraints-based formalism to perform variation-like automatic reasoning over large-scale data from molecular biology.
  • Construction of model hierarchies for data interpretations (fatty acid metabolism regulation, initiation of sea-urchin translation).
  • Graph description of fractal boundaries and topological properties. Application to Markov partitions for toral automorphisms and purely periodic beta-expansions.
  • Combinatorial rules to iterately build discrete plane by making use of Z2 action.

Additional links

  • French summary of activites pdf
  • Paper abstracts in systems biology
  • Paper abstracts in numeration and symbolic dynamical systems Overview of work and paper abstracts
  • Sofware : Bioquali (analysis of compatibilities between an interaction graph and micro-array data) Web access

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