The thesis will be with the COMORE team, INRIA Sophia-Antipolis. It will address
the problem of controlling the class of systems of piecewise affine differential
equations, under biologically appropriate restrictions. Piecewise affine (PWA)
differential systems constitute an intuitive theoretical framework for the study
of genetic regulatory networks, as they are based on a qualitative description
of the systems that can be easily compared with the experimental data obtained
from gene and protein expression. In general, the parameters of PWA systems
represent synthesis and degradation rates of the molecular components of the
biological network, and the solutions represent the evolution of the system in
"rectangles" in the state space with well defined dynamical properties. The
"inputs" will be some of the synthesis and/or degradation rates, and possible
control functions will be in the form of piecewise constant inputs to the system
(constant in time intervals or in regions of space), and ranging in a qualitative
scale. In a more advanced stage, control laws that depend on the variables of the
system or dynamic feedback laws will also be explored.
Control problems can be related to generating invariant regions, stabilization to
a given steady state, generating periodic solutions. The project will study these
control problems for small circuits (motifs such as simple positive and negative
loops, feedforward loops) and then investigate the insertion of each motif and
its control method into a larger network. The methods developed will be applied
to the genetic network that regulates growth in E. coli (collaboration with IBIS team).
Requirements: We are looking for an applied mathematician (master level) , or
computer scientist, with a background in analysis of dynamical systems, and
preferably familiar with hybrid systems theory and/or control theory. In addition,
we expect a strong motivation to work on applications in genomics.
Contact: JL Gouzé, INRIA COMORE, gouze@sophia.inria.fr
Initial gross income is 1947,80 euros / month. Knowledge of French is not requested.
Application deadline is May 4th, 2010. Additional information and application can
be found at http://www.inria.fr/travailler/opportunites/doc.en.html
equations, under biologically appropriate restrictions. Piecewise affine (PWA)
differential systems constitute an intuitive theoretical framework for the study
of genetic regulatory networks, as they are based on a qualitative description
of the systems that can be easily compared with the experimental data obtained
from gene and protein expression. In general, the parameters of PWA systems
represent synthesis and degradation rates of the molecular components of the
biological network, and the solutions represent the evolution of the system in
"rectangles" in the state space with well defined dynamical properties. The
"inputs" will be some of the synthesis and/or degradation rates, and possible
control functions will be in the form of piecewise constant inputs to the system
(constant in time intervals or in regions of space), and ranging in a qualitative
scale. In a more advanced stage, control laws that depend on the variables of the
system or dynamic feedback laws will also be explored.
Control problems can be related to generating invariant regions, stabilization to
a given steady state, generating periodic solutions. The project will study these
control problems for small circuits (motifs such as simple positive and negative
loops, feedforward loops) and then investigate the insertion of each motif and
its control method into a larger network. The methods developed will be applied
to the genetic network that regulates growth in E. coli (collaboration with IBIS team).
Requirements: We are looking for an applied mathematician (master level) , or
computer scientist, with a background in analysis of dynamical systems, and
preferably familiar with hybrid systems theory and/or control theory. In addition,
we expect a strong motivation to work on applications in genomics.
Contact: JL Gouzé, INRIA COMORE, gouze@sophia.inria.fr
Initial gross income is 1947,80 euros / month. Knowledge of French is not requested.
Application deadline is May 4th, 2010. Additional information and application can
be found at http://www.inria.fr/travailler/opportunites/doc.en.html
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