New Mathematical Approaches in Biology, with applications
Research Contract within the Excellence Research Programme of ANCS
October 2006 - November 2008
Our aim is to solve a number of mathematical problems relevant for: molecular and cellular biology, population genetics, tomography and internal medicine.
Computing with membranes (P systems) is a branch of Molecular Computing initiated by Gheorghe Paun, is a recent very active domain in mathematical and computer science research. The aim is to obtain new paradigma for the description and control of complex biological and biochemical systems with very large numbers of molecules, cells or even organisms.
The development of new methods for retrogenetics analysis and to determine genetic events that previously have been observed in experiments, by direct observation or from partial paleogenetic information: to determine the moment and even the place of a mutation that happened in the past or postdiction of an original genetic sequence. We plan to obtain instruments for the understanding of the spatial and temporal evolution of genetic diseases, with a potential practical impact.
The time and space analysis of epidemia by using complex mathematical techniques: the Fisher information distance, connections between differential geometry and statistics, ergodic properties of discrete dynamical systems, the analysis of some partial differential equations modeling nonlinear transport.
Tomography, as a bioengineering technique allows to obtain internal images of patients. The mathematical methods used are: computational algebraic geometry and combinatorial commutative algebra.
Algorithms for anticoagulant treatment; incorect dosing may cause death by hemoragy or stroke. We plan to develop algorithms and software that will take into account genetic, biochemic and farmacodynamical information.