By Tatsuya Akutsu, Morihiro Hayashida, Takeyuki Tamura (auth.), Katsuhisa Horimoto, Georg Regensburger, Markus Rosenkranz, Hiroshi Yoshida (eds.)
This booklet constitutes the refereed lawsuits of the 3rd overseas convention on Algebraic Biology, AB 2008, held on the fort of Hagenberg, Austria in July 2008 as a part of the RISC summer time 2008, prepared via the study Institute for Symbolic Computation.
The 14 revised complete papers awarded including three educational lectures have been conscientiously reviewed and chosen from 27 submissions. The convention is the interdisciplinary discussion board for the presentation of study on all features of purposes of symbolic computation (computer algebra, computational common sense, and comparable tools) to varied concerns in biology and existence sciences in addition to different difficulties in biology being approached with symbolic methods.
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Additional info for Algebraic Biology: Third International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008 Proceedings
See also . The differential elimination processes that are presented in this paper take as input two parameters: a system of polynomial (thus nonlinear) differential equations, ordinary or with partial derivatives1 and a ranking2 . They produce on the output an equivalent finite set of polynomial differential systems, which are simpler, in the sense that they involve some differential equations which are consequences of the input system but were somehow hidden. The output may consist of more than one differential system because the differential elimination process may need to split cases.
The integer number n is a parameter of the system. This study was motivated by the activity of a working group aiming at modeling the circadian clock of the green alga ostreococcus tauri. The addressed question was: does there exist biologically meaningful parameters values which make this circuit oscillate? More technically: does there exist biologically meaningful parameters values which make a Poincar´e-Andronov-Hopf bifurcation occur? One refers to  for a more detailed motivation of the addressed question and to  for a related work.
5 Parameters Estimation The problem which is addressed in this section can be stated as follows: given a parametric ordinary differential system and files of measures for some of the dependent variables, estimate the values of the unknown parameters. In this context, differential elimination somehow transforms a nonlinear least squares problem into a linear one by guessing a starting point for a Newton-like method. The approach described in this section was published in [30,13]. It was implemented in a software based on the BLAD libraries [31,14].