39 citations · 219 across the 22 of their papers we have counts for
22 papers
Pseudo-Complex Quantifier Elimination
Nicolas Faroß, Thomas Sturm
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts,…
A Computational Approach to Polynomial Conservation Laws
Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders +4
For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. F…
Reduction of Chemical Reaction Networks with Approximate Conservation Laws
Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders +4
Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integra…
ODEbase: A Repository of ODE Systems for Systems Biology
Christoph Lüders, Thomas Sturm, Ovidiu Radulescu
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symb…
Parametric Toricity of Steady State Varieties of Reaction Networks
Hamid Rahkooy, Thomas Sturm
We study real steady state varieties of the dynamics of chemical reaction networks. The dynamics are derived using mass action kinetics with parametric reaction rates. The models s…
Algorithmic Reduction of Biological Networks With Multiple Time Scales
Niclas Kruff, Christoph Lüders, Ovidiu Radulescu +2
We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks whic…