77 citations · 128 across the 12 of their papers we have counts for
13 papers
Decomposable and essentially univariate mass-action systems: Extensions of the deficiency one theorem
Abhishek Deshpande, Stefan Müller
The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with…
A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks
Marcus S. Aichmayr, Stefan Müller, Georg Regensburger
We present our SageMath package elementary_vectors for computing elementary and sign vectors of real subspaces. In this setting, elementary vectors are support-minimal vectors that…
Parametrized systems of generalized polynomial inequalitites via linear algebra and convex geometry
Stefan Müller, Georg Regensburger
We provide fundamental results on positive solutions to parametrized systems of generalized polynomial (with real exponents and positive parameters), includ…
Sufficient conditions for linear stability of complex-balanced equilibria in generalized mass-action systems
Stefan Müller, Georg Regensburger
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for…
A new decomposition of the graph Laplacian and the binomial structure of mass-action systems
Stefan Müller
We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible , the vector…
Complex-balanced equilibria of generalized mass-action systems: Necessary conditions for linear stability
Balazs Boros, Stefan Müller, Georg Regensburger
It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-ba…
The center problem for the Lotka reactions with generalized mass-action kinetics
Balázs Boros, Josef Hofbauer, Georg Regensburger +1
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar…
On global stability of the Lotka reactions with generalized mass-action kinetics
Balázs Boros, Josef Hofbauer, Stefan Müller
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species…
Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis
Stefan Müller, Georg Regensburger
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations…
Generalized Mass-Action Systems and Positive Solutions of Polynomial Equations with Real and Symbolic Exponents
Stefan Müller, Georg Regensburger
Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides…
Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
Stefan Müller, Elisenda Feliu, Georg Regensburger +3
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthan…
Enzyme allocation problems in kinetic metabolic networks: Optimal solutions are elementary flux modes
Stefan Müller, Georg Regensburger, Ralf Steuer
The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In par…
Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces
Stefan Müller, Georg Regensburger
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative…