77 citations · 337 across the 28 of their papers we have counts for
31 papers
Disguised complex balance via positive algebraic geometry
Stefan Müller, Abhishek Deshpande, Georg Regensburger
We study dynamical systems arising from reaction networks under mass-action kinetics. For certain choices of the rate constants (parameters), such systems are complex-balanced (ver…
The integro-differential closure of a commutative differential ring
Clemens G. Raab, Georg Regensburger
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a…
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…
How to automatise proofs of operator statements: Moore-Penrose inverse -- a case study
Klara Bernauer, Clemens Hofstadler, Georg Regensburger
We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we pres…
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…
Parametrized systems of generalized polynomial equations: first applications to fewnomials
Stefan Müller, Georg Regensburger
We consider positive solutions to parametrized systems of generalized polynomial equations (with real exponents and positive parameters). By a fundamental result obtained in parall…
The fundamental theorem of calculus in differential rings
Clemens G. Raab, Georg Regensburger
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notio…
Universal truth of operator statements via ideal membership
Clemens Hofstadler, Clemens G. Raab, Georg Regensburger
We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements ab…
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…
Computing elements of certain form in ideals to prove properties of operators
Clemens Hofstadler, Clemens G. Raab, Georg Regensburger
Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this b…
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
Dragana S. Cvetković-Ilić, Clemens Hofstadler, Jamal Hossein Poor +3
When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some o…
Compatible rewriting of noncommutative polynomials for proving operator identities
Cyrille Chenavier, Clemens Hofstadler, Clemens G. Raab +1
The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators,…
Formal proofs of operator identities by a single formal computation
Clemens G. Raab, Georg Regensburger, Jamal Hossein Poor
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators…
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…
Characterizing injectivity of classes of maps via classes of matrices
Elisenda Feliu, Stefan Müller, Georg Regensburger
We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characteriz…
On the bijectivity of families of exponential/generalized polynomial maps
Stefan Müller, Josef Hofbauer, Georg Regensburger
We start from a parametrized system of generalized polynomial equations (with real exponents) for positive variables, involving generalized monomials with positive…
Planar S-systems: Global stability and the center problem
Balázs Boros, Josef Hofbauer, Stefan Müller +1
S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equili…
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…
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…
Symbolic Derivation of Mean-Field PDEs from Lattice-Based Models
Christoph Koutschan, Helene Ranetbauer, Georg Regensburger +1
Transportation processes, which play a prominent role in the life and social sciences, are typically described by discrete models on lattices. For studying their dynamics a continu…
Planar Linkages Following a Prescribed Motion
Matteo Gallet, Christoph Koutschan, Zijia Li +3
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also…
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…
Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems
Anja Korporal, Georg Regensburger
We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a ce…