Prof. Dr. Georg Regensburger

Computeralgebra

Bild: Prof. Dr. Georg Regensburger

E-Mail: regensburger[at]mathematik.uni-kassel[dot]de

Website: http://gregensburger.com/

Standort: Heinrich-Plett-Straße 40
34132 Kassel

Raum: Heinr.-Plett-Str., Raum 3306

Sprechstunde

In der Vorlesungszeit: Dienstags 11-12 Uhr.

In der Vorlesungsfreien Zeit: Nach Vereinbarung.

Bitte melden Sie sich vorher an.

Research	Publications	Theses	Edited Volumes

A unifying theme in my research is the combination of algebraic and geometric methods and symbolic computation to treat problems coming from analysis and applications. I am interested in aspects ranging from purely algebraic over constructive and algorithmic considerations to the development of software for computer algebra systems.

Recent research interests

Applied algebra, symbolic computation, and computer algebra systems
Integro-differential algebras, equations, and boundary problems
Operator algebras and algebraic systems theory
Positive solutions of generalized polynomial equations
Reaction networks and applications in systems biology
Polyhedral geometry and optimization with applications in metabolic networks

My online research profiles can be found here:

ORCID – Google Scholar – Scopus

Submitted

(with C. Hofstadler and C.G. Raab) Universal truth of operator statements via ideal membership, (2024), 50 pages. arXiv
(with S. Müller) Parametrized systems of polynomial inequalities with real exponents via linear algebra and convex geometry, (2023), 24 pages. arXiv
(with S. Müller) Parametrized systems of polynomial equations with real exponents: applications to fewnomials, (2023), 29 pages. arXiv

Refereed Publications

(with Marcus S. Aichmayr and S. Müller) A SageMath Package for elementary and sign vectors with applications to chemical reaction networks, Proceedings of ICMS 2024 (eds. K. Buzzard, A. Dickenstein, B. Eick, A. Leykin, Y. Ren), Lecture Notes in Comput. Sci. 14749, Springer, Cham, pp. 155-164, 2024. DOI \| arXiv
(with C.G. Raab) The fundamental theorem of calculus in differential rings, Advances in Mathematics 447(2024) 109676, 50 pages. DOI \| arXiv
(with S. Müller) Sufficient conditions for linear stability of complex-balanced equilibria in generalized mass-action systems, SIAM Journal on Applied Dynamical Systems 23 (2024) 325-357. DOI \| arXiv
(with K. Bernauer and C. Hofstadler) How to automatise proofs of operator statements: Moore-Penrose inverse – a case study, (2023), Proceedings of CASC 2023, (eds. F. Boulier, M. England, I. Kotsireas, T.M. Sadykov, E.V. Vorozhtsov), Lecture Notes in Comput. Sci. 14139, Springer Nature Switzerland, pp. 39-68, 2023. DOI \| arXiv
(with C. Hofstadler and C.G. Raab) Computing elements of certain form in ideals to prove properties of operators, Mathematics in Computer Science 16 (2022) 17, 19 pages. DOI \| arXiv
(with D.S. Cvetković-Ilić, C. Hofstadler, J. Hossein Poor, J. Milošević, C.G. Raab) Algebraic proof methods for identities of matrices and operators: improvements of Hartwig’s triple reverse order law, Applied Mathematics and Computation 409 (2021) 126357, 10 pages. DOI \| arXiv
(with C.G. Raab and J. Hossein Poor) Formal proofs of operator identities by a single formal computation, Journal of Pure and Applied Algebra 225(5) (2021) 106564, 20 pages. DOI \| arXiv
(with C. Chenavier, C. Hofstadler, C.G. Raab) Compatible rewriting of noncommutative polynomials for proving operator identities, Proceedings of ISSAC 2020 (ed. A. Mantzaflaris), pp. 83–90, 2020. DOI \| arXiv.
(with Alban Quadrat) Computing polynomial solutions and annihilators of integro-differential operators with polynomial coefficients, in Algebraic Methods and Symbolic Computation Methods in Dynamical Systems, (eds. A. Quadrat and E. Zerz), Springer, Cham, pages 87–114, 2020. DOI \| pdf \| hal
(with B. Boros and S. Müller) Complex-balanced equilibria of generalized mass-action systems: Necessary conditions for linear stability, Mathematical Biosciences and Engineering 17 (2020) 442-459. DOI \| arXiv
(with C. Hofstadler and C.G. Raab) Certifying operator identities via noncommutative Gröbner bases, ACM Communications in ComputerAlgebra 53 (2019) 49-52. Software presentation at ISSAC 2019. DOI \| pdf
(with E. Feliu and S. Müller) Characterizing injectivity of classes of maps via classes of matrices, Linear Algebra and Its Applications 580 (2019) 236-261. DOI \| arXiv
(with S. Müller and J. Hofbauer) On the bijectivity of families of exponential/generalized polynomial maps, SIAM Journal on Applied Algebra and Geometry 3(2019) 412-438. DOI \| arXiv
(with B. Boros, J. Hofbauer, S. Müller) Planar S-systems: Global stability and the center problem, Discrete and Continuous DynamicalSystems. Series A 39 (2019) 707-727. DOI \| arXiv
(with M. P Gerstl, S. Müller, J. Zanghellini) Flux tope analysis: studying the coordination of reaction directions in metabolic networks, Bioinformatics 35 (2019) 266–273. DOI
(with T. Cluzeau, J. Hossein Poor, A. Quadrat, C.G. Raab) Symbolic computation for integro-differential-time-delay operators with matrix coefficients, 14th IFAC Workshop on Time Delay Systems, IFAC-PapersOnLine 51(14) (2018) 153-158. DOI \| pdf
(with B. Boros, J. Hofbauer, S. Müller) The center problem for the Lotka reactions with generalized mass-action kinetics, Qualitative Theory of Dynamical Systems17 (2018) 403-410. arXiv \| DOI
(with S. Klamt, S. Müller, J. Zanghellini) A mathematical framework for yield (versus rate) optimization in constraint-based modeling and applications in metabolic engineering, Metabolic Engineering47 (2018) 153-169. DOI
(with J. Hossein Poor and C.G. Raab) Algorithmic operator algebras via normal forms in tensor rings, Journal of Symbolic Computation85 (2018) 247-274. pdf \| DOI
(with S. Klamt, M. P Gerstl, C. Jungreuthmayer, S. Schuster, R. Mahadevan, J. Zanghellini, S. Müller) From elementary flux modes to elementary flux vectors: metabolic pathway analysis with arbitrary linear flux constraints, PLOS Computational Biology13(4): e1005409, 2017. DOI
(with C. Jungreuthmayer, M. P. Gerstl, M. Hanscho, G. Nair, S. Müller, J. Zanghellini) Toward genome-scale metabolic pathway analysis, in Industrial Biotechnology: Microorganisms, (eds. C. Wittmann and J.C. Liao),Wiley, pp. 111-123, 2017. DOI
(with M. Gallet, C. Koutschan, Z. Li, J. Schicho, N. Villamizar) Planar linkages following a prescribed motion, Mathematics of Computation 86 (2017) 473-506 arXiv \| Animations and Software \| DOI
(with J. Hossein Poor and C.G. Raab) Algorithmic operator algebras via normal forms for tensors, Proceedings of ISSAC 2016, (ed. M. Rosenkranz), New York, ACM, pp. 397-404, 2016. pdf \| DOI
Symbolic computation with integro-differential operators, Proceedings of ISSAC 2016, (ed. M. Rosenkranz), New York, ACM, pp. 17-18, 2016. Tutorial, extended abstract. pdf \| DOI
(with J. Hossein Poor and C.G. Raab) Normal forms for operators via Gröbner bases in tensor algebras, Mathematical Software – ICMS 2016, (eds. G-M. Greuel, T. Koch, P. Paule, A. Sommese), Lecture Notes in Comput. Sci. 9725, Springer International Publishing, pp. 505-513, 2016.pdf \| DOI
(with Stefan Müller) Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis, Frontiers in Genetics (2016) 7:90 pp. 11. arXiv \| DOI
(with F. Boulier, F. Lemaire, J. Lallemand, M. Rosenkranz) Additive normal forms and integration of differential fractions, Journal of Symbolic Computation 77 (2016) 16-38. DOI \| hal
(with S. Müller, E. Feliu, C. Conradi, A. Shiu, A. Dickenstein) Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry, Foundations of Computational Mathematics 16 (2016) 69-97. arXiv \| DOI
(with C. Koutschan, H. Ranetbauer, M-T. Wolfram) Symbolic derivation of mean-field PDEs from lattice-based models, Proceedings of SYNASC 2015, 27-33, IEEE Computer Society Conference Publishing Services (CPS), 2015. arXiv \| DOI
(with S. Müller and R. Steuer) Resource allocation in metabolic networks: kinetic optimization and approximations by FBA, Biochemical Society Transactions 43 (2015) 1195-1200. pdf \| supp_pdf \| DOI
(with Anja Korporal) On the product of projectors and generalized inverses, Linear and Multilinear Algebra 62 (2014) 1567-1582. arXiv \| DOI
(with Stefan Müller) Generalized mass-action systems and positive solutions of polynomial equations with real and symbolic exponents, Proceedings of CASC 2014, (eds. V.P. Gerdt, W. Koepf, W.M. Seiler, E.H. Vorozhtsov), Lecture Notes in Comput. Sci. 8660, Springer International Publishing, pp. 302-323, 2014. arXiv \| DOI
(with S. Müller and R. Steuer) Enzyme allocation problems in kinetic metabolic networks: Optimal solutions are elementary flux modes, Journal of Theoretical Biology 347 (2014) 182-190. arXiv \| DOI
(with L. Guo and M. Rosenkranz) On integro-differential algebras, Journal of Pure and Applied Algebra 218 (2014) 456-473. arXiv \| DOI
(with Anja Korporal) Composing and factoring generalized Green’s operators and ordinary boundary problems, AADIOS 2012, (eds. with M. Barkatou, T. Cluzeau, M. Rosenkranz), Lecture Notes in Comput. Sci. 8372, Berlin/Heidelberg, Springer, pp. 116-134, 2014. arXiv \| DOI
(with F. Boulier, F. Lemaire, M. Rosenkranz) On the integration of differential fractions, Proceedings of ISSAC 2013, (ed. M. Kauers), New York, ACM, pp. 101-108, 2013. pdf \| DOI
(with Alban Quadrat) Polynomial solutions and annihilators of ordinary integro-differential operators, 5th IFAC Symposium on System Structure and Control, IFAC Proceedings Volumes 42(2) (2013) 308-313. pdf \| DOI
(with H. Albrecher, C. Constantinescu, Z. Palmowski, M. Rosenkranz) Exact and asymptotic results for insurance risk models with surplus-dependent premiums, SIAM Journal on Applied Mathematics 73 (2013) 47-66. pdf \| arXiv \| DOI
(with Stefan Müller) Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces, SIAM Journal on Applied Mathematics 72 (2012) 1926-1947. pdf \| arXiv \| DOI
(with A. Korporal and M. Rosenkranz) Symbolic computation for ordinary boundary problems in Maple, ACM Communications in ComputerAlgebra 46 (2012) 154-156. Software presentation at ISSAC 2012. pdf \| DOI
(with M. Rosenkranz, L. Tec, B. Buchberger) Symbolic analysis for boundary problems: From rewriting to parametrized Gröbner bases, in Numerical and Symbolic Scientific Computing: Progress and Prospects, (eds. U. Langer and P. Paule), Vienna, SpringerWienNew York, 2012, pp. 273-331. pdf \| arXiv \| DOI
(with A. Korporal and M. Rosenkranz) Regular and singular boundary problems in Maple, Proceedings of CASC 2011, (eds. V.P. Gerdt, W. Koepf, E.W. Mayr, E.H. Vorozhtsov), Lecture Notes in Comput. Sci. 6885 , Berlin/Heidelberg, Springer, pp. 280-293, 2011. pdf \| arXiv \| DOI
(with A. Korporal and M. Rosenkranz) A Maple package for integro-differential operators and boundary problems, ACM Communications in Computer Algebra 44 (2010) 120-122. Poster presentation at ISSAC 2010. pdf \| DOI
(with L. Tec and M. Rosenkranz) An automated confluence proof for an infinite rewrite system parametrized over an integro-differential algebra, Mathematical Software – ICMS 2010, (eds. K. Fukuda, J. van der Hoeven, M. Joswig, N. Takayama), Lecture Notes in Comput. Sci. 6327, Berlin/Heidelberg, Springer, pp. 245-248, 2010. pdf \| DOI
(with H. Albrecher, C. Constantinescu, G. Pirsic, M. Rosenkranz) An algebraic operator approach to the analysis of Gerber-Shiu functions, Insurance: Mathematics and Economics 46 (2010) 42-51. pdf \| DOI
(with M. Rosenkranz, L. Tec, B. Buchberger) A symbolic framework for operations on linear boundary problems, Proceedings of CASC 2009, (eds. V.P. Gerdt, E.W. Mayr, E.H. Vorozhtsov), Lecture Notes in Comput. Sci. 5743, Berlin/Heidelberg, Springer, pp. 269-283, 2009. pdf \| DOI
(with M. Rosenkranz and J. Middeke) A skew polynomial approach to integro-differential operators, Proceedings of ISSAC 2009, (ed. J.P. May), New York, ACM, pp. 287-294, 2009. pdf \| DOI
(with Markus Rosenkranz) An algebraic foundation for factoring linear boundary problems, Annali di Matematica Pura ed Applicata (4) 188 (2009) 123-151. pdf \| DOI
(with Markus Rosenkranz) Integro-differential polynomials and operators, Proceedings of ISSAC 2008, (ed. D. Jeffrey), New York, ACM, pp. 261-268, 2008. pdf \| DOI
(with B. Buchberger, M. Rosenkranz, L. Tec) General polynomial reduction with Theorema functors: Applications to integro-differential operators and polynomials, ACM Communications in ComputerAlgebra 42 (2008) 135-137. Poster presentation at ISSAC 2008. pdf \| DOI
(with Markus Rosenkranz) Solving and factoring boundary problems for linear ordinary differential equations in differential algebras, Journal of Symbolic Computation 43 (2008) 515-544. pdf \| DOI
Max-plus linear algebra in Maple and generalized solutions for first-order ordinary BVPs via max-plus interpolation, in Milestones in Computer Algebra MICA 2008, (eds. M. Moreno Maza and S.M. Watt), Stonehaven Bay, Trinidad and Tobago, University of Western Ontario, pp. 177-182, 2008. pdf
Applications of filter coefficients and wavelets parametrized by moments, in Gröbner Bases in Control Theory and Signal Processing, (eds. with H. Park), Berlin, de Gruyter, pp. 191-214, 2007. pdf \| DOI
Parametrizing compactly supported orthonormal wavelets by discrete moments, Appl. Algebra Engrg. Comm. Comput. 18 (2007) 583-601. pdf \| DOI
(with Otmar Scherzer) Symbolic computation for moments and filter coefficients of scaling functions, Annals of Combinatorics 9 (2005) 223-243. pdf \| DOI
(with Herwig Hauser) Explizite Auflösung von ebenen Kurvensingularitäten in beliebiger Charakteristik (German) [Explicit resolution of plane curve singularities in arbitrary characteristic], L’Enseignement Mathématique 50 (2004) 305-353. pdf \| DOI
(with Andreas Matt) An adaptive clustering method for model-free reinforcement learning, Proceedings of IEEE INMIC 2004, Lahore, Pakistan, pp. 362-367, 2004. pdf \| DOI
(with Andreas Matt) Approximate policy iteration for several environments and reinforcement functions, Proceedings of EWRL-6, (eds. A. Dutech and O. Buffet), Nancy, France, pp. 15-17, 2003. pdf
(with Andreas Matt) Generalization over environments in reinforcement learning, IberoAmerican Journal of Artificial Intelligence 7 (2003) 47-53. pdf \| url
(with Andreas Matt) Generalization over environments in reinforcement learning, Proceedings of ASAI 2002, (eds. J.M. Santos and A. Zapico), Santa Fe, Argentina, pp. 100-109, 2002. pdf
(with Johannes Otepka) Hybride 3D Ausgleichung von GPS-, Tachymeter-, und Nivellementbeobachtungen, Österreichische Zeitschrift für Vermessung und Geoinformation (VGI) 2/02 (2002) 46-52. pdf \| url
(with Andreas Matt) Policy improvement for several environments, Proceedings of EWRL-5, (ed. M.A. Wiering), Utrecht, Netherlands, pp. 30-32, 2001. pdf \| url

Algebraic and algorithmic methods for analysis: Integro-differential equations, positive steady states, and wavelets. Habilitation thesis, Johannes Kepler University Linz, 2019.
(with Andreas Matt) Reinforcement Learning for Several Environments: Theory and Applications. PhD thesis, University of Innsbruck, 2004. Supervised by Prof. Ulrich Oberst. pdf
Auflösung von ebenen Kurvensingularitäten. Master’s thesis, University of Innsbruck, 1999. Supervised by Prof. Herwig Hauser. pdf

(with M. Barkatou, T. Cluzeau, A. Ovchinnikov, M. Rosenkranz) Preface: Special issue on computational aspects of differential/difference algebra and integral operators, Advances in Applied Mathematics72 (2016) 1–3. DOI
(with M. Barkatou, T. Cluzeau, and M. Rosenkranz, editors) Algebraic and Algorithmic Aspects of Differential and Integral Operators, 5th International Meeting, AADIOS 2012, Held at the Applications of Computer Algebra Conference, ACA 2012, Sofia, Bulgaria, June 25-28, 2012. Selected and Invited Papers, Lecture Notes in Comput. Sci. 8372, Springer-Verlag, 2014. DOI
(with M. Rosenkranz and W.Y. Sit) Foreword, Special Issue on “Algebraic and Algorithmic Aspects of Differential and Integral Operators”, Mathematics in Computer Science4(2–3) (2010) 139–141. pdf \|DOI
(with K. Horimoto, M. Rosenkranz, and H. Yoshida, editors) Algebraic Biology, Third International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008, Proceedings, Lecture Notes in Comput. Sci. 5147, Springer-Verlag, 2008. DOI Preprints of all papers are available here.
(with K. Horimoto, M. Rosenkranz, and H. Yoshida, editors) Algebraic Biology, Third International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008, Invited Talks and Short Communications 2008. pdf
(with Hyungju Alan Park, editor) Gröbner bases in control theory and signal processing, Radon Series on Computational and Applied Mathematics 3, de Gruyter, 2007. Papers from the D3 Workshop held in Linz, May 18–19, 2006. DOI

Prof. Dr. Georg Regensburger

Computeralgebra

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