(with B. Boros, J. Hofbauer, S. Müller) Planar S-systems: Global stability and the center problem, 26 pages, 2017. Submitted. arXiv

(with M. P Gerstl, S. Müller, J. Zanghellini) Flux topes rather than elementary flux modes can be enumerated in genome-scale metabolic networks, 9 pages, 2017. Submitted.

Refereed Publications

(with J. Hossein Poor and C.G. Raab) Algorithmic operator algebras via normal forms in tensor rings, Journal of Symbolic Computation, 33 pages, 2017. pdf | DOI

(with B. Boros, J. Hofbauer, S. Müller) The center problem for the Lotka reactions with generalized mass-action kinetics, Qualitative Theory of Dynamical Systems, 8 pages, 2017. arXiv | DOI

(with Alban Quadrat) Computing polynomial solutions and annihilators of integro-differential operators with polynomial coefficients, 26 pages, 2017. To appear. pdf | hal

(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 Biology 13(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) pp. 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, Proceedings of 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 (2016) 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) pp. 16-38. DOI

(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, Proceedings of SSSC (5th IFAC Symposium on System Structure and Control) 2013, IFAC, pp. 308-313, 2013. 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 Commun. Comput. Algebra. 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 Commun. Comput. 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, Proceedings of 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 Commun. Comput. Algebra 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

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 (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


(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

Edited Volumes

(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 Mat
hematics 72 (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 Science
4(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.