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Publications
Preprints
O. Fogelklou. Estimation of the diffusion coefficient by interval methods, level curves and bicubic splines. [ preprint ]
A. Danis, S. Ueckert, A. Hooker, and W. Tucker. Rigorous parameter estimation for noisy mixed-effects models. [ preprint ]
To appear
O. Fogelklou, T. Konstantopoulos, and W. Tucker. On the global stability of a peer-to-peer network model. To appear in OR Letters, 2012. [ doi ]
T. Johnson and W. Tucker. On a fast and accurate method to enclose all zeros of an analytic function on a triangulated domain. To appear in Lecture Notes in Computer Science. [ bib | preprint | code ]
2011
O. Fogelklou, G. Kreiss, and W. Tucker. A Computer--assisted Proof of the Existence of Traveling Wave Solutions to the Scalar Euler Equations with Artificial Viscosity. Nonlinear Differential Equations and Applications, 19(1):97-13, 2011. [ doi ]
T. Johnson and W. Tucker. On a computer-aided approach to the computation of Abelian integrals. BIT, 51(3):653-667, 2011. [ doi ]
P. Gennemark, A. Danis, J. Nyberg, A. Hooker, and W. Tucker. Optimal design in population kinetic experiments by set-valued methods. AAPS Journal, 13(4):495-507, 2011. [ code | doi ]
W. Tucker. Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press, ISBN-13: 978-0691147819, 2011. [ www ]
Z. Galias and W. Tucker. Validated Study of Short Cycles for Chaotic Systems using Symbolic Dynamics and Interval Tools. International Journal of Bifurcation and Chaos, 21(2):551-563, 2011. [ doi ]
T. Johnson and W. Tucker. A note on the convergence of parametrised non-resonant invariant manifolds. Qualitative Theory of Dynamical Systems, 10(1):107-121, 2011. [ bib | doi ]
O. Fogelklou, G. Kreiss, M. Siklosi, and W. Tucker. A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition. Communications in Nonlinear Science and Numerical Simulation, 16(3):1227-1243, 2011. [ bib | doi ]
2010
A. Danis, A. Hooker, and W. Tucker. Rigorous parameter estimation for noisy mixed-effects models. Proceedings of International Symposium on Nonlinear Theory and its Applications 67-70, 2010. [ bib | article ]
T. Johnson and W. Tucker. An improved lower bound on the number of limit cycles bifurcating from a Hamiltonian planar vector field of degree 7. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20(5):1-8, 2010. [ bib | doi | code ]
T. Johnson and W. Tucker. An improved lower bound on the number of limit cycles bifurcating from a quintic hamiltonian planar vector field under quintic perturbation. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20(1):63-70, 2010. [ bib | doi | code ]
2009
Z. Galias and W. Tucker. Symbolic Dynamics Based Method for Rigorous Study of the Existence of Short Cycles for Chaotic Systems. Proceedings of IEEE Int. Symposium on Circuits and Systems, ISCAS'09, 1907-1910, 2009. [ paper ]
D. Gaidashev and T. Johnson. Dynamics of the universal area-preserving map associated with period doubling: Stable sets. Journal of Modern Dynamics 3(4):555-587, 2009. [ bib | doi ]
D. Gaidashev and T. Johnson. Dynamics of the universal area-preserving map associated with period doubling: Hyperbolic sets. Nonlinearity, 22:2487-2520, 2009. [ bib | doi | code ]
W. Tucker and D. Wilczak. A rigorous lower bound for the stability regions of the quadratic map. Physica D, 238(18):1923-1936, 2009. [ bib | doi | code ]
T. Johnson and W. Tucker. Automated computation of robust normal forms of planar analytic vector fields. Discrete and Continuous Dynamical Systems: Series B, 12(4):769-782, 2009. [ bib | doi | code ]
T. Johnson and W. Tucker. Enclosing all zeros of an analytic function - a rigorous approach. J. Comput. Appl. Math., 228(1):418-423, 2009. [ bib | doi | code ]
W. Tucker. Fundamental of chaos. Kocarev, Ljupco (ed.) et al., Intelligent computing based on chaos. Berlin: Springer. Studies in Computational Intelligence 184, 1-23, 2009. [ bib | doi | book ]
T. Johnson and W. Tucker. A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five. Dyn. Syst., 24(2):237-247, 2009. [ bib | doi | code ]
2008
Z. Galias and W. Tucker. Rigorous study of short periodic orbits for the Lorenz system. In Proc. IEEE Int. Symposium on Circuits and Systems, ISCAS'08, pages 764-767, Seattle, May 2008. [ bib | doi ]
T. Johnson and W. Tucker. Rigorous parameter reconstruction for differential equations with noisy data. Automatica, 44(9):2422-2426, 2008. [ bib | doi | code ]
Z. Galias and W. Tucker. Short periodic orbits for the Lorenz system. In Proc. Int. Conference on Signals and Electronic Systems, ICSES'08, pages 285-288, Krakow, 2008. [ bib | doi ]
T. Johnson. Lp spectral radius estimates for the Lamé system on an infinite sector. Experiment. Math., 17(3):333-339, 2008. [ bib | paper ]
2007
W. Tucker, Z. Kutalik, and V. Moulton. Estimating parameters for generalized mass action models using constraint propagation. Math Biosci, 208(2):607-20, Aug. 2007. [ bib | doi | code ]
Z. Kutalik, W. Tucker, and V. Moulton. S-system parameter estimation for noisy metabolic profiles using newton-flow analysis. IET Syst Biol, 1(3):174-80, May 2007. [ bib | doi | supplements ]
I. Mitrea and W. Tucker. Interval analysis techniques for boundary value problems of elasticity in two dimensions. J. Differ. Equations, 233(1):181-198, 2007. [ bib | doi ]
2006 and older
W. Tucker and V. Moulton. Parameter reconstruction for biochemical networks using interval analysis. Reliab. Comput., 12(5):389-402, 2006. [ bib | doi ]
W. Tucker and V. Moulton. Reconstructing metabolic networks using interval analysis. In Algorithms in bioinformatics, volume 3692 of Lecture Notes in Comput. Sci., pages 192-203. Springer, Berlin, 2005. [ bib | doi ]
W. Tucker. Validated numerics for pedestrians. In European Congress of Mathematics, pages 851-860. Eur. Math. Soc., Zürich, 2005. [ bib | book | paper ]
W. Tucker. Robust normal forms for saddles of analytic vector fields. Nonlinearity, 17(5):1965-1983, 2004. [ bib | doi ]
I. Mitrea and W. Tucker. Some counterexamples for the spectral-radius conjecture. Differ. Integral Equ., 16(12):1409-1439, 2003. [ bib | paper | code ]
W. Tucker. Computing accurate Poincaré maps. Physica D, 171(3):127-137, 2002. [ bib | doi | code ]
W. Tucker. A rigorous ODE solver and Smale's 14th problem. Found. Comput. Math., 2(1):53-117, 2002. [ bib | doi | html | paper ]
W. Tucker. Computational algorithms for ordinary differential equations. In International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), pages 71-76. World Sci. Publ., River Edge, NJ, 2000. [ bib | paper ]
W. Tucker. The Lorenz attractor exists. C. R. Acad. Sci. Paris Sér. I Math., 328(12):1197-1202, 1999. [ bib | doi ]
S. Luzzatto and W. Tucker. Non-uniformly expanding dynamics in maps with singularities and criticalities. Inst. Hautes Études Sci. Publ. Math., (89):179-226 (2000), 1999. [ bib | doi ]