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9 results on '"Ligon, Thomas S."'

2. The symmetry of the Kepler problem, the inverse Ligon-Schaaf mapping and the Birkhoff conjecture

Author

Ligon, Thomas S.

Subjects
Mathematics - Symplectic Geometry, Mathematical Physics
Abstract

The Ligon-Schaaf regularization (LS mapping) was introduced in 1976 and has been used several times. However, we are not aware of any direct usage of the inverse mapping, perhaps since it appears at first sight to be quite complex and involves the use of a transcendental equation (referred to as the generalized Kepler equation) that cannot be solved in closed form. Here, we provide some insight into the significance of this equation, along with a very simple derivation and confirmation of the inverse LS mapping. Then we use numerical methods to investigate three applications: 1) solutions of the Kepler function, 2) calculation of orbits including time-of-flight data based on the Delaunay Hamiltonian, and 3) numerical evidence for the Birkhoff conjecture for the circular restricted 3-body problem., Comment: The original preprint included the supplementary information document, which is now available on the PLoS ONE site

Published
2018
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5. GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models

Author

European Commission, German Research Foundation, Ligon, Thomas S., Fröhlich, Fabian, Chis, O., Banga, Julio R., Balsa-Canto, Eva, Hasenauer, Jan, European Commission, German Research Foundation, Ligon, Thomas S., Fröhlich, Fabian, Chis, O., Banga, Julio R., Balsa-Canto, Eva, and Hasenauer, Jan

Abstract

Motivation Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models.

Published
2018

8. GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models.

Author

Ligon, Thomas S, Fröhlich, Fabian, Chiş, Oana T, Banga, Julio R, Balsa-Canto, Eva, and Hasenauer, Jan

Subjects
*BIOLOGICAL mathematical modeling, *DIFFERENTIAL equations, *BIOCHEMISTRY technique, *BIOINFORMATICS software, *MESSENGER RNA
Abstract

Motivation: Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results: We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models. [ABSTRACT FROM AUTHOR]

Published
2018
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9. Galois theory in monoidal categories

Author

Ligon, Thomas S.

Subjects
Mathematics::Category Theory, FOS: Mathematics, Galois theory, monoidal categories
Abstract

The Galois theory of Chase and Sweedler [11], for commutative rings, is generalized to encompass commutative monoids in an arbitrary symmetric, closed, monoidal category with finite limits and colimits. The primary tool is the Morita theory of Pareigis [35, 36, 37], which also supplies a suitable definition for the concept of a “finite” object in a monoidal category. The Galois theory is then extended by an examination of “normal” sub-Hopf-monoids, and examples in various algebraic and topological categories are considered. In particular, symmetric, closed, monoidal structures on various categories of topological vector spaces are studied with respect to the existence of “finite” objects.

Published
1978
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