Embedded Files
Fall 2022
Fall 2022
Title: Morpho-elasticity of thin living tissues: from leaves to epithelia
Title: Morpho-elasticity of thin living tissues: from leaves to epithelia
Name: Martine Ben Amar
Name: Martine Ben Amar
École normale supérieure
École normale supérieure
Laboratoire de Physique Statistique
Laboratoire de Physique Statistique
Sorbonne Université
Sorbonne Université
Faculté de Médecine
Faculté de Médecine
Institut Universitaire de Cancérologie
Institut Universitaire de Cancérologie
Title: Incorporating growth models in Riemannian shape spaces
Title: Incorporating growth models in Riemannian shape spaces
Name: Laurent Younes
Name: Laurent Younes
Johns Hopkins University
Johns Hopkins University
Department of Applied Mathematics and Statistics
Department of Applied Mathematics and Statistics
Center for Imaging Science
Center for Imaging Science
Mathematical Institute for Data Science
Mathematical Institute for Data Science
Institute for Computational Medicine
Institute for Computational Medicine
Title: Born to Run: Experimental Evolution of Exercise Behavior and Physiology in a Vertebrate Model Organism
Title: Born to Run: Experimental Evolution of Exercise Behavior and Physiology in a Vertebrate Model Organism
Name: Ted Garland
Name: Ted Garland
University of California, Riverside
University of California, Riverside
Department of Evolution Ecology and Organismal Biology
Department of Evolution Ecology and Organismal Biology
Title: Mechanics of Multi-articular Muscles
Title: Mechanics of Multi-articular Muscles
Name: Henry Astley
Name: Henry Astley
University of Akron
University of Akron
Department of Biology
Department of Biology
Department of Polymer Science
Department of Polymer Science
Biomimicry Research & Innovation Center
Biomimicry Research & Innovation Center
Title: The Morphomechanical Basis of Seashell Form
Title: The Morphomechanical Basis of Seashell Form
Name: Derek E. Moulton
Name: Derek E. Moulton
University of Oxford
University of Oxford
Mathematical Institute
Mathematical Institute
Spring 2023
Spring 2023
Title: Statistical Challenges in Shape Prediction of Biomolecules
Title: Statistical Challenges in Shape Prediction of Biomolecules
Name: Kanti Mardia
Name: Kanti Mardia
University of Leeds
University of Leeds
Department of Statistics
Department of Statistics
University of Oxford
University of Oxford
Department of Statistics
Department of Statistics
Title: Statistical Challenges in Shape Prediction of Biomolecules
Title: Statistical Challenges in Shape Prediction of Biomolecules
Name: Stephan Huckemann
Name: Stephan Huckemann
Georg-August-Universität Göttingen
Georg-August-Universität Göttingen
Institut für Mathematische Stochastik
Institut für Mathematische Stochastik
Literature
- Mardia, K. V., Wiechers, H., Eltzner, B., Huckemann, S. F. (2022).
- Wiechers, H., Eltzner, B., Mardia, K. V., Huckemann, S. F. (2021).
Title: Modelling phenotypic traits evolution in deep times: a phylogenetic approach
Title: Modelling phenotypic traits evolution in deep times: a phylogenetic approach
Name: Julien Clavel
Name: Julien Clavel
Université Lyon 1
Université Lyon 1
Laboratoire d'Ecologie des Hydrosystèmes Naturels et Anthropisés
Laboratoire d'Ecologie des Hydrosystèmes Naturels et Anthropisés
Title: An introduction to shape analysis and deep learning for optimal reparametrizations of shapes
Title: An introduction to shape analysis and deep learning for optimal reparametrizations of shapes
Name: Elena Celledoni
Name: Elena Celledoni
Norwegian University of Science and Technology
Norwegian University of Science and Technology
Department of Mathematical Sciences
Department of Mathematical Sciences
AbstractShape analysis is a mathematical approach to problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where it is interesting to compare curves or surfaces independently of their parametrisation. Considering a smooth setting where the parametrized curves or surfaces belong to an infinite dimensional Riemannian manifold, one defines the corresponding shapes to be equivalence classes of curves differing only by their parametrization. Under appropriate assumptions, the Riemannian metric can be used to obtain a meaningful measure of distance on the space of shapes. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform, and we have proposed a generalisation of this approach to shapes on Lie groups and homogeneous manifolds. The Lie group approach can be effective when dealing with skeletal animation data coming for example from human motion.
A demanding task when approximating shape distances is finding the optimal reparametrization. The problem can be phrased as an optimisation problem on the infinite dimensional group of orientation preserving diffeomorphisms Diff+(Ω), where Ω is the domain where the curves or surfaces are defined. In the case of curves, one robust approach to compute optimal reparametrizations is based on dynamic programming, [10], but this method seems difficult to generalize to surfaces.
We consider here a method where the approximations are obtained composing in succession a number of elementary diffeomorphism and optimising simultaneously over a larger number of parameters. This approach is reminiscent of deep learning with ResNets and the optimal control interpretation of deep learning.
If time permits I will discuss connection to structure preserving numerical discretization of differential equations, structure preserving deep learning andequivariant neural networks. This talk is built on material taken from [5, 6, 7, 11, 1, 3, 2].
References[1] M. Benning, E. Celledoni, M. J. Ehrhardt, B. Owren, and C. B. Sch ̈onlieb, Deep learning as optimal control problems: models and numerical methods. Journal of Computational Dynamics, 6(2):171–198, 2019.[2] E. Celledoni, H. Gl ̈ockner, J. Riseth, A. Schmeding, Deep learning of diffeomorphisms for optimal reparametrizations of shapes, arXiv:2207.11141.[3] E. Celledoni, M. J. Ehrhardt, C. Etmann, R. I. McLachlan, B. Owren, C. B. Sch ̈onlieb, F. Sherry, (2021) Structure preserving deep learning.European journal of applied mathematics.[4] E. Celledoni, M. J. Ehrhardt, C. Etmann, B. Owren, C. B. Sch ̈onlieb, F. Sherry, (2021), Equivariant neural networks for inverse problems. Inverse Problems.[5] E. Celledoni, M. Eslitzbichler, and A. Schmeding, Shape analysis on Lie groups with applications in computer animation. J. Geom. Mech., 8 (3) :273–304, 2016.[6] E. Celledoni, S. Eidnes, A. Schmeding, (2018) Shape analysis on homogeneous spaces: a generalised SRVT framework. Abel Symposia. vol. 13.[7] E. Celledoni, P. E. Lystad, N. Tapia, (2019) Signatures in Shape analysis: An efficient approach to motion identification. Lecture Notes in Computer Science (LNCS). vol. 11712 LNCS.[8] S. Kurtek, E. Klassen, J. C. Gore, Z. Ding, A. Srivastava, Elastic geodesic paths in shape space of parameterized surfaces, IEEE trans-actions on pattern analysis and machine intelligence, 2012.[9] M. Mani, S. Kurtek, C. Barillot, A. Srivastava, A comprehensive Riemannian framework for the analysis of withe matter fiber tracts IEEE Symposium on Biomedical Imaging, pp. 1101–1104, 2010.[10] T. B. Sebastian, P. N. Klein, B. B. Kimia, On aligning of curves, IEEE transactions on pattern analysis and machine intelligence, 2003.[11] J. N. Riseth, Gradient-based algorithms in shape analysis for reparametrization of parametric curves and surfaces, Feb. 2021, Master thesis, NTNU.
A demanding task when approximating shape distances is finding the optimal reparametrization. The problem can be phrased as an optimisation problem on the infinite dimensional group of orientation preserving diffeomorphisms Diff+(Ω), where Ω is the domain where the curves or surfaces are defined. In the case of curves, one robust approach to compute optimal reparametrizations is based on dynamic programming, [10], but this method seems difficult to generalize to surfaces.
We consider here a method where the approximations are obtained composing in succession a number of elementary diffeomorphism and optimising simultaneously over a larger number of parameters. This approach is reminiscent of deep learning with ResNets and the optimal control interpretation of deep learning.
If time permits I will discuss connection to structure preserving numerical discretization of differential equations, structure preserving deep learning andequivariant neural networks. This talk is built on material taken from [5, 6, 7, 11, 1, 3, 2].
References[1] M. Benning, E. Celledoni, M. J. Ehrhardt, B. Owren, and C. B. Sch ̈onlieb, Deep learning as optimal control problems: models and numerical methods. Journal of Computational Dynamics, 6(2):171–198, 2019.[2] E. Celledoni, H. Gl ̈ockner, J. Riseth, A. Schmeding, Deep learning of diffeomorphisms for optimal reparametrizations of shapes, arXiv:2207.11141.[3] E. Celledoni, M. J. Ehrhardt, C. Etmann, R. I. McLachlan, B. Owren, C. B. Sch ̈onlieb, F. Sherry, (2021) Structure preserving deep learning.European journal of applied mathematics.[4] E. Celledoni, M. J. Ehrhardt, C. Etmann, B. Owren, C. B. Sch ̈onlieb, F. Sherry, (2021), Equivariant neural networks for inverse problems. Inverse Problems.[5] E. Celledoni, M. Eslitzbichler, and A. Schmeding, Shape analysis on Lie groups with applications in computer animation. J. Geom. Mech., 8 (3) :273–304, 2016.[6] E. Celledoni, S. Eidnes, A. Schmeding, (2018) Shape analysis on homogeneous spaces: a generalised SRVT framework. Abel Symposia. vol. 13.[7] E. Celledoni, P. E. Lystad, N. Tapia, (2019) Signatures in Shape analysis: An efficient approach to motion identification. Lecture Notes in Computer Science (LNCS). vol. 11712 LNCS.[8] S. Kurtek, E. Klassen, J. C. Gore, Z. Ding, A. Srivastava, Elastic geodesic paths in shape space of parameterized surfaces, IEEE trans-actions on pattern analysis and machine intelligence, 2012.[9] M. Mani, S. Kurtek, C. Barillot, A. Srivastava, A comprehensive Riemannian framework for the analysis of withe matter fiber tracts IEEE Symposium on Biomedical Imaging, pp. 1101–1104, 2010.[10] T. B. Sebastian, P. N. Klein, B. B. Kimia, On aligning of curves, IEEE transactions on pattern analysis and machine intelligence, 2003.[11] J. N. Riseth, Gradient-based algorithms in shape analysis for reparametrization of parametric curves and surfaces, Feb. 2021, Master thesis, NTNU.
Title: Curved feet: How humans roll along while walking
Title: Curved feet: How humans roll along while walking
Name: Anne Elizabeth Martin
Name: Anne Elizabeth Martin
Pennsylvania State University
Pennsylvania State University
Department of Mechanical Engineering
Department of Mechanical Engineering
Title: TBD
Title: TBD
Date: TBD
Date: TBD
Name: Antonio DeSimone
Name: Antonio DeSimone
Scuola Internazionale Superiore di Studi Avanzati
Scuola Internazionale Superiore di Studi Avanzati
Mathematics Area
Mathematics Area
Title: TBD
Title: TBD
Date: TBD
Date: TBD
Name: TBD
Name: TBD
University of TBD
University of TBD
Department TBD
Department TBD
Page updated
Google Sites
Report abuse