Browsing Nord Open Research Archive by Author "Schmeding, Alexander"
Now showing items 113 of 13

Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application
Schmeding, Alexander (Chapter; Peer reviewed, 2021)This chapter examines the interaction of algebra and geometry in the guise of Hopf algebras and certain associated character groups. The geometry mirrors the algebra in that equation becomes a Lie group antihomomorphism. ... 
Applications of inﬁnitedimensional geometry and Lie theory
Schmeding, Alexander (Others, 2021)Infinitedimensional manifolds and Lie groups arise from problems related to differential geometry, fluid dynamics, and the symmetry of evolution equations. Among the most prominent examples of infinitedimensional manifolds ... 
Continuity of ChenFliess series for applications in system identification and machine learning
Dahmen, Rafael; Gray, W. Steven; Schmeding, Alexander (Peer reviewed; Journal article, 2021)Model continuity plays an important role in applications like system identification, adaptive control, and machine learning. This paper provides sufficient conditions under which inputoutput systems represented by locally ... 
Continuity of Formal Power Series Products in Nonlinear Control Theory
Gray, W. Steven; Palmstrøm, Mathias; Schmeding, Alexander (Peer reviewed; Journal article, 2022) 
Deep neural networks on diffeomorphism groups for optimal shape reparametrization
Celledoni, Elena; Glöckner, Helge; Riseth, Jørgen Nilsen; Schmeding, Alexander (Peer reviewed; Journal article, 2023)One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally ... 
Geometric rough paths on infinite dimensional spaces
Grong, Erlend; Nilssen, Torstein; Schmeding, Alexander (Peer reviewed; Journal article, 2022)Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For α ∈ (1/3,1/2), we give criteria for when we can approximate Banach spacevalued ... 
Incompressible Euler equations with stochastic forcing : A geometric approach
Maurelli, Mario; Modin, Klas; Schmeding, Alexander (Peer reviewed; Journal article, 2023)We consider a stochastic version of Euler equations using the infinitedimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) ... 
An Introduction to InfiniteDimensional Differential Geometry
Schmeding, Alexander (Cambridge Studies in Advanced Mathematics;, Book, 2022) 
Lie theory for asymptotic symmetries in general relativity : The BMS group
Prinz, David Nicolas; Schmeding, Alexander (Peer reviewed; Journal article, 2022)We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinitedimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness ... 
Lie theory for asymptotic symmetries in general relativity : The NU group
Prinz, David Nicolas; Schmeding, Alexander (Peer reviewed; Journal article, 2022)We study the NewmanUnti (NU) group from the viewpoint of infinitedimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this ... 
Manifolds of mappings on Cartesian products
Glöckner, Helge; Schmeding, Alexander (Peer reviewed; Journal article, 2022) 
On the unit component of the NewmanUnti group
Schmeding, Alexander (Peer reviewed; Journal article, 2023) 
Universal Zero Dynamics : The SISO Case
Gray, W. Steven; EbrahimiFard, Kurusch; Schmeding, Alexander (Peer reviewed; Chapter, 2021)Given a singleinput, singleoutput (SISO) system with a ChenFliess series representation whose generating series has a well defined relative degree, it is shown that there is a notion of universal zero dynamics that ...