Research

My primary research interests are related to medical data analysis, using machine learning, and algebraic and combinatorial aspects of geometric numerical integration, image processing and data analysis.

Some key tools and concepts related to my work in geometric numerical integration includes: the combinatorics of trees and partitions, pre-Lie and post-Lie algebras, Hopf algebras, Lie group integrators, Lie–Butcher series, and flows on homogeneous manifolds.

More details can be found in the papers linked to below. A convenient starting point is perhaps the survey paper On algebraic structures of numerical integration on vector spaces and manifolds, or these slides.

I'm a member of ICT Engineering (also called DISTECH) at Western Norway University of Applied Sciences, a NILS project on discrete mechanics and geometric integration, and a project involving mathematical image- and signal processing, sponsored by UH-Nett Vest: computationalmedicine.no. As part of the latter project I'm studying functional and structural networks of the brain using fMRI and MRI data.

I'm also a member of the multidisciplinary research group Idrett, Helse og Funksjon (Sports, health and function) at HVL, where I'm working on a MRI/fMRI project within exercise physiology, and a physiological modelling project whose aim it is to construct a realistic model for simulating airflow through the larynx.

I'm a "Secondary Proposer" for a recently (Oct. 2016) selected COST action proposal "Magnetic Resonance Imaging Biomarkers for Chronic Kidney Disease" (PARENCHIMA, OC-2016-1-20493).

I am part of the organizing committees for

In addition to the members of ICT engineering my collaborators include Hans Munthe-Kaas, Kurusch Ebrahimi-Fard, Arvid Lundervold, Dominique Manchon, Simon Malham and Anke Wiese.


Publications

Post-Lie algebras and isospectral flows
with K. Ebrahimi-Fard, I. Mencattini, H.Z. Munthe-Kaas Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 11, 093, 2015
arXiv version
On the Lie enveloping algebra of a post-Lie algebra
with K. Ebrahimi-Fard and H.Z. Munthe-Kaas, Journal of Lie Theory, Vol. 25, No. 4, 1139--1165, 2015
arXiv version
On algebraic structures of numerical integration on vector spaces and manifolds
with H.Z. Munthe-Kaas, IRMA Lectures in Mathematics and Theoretical Physics Vol. 21, 2015
arXiv version
Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras
with K. Ebrahimi-Fard and D. Manchon, International Journal of Algebra and Computation, Volume 24, Issue 5, 2014
arXiv version
On post-Lie algebras, Lie–Butcher series and moving frames
with H.Z. Munthe-Kaas, Foundations of Computational Mathematics, Volume 13, Issue 4, 2013
arXiv version
Backward error analysis and the substitution law for Lie group integrators
with H.Z. Munthe-Kaas, Foundations of Computational Mathematics, Volume 13, Issue 2, 2013
arXiv version
Algebraic structure of stochastic expansions and universally accurate simulation
with K. Ebrahimi-Fard, S.J.A. Malham, H.Z. Munthe-Kaas, A. Wiese, Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, Volume 468 (2144), 2012
arXiv version

Abstracts, preprints and in preparation

Python-based software for medical imaging and machine learning - an example from brain imaging in IBS
with K. Le Cornec, O. Verdier, V. Barra, and A. Lundervold, Abstract and poster at MedViz 2016
Title TBD. Keywords: Operator-valued probability, incidence Hopf algebras
with K. Ebrahimi-Fard
Noncommutative incidence Hopf algebras
with D. Manchon

Conferences and travel

Recent and upcoming

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PhD thesis