CHallenges in Preservation of Structure

Livrables

Software 2

Publication of open source software

Workshops with industry

Workshop 7 where early stage researchers meet industry (task 8.3). Workshop 8 with SMEs (task 8.4).

Workshop 4

Workshop organized by La Trobe.

Talks 3

Presentations at the conference FoCM, 2017

Workshop 6

Workshop at Massey.

Talks at FoCM

Presentations at the FoCM meeting, 2017. Delivery month is tentative because the date of the FoCM conference is not known at the moment.

Software 3

Open source software package implementing the algorithms developed in tasks 7.1-7.4 and incorporating standard test cases.

SDEs

School on SDEs (see task 8.9).

Talks

Reports on tasks 3.1-3.2 at the SciCADE meeting, D 3.1-3.2, Bath, UK, 2017.

Workshop 5 and MaGIC

Workshop 5: The Abel symposium, August 16-19, 2016, Rosendal, Norway WP5 MaGIC Workshop WP8

Talks 2

Presentations at the SciCADE conference, Bath, UK, 2017.

Workshops organized by UCAM

Workshops at the Newton institute (Cambridge): -Workshop 1: Variational methods new optimization techniques and new fast numerical algorithms, (tasks 2.5, 2.6). -Workshop 2: Generative models, parameter learning and sparsity, (task 2.6). -Workshop 3: Flows, Mappings and Shapes, (task 2.7). Final CHiPS Workshop (event 12 table 3).

Software 1

Implementation of integrators in D 3.3-3.4 in open-spurce software.

School lecture

Science festival Gothenburg, school lecture.

Videos

Production of short instruction videos explaining the basics of Discrete Gradients, and corresponding methods. (WP 4) Production of short instructive videos giving the elementary background to elementary Geometric Mechanics targeted at new MSc and PhD students. (WP 3)

Report on the polarization

Report on the polarization technique generalizing Kahan’s method to higher degree polynomial vector fields.

Model Reduction/ Port-Hamiltonian

Report on structure-preserving model reduction and on port-Hamiltonian systems.

Reports Bayesian

Reports on geometric integrators for Bayesian inference (tasks 7.1-7.4)

Report on modified invariant measure

Report on modified invariant measure for new classes of completely integrable quadratic vector fields.

Symplectic

Reports on tasks 3.3-3.4

Case study/Convergence/Continuous model

Case study of the use of discrete gradient methods in image processing, report. Convergence of discrete gradients, report (task 2.2). Approximation of the continuous model, (task 2.4).

Reports HOsC

Publications in relevant journals on Structure preservation in partial differential equations with highly oscillatory solutions (delivered also on month 12)

Reports on algebraic combinatorics

Publications in algebraic combinatorics with applications

Publications

Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations

Auteurs: Changying Liu, Arieh Iserles, Xinyuan Wu
Publié dans: Journal of Computational Physics, Numéro 356, 2018, Page(s) 1-30, ISSN 0021-9991
Éditeur: Academic Press
DOI: 10.1016/j.jcp.2017.10.057

Discretization of polynomial vector fields by polarization

Auteurs: Elena Celledoni, Robert I. McLachlan, David I. McLaren, Brynjulf Owren, G. R. W. Quispel
Publié dans: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Numéro 471/2184, 2015, Page(s) 20150390, ISSN 1364-5021
Éditeur: Royal Society of London
DOI: 10.1098/rspa.2015.0390

Geometry of Discrete-Time Spin Systems

Auteurs: Robert I. McLachlan, Klas Modin, Olivier Verdier
Publié dans: Journal of Nonlinear Science, Numéro 26/5, 2016, Page(s) 1507-1523, ISSN 0938-8974
Éditeur: Springer Verlag
DOI: 10.1007/s00332-016-9311-z

Geometry of matrix decompositions seen through optimal transport and information geometry

Auteurs: Klas Modin
Publié dans: Journal of Geometric Mechanics, Numéro 9/3, 2017, Page(s) 335-390, ISSN 1941-4889
Éditeur: American Institute of Mathematical Sciences
DOI: 10.3934/jgm.2017014

Geometric and integrability properties of Kahan's method

Auteurs: Celledoni, Elena; McLaren, David; Owren, Brynjulf; Quispel, Reinout
Publié dans: Journal of Physics A, Numéro 1, 2019, ISSN 1751-8113
Éditeur: Institute of Physics Publishing

Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images

Auteurs: Calatroni, Luca; van Gennip, Yves; Schönlieb, Carola-Bibiane; Rowland, Hannah; Flenner, Arjuna
Publié dans: Journal of Mathematical Imaging and Vision, Numéro 16, 2017, ISSN 0924-9907
Éditeur: Kluwer Academic Publishers
DOI: 10.17863/CAM.31490

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Auteurs: De los Reyes, JC; Schonlieb, C-B; Valkonen, T
Publié dans: JOURNAL OF MATHEMATICAL IMAGING AND VISION, Numéro 11, 2018, ISSN 0924-9907
Éditeur: Kluwer Academic Publishers
DOI: 10.13039/501100000735

Two classes of quadratic vector fields for which the Kahan discretization is integrable

Auteurs: Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Publié dans: Journal of Physics A, Numéro 7, 2019, ISSN 1751-8113
Éditeur: Institute of Physics Publishing

Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation

Auteurs: van der Kamp, Peter H.; Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Publié dans: Journal of Physics A, Numéro 1, 2019, ISSN 1751-8113
Éditeur: Institute of Physics Publishing

The Joy and Pain of Skew Symmetry

Auteurs: Arieh Iserles
Publié dans: Foundations of Computational Mathematics, Numéro 16/6, 2016, Page(s) 1607-1630, ISSN 1615-3375
Éditeur: Springer Verlag
DOI: 10.1007/s10208-016-9321-0

Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential

Auteurs: Philipp Bader, Arieh Iserles, Karolina Kropielnicka, Pranav Singh
Publié dans: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Numéro 472/2193, 2016, Page(s) 20150733, ISSN 1364-5021
Éditeur: Royal Society of London
DOI: 10.1098/rspa.2015.0733

Shape analysis on Lie groups with applications in computer animation

Auteurs: Elena Celledoni, Markus Eslitzbichler, Alexander Schmeding
Publié dans: Journal of Geometric Mechanics, Numéro 8/3, 2016, Page(s) 273-304, ISSN 1941-4889
Éditeur: American Institute of Mathematical Sciences
DOI: 10.3934/jgm.2016008

A classification of volume preserving generating forms in $\mathbb{R}^3$

Auteurs: Olivier Verdier, Huiyan Xue, Antonella Zanna
Publié dans: Discrete and Continuous Dynamical Systems, Numéro 36/4, 2016, Page(s) 2285-2303, ISSN 1078-0947
Éditeur: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2016.36.2285

High Order Semi-Lagrangian Methods for the Incompressible Navier–Stokes Equations

Auteurs: Elena Celledoni, Bawfeh Kingsley Kometa, Olivier Verdier
Publié dans: Journal of Scientific Computing, Numéro 66/1, 2016, Page(s) 91-115, ISSN 0885-7474
Éditeur: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-015-0015-6

The averaged Lagrangian method

Auteurs: Elena Celledoni, Eirik Hoel Høiseth
Publié dans: Journal of Computational and Applied Mathematics, Numéro 316, 2017, Page(s) 161-174, ISSN 0377-0427
Éditeur: Elsevier BV
DOI: 10.1016/j.cam.2016.09.047

Geometric integration of non-autonomous linear Hamiltonian problems

Auteurs: Håkon Marthinsen, Brynjulf Owren
Publié dans: Advances in Computational Mathematics, Numéro 42/2, 2016, Page(s) 313-332, ISSN 1019-7168
Éditeur: Kluwer Academic Publishers
DOI: 10.1007/s10444-015-9425-0

Graph Clustering, Variational Image Segmentation Methods and Hough Transform Scale Detection for Object Measurement in Images

Auteurs: Luca Calatroni, Yves van Gennip, Carola-Bibiane Schönlieb, Hannah M. Rowland, Arjuna Flenner
Publié dans: Journal of Mathematical Imaging and Vision, 2016, ISSN 0924-9907
Éditeur: Kluwer Academic Publishers
DOI: 10.1007/s10851-016-0678-0

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Auteurs: J. C. De los Reyes, C.-B. Schönlieb, T. Valkonen
Publié dans: Journal of Mathematical Imaging and Vision, 2016, ISSN 0924-9907
Éditeur: Kluwer Academic Publishers
DOI: 10.1007/s10851-016-0662-8

The structure of optimal parameters for image restoration problems

Auteurs: J.C. De Los Reyes, C.-B. Schönlieb, T. Valkonen
Publié dans: Journal of Mathematical Analysis and Applications, Numéro 434/1, 2016, Page(s) 464-500, ISSN 0022-247X
Éditeur: Academic Press
DOI: 10.1016/j.jmaa.2015.09.023

Individual Tree Species Classification From Airborne Multisensor Imagery Using Robust PCA

Auteurs: Juheon Lee, Xiaohao Cai, Jan Lellmann, Michele Dalponte, Yadvinder Malhi, Nathalie Butt, Mike Morecroft, Carola-Bibiane Schonlieb, David A. Coomes
Publié dans: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Numéro 9/6, 2016, Page(s) 2554-2567, ISSN 1939-1404
Éditeur: Institute of Electrical and Electronics Engineers
DOI: 10.1109/JSTARS.2016.2569408

Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ L p Spaces

Auteurs: Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola-Bibiane Schönlieb
Publié dans: Journal of Mathematical Imaging and Vision, Numéro 55/3, 2016, Page(s) 343-369, ISSN 0924-9907
Éditeur: Kluwer Academic Publishers
DOI: 10.1007/s10851-015-0624-6

Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation

Auteurs: Stig Larsson, Matteo Molteni
Publié dans: Computational Methods in Applied Mathematics, Numéro 17/1, 2017, ISSN 1609-4840
Éditeur: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2016-0027

Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

Auteurs: Rikard Anton, David Cohen, Stig Larsson, Xiaojie Wang
Publié dans: SIAM Journal on Numerical Analysis, Numéro 54/2, 2016, Page(s) 1093-1119, ISSN 0036-1429
Éditeur: Society for Industrial and Applied Mathematics
DOI: 10.1137/15M101049X

Weak error analysis for semilinear stochastic Volterra equations with additive noise

Auteurs: Adam Andersson, Mihály Kovács, Stig Larsson
Publié dans: Journal of Mathematical Analysis and Applications, Numéro 437/2, 2016, Page(s) 1283-1304, ISSN 0022-247X
Éditeur: Academic Press
DOI: 10.1016/j.jmaa.2015.09.016

A Weak Space-Time Formulation for the Linear Stochastic Heat Equation

Auteurs: Stig Larsson, Matteo Molteni
Publié dans: International Journal of Applied and Computational Mathematics, 2016, ISSN 2349-5103
Éditeur: Springer India
DOI: 10.1007/s40819-016-0134-2

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

Auteurs: Adam Andersson, Stig Larsson
Publié dans: Mathematics of Computation, Numéro 85/299, 2016, Page(s) 1335-1358, ISSN 0025-5718
Éditeur: American Mathematical Society
DOI: 10.1090/mcom/3016

Duality in refined Sobolev–Malliavin spaces and weak approximation of SPDE

Auteurs: Adam Andersson, Raphael Kruse, Stig Larsson
Publié dans: Stochastics and Partial Differential Equations Analysis and Computations, Numéro 4/1, 2016, Page(s) 113-149, ISSN 2194-0401
Éditeur: Springer US
DOI: 10.1007/s40072-015-0065-7

Gradient flows: from theory to application

Auteurs: Bertram Düring, Carola-Bibiane Schönlieb, Marie-Therese Wolfram
Publié dans: ESAIM: Proceedings and Surveys, Numéro 54, 2016, Page(s) I-VIII, ISSN 2267-3059
Éditeur: EDP Science
DOI: 10.1051/proc/201654000

Discrete gradient methods for solving variational image regularisation models

Auteurs: V Grimm, Robert I McLachlan, David I McLaren, G R W Quispel, C-B Schönlieb
Publié dans: Journal of Physics A: Mathematical and Theoretical, Numéro 50/29, 2017, Page(s) 295201, ISSN 1751-8113
Éditeur: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aa747c

8. Bilevel approaches for learning of variational imaging models

Auteurs: Luca Calatroni, Chung Cao, Juan Carlos De los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
Publié dans: Variational Methods - In Imaging and Geometric Control, 2016, ISBN 9783-110430394
Éditeur: De Gruyter
DOI: 10.1515/9783110430394-008

Learning Filter Functions in Regularisers by Minimising Quotients

Auteurs: Martin Benning, Guy Gilboa, Joana Sarah Grah, Carola-Bibiane Schönlieb
Publié dans: cale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings, 2017, Page(s) 511-523
Éditeur: Springer International Publishing
DOI: 10.1007/978-3-319-58771-4_41

Nonlinear Spectral Image Fusion

Auteurs: Martin Benning, Michael Möller, Raz Z. Nossek, Martin Burger, Daniel Cremers, Guy Gilboa, Carola-Bibiane Schönlieb
Publié dans: Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings, 2017, Page(s) 41-53
Éditeur: Springer International Publishing
DOI: 10.1007/978-3-319-58771-4_4

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