CHallenges in Preservation of Structure

Resultado final

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

Publicaciones

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

Autores: Changying Liu, Arieh Iserles, Xinyuan Wu
Publicado en: Journal of Computational Physics, Edición 356, 2018, Página(s) 1-30, ISSN 0021-9991
Editor: Academic Press
DOI: 10.1016/j.jcp.2017.10.057

Discretization of polynomial vector fields by polarization

Autores: Elena Celledoni, Robert I. McLachlan, David I. McLaren, Brynjulf Owren, G. R. W. Quispel
Publicado en: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Edición 471/2184, 2015, Página(s) 20150390, ISSN 1364-5021
Editor: Royal Society of London
DOI: 10.1098/rspa.2015.0390

Geometry of Discrete-Time Spin Systems

Autores: Robert I. McLachlan, Klas Modin, Olivier Verdier
Publicado en: Journal of Nonlinear Science, Edición 26/5, 2016, Página(s) 1507-1523, ISSN 0938-8974
Editor: Springer Verlag
DOI: 10.1007/s00332-016-9311-z

Geometry of matrix decompositions seen through optimal transport and information geometry

Autores: Klas Modin
Publicado en: Journal of Geometric Mechanics, Edición 9/3, 2017, Página(s) 335-390, ISSN 1941-4889
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/jgm.2017014

Geometric and integrability properties of Kahan's method

Autores: Celledoni, Elena; McLaren, David; Owren, Brynjulf; Quispel, Reinout
Publicado en: Journal of Physics A, Edición 1, 2019, ISSN 1751-8113
Editor: Institute of Physics Publishing

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

Autores: Calatroni, Luca; van Gennip, Yves; Schönlieb, Carola-Bibiane; Rowland, Hannah; Flenner, Arjuna
Publicado en: Journal of Mathematical Imaging and Vision, Edición 16, 2017, ISSN 0924-9907
Editor: Kluwer Academic Publishers
DOI: 10.17863/CAM.31490

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Autores: De los Reyes, JC; Schonlieb, C-B; Valkonen, T
Publicado en: JOURNAL OF MATHEMATICAL IMAGING AND VISION, Edición 11, 2018, ISSN 0924-9907
Editor: Kluwer Academic Publishers
DOI: 10.13039/501100000735

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

Autores: Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Publicado en: Journal of Physics A, Edición 7, 2019, ISSN 1751-8113
Editor: Institute of Physics Publishing

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

Autores: van der Kamp, Peter H.; Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; Quispel, G. R. W.
Publicado en: Journal of Physics A, Edición 1, 2019, ISSN 1751-8113
Editor: Institute of Physics Publishing

The Joy and Pain of Skew Symmetry

Autores: Arieh Iserles
Publicado en: Foundations of Computational Mathematics, Edición 16/6, 2016, Página(s) 1607-1630, ISSN 1615-3375
Editor: Springer Verlag
DOI: 10.1007/s10208-016-9321-0

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

Autores: Philipp Bader, Arieh Iserles, Karolina Kropielnicka, Pranav Singh
Publicado en: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Edición 472/2193, 2016, Página(s) 20150733, ISSN 1364-5021
Editor: Royal Society of London
DOI: 10.1098/rspa.2015.0733

Shape analysis on Lie groups with applications in computer animation

Autores: Elena Celledoni, Markus Eslitzbichler, Alexander Schmeding
Publicado en: Journal of Geometric Mechanics, Edición 8/3, 2016, Página(s) 273-304, ISSN 1941-4889
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/jgm.2016008

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

Autores: Olivier Verdier, Huiyan Xue, Antonella Zanna
Publicado en: Discrete and Continuous Dynamical Systems, Edición 36/4, 2016, Página(s) 2285-2303, ISSN 1078-0947
Editor: 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

Autores: Elena Celledoni, Bawfeh Kingsley Kometa, Olivier Verdier
Publicado en: Journal of Scientific Computing, Edición 66/1, 2016, Página(s) 91-115, ISSN 0885-7474
Editor: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-015-0015-6

The averaged Lagrangian method

Autores: Elena Celledoni, Eirik Hoel Høiseth
Publicado en: Journal of Computational and Applied Mathematics, Edición 316, 2017, Página(s) 161-174, ISSN 0377-0427
Editor: Elsevier BV
DOI: 10.1016/j.cam.2016.09.047

Geometric integration of non-autonomous linear Hamiltonian problems

Autores: Håkon Marthinsen, Brynjulf Owren
Publicado en: Advances in Computational Mathematics, Edición 42/2, 2016, Página(s) 313-332, ISSN 1019-7168
Editor: 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

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

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

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

The structure of optimal parameters for image restoration problems

Autores: J.C. De Los Reyes, C.-B. Schönlieb, T. Valkonen
Publicado en: Journal of Mathematical Analysis and Applications, Edición 434/1, 2016, Página(s) 464-500, ISSN 0022-247X
Editor: Academic Press
DOI: 10.1016/j.jmaa.2015.09.023

Individual Tree Species Classification From Airborne Multisensor Imagery Using Robust PCA

Autores: Juheon Lee, Xiaohao Cai, Jan Lellmann, Michele Dalponte, Yadvinder Malhi, Nathalie Butt, Mike Morecroft, Carola-Bibiane Schonlieb, David A. Coomes
Publicado en: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Edición 9/6, 2016, Página(s) 2554-2567, ISSN 1939-1404
Editor: 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

Autores: Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola-Bibiane Schönlieb
Publicado en: Journal of Mathematical Imaging and Vision, Edición 55/3, 2016, Página(s) 343-369, ISSN 0924-9907
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10851-015-0624-6

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

Autores: Stig Larsson, Matteo Molteni
Publicado en: Computational Methods in Applied Mathematics, Edición 17/1, 2017, ISSN 1609-4840
Editor: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2016-0027

Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

Autores: Rikard Anton, David Cohen, Stig Larsson, Xiaojie Wang
Publicado en: SIAM Journal on Numerical Analysis, Edición 54/2, 2016, Página(s) 1093-1119, ISSN 0036-1429
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/15M101049X

Weak error analysis for semilinear stochastic Volterra equations with additive noise

Autores: Adam Andersson, Mihály Kovács, Stig Larsson
Publicado en: Journal of Mathematical Analysis and Applications, Edición 437/2, 2016, Página(s) 1283-1304, ISSN 0022-247X
Editor: Academic Press
DOI: 10.1016/j.jmaa.2015.09.016

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

Autores: Stig Larsson, Matteo Molteni
Publicado en: International Journal of Applied and Computational Mathematics, 2016, ISSN 2349-5103
Editor: Springer India
DOI: 10.1007/s40819-016-0134-2

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

Autores: Adam Andersson, Stig Larsson
Publicado en: Mathematics of Computation, Edición 85/299, 2016, Página(s) 1335-1358, ISSN 0025-5718
Editor: American Mathematical Society
DOI: 10.1090/mcom/3016

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

Autores: Adam Andersson, Raphael Kruse, Stig Larsson
Publicado en: Stochastics and Partial Differential Equations Analysis and Computations, Edición 4/1, 2016, Página(s) 113-149, ISSN 2194-0401
Editor: Springer US
DOI: 10.1007/s40072-015-0065-7

Gradient flows: from theory to application

Autores: Bertram Düring, Carola-Bibiane Schönlieb, Marie-Therese Wolfram
Publicado en: ESAIM: Proceedings and Surveys, Edición 54, 2016, Página(s) I-VIII, ISSN 2267-3059
Editor: EDP Science
DOI: 10.1051/proc/201654000

Discrete gradient methods for solving variational image regularisation models

Autores: V Grimm, Robert I McLachlan, David I McLaren, G R W Quispel, C-B Schönlieb
Publicado en: Journal of Physics A: Mathematical and Theoretical, Edición 50/29, 2017, Página(s) 295201, ISSN 1751-8113
Editor: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aa747c

8. Bilevel approaches for learning of variational imaging models

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

Learning Filter Functions in Regularisers by Minimising Quotients

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

Nonlinear Spectral Image Fusion

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

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