Report on the 23rd Annual Meeting of the SIAM UK and Republic of Ireland Section

The 23rd Annual Meeting of the SIAM UK and Republic of Ireland Section was held on Friday 11th of January 2019 at the Mathematical Institute at the University of Oxford. Around 90 participants attended the meeting.

The invited speakers were: Lisa Fauci (Tulane University, Incoming SIAM President), Des Higham (Strathclyde University), Carola-Bibiane Schoenlieb (IMA sponsored speaker, University of Cambridge), Kirk Soodhalter (Trinity College Dublin)and Konstantinos Zygalakis (University of Edinburgh), and brief summaries of their lectures are given below.

The meeting also included a poster session for PhD students and postdocs, held over lunchtime, and a preceeding `poster blitz’ where each poster presenter gave a brief summary of their work.

At the end of the meeting, four prizes for best poster were awarded to Abigail Cocks (University of Nottingham), James Fannon (University of Limerick), Yury Korolev (University of Cambridge) and Carolina Urzua-Torres (University of Oxford).

Attendees of the meeting enjoyed the excellent facilities of the Andrew Wiles Building
at the Mathematical Institute, University of Oxford, and excellent lunch and refreshments. The local organisation was handled most ably by Dr Alberto Paganini and Dr Abdul-Lateef Haji-Ali.

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Des Higham gave a talk with the intriguing title: `Our Friends are Cooler than Us‘. He started by explaining the `Friendship Paradox’ (first identified by Scott Field) which essentially says that `on average our friends have more friends than we do’. This is obtained by analysing graphs which model individuals as nodes and friendships as edges. He went on to explain how this can be applied to any mutual pairwise
interactions, for example the `Happiness paradox’ – which asserts that our friends are happier than us on average, and how the concept is useful as a method of informing immunization strategies. He then went on to describe the abstraction of this idea into the more general concept of node centrality, and the associated `centrality paradox’ and gave examples arising in general principles of linear algebra applied to graphs, such as the eigenvector calculation leading to the Fiedler vector of a graph.

The meeting welcomed Lisa Fauci on one of the first official engagements of her SIAM Presidency. Lisa’s title was`Complex dynamics of fibers in flow at the microscale‘. She started by showing experiments detailing the behaviour of micro-organisms (e.g. sperm cells, E. Coli or diatom chains) immersed in fluids. She described theoretical work on the role of flexibility in diatom chains and explained the difficulty of computation of elastic properties of such complex media in the microscopic context. She then described mathematical work on the modeling of fibers in flow governed by the Navier-Stokes and Stokes equations, in the latter case using boundary potentials and fast summation techniques for speeding up the computation of the composite potential. The talk then went on to present beautiful computational simulations and to describe their relation to lab experiments for several examples including helical swimmers, passive fibers in shear flow and in straining flow.

Kirk Soodhalter talked on `Augmented Arnoldi-Tikhonov Methods for Ill-posed Problems‘. Using a motivating example from image deblurring, the speaker described the ill-posed problem of determining a sharp image from blurred and noisy input data. Given that the problem size of these types of problems is large, the focus was on the use of iterative methods and in particular on projection approaches to update the approximation of the solution vector. Due to the ill-conditioning of the linear systems, some form of regularisation is needed to be able to compute a useful approximation and Tikhonov regularisation was considered. The idea of the augmented approach is to use a low-dimensional user-supplied subspace to augment the projection space. The augmented subspace is constructed from vectors which are able to represent known
features of the desired solution. The talk concluded with a numerical example indicating the improved performance of the augmented method for a problem containing a step discontinuity.

Konstantinos Zygalakis gave a talk on `Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems‘.  This talk explored how ordinary and stochastic differential equations can be used as a basis for designing algorithms to solve optimisation and sampling tasks in Bayesian inverse problems. These kinds of problems frequently appear in applied mathematics and machine learning, for example
in the context of imaging. Utilising the connection to (stochastic) differential equations allows for the design of novel optimisation and sampling algorithms based on the numerical analysis of differential equations. The talk showed how a gradient flow naturally leads to optimisation algorithms, and how Langevin dynamics can be used for sampling. The focus of the talk was on incorporating sophisticated numerical time stepping methods with good stability properties in order to obtain computationally efficient algorithms. This is of great importance in problems of practical interest, where the objective function is often very high-dimensional and expensive to evaluate.

The final talk of the day was by Carola-Bibiane Schoenlieb (the IMA sponsored speaker), whose title was `Variational models and partial differential equations for mathematical imaging‘. The talk started by framing inverse image analysis problems within a variational context. Such problems are inherently ill-posed and require some form of regularisation. An example using total variation regularisation was given for a problem involving the use of undersampled magnetic resonance tomography data. Further examples were presented including the segmentation and classification of biological cells as they change morphology during the cell cycle. The developed algorithm and software is being used by biologists in the development of anti-mitotic treatments for cancer. The talk also highlighted the myriad of mathematical and numerical challenges in the area of imaging and suggested that future hybrid methods would possibly involve a combination with machine learning.

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Registration now open for 2019 SIAM-UKIE annual meeting

Registration is now open for the 23rd  Annual Meeting of the SIAM UKIE Section, taking place at

The Mathematical Institute, University of Oxford on Friday 11th of January 2019.

The meeting features five invited speakers and a poster session. We will also have a “poster blitz” session and offer travel support to students and postdocs presenting posters.

The confirmed invited speakers are:

Lisa Fauci, Tulane University, Incoming SIAM President

Des Higham,  Strathclyde University

Carola-Bibiane Schoenlieb, University of Cambridge

Kirk Soodhalter, Trinity College Dublin

Konstantinos Zygalakis, University of Edinburgh

To register, please visit

https://www.maths.ed.ac.uk/siamukie/meetings.html

The 27th Biennial Conference on Numerical Analysis

The 27th Biennial Conference in Numerical Analysis took place at the University of Strathclyde, 27-30 June.

The series began at St. Andrews University in 1965, then spent many happy years at the University of Dundee, and finally moved to Glasgow in 2009. A full history, up to 2005, can be found on Alistair Watson’s website, and comments on the 50th Anniversary Meeting can be found on Nick Higham’s blog.

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Pens from the 20th, 21st, and 22nd biennial conferences on Numerical Analysis.

The conference has a traditional feel in that, whereas many meetings of its scale are held at hotels and conference centres, this one is entirely organised by academics, and hosted on a university campus. This traditional feel contrasts with a modern focus: through its twelve plenary talks, fifteen mini-symposia, and numerous contributed talks, the Biennial Conference reflects the many recent innovations in numerical analysis.

The plenary talks are at the core of this meeting, which opened with Christian Lubich (Tubingen) presenting recent developments in dynamic low-rank approximation, and Valeria Simoncini’s talk on methods for large-scale Sylvester equations (and related problems). David Keyes kept the focus on (extremely) large-scale problems, exhorting the numerical analysis community to develop algorithms that keep pace with modern hardware. The (now) classical roots of numerical analysis, and their influence on current trends were the focus of, for example, the Fletcher-Powell lecture, given by Philip Gill (San Diego). And that was all on Day 1, which concluded with a civic reception hosted by The City of Glasgow in the spectacular City Chambers.

 

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Donald Estep (Colorado) making the case for computational measure theory

Wednesday’s plenaries were delivered by Donald Estep (Colorado), Ilaria Perugia (Vienna), and Gerlind Plonka-Hoch on, respectively, “computational measure theory” (with applications to modelling extreme weather events), completely discontinuous finite elements, and sublinear sparse FFT methods.

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Anna-Karin Tornberg (KTH) on Quadrature by expansion (source: Heather Yorston)

Anna-Karin Tornberg (KTH; above) opened Thursday’s sessions. She was followed by Endre Suli (Oxford) who married the classical and modern, where he outlined the analysis of finite element approximations for viscous incompressible fluids, accompanied by a live demonstration with tooth-paste.

Through out the meeting, it is clear that the distinctions between numerical analysis and computer science are becoming increasingly blurred, particularly in the field of networks, where algorithms for graphs and matrices are of core importance. This featured in the A.R. Mitchell lecture, delivered by Andrew Stuart (Caltech). He discussed machine learning and for classification algorithms applied on large graphs.

That evening the conference dinner was hosted in the remarkable Trades Hall, which was designed and built between 1791 and 1794. The after dinner speech, which was both humorous and thoughtful,  was given by Ivan Graham (Bath).

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View from the top table (source: David Gleich)

Arguably, the best was saved until last. In Friday morning’s first plenary lecture, Francoise Tisseur (Manchester) made a compelling case for the use of tropical algebra in
numerical analysis, with the applications to incomplete factorisations being particularly compelling. She was followed by David Gleich (Purdue), who explained the motivation and methods for locating motifs (such as triangles) in networks.

Of course, there was much more to the conference than the plenary talks and receptions. There were 15 minisymposia on topics ranging from “M1” on non-local problems (such as the en vogue fractional differential equations) to “M15” on Chebfun, as well as contributed talks. In particular, there were numerous presentations by student participants. Three of these were awarded prizes by the UK and Ireland section of SIAM:

  • Denis Devaud, ETH Zurich, Switzerland, “Exponential convergence in
    H^1/2 of hp-approximation for parabolic equations”
  • James Rynn, University of Manchester, UK, “Using Surrogate Models to
    Accelerate Bayesian Inverse Uncertainty Quantification”
  • Florian Wechsung, University of Oxford, UK, “Shape Optimization with
    Geometric Constraints Using Moreau-Yosida Regularization”

The judging panel was Ivan Graham (Bath), Natalia Kopteva  (Limerick) and John Mackenzie (Strathclyde).

To conclude, the 27th conference was at least as successful as the previous 26. For that, the numerical analysis community owes its gratitude to the University of Strathclyde’s Numerical Analysis and Scientific Computing Group and, in particular, Philip Knight, John Mackenzie and Alison Ramage.

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The conference dinner took place in one of Glasgow’s historic buildings: the Glasgow Trades Hall.

Three SIAM Student Prizes at BAMC 2016

We congratulate the three winners of SIAM Student Prizes at the BAMC 2016 held at the University of Oxford, April 5-8, 2016:

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Best Presentation
Will Rowley – University of Manchester
Design of an Acoustic Beam Shifter

 

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Best Presentation
Doireann O’Kiely – University of Oxford
Stretching and Buckling of Thin Viscous Sheets

 

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Best Poster
Roxana Feier – University of Oxford
Community detection in product-purchase networks