NAIS Members

(Members are associated research staff, typically at the three NAIS core institutions, who are involved with NAIS workshops, events, or projects.)

Lyonell Boulton Department of Mathematics Heriot-Watt University Riccarton, EH14 4AS +131 4513973 L.Boulton@hw.ac.uk

The estimation of eigenvalues of linear operators in gaps of the essential spectrum has been a long-standing problem in numerical analysis. Successful solutions to this problem find applications in the theory of elasticity, electromagnetism and relativistic quantum mechanics. In my papers [1-3], and the references therein, I have explored the use of non-self-adjoint methods based on quadratic matrix polynomials, capable of finding certified eigenvalue enclosures, no matter their position relative to the essential spectrum. This method seems to be quite robust and reliable. It never pollutes and it always provides two-sided estimates of the eigenvalue to be approximated. As the underlying eigenvalue problem is non-self-adjoint, HPC tools are of prime importance for achieving accurate eigenvalue enclosures. Lots of interesting and important computational and theoretical problems, lying in the boundary between rigorous functional analysis, numerical analysis and mathematical physics, are still remain open in this area of research. [1]L.Boulton and M. Strauss, On the convergence of second order spectra and multiplicity, Proc. R. Soc. A, vol. 467, pp. 264-284 (2011) [2]L. Boulton and N. Boussaid, Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials. LMS J. Comput Math vol. 13, pp. 10-32 (2010) [3]L. Boulton, Limiting set of second order spectra. Math. Comp. vol. 75, pp. 1367-1382 (2006)

Coralia Cartis School of Mathematics, University of Edinburgh The King's Buildings Edinburgh EH9 3JZ +44 (0)131 650 5127 Coralia.Cartis@ed.ac.uk

My research addresses the development, analysis and implementation of algorithms for linear and nonlinear nonconvex smooth optimization problems, suitable for large-scale problems; see for example [1, 2, 3]. I am also interested in the interconnections between dynamical systems and continuous optimization; and optimization aspects of compressed sensing and sparse approximation. [1]C. Cartis, N. I. M. Gould, and Ph. L. Toint, Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results, Math. Program., vol. 127, no. 2, pp. 245-295 (2011) [2]C. Cartis, N. I. M. Gould, and Ph. L. Toint, Trust-region and other regularisations of linear least-squares problems, BIT, vol. 49, no.1, pp. 21-53 (2009) [3]S. Bellavia, C. Cartis, N. I. M. Gould, B. Morini and Ph. L. Toint, Convergence of a Regularized Euclidean Residual algorithm for nonlinear least-squares, SIAM J. Num. Analysis, vol. 48, no. 1, pp. 1-29 (2010)

Jacek Gondzio

Andreas Grothey JCMB 6215 University of Edinburgh Edinburgh EH9 3JZ 0131 6505747 A.Grothey@ed.ac.uk

Many of todays challenging optimization problems are not only large (exceeding 1 million variables routinely), but also display exploitable structure. This structure is usually a signature of the model generating process which often features discretizations over time, space or (in the case of stochastic problems) probability spaces. Such a structure leand itself to parallelisation either on traditional computing clusters or recently grid, GPU or hybrid architectures. In many cases achieving maximal efficiency requires not only organising computing tasks and data on the machine, but also inestigating new or modified algorithm that avoid computational bottlenecks (e.g. synchronization avoidance). [1]M. Colombo, J. Gondzio and A. Grothey, A Warm-Start Approach for Large-Scale Stochastic Linear Programs, Mathematical Programming, published online 30 May 2009. [2]M. Colombo, A. Grothey, J. Hogg, K. Woodsend and J. Gondzio, A Structure-Conveying Modelling Language for Mathematical and Stochastic Programming. Mathematical Programming Computation, Volume 1/4, pp. 223-247 (2009) [3]J. Gondzio and A. Grothey, Direct Solution of Linear Systems of Size 10^9 Arising in Optimization with Interior Point Methods, R. Wyrzykowski (ed.), Parallel Processing and Applied Mathematics, Lecture Notes in Computer Sciences 3911.

Julian Hall School of Mathematics University of Edinburgh JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK J.A.J.Hall@ed.ac.uk

Development of algorithmic and computational techniques for solving large scale linear programming (LP) problems using the revised simplex method on both serial and parallel computers. Consequential research interest is the application of these techniques in other areas of computational optimization and linear algebra. [1]J. A. J. Hall, Towards a practical parallelisation of the simplex method, Computational Managment Science vol: 7, pp 139-170 (2010) [2]G. Al-Jeiroudi, J. Gondzio and J. A. J. Hall, Preconditioning Indefinite Systems in Interior Point Methods for Large Scale Linear Optimization, Optimization Methods & Software vol: 23, pp 345-363 (2008)

Douglas Heggie University of Edinburgh School of Mathematics Edinburgh +44 131 650 5035 d.c.heggie@ed.ac.uk

Computer simulation of rich star clusters, including astrophysical ingredients such as stellar evolution in addition to dynamics. The simulations use the GPU-enabled version of the code NBODY6[1], and focus on the globular star cluster M4, for which initial conditions have been published[2]. [1]S.J. Aarseth, Gravitational N-Body Simulations: Tools and Algorithms, CUP (2003) [2]D.C. Heggie and M.Giersz, Monte Carlo Simulations of Star Clusters - V. The Globular Cluster M4, MNRAS, vol.389,pp.1858-1870 (2008)

Nick Johnson 2407 JCMB King's Buildings Mayfield Road 1316513388 nick.johnson@ed.ac.uk

Anthony Kennedy JCMB 4404 King's Buildings +44 (131) 447 0086 adk@ph.ed.ac.uk

Michael O'Boyle University of Edinburgh School of Informatics 10 Crichton Street, Edinburgh mob@inf.ed.ac.uk

The primary research question I am interested in is: how can compiler technology best exploit the potential of high performance architectures? Recently we have developed innovative approaches to this problem using machine learning where it outperforms hand designed approaches. I am interested in their interaction with architecture and in particular compiler/architecture co-design . My research interests include: Adaptive compilation. Compilers are unable to keep up with the sustained evolution of computer architecture. I am working on techniques which allow the compiler to learn about the underlying parallel architecture by exploring a transformation based optimisation space. Machine learning based Optimisation. I'm interested in how predictive modelling and feature generation can be used to automate the design of compilers. Compiler/Architecture co-design space exploration. We are investigating the use of predictive models to predict the best compiler optimisations for any architecture. Auto-parallelising compilers. This is a tough problem. I am currently investigating the use of dynamic, probabilistic analysis in conjunction with machine learning to develop a new approach that gives future proof scalable code for multi-cores. Heterogeneous and GPGPU multi-core platforms. I am interested in how we can use smart compiler analysis and adaptation to exploit the potential of such architectures. Very High level programming languages. I am interested in how languages such as Matlab, which provide great expressive power may be implemented on multi-cores. [1]G. Tournavitis, Z. Wang, B. Franke, MFP O'Boyle, Towards Automatic Parallelisation using Dynamic Analysis and Machine-Learning, ACM SIGPLAN 2009 Conference on Programming Language Design and Implementation (PLDI), (2009) [2]Zheng Wang and MFP. O'Boyle. Mapping Parallelism to Multi-cores: A Machine Learning Based Approach, 14th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP), (2009) [3]C. Dubach, T. Jones, MFP. O'Boyle, Exploring and predicting the architecture/optimising compiler co-design space, CASES 2008: 31-40 (2008)

Nikola Popovic University of Edinburgh, School of Mathematics James Clerk Maxwell Building, King's Buildings Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom +44 131 651 7031 Nikola.Popovic@ed.ac.uk

I am an applied mathematician whose research interests lie in dynamical systems and differential equations, with an emphasis on mathematical modelling in the biological and physical sciences. My current research focuses on the development of techniques for reducing the complexity of the resulting models; my approach relies on a combination of analytical techniques and numerical simulation. In previous work, I have investigated how micromagnetic phenomena can be treated efficiently by combining finite element methods with hierarchical matrix techniques. The variational model due to Landau and Lifshitz is frequently applied in this context. In [1], we employed hierarchical matrices to approximate the densely populated stiffness matrices which arise in the numerical simulation of the model. In the follow-up article [2], we investigated how the associated stray field can be computed in linear complexity, even on unstructured meshes. Finally, in [3], we considered formulae for the magnetic forces between microscopic magnetised bodies: we stated and proved rigorously two such formulae under rather general regularity assumptions. We then studied the formulae comparatively in a series of numerical simulations, providing numerical data for a comparison with real-life experiments. [1]N. Popovic and D. Praetorius, Applications of H-Matrix Techniques in Micromagnetics, Computing, vol. 74, no. 3, pp. 177-204 (2005) [2]N. Popovic and D. Praetorius, H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics, Lecture Notes in Comput. Sci., vol. 3743, pp. 102-110 (2006) [3]N. Popovic, D. Praetorius and A. Schloemerkemper, Analysis and Numerical Simulation of Magnetic Forces between Rigid Polygonal Bodies, Contin. Mech. Thermodyn., vol. 19, no. 1-2, pp. 67-109 (2007)

Peter Richtarik 6317 James Clerk Maxwell Building Kings Buildings Mayfield Road +44 (131) 6505-049 peter dot richtarik at ed dot ac dot uk

In my work I focus on developing and analyzing efficient gradient algorithms for large-scale optimization problems. Together with several coauthors, we have developed GPower, a generalized power method for sparse principal component analysis [1]. The method is able to achieve significant speedups (5-10x) when compared to the best prior methods. Recently, I have worked on estimating iteration complexity (counting the number of iterations) and efficient implementation of block coordinate descent methods for minimizing a composite convex objective function [2] (a composite function is a sum of two convex terms: a smooth and a simple nonsmooth block-separable term). An important problem of this form is sparse regression, where the smooth part is a quadratic and the nonsmooth part is formed by the L1 norm. Applications include truss topology design, training linear support vector machines and finding c-optimal designs of experiments. In [3], together with my student, we have shown that coordinate descent methods can be accelerated on a graphical processing unit (GPU), leading to speedups of up to two orders of magnitude. [1]M. Journée, Yu. Nesterov, P. Richtárik and R. Sepulchre, Generalized power method for sparse principal component analysis, Journal of Machine Learning Research, vol. 11, pp. 517–553 (2010) . [2]P. Richtárik and M. Takáč, Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function, ERGO Tech. Report 11-011 (2011) . [3]P. Richtárik and M. Takáč, Efficient serial and parallel coordinate descent methods for huge-scale truss topology design, ERGO Tech. Report 11-012 (2011)

Jared Tanner School of Mathematics, University of Edinburgh The King's Buildings Edinburgh EH9 3JZ +44 (0)131 650 5057 Jared.Tanner@ed.ac.uk

Many of the most timely scientific questions of the day have the collection and analysis of data as central tasks. Research on this topic has typically been conducted by statisticians, but is now also being studied extensively in the signal/image processing community. My research focus is on the construction, analysis, and application of algorithms for sparse representation and compressed sensing. Some of the questions can be analysed exactly [1], and others are only understood through large scale numerical experimentation [2] and [3]. [1]D. L. Donoho and J. Tanner, Counting faces of randomly-projected polytopes when the projection radically lowers dimension, J. of the AMS, vol. 22, no. 1, pp. 1-53 (2009). [2]D. L. Donoho and J. Tanner, Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing, Phil. Trans. of the Royal Society A, vol. 367, no. 1906, pp. 4273-4293 (2009). [3]D. L. Donoho and J. Tanner, Precise Undersampling Theorems, Proc. of the IEEE, vol. 98, no. 6, pp. 913-924 (2010).

Arthur Trew EPCC, The University of Edinburgh Mayfied Road Edinburgh EH9 3JZ a.s.trew@ed.ac.uk

Prior to becoming a founder member of EPCC in 1990, Arthur Trew was a Research Fellow in the Department of Physics and Astronomy at Edinburgh working on simulations of many-body problems. In 1995, he became Director of EPCC; in this role one of his key aims is exploiting computational science linkages between academic disciplines and between academia and industry. In 2001, he became the Deputy Director of the National e-Science Centre (NeSC); he is also a Director of UOE HPCx Ltd, a wholly-owned subsidiary of the University of Edinburgh, which was formed to manage the £54M HPCx, and more recently the £113M HECToR, projects. As the Service Director, he is the main link to the Research Councils for both projects. Today, he holds a wide range of Research Grants and contracts, and, since 2006, has the Chair of Computational Science. He is now the Head of School of Physics and Astronomy.