1. John Reid’s influence in informatics and mathematical modelling Kaj Madsen Technical University of Denmark

2. Numerical Analysis Group Computer Science and Systems Division A.E.R.E. Harwell Allan Curtis Roger Fletcher Mike Powell John Reid August 1973

5. Space Mapping Physical problem R f fine model R c coarse model Connect similar residuals. xf*. xf*. xc*. xc* P John Bandler, 1993

7. Fortran programming Polynomial zeros

10. Spring 1974: John was Visiting Professor at Institute for Numerical Analysis Technical University of Denmark

12. Owe Axelson: Solution of linear systems of equations: iterative methods J. Alan George: Solution of linear systems of equations: direct methods for finite element problems John K. Reid: Solution of linear systems of equations: direct methods (general) Axel Ruhe: Computation of eigenvalues and eigenvectors

13. Numerical Analysis Per Christian Hansen T. K. Jensen and P. C. Hansen, Iterative regularization with minimum-residual methods, BIT, 47 (2007), pp. 103–120. Scientific Computing

14. Image Deblurring deblurring Io (moon of Jupiter) blurring

15. John Reid & Conjugate Gradients It took a few years for researchers to realize that it was more fruitful to consider the conjugate gradient method truly iterative. In 1972, John Reid was one of the first to point in this direction. Henk A. van der Vorst Krylov Subspace Iterations Computing in Science and Engineering, IEEE, 2000 J. K. Reid, The Use of Conjugate Gradients for Systems of Equations Possessing ’Property A’, SIAM J. Numerical Analysis, 9 (1972), pp. 325–332.

16. T. K. Jensen and P. C. Hansen, Iterative regularization with minimum-residual methods, BIT, 47 (2007), pp. 103–120. Example (295  390  3 = 345150 unknowns)

17. Scientific Computing Computer Science

18. Wireless Networks for Smart Energy Devices join and leave a secure wireless network as described by a Markov Chain. When devices leave there is a risk that the security is compromised. ZigBee devices  contain tiny microprocessors  have limited memory, and  are deployed in home and industrial settings. What is the trade-off between installing new security keys and the risk of security flaws?

19. Wireless Networks for Smart Energy The question: The model: The matrix: ZigBee devices  contain tiny microprocessors  have limited memory, and  are deployed in home and industrial settings.

20. Scientific Computing Operations Research Statistics Image Processing Computer Science

21. Principal Component Analysis (PCA) [Karl Persson (1901)]

22. Brain Morphometry Image from temagami.carleton.ca The corpus callosum is the nerve fiber bundle that connects the two hemispheres of the brain. Local atrophy correlates to loss of particular ability, e.g walking speed, verbal fluency (age-related degeneracy) F M S A P/T V In a study of 600 elderly the CC outline was extracted using automated image analysis on MRI brain images Each outline is represented by a list of corresponding ”landmark” coordinates sampled along the outline We want to find local (sparse) variations from the mean CC shape to be used in predicition of cognitive and clinical parameters such as max. walking speed and verbal fluency The shape coordinates are projected onto the first few (sparse) principal components before regression

23. Reconstruction error Transformation to PCA space and back Sparse principal components Transformation to k-D PCA-space Elastic net type regularization Keep loading matrix L near orthogonal For    k = 0, A = L is the ordinary principal component loadings. For positive  ’s L is sparse mean slower Walking Speed Regression of walking speed on the sparse eigen modes identifies two significant modes representing atrophy in the nerve fibers connect the motor control centres and cognitive centres of the brain, respectively Sparse Decomposition and Modeling of Anatomical Shape Variation Sjöstrand, Karl ; Rostrup, Egill ; Ryberg, Charlotte ; Larsen, Rasmus ; Studholme, Colin ; Baezner, Hansjoerg ; Ferro, Jose ; Fazekas, Franz ; Pantoni, Leonardo ; Inzitari, Domenico ; Waldemar, Gunhild in journal: IEEE Transactions on Medical Imaging (ISSN: 0278-0062), vol: 26, issue: 12, pages: 1625-1635, 2007

24. Scientific Computing Operations Research Statistics Image Processing Signal Analysis Computer Science

25. … A 1,1 A 2,1 A 1,2 The CocKtail Party Problem

26. References [1] P. Comon, Independent component analysis, A new concept?, Signal Processing (36)287-314,1994 [2] T. Bell, T. Sejnowski, An information maximisation approach to blind separation and blind deconvolution, Neural Computation (7) 1129-1159, 1995 [3] L. K. Hansen, J. Larsen and T. Kolenda, On Independent Component Analysis for Multimedia Signals, Multimedia Image and Video Processing, 175-199, 2000

27. The CocKtail Party Problem … A 1,1 A 2,1 A 1,2 Solution: As the distribution of unmixed speech signals are sparse optimizing for such that becomes sparse solves the above ambiguity up to scale and permutation of the sources. This solution can be obtained through a method named Independent Component Analysis (ICA) [1-3], i.e: ICA solution for SMixture X True sources S Problem: From mixture recover mixing matrix and underlying sources. There are infinitely many potential solutions, i.e. where is an invertible matrix. Mixed signals X are not in general as sparse as true underlying sources S.

28. Happy Birthday, John !