John Reid’s influence in informatics and mathematical modelling

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

2. August 1973 Numerical Analysis GroupComputer Science and Systems DivisionA.E.R.E. Harwell Allan CurtisRoger FletcherMike Powell John Reid

5. Space Mapping Physical problem Rf finemodel Rc coarse model .xc* P .xf* Connect similar residuals JohnBandler, 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. Scientific Computing Numerical Analysis Per Christian Hansen T. K. Jensen and P. C. Hansen, Iterative regularization with minimum-residual methods, BIT, 47 (2007), pp. 103–120.

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

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

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. What is the trade-off between installing new security keys and the risk of security flaws? • ZigBee devices • contain tiny microprocessors • have limited memory, and • are deployed in home and industrial settings.

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

20. Scientific Computing Operations Research Statistics Image Processing Computer Science

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

22. 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) S A M P/T V F Brain Morphometry 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 Image from temagami.carleton.ca

23. Reconstruction error Transformation to PCA space and back Transformation to k-D PCA-space Elastic net type regularization Keep loading matrix L near orthogonal Sparse principal components mean Walking Speed slower For d1 = ... = dk = 0, A = L is the ordinary principal component loadings. For positived’s L is sparse 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. A1,1 A2,1 A1,2 … 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. A1,1 A2,1 A1,2 … The CocKtail Party Problem Problem: From mixture recover mixing matrix and underlying sources . There are infinitely many potential solutions, i.e. where is an invertible matrix. 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: Mixed signals X are not in general as sparse as true underlying sources S. True sourcesS Mixture X ICA solution forS

28. Happy Birthday, John !