Dave Broomhead

Professor in Applied Mathematics

Qualifications: MA, DPhil, CMath, FIMA

Room No. 2.230 (Alan Turing)

(photograph taken in Aberdeen in September 2007

at the conference to celebrate Celso Grebogi's 60th birthday

l to r: Steven Schiff, Floris Takens, Celso Grebogi, DSB)

General:

I am Professor of Applied Mathematics in the School of Mathematics in the University of Manchester and an Associate Member of the Manchester Interdisciplinary Biocentre (MIB). I am director of the Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) recently created within the University of Manchester and funded jointly by the University and with the aid of a £2m grant from EPSRC. I am also a member of the management team of the Manchester Centre for Integrated Systems Biology (MCISB). Within the School of Mathematics my interests are largely focussed around those of the Dynamical Systems Group and the Mathematical Biology Group.

My original appointment in Manchester was to a chair at UMIST where I moved in 1995 after spending 12 years working in the scientific civil service. I had been employed at the Royal Signals and Radar Establishment (RSRE) at Malvern (which has latterly become QinetiQ) where I was a Senior Principal Scientific Officer (Individual Merit). It is an ill-kept secret that my first degree was in chemistry. However, following a DPhil in theoretical chemistry (under the supervision on P.W.Atkins) I became interested in nonlinear dynamics while holding a NATO Postdoctoral Fellowship in the Department of Physics at the University of Kyoto (working in the group of Professor K. Tomita).

Thus far in my research career I have studied nonlinear dynamical systems theory and done interdisciplinary research through application of these ideas to a wide range of areas. I have worked with mathematicians, physicists, signal processors and electrical engineers while in Malvern and, since moving to Manchester, I have additionally developed strong collaborations with life scientists and systems biologists. From 1989 to 1992 I was Coordinator of the EPSRC’s Nonlinear Mathematics Initiative; I have been a Visiting Professor at University College, London; a Senior Visiting Research Fellow in the Department of Atmospheric Physics, Oxford; a Mombusho (Japanese Ministry of Education) Visiting Research Fellow at the University of Hiroshima; I am a Fellow of the Institute of Mathematics and its Applications (IMA), have been a member of IMA Council since 1998 and the Chair of the Editorial Board of Mathematics Today since 2002. For my work on radial basis function (neural) networks, I was awarded in 1989 (with Dr D. Lowe and Dr A.R. Webb) the John Benjamin Memorial Prize.

Research:

For a long time I have been interested in the development of methods for time series analysis and nonlinear signal processing using techniques from the theory of nonlinear dynamical systems. Most recently, I—mainly working with friends Jerry Huke, Mark Muldoon and Jaroslav Stark—have been looking at the extension of these methods to iterated function systems thereby establishing a basis for the use of these as models of (nonlinear) digital communications channels. This work has led me to become interested in iterated function systems per se, in particular the structure of their invariant measures (see work with Matt Nicol (who is now in Houston), Nikita Sidorov and James Montaldi). This is an area where abstraction and application become closely connected, in particular, classical quantities such as the channel capacity are related to the invariant measure of the corresponding iterated function model (work with Nikita Sidorov). Iterated function systems also provide a way to define differential operators on a class of complex (fractal) sets by providing a sequence of graphical approximations on which the graph laplacians have a nice renormalisable structure. Recently, Caroline Riley, who was then my PhD student, and I have been using this approach to study reaction-diffusion equations on complex spatial domains. The latter work relates to my developing interest in mathematical biology. I have been and am working on: the modelling of social insect behaviour with my former PhD student David Sumpter; the dynamics of plankton in the mixed layer of the ocean with Trevor Platt, Shubha Sathyendranath and Andy Edwards and recently with Shovonlal Roy (who is a Royal Society Incoming Fellow from India); on a number of long term projects on neural control of eye movements Richard Abadi, Richard Clements (Institute of Child Health) and with my former PhD students Ozgur Akman and Ioanna Tsolaki. Most recently, I have begun to develop a nonlinear dynamics approach to systems biology in collaboration with a number of researchers in the MIB (Douglas Kell, John McCarthy and Hans Westerhoff ) at Manchester and with workers in Liverpool University (Michael White), Warwick University (David Rand) and Edinburgh University (Andrew Millar).

Publications:

Refereed Journal papers - click here

Patents

i. D.S. Broomhead, R. Jones, J.G. McWhirter and T.J. Shepherd 1989 Heuristic Processor British Patent Application 8903091
ii. M. Johnson, R. Jones and D.S. Broomhead 1990 Digital Processor for Simulating Operation of a Parallel Processing Array British Patent Application 9018048
iii. D.S. Broomhead, R. Jones and M. Johnson 1991 Dynamical System Analyser British Patent Application 9106082.2

Books

B 1. ‘Dynamics of Numerics and Numerics of Dynamics’ eds. D.S. Broomhead and A. Iserles, Clarendon Press, Oxford 1992
B 2. ‘Stochastic and Chaotic Dynamical Systems in the Lakes’ eds. D.S.Broomhead, E.A.Luchinskaya, P.V.E McLintock, Tom Mullin, AIP Conference Proceedings 502, 1999

Articles and Pamphlets

A 1. D.S. Broomhead and D.G. Crighton The Remarkable World of Nonlinear Systems, published by the Nonlinear Mathematics Initiative of the SERC 1989
A 2. D.S. Broomhead Keeping a Close Check on Chaos (a review) Physics World 1990 3 - July issue 23
A 3. D.S. Broomhead Guidance on the Control of Chaos (a review) Physics World 1992 5 - August issue 19
A 4. D.S. Broomhead Model Solution to Chaotic Confusion (a review) Physics World 1994 7 - February issue 19 2
A 5. D.S. Broomhead Chaos Moves on from Mythology (a review) Physics World 1995 8 - June issue 53
A 6. D.S. Broomhead Defence Sale is a Big Mistake, The Times Higher Education Supplement, July 28 2000, 18
A 7. Since July 2002 I have been writing a regular editorial for Mathematics Today (which has six issues per year).

Conference proceedings – not refereed

C 1. D.S. Broomhead, J.G. Harp, J.G. McWhirter, K.J. Palmer and J.B.G. Roberts 1985 A Practical Comparison of the Systolic and Wavefront Array Processing Architectures Proc. IEEE Int. Conf. Acoustics Speech and Signal Processing (Tampa, Florida) 296 - 300
C 2. R. Jones and D.S. Broomhead 1989 Phase Spaces from Experimental Time Series Proc. European Conference on Circuit Theory and Design 308 542 - 546
C 3. D.S. Broomhead, R. Jones, J.G. McWhirter and T.J. Shepherd 1989 A Parallel Architecture for Nonlinear Adaptive Filtering and Pattern Recognition Proc. 1st IEE International Conference on Artificial Neural Networks 313 265 - 269
C 4. D.S. Broomhead, R. Jones, J.G. McWhirter and T.J. Shepherd 1990 A Systolic Array for Nonlinear Adaptive Filtering and Pattern Recognition Proc. IEEE Int. Symposium on Circuits and Systems New Orleans 962 - 965
C 5. T.J. Shepherd and D.S. Broomhead 1990 Nonlinear Signal Processing using Radial Basis Functions Proc. SPIE 1348 Advanced Signal Processing: Algorithms, Architectures and Implementations ed. F. T. Luk
C 6. D.S. Broomhead 1991 Signal Processing for Nonlinear Systems (keynote address) Proc. SPIE 1565 Adaptive Signal Processing, 228 - 243
C 7. M.A.S. Potts, D.S. Broomhead 1991 Time Series Prediction with a Radial Basis Function Neural Network Proc. SPIE 1565 Adaptive Signal Processing, 255 -266
C 8. D.S. Broomhead and J.P. Huke 1994 Filtering Time Series with Topology Proc. SPIE 2296 Advanced Signal Processing: Algorithms, Architectures and Implementations V ed. F.T. Luk, 305–316
C 9. D.S. Broomhead and J.P. Huke 1996 Nonlinear Inverse Filtering in the Presence of Noise in Chaotic Fractal and Nonlinear Signal Processing ed. R.A. Katz AIP Conference Proc. 375 AIP Press New York 337–359
C 10. D.S. Broomhead, J.P. Huke and M.R. Muldoon 2000 Digital Channels, Proceedings of IEEE 2000 Adaptive Systems for Signal Processing, Communications and Control Symposium, 123–128 3
C 11. R.A. Clement, R.V. Abadi, D.S. Broomhead and J. P. Whittle 2002 Periodic forcing of congenital nystagmus, Experimental Chaos: 6th Experimental Chaos Conference, AIP Conference Proceedings 622 (edited by S. Boccaletti, B.J. Gluckman, J. Kurths, L.M. Pecora and M.L Spano), 149–154

Contributions to edited works

E 1. D.S. Broomhead and G.P. King 1986 On the Qualitative Analysis of Experimental Dynamical Systems in ‘Nonlinear Phenomena and Chaos’ ed. S. Sarkar, Adam Hilger: Bristol 113 - 144
E 2. D.S. Broomhead, R. Jones, G.P. King and E.R. Pike 1987 Singular System Analysis with Application to Dynamical Systems in ‘Chaos, Noise and Fractals’ ed. E.R. Pike and L.A. Lugiato Adam Hilger: Bristol 15 - 27
E 3. D.S. Broomhead 1987 Fractals in ‘Continuum Models of Discrete Systems’ ed. A.J.M. Spencer A.A. Balkema: Rotterdam, Paris 27 - 34
E 4. D.S. Broomhead 1992 The Geometry of Dynamics, in ‘Dynamics of Numerics
and Numerics of Dynamics’ eds. D.S. Broomhead and A. Iserles, Clarendon Press, Oxford
E 5. D.S. Broomhead 1994 Nonlinear Signal Processing, Proc. IMA Conf. on ‘Mathematics in Signal Processing’ ed. J. G. McWhirter, Clarendon Press, Oxford
E 6. D.S. Broomhead, J.P. Huke and M.R. Muldoon 1998 Fractals, Linear Channels and Delay Methods, Proc. 4th Institute of Mathematics Conference, ‘Mathematics of Signal Processing’ ed. J.G. McWhirter & I.K. Proudler, Clarendon Press, Oxford.
E 7. D.S. Broomhead, J.P. Huke, M.R. Muldoon and A.G. Brown 2001 Nonlinear Thoughts about Linear Signal Processing, Proc. 5th Institute of Mathematics Conference, ‘Mathematics of Signal Processing’ ed. J.G. McWhirter & I.K. Proudler, Clarendon Press, Oxford.
E 8. D. J. T. Sumpter and D. S. Broomhead, (1998), Formalising the Link Between Worker and Society in Honeybee Colonies, Lecture Notes in Artificial Intelligence, 1534, 95–110

Professor D S Broomhead
Mathematics Department
Room 2.230, Alan Turing Building
Upper Brook Street, Manchester
UK
(0161) 306 3680 (+ 44 161 306 3680 from overseas)
Fax: (0161) 306 3669
Email: david.broomhead[at]manchester.ac.uk