UK Nonlinear News , August 1998


Winter School on Time Series Analysis

Max Planck Institute Dresden, 11-20 February 1998

By James Heald

This was my first experience of a residential school, and (as one of the other students later emailed me), how lucky I was to start with such a nice one!

I had a feeling that it would be a special fortnight right from the moment when Paddy and I rolled up in the land rover, and were shown to our de-luxe accommodation in a brand new apartment -- really rather good for a couple of random students! The institute, which only opened last year, has three little blocks of these apartments, separated across a rather attractively landscaped mini-campus, from its spacious and pleasantly airy main building. The 45 participants were all put up in some comfort. But as Holger Kantz was keen to remind us, this was not a hotel: the school he had organised with Thomas Schreiber and Danny Kaplan for us had a lot more than just that to offer...

Certainly we, the students, were kept quite busy. The morning session started at 9am and was intensive, with a series of exceptionally clear lectures that made up the backbone of the course. These were divided between Holger and Thomas, who gave a thorough review of the dynamical systems approach to time series analysis, and the properties of dynamical invariants; and a second strand on statistical properties of time series, and surrogate-data methods, given by Danny and James Theiler. But the school was not just about abstract theory. Thanks to a set of Matlab scripts by Danny, and two suites of C and Fortran code by Thomas and Holger, there was time in the afternoon to work though the morning's lecture material on the institute's superb new DEC alpha cluster, and to experiment with the algorithms. (This code is all now publicly accessible, and can be downloaded from the links below).

This was also a great opportunity for co-operation and for the students to get to know each other, we had all been encouraged to bring along their own datasets for analysis. As well as the extraordinarily cohesive and friendly atmosphere, the sheer range of subjects and experience represented was remarkable, both theory and an enormous diversity of real world applications, from spatiotemporal fluid mechanics to laser engineering, biomechanics to astrophysics, and all points in between. This was underlined by the large number of very impressive contributions in the poster sessions and student presentations. It was fascinating to meet so many people from so many backgrounds, and to gain an insight into how wide the scope is for nonlinear dynamics and nonlinear time-series analysis.

Finally, these strands were complemented by a truly exciting series of stand-out lectures in the evenings on the high frontiers of the subject, kicked off in storming fashion by Celso Grebogi with two adrenaline saturated lectures on the importance of chaos, firstly in chaotic control and then chaotic mixing. These were followed by fascinating lectures from Lenny Smith on the dynamics of uncertainty in weather prediction and the rival schemes (and teams) coping with it; from James Yorke on some of the latest results in embedding theory; from Peter Grassberger on the important subject of synchronisation between chaotic systems; and from Freddy Christiansen on the interesting promise of periodic orbit theory.

But perhaps the images that will stay with me longest are those from the lecture by Klaus Lehnertz on epilepsy, with its graphic video footage of the effects of this disease. This was also a useful lesson in the dangers of hubris. It can be tempting to look down from a great height on the use of dimension calculations from short unstable datasets, and to carelessly dismiss the results as 'statistically unfounded'. As Dr Lehnertz showed, such blind high-handedness would be a great mistake. While such calculations may 'only' be useful complexity measures, rather than meaningfully quantifying dimensionality, I don't think anybody who saw his footage of their effectiveness giving advanced warning of seizures from EEG data will ever be quite so quick to belittle them again.

All this, and I haven't mentioned the joys of the excellent Dresden Opera (which sent a good many of us rushing back to the Net afterwards, to find out what it was about); the outstanding collections of the Zwinger palace; the efficient trams, historic 'old stones' and pleasant relaxed boulevards of Dresden; the picturesque beauty of the rock stacks further up the river Elbe where Holger took us for a Sunday ramble. I could go on and on...

What was most impressive was the really warm and exciting atmosphere of people having a good time and working well together, and the real buzz of discussion and enthusiasm, which you could see infecting and visibly relaxing everyone, teachers and students alike. I offer my most sincere thanks to the Max Planck Society, and the institute in Dresden, for inviting us; and to Danny Kaplan, Thomas Schreiber and Holger Kantz for planning and organising this excellent event. It was one of the busiest, happiest and most stimulating ten days I have ever spent anywhere.

James Heald ( )
Centre for Nonlinear Dynamics and its Applications, University College, London.


The TISEAN WWW page is at:

As well as links to the original programme, this page contains links to the WWW homepages of the organisers, participants and many of the students; links to the TISEAN software packages; and information about the recent books by the organisers which inspired the core lectures.

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Last Updated: 7th August 1998.