Research Interests

Scientific Interests: My PhD work was on weak decays of K mesons, under the supervisions of Prof. W. Thirring and Dr. H. Pietschmann. After finishing the PhD I went to Bonn University, where I joined the group around Dr. Sandhas working on scattering theory. Stimulated by claims made by S. Lovelace, we studied in particular non-relativistic three-body scattering and scattering of bound states ("Fadeev theory"). Our main contribution in this field was the formulation of formally exact equations for bound state scattering ("Alt-Grassberger-Sandhas equations"). These papers were much quoted (our first paper has nearly 600 citations) and are still used in atomic and nuclear physics. But when it became clear that Lovelace's more excessive claims about relevance for particle physics failed, I left the field.

First, I went for two years to Kabul, vAfghanistan, where I took a position as professor for physics at the University. Research was of difficult there, although I managed to continue the work on scattering theory and to do some experimental work, together with another German colleague in our team, on geophysics of sand dunes.

After coming back to Bonn, I worked on exact consequences of basic assumptions such as Lorentz invariance, positivity, and analyticity, for pion-pion scattering. This was mainly triggered by work done by Andre Martin at CERN, who had shown that these basic requirements lead to non-trivial consequences. This field was also the subject of my habilitation thesis, and I continued with it for some time when I came to CERN as a fellow. But again it became clear that the original hopes were too high, and that this approach would not give really interesting results.

Thus I switched to hadron phenomenology. These were at CERN the high days of reggeon field theory (RFT). But there were rumors that Feynman had suggested that the results of RFT should be understandable in terms of stochastic concepts centered around soft ("wee") partons and their interactions. After spending a substantial effort to understand the relationship between quantum and stochastic theories (which were at that time not very well understood!), I finally realized that RFT is a stochastic theory. More precisely, it is (after augmenting it with some regularizing term) exactly equivalent to the "contact process", and is in the same universality class as directed percolation. This work I consider as my second major achievement.

After this, I left particle physics and turned my full attention to statistical physics and dynamical systems. Here I worked on a multitude of different problems: reaction-diffusion systems, cellular automata, fractals, Ising model, Griffiths phases, self organized criticality, possible operational definitions of the concept of "complexity", percolation, heat conduction in low dimensional systems, etc.

But my best known work was on strange attractors. Apart from a method for estimating attractor dimensions I wrote a well received paper on strange repellers Two of my papers with I. Procaccia were cited now about 2000 times, and several other ones were cited a few hundred times. Apart from a method for estimating attractor dimensions I wrote a well received paper on strange repellers with H. Kantz, another with him on generating partitions, and a series of papers on nonlinear methods for noise reduction. Finally, together with A. Pikovsky we were the first to recognize the importance of Milnor attractors (now known as ``riddled" attractors) in coupled dynamical systems. This line of work still continues, along two lines. On the one hand I have still an ongoing collaboration with medical doctors, dealing with the application of these methods in epileptology. Here we are mainly concerned with predicting seizures and with locating the epileptic focus. Some of the methods we developed for this include some new measures for interdependencies among two time series. The other line which derived from my earlier work on strange attractors involves novel estimators of mutual information, and their application to independent component analysis (ICA). The latter has numerous applications in a wide range of fields. Two problems we studied explicitly are the extraction of fetal ECG from the ECG of a pregnant woman, and a new simulated annealing approach to the analysis of infrared spectra.

Finally, a large part of my work during the last 12 years deals with sequential sampling algorithms, mostly applied to polymer systems. Non-trivial sequential sampling algorithms started on the one hand with Rosenbluth & Rosenbluth's work in the 50's on sampling of self avoiding random walks, on the other hand with Ulam & von Neumann's ``Russian Roulette and Splitting". The latter has survived up to the present day in neutron transport theory and in quantum Monte Carlo, but it has spread very little outside these disciplines. Which led to its repeated rediscovery. When I rediscovered it and applied it with some modifications to polymers, I called it PERM ("pruned-enriched Rosenbluth method"). Since then, PERM has been applied to a vast range of problems, ranging from reaction-diffusion systems to finding the ground states of lattice protein models. The last major finished project using PERM involved lattice animals and lattice trees, and in particular their collapse transitions. I have also a project with R. Bundschuh where we apply it to generate more efficient surrogates for sequence alignment, and with M. Paczuski where we use it for generating constrained random graphs.

At present I would describe myself as a physicist mainly using computational tools, but with the ambition to perform high quality work on moderate scale equipment. With this I connect the hope that I can encourage scientists in lesser developped countries without access to heavy hardware that they still can do relevant work. I have a rather broad interest in many fields of science, but mostly I am interested in ``complex" systems, of which biology is of course the prime example. I am aware of the fact that my work sometimes concentrates too much on details, but it is my conviction that only meticulous observation of details can prevent one from loosing the ground under one's feet. I would consider my work as intermediate between pure and applied science, ``pure" in the sense that I do not care too much for financial benefits resulting from it, but ``applied" in the sense that I believe all good scientific work must transgress its narrow boundaries and must relate in some way to other human interests.