# Peter Grassberger

Per Bak Foundation Fellow

Former Visiting iCORE Research Professor,

joint appointment with the Institute for Biocomplexity & Informatics (IBI).

## 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.

## Curriculum Vitae

Born May 17th, 1940 in Vienna, Austria;

Father: Dr. Johann Grassberger

Mother: Helene Grassberger

Austrian citizen

Education:

1950-58: ``Gymnasium" (high school) in Steyr, Upper Austria

1959-65: University of Vienna (physics, mathematics)

1965: Dr. Phil. (theoretical high energy physics) at the University of Vienna

1973: ``Habilitation" in theoretical physics at Bonn University

1958-59: Military service in the Austrian Air Force

Employment:

1965-68: Postdoctoral fellow at Bonn University

1969-71: Professor (`Pohand'), University of Kabul (Afghanistan)

1971-73: Assistent professor (H1) at Bonn University

1973-75: Fellow, CERN (Geneva)

1975-77: Maitre de Conferences associe, Universite de Nice (France)

1977-2005 : Professor (C3), University of Wuppertal (Germany)

1. 9. 1996 - 31.7. 2005: leave of absence from Univ. of Wuppertal, head of the Complex Systems Research Group at the John-von-Neumann Institute, Forschungszentrum J\"ulich (Germany)

Visiting Professorships:

Aug. 1978: CERN, Geneva

Aug. 1979: Stanford Linear Accelerator Center, Stanford (USA)

Feb.-Aug. 1982: Weizmann Institute, Rehovot (Israel)

Aug. 1986: Los Alamos National Lab, Los Alamos (USA)

Sept. 1986: James Franck Institute, University of Chicago (USA)

July-August 1987: MIDIT, Technical University of Copenhagen (Denmark)

July 1988: Mathem. Department, University of Warwick (England)

Oct.-Dec. 1988: Los Alamos National Lab, Los Alamos (USA)

Jan.-March 1989: Niels Bohr Institute, Copenhagen (Denmark)

July 1991, July 1992: Institute of Scientific Interchange, Torino (Italy)

Oct.-Dec. 1993: Istituto Nazionale di Ottica, Florence (Italy)

Jan.-March 1994: Universita di Roma I (Italy)

Jan.-Feb. 1999: University of Stellenbosch (South Africa)

February 2001: Institute for Theoretical Physics, UCSB, Santa Barbara (USA)

Oct.-Nov. 2002: Korean Institute for Advanced Studies, Seoul (Korea)

Jan.-Feb. 2005: Korean Institute for Advanced Studies, Seoul (Korea)

July-August 2005: Perimeter Institute, Waterloo (Canada)

Sept.-Dec. 2005: Kramers Professor, University of Utrecht (Netherlands)

Feb.-April 2006: School for Scientific Computing, Florida State University, Tallahassee (USA)

1. 8. 2006 - present: Visiting Research Professor, Department of Physics and Astronomy, University of Calgary (Canada)

Memberships in Editorial Boards:

1987-1991, 1998 - : Journal of Physics A (Inst. of Physics Publishing Ltd)

1991-1997: Nonlinearity (Inst. of Physics Publishing Ltd)

1991-2003: CHAOS (American Inst. of Physics)

1995 - : Complexity (Wiley)

1991 - : International Journal of Bifurcations & Chaos (Pergamon Press)

2001 - : SIAM Journal on Applied Dynamical Systems

2003 - : Journal of Statistical Physics

Refereeing work:

Referee for numerous journals in addition to those listed above:

Physical Review A - E, Physical Review Letters, Physics Letters A\&B, Nuclear Physics A\&B, Europhysics Letters, Journal of Chemical Physics, Journal of Hydrology, Nature, Electroencephalography and Clinical Neurophysiology.

Advisor for several national Science Boards:

Austria, Canada, Denmark, Germany, Netherlands, Norway, Sweden

Scientific Collaborators:

E.O. Alt, R.G. Andrzejak, S.A. Astakhov, R. Badii, G. Barkema, U. Bastolla, A. Ben-Mizrahi, B.A. Berg, D. Braess, L. Caneschi, M.S. Causo, J. Cardy, H. Chate, B. Coluzzi, A. Crisanti, J. Davidsen, C.E. Elger, J.G. Foster, D.V. Foster, H. Frauenkron, H. Freund, J.A.C. Gallas, F. Guerin, S. Havlin, R. Hegger, H.G.E. Hentschel, H. Herrmann, H.-P. Hsu, H. Kantz, H. Kuehnelt, F. Krause, D.V. Ktitarev, J. Kubar-Andre, K. Lehnertz, S. Luebeck, S. Majumdar, S.S. Manna, V. Mehra, C. Michael, H.I. Miettinen, F. Mormann, W. Nadler, M. Paczuski, A.S. Pikovsky, A. Politi, V.B. Priezzhev, I. Procaccia, R. Quian Quiroga, G. Rousseau, B. Samuelson, W. Sandhas, L. Schaefer, M. Scheunert, T. Schreiber, D. Schwela, A. Shreim, J.E.S. Socolar, D. Stauffer, K. Sundermeyer, H. Taitelbaum, A. Torcini, A. de la Torre, T. von der Twer, P. Ueberholz, L. Yang, D. Zambella, Y.-C. Zhang

PhD and Diploma Students:

J. Arnhold, H.-M. Broeker, H. Frauenkron, H. Freund, E. Gerstner, R. Hegger, H. Kantz, A. Kraskov, T. Kreuz, R. Leuverink, U. Moenig, C. Schaffrath, P. Schneider, T. Schreiber, T. Schuermann, H. Stoegbauer, R. Wolter

Grants etc.:

1980 - 1981: Postdoc position for 2 years from Deutsche Forschungsgemeinschaft (M. Scheunert)

1987 - 1988: Postdoc position for 2 years from Volkswagen-Stiftung (H. Freund)

1989 - 1991: Humboldt fellowship (A. Pikovsky)

1996 - 1997: Postdoc position for one year from European Union (A. Torcini)

1988 - 2002: Member of SFB (research unit) 237, ``Disorder and large fluctuations" (implied 1 PhD student position during entire period)

1994 - 2001: Member of Graduate College ``Field theoretic and numerical methods in particle and statistical physics" (implied 1 to 2 PhD student positions during entire period)

2001 - : Member of SFB-TR3 ``Mesial Temporal Lobe Epilepsies"

since 1997: External member of the Max-Planck-Society

## Recent publications

Copies of them can be got from there.

- ``Graph animals, subgraph sampling and motif search in large networks" K. Baskerville, P. Grassberger, and M. Paczuski, e-print q-bio.MN/0702029 (2007)
- ``Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity" J. Davidsen, P. Grassberger, and M. Paczuski, e-print physics/0701190 (2007)
- ``Network Analysis of the State Space of Discrete Dynamical Systems" A. Shreim, P. Grassberger, W. Nadler, B. Samuelsson, J.E.S. Socolar, and M. Paczuski, e-print cond-mat/0610447 (2006)
- ``Link likelihoods in random networks with fixed and partially fixed degree sequence" J.G. Foster, D.V. Foster, P. Grassberger, and M. Paczuski, e-print cond-mat/0610446 (2006)
- ``Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition" S.A. Astakhov, H. Stoegbauer, A. Kraskov, and P. Grassberger, Anal. Chem. 78, 1620 (2006); e-print physics/0601161
- ``Tricritical directed percolation in 2+1 dimensions" P. Grassberger, J. Stat. Mech. P01004 (2006); e-print cond-mat/0510428
- ``Temporal scaling at Feigenbaum points and non-extensive thermodynamics" P. Grassberger; Phys. Rev. Lett. 95, 140601 (2005); e-print cond-mat/0508110 (2005)
- ``Earthquake recurrence as a record breaking process" J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res Lett., 33, L11304 (2006); e-print physics/0507082 (2005)
- ``Collapsing lattice animals and lattice trees in two dimensions" H.-P. Hsu and P. Grassberger, J. Stat. Mech. P06003 (2005); e-print cond-mat/0504678
- ``Spectral Mixture Decomposition by Least Dependent Component Analysis" S.A. Astakhov, H. Stoegbauer, A. Kraskov, and P. Grassberger, e-print physics/0412029 (2004)
- ``The coil-globule transition of confined polymers" H.-P. Hsu and P. Grassberger, J. Stat. Mech. P01007 (2005); e-print cond-mat/0412029 (2004)
- ``Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces" H.-P. Hsu, W. Nadler, and P. Grassberger, Phys. Rev. E 71, 065104R (2005); e-print cond-mat/0411262
- ``Simulations of grafted polymers in a good solvent" P. Grassberger, J. Phys. A: Math. Gen. 38, 323 (2005); e-print cond-mat/0410055
- ``Hierarchical Clustering Using Mutual Information" H. Stoegbauer, A. Kraskov, R.G. Andrzejak, and P. Grassberger, Europhys. Lett. 70, 278 (2005); e-print q-bio.QM/0311037
- ``Reliability of ICA estimates with mutual information" H. Stoegbauer, R.G. Andrzejak, A. Kraskov, and P. Grassberger; Lecture Notes in Computer Science 3195, 209 (2004)
- ``Measure profile surrogates: A method to validate the performance of epileptic seizure prediction algorithms T. Kreuz, R.G. Andrzejak, F. Mormann, A. Kraskov, H. Stoegbauer, C.E. Elger, K. Lehnertz, and P. Grassberger, Phys. Rev. E 69, 061915 (2004)
- ``Extracting Phases from Aperiodic Signals" A. Kraskov, T. Kreuz, R.G. Andrzejak, H. Stoegbauer, W. Nadler, and P. Grassberger, e-print cond-mat/0409382 (2004)
- ``Hierarchical Clustering Based on Mutual Information" H. Stoegbauer, A. Kraskov, R.G. Andrzejak, and P. Grassberger, e-print q-bio.QM/0311039 (2004)
- ``Least Dependent Component Analysis Based on Mutual Information" H.-P. Hsu, W. Nadler, and P. Grassberger, Macromolecules 37, 4658 (2004); e-print cond-mat/0310534
- ``Polymers confined between two parallel plane walls" H.-P. Hsu and P. Grassberger, J. Chem. Phys. 120, 2034 (2004)
- ``Entropy Estimates from Insufficient Samplings" P. Grassberger, e-print physics/0307138 (2003)
- ``Least Dependent Component Analysis Based on Mutual Information" H. Stoegbauer, A. Kraskov, S.A. Astakhov, and P. Grassberger, Phys. Rev. E 70, 066123 (2004); e-print cs/0405044 (2004)
- ``Sequential Monte Carlo Methods for Protein Folding" P. Grassberger, in ``NIC Symposium 2004", eds. D. Wolf at el. (NIC, Juelich, 2004); e-print cond-mat/0408571
- ``Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations" H.-P. Hsu, B.A. Berg, and P. Grassberger, in ``NIC Symposium 2004", eds. D. Wolf at el. (NIC, Juelich, 2004); e-print cond-mat/0408572
- ``Simulations of Lattice Animals and Trees" H.-P. Hsu, W. Nadler, and P. Grassberger, J. Phys. A: Math. Gen. 38, 775 (2005); e-print cond-mat/0408061 (2004)
- ``Effective Interactions between Star Polymers" H.-P. Hsu and P. Grassberger, Europhys. Lett. 66, 874-880 (2004); e-print cond-mat/0312194
- ``Scaling of Star Polymers with one to 80 Arms" H.-P. Hsu, W. Nadler, and P. Grassberger, Macromolecules 37, 4658 (2004); e-print cond-mat/0310534
- ``Polymers confined between two parallel plane walls" H.-P. Hsu and P. Grassberger, J. Chem. Phys. 120, 2034 (2004)
- ``Entropy Estimates from Insufficient Samplings" P. Grassberger, e-print physics/0307138 (2003)
- ``Comment on `Linguistic Analysis of the Human Heartbeat Using Frequency and Rank Order Statistics'" A. Kraskov, W. Nadler, H. Stogbauer, and P. Grassberger, Phys. Rev. Lett. 92, 109801 (2004)
- ``Measure Profile Surrogates: A Method to Validate the Performance of epileptic seizure prediction algorithms" with T. Kreuz, R.G. Andrzejak, F. Mormann, A. Kraskov, H. Stoegbauer, C.E. Elger, K. Lehnertz, and P. Grassberger, Phys. Rev. E 69, 061915 (2004)
- ``Estimating Mutual Information" A. Kraskov, H. Stoegbauer, and P. Grassberger, Phys. Rev. E 69, 066138 (2004); e-print cond-mat/0305641
- ``2-Dimensional Polymers Confined in a Strip" H.-P. Hsu and P. Grassberger, European Physical Journal B 36, 209 (2003); e-print cond-mat/0308276
- ``Are there really phase transitions in 1-d heat conduction models?" P. Grassberger and L. Yang, e-print cond-mat/0306173 (2003);
- ``Structure optimization in an off-lattice protein model" H.-P. Hsu, V. Mehra, and P. Grassberger, Phys. Rev. E 68, 037703 (2003); e-print cond-mat/0302545
- ``Growth-based Optimization Algorithm for Lattice Heteropolymers" H.-P. Hsu, V. Mehra, W. Nadler, and P. Grassberger, Phys. Rev. E 68, 021113 (2003); e-print cond-mat/0209366
- ``Critical Percolation in High Dimensions" P. Grassberger, Phys. Rev. E 67, 036101 (2003); e-print cond-mat/0202144
- ``A Simple Model for the DNA Denaturation Transition" M.S. Causo and B. Coluzzi, and P. Grassberger, Physica A 314, 607 (2002)

## Citations

According to the Science Citation Index, my papers have been cited more than 13,000 times (by October 2006), qualifying me as ``highly cited researcher" and placing me among the 200 most cited physicists.

My 10 most cited papers are (citations up to 21. Oct. 2006):

- ``Measuring the Strangeness of Strange Attractors", P. Grassberger and I. Procaccia, Physica D 9, 189 (1883); 2045 citations
- ``Characterization of Strange Attractors", P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983); 1716 citations
- ``Reduction of the 3-Particle Collision Problem to Multichannel 2-Particle Lippmann-Schwinger Equations", E.O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. B 2, 167 (1967); 583 citations
- ``Estimating the Kolmogorov Entropy from a Chaotic Signal", P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983); 482 citations
- ``Generalized Dimensions of Strange Attractors", P. Grassberger, Phys. Lett. A 97, 227 (1983); 419 citations
- ``Dimensions and Entropies of Strange Attractors from a Fluctuating Dynamics Approach", P. Grassberger and I. Procaccia, Physica D 13, 34 (1984); 396 citations
- ``Reggeon Field Theory (Schloegl's First Model) on a Lattice: Monte Carlo Calculations of Critical Behavior", P. Grassberger and A. de la Torre, Annals of Physics 122, 373 (1979); 384 citations
- ``Scaling Laws for Invariant Measures on Hyperbolic and Non-Hyperbolic Attractors", P. Grassberger, R. Badii, and A. Politi, J. Stat. Phys. 51, 135 (1988); 329 citations
- ``On Phase Transitions in Schloegl's 2nd Model", P. Grassberger, Z. Physik B 47, 365 (1982); 293 citations
- ``The Long-Time Properties of Diffusion in a Medium with Static Traps", P. Grassberger and I. Procaccia, J. Chem. Phys. 77, 6281 (1982); 265 citations