Workshop on

"Hitting, returning and matching in dynamical systems,
information theory & mathematical biology"

November 3-7, 2008

EURANDOM, Eindhoven, The Netherlands

Programme | Abstracts| Speakers | Participants |Registration | Practical Information

Summary

The purpose of this workshop is to gather people from various areas dealing with probabilistic aspects of the occurrence and the repetition of events.

In the context of ergodic theory and dynamical systems, one deals with hitting and return times to “shrinking” sets, e.g., cylinder sets, balls, Bowen balls. The exponential rate of return to shrinking typical cylinders is the entropy of the system [5]. In hyperbolic systems, the return time to a typical ball scales as a power law, with exponent the Hausdorff dimension of the invariant measure. The smallest return time to ball is related to Lyapunov exponents [2]. Another subject is the search for limit laws of (rescaled) hitting and return times. For “chaotic" systems, this limiting law is exponential. The control of fluctuations relies on the control of the Poisson approximation [1].

The link between entropy and recurrence rate to cylinders was actually established in the context of information theory in the 1990’s, in relation with data compression; see [5]. In this field, one is interested in pattern matching, perfect or approximate (lossy data compression) [3]. In the theory of image compression, Gibbsian random fields naturally arise.

In mathematical biology, one analyses word occurrences in, e.g., DNA and protein sequences. A well-known algorithm for DNA matching, namely BLAST, relies on a Poisson approximation of the distribution of words. The validity and quality of this approximation is a current object of study.

People from the areas mentioned above deal with common objects (often under different names) with different motivations, applications and techniques. This meeting will be the opportunity to share expertises, ideas and sustain future projects and colloborations.

To summarise, we aim at covering the following subjects in the workshop:

·                 Entropy, hitting and return times in ergodic theory;

·                 Sequence alignment and occurrence of words in biological sequences;

·                 Occurrence and matching of patterns in stochastic processes and random fields;

·                 Pattern matching and data compression in information theory.

References

[1]  M. Abadi and A. Galves. Inequalities for the occurrence times of rare events in mixing processes. The state of the art. Inhomogeneous random systems (Cergy-Pontoise, 2000). Markov Process. Related Fields  (2001), no. 1, 97–112.

[2]  L. Barreira. Hyperbolicity and recurrence in dynamical systems: a survey of recent results. Resenhas  (2002), no. 3, 171–230.

[3]  A. Dembo and I. Kontoyiannis. Source coding, large deviations, and approximate pattern matching. Special issue on Shannon theory: perspective, trends, and applications. IEEE Trans. Inform. Theory  (2002), no. 6, 1590–1615.

[4]  G. Reinert, S. Schbath, and M.S. Waterman. Probabilistic and Statistical Properties of Finite Words in Finite Sequences. In: Lothaire: Applied Combinatorics on Words, Cambridge University Press, J. Berstel, D. Perrin, eds. (2005).

[5]  P.C. Shields. The ergodic theory of discrete sample paths. Graduate Studies in Mathematics . American Mathematical Society, Providence, RI, 1996.

PARTICIPANTS

SPEAKERS

David Coupier, Laboratoire Paul Painlevé & Université Lille 1
Tomasz Downarowicz, Institute of Mathematics Computer Science, Wroclaw University of Technology
Jorge Freitas, Universidade do Porto
Stefano Galatolo, Dipartimento di matematica applicata "U. Dini" 
Marc Kesseböhmer, Universität Bremen
Ioannis Kontoyiannis, Athens University of Economics & Business
Yves Lacroix, Centre de Physique Théorique
Jérôme Rousseau, CNRS & Université de Bretagne Occidentale
Benoît Saussol, CNRS & Université de Bretagne Occidentale
Sophie Schbath, Institut National de la Recherche Agrononique
Sandro Vaienti, Centre de Physique théorique, Luminy
Nicolas Vergne, CNRS - Université d'Evry
Benjamin Weiss, The Hebrew University of Jerusalem
Roland Zweimüller, University of Vienna

PROGRAMME

There will be three minicourses of 3 hours each, by Benoît Saussol (ergodic theory), Sophie Schbath (mathematical biology), and Ioannis Kontoyiannis (information theory).

Monday - Tuesday - Wednesday - Thurday - Friday

Monday November 3, 2008

Tuesday November 4, 2008

Wednesday November 5, 2008

Thursday November 6, 2008

Friday November 7, 2008

Practical Information

REGISTRATION

There is no registration fee.

PLEASE REGISTER BY FILLING IN THE FORM

PRACTICAL INFORMATION

Conference Location and Travel

The workshop location is EURANDOM,  Den Dolech 2, 5612 AZ Eindhoven, Laplace Building, 1st floor, LG 1.105.

EURANDOM is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).

For information on how to come to Eindhoven, please check www.eurandom.tue.nl/Location.htm

Hotel

EURANDOM made a preliminary group reservation in

- Sandton Hotel Eindhoven City, Stratumsedijk 23d/f, Eindhoven. Special price single room  87^* euro, double room 97^* euro (breakfast included).

- Hotel Queen, Markt 7, Eindhoven, 040-2452480, Special price single room 92,50*,  double room 112,50* euro (breakfast included).

 * excl. tourist tax 3,50 euro per night.

If you want EURANDOM to make a reservation, indicate the requested nights on the registration page.

For private bookings we suggest you consult the web pages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.

Lunches/dinner

November 3-7, 2008 lunches are being organised; these are free of costs for all participants, if ordered on the registration form.

On  November 4, there will be a conference dinner. For non-invitees an amount of 35 euro is requested, to be paid at arrival in cash (preferably exact amount in euros). Indicate your attendance on the registration form.

Contact

For more information,  please contact Mrs. Lucienne Coolen, workshop officer of  EURANDOM, at coolen 'at' eurandom.tue.nl

Organisers

Jean-René Chazottes, CNRS / École Polytechnique (jeanrene'at'cpht.polytechnique.fr)
Frank den Hollander, Universiteit Leiden (denholla'at'math.leidenuniv.nl)
Frank Redig, Mathematisch Instituut Universiteit Leiden (redig'at'math.leidenuniv.nl)

Last modified: 24-02-09
Maintained by Lucienne Coolen