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Colloquia Patavina: Phase Synchronization and Cointegration: Bridging Two Theories

Martedì 25 Giugno 2013, ore 14:30 - Aula: 1A150 - Rainer Dahlhaus

ARGOMENTI: Seminari

Martedì 25 Giugno 2013 alle ore 14:30 in aula 1A150 della Torre Archimede, Rainer Dahlhaus (University of Heidelberg) terrà una conferenza della serie Colloquia Patavina.

La Commissione Colloquia
C. Bonotto, M.A. Garuti, M. Pavon, F. Rossi

Titolo
Phase Synchronization and Cointegration: Bridging Two Theories

Conferenziere
Rainer Dahlhaus (University of Heidelberg)

Riassunto
The theory of cointegration has been the leading theory in econometrics with powerful applications to macroeconomics during the last decades. On the other hand phase synchronization for oscillators has been a major research topic in physics for some 15 years with many applications in different areas of science. In particular in neuroscience the understanding of phase synchronization is of importance since phase synchronization is regarded as essential for functional coupling of different brain regions. In an abstract sense both theories describe the dynamic fluctuation around some equilibrium. In this talk we point out that, after some mathematical transformation, there exists a close connection between both subjects. As a consequence several techniques on statistical inference for cointegrated systems can immediately be applied for statistical inference on phase synchronization based on empirical data. This includes tests for phase synchronization, tests for unidirectional coupling and the identification of the equilibrium from data including phase shifts. We give an example where a chaotic Rössler-Lorenz system is identified with the methods from cointegration. Cointegration may also be used to investigate phase synchronization in complex networks. We also discuss some open problems and the research subject as a whole at the edge between econometrics, statistics, physics and neuroscience.

Breve biografia
Education/Profession
Diploma in Mathematics at the University of Munster, Germany
Dr. rer. nat. and Habilitation in Mathematics at the University of Essen, Germany
June 6, 1986: Habilitation at the University of Essen
1978 - 1988: Scientic Assistant, Department of Mathematics, University of Essen, Germany
1984/1985: Visiting Research Fellow, University of California, Berkeley
since 1988: Full Professor, Department of Mathematics, University of Heidelberg, Germany
1996-1998: Dean, Faculty of Mathematics, University of Heidelberg
since 2002: Director of the Institute of Applied Mathematics
Memberships and Professional Activities
Member of the German Mathematical Association (DMV), Bernoulli Society, Institute of Mathematical Statistics.
Elected fellow of the Institute of Mathematical Statistics.
Member of the scientic board and the "Gesellschaft fur Mathematische Forschung e.V." at the mathematical research institute Oberwolfach.
Associate Editor, Annals of Statistics (1996 - 2006).
Associate Editor, Journal of Time Series (2003 - present).
Associate Editor, Statistics Surveys (2007 - present).

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