Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Donnerstag
DY 46.11 Do 16:00 Poster D
Magnification control of concave/convex learning in selforganizing
neural maps and neural gas — Thomas Villmann 1
and •Jens Christian Claussen 2 — 1 Cl. for Psychotherapy,
University Leipzig — 2 Theoretical Physics, University Kiel
The self-organizing neural maps (SOM) by Kohonen and the neural
gas (NG) by Martinetz are paradigms of neural winner-take all feedforward
computation and are widely applied for vector quantization tasks.
A data representation maximizing mutual information corresponds to an
magnification exponent of 1, which is not reached by SOM and (finitedimensional)
NG. Recently we presented magnification approaches for
NG by an additive winner-relaxing term [1] (extending an approach for
SOM [2, 3, 4]) as an alternative to localized learning [4].
In this work [5] an alternative learning rule, the concave/convex learning
[6], is investigated with respect to its magnification behaviour. We
present an analytical derivation of the magnification exponent for SOM
(in 1D) and for NG in arbitrary dimensions from a continuum theory. The
results are validated by numerical calculation of the entropy for a standardized
test system. We observe a dependence on the learning exponent
in agreement with the theoretical predictions.
[1] J.C.C. and T.V., Proc. ESANN 2003; J.C.C. and T.V. (subm.)
[2] J.C.C. cond-mat/0208414; [3] J.C.C. Complexity 8(4), 15 (2003).
[4] J.C.C., Math.Mod.Comp.Biol.Med. p.17, ed.V.Capasso, Bologna, 2003.
[5] M. Hermann, T.V., Proc. ICANN 1997.
[6] T.V. and J.C.C., Proc. WSOM 2003; T.V. and J.C.C. (subm.)
[7] Y.Zheng, J.F.Greenleaf, IEEE Trans. Neur. Netw. 7, 87 (1996).
DY 46.12 Do 16:00 Poster D
The Dynamics of Learning Vector Quantization — •Michael
Biehl 1,2 , Ansgar Freking 2 , and Georg Reents 2 — 1 Institute for
Mathematics and Computing Science, University of Groningen, P.O. Box
800, NL-9700 AV Groningen — 2 Institut fuer Theoretische Physik und
Astrophysik, Universitaet Wuerzburg, Am Hubland, D-97074 Wuerzburg
Learning Vector Quantization (LVQ) is a widely used method for the
implementation of classification schemes, in particular in the context of
structured (”clustered”) data. Here, we analyse LVQ by means of the
statistical physics theory of on-line learning in high-dimensional weight
space.
We show how variations of LVQ can be interpreted as interpolating between
”unsupervised clustering” (without a teacher) and the supervised
learning of a rule. The focus is on the phenomen of symmetry breaking
phenomena and the role of initial conditions for the learning process.
DY 46.13 Do 16:00 Poster D
Parameters estimation of hidden diffusion processes —
•Abdelhadi Benabdallah and Günter Radons — TU Chemnitz,
Institut für Physik , D-09107 Chemnitz, Germany
Diffusion processes, continuous in time and space, often cannot be
observed directly but only via functions reflecting the measurement process.
Within this work we investigate the parameter estimation problem
for hidden diffusion processes in a periodic potential. We propose a discrete
model as an approximation of continuous partially observed diffusion
Processes. Using the EM (Expectation-Maximisation) algorithm
we estimate the drift and the diffusion parameters which characterise
the diffusing state variable via an approximation by a discrete random
walk.A comparison with the particle filter are made. Numerical results
confirm our analytical estimation.
DY 46.14 Do 16:00 Poster D
Duality Transformation for Quantum Ratchets — •Joël Peguiron
1,2 and Milena Grifoni 2 — 1 Departement of Nanoscience, Delft
University of Technology, 2628 CJ Delft, The Netherlands — 2 Institut
für Theoretische Physik, Universität Regensburg, 93040 Regensburg
We investigate a duality transformation between weak-binding models
and tight-binding models for quantum ratchet systems. Ratchets are periodic
structures with broken spatial symmetry yielding the possibility of
a directed current in presence of noise and unbiased external forces. The
duality transformation would allow to relate results that we obtained on
few-bands quantum ratchets in the incoherent tunneling regime [1] with
existing results on weakly corrugated ratchets [2]. It would also make
possible to extend the parameter range of applicability of these results
and especially check their classical limit. We are also interested to see
how the symmetry conditions under which the ratchet current vanishes
in both models map onto each other.
[1] M. Grifoni et al., PRL 89, 146801 (2002)
[2] S. Scheidl and V. M. Vinokur, PRB 65, 195305 (2002)
DY 46.15 Do 16:00 Poster D
Velocity fluctuations in ratchets — •Lukasz Machura 1,2 and Peter
Hänggi 1 — 1 Theoretishe Physik I, Institut für Physik, Universität
Augsburg, Germany — 2 Department of Theoretical Physics, Institute of
Physics, University of Silesia, Poland
The quantity of foremost interest in the context of transport in periodic
systems, like Brownian ratchets, is the mean velocity of the particle.
However, the quality of the transport depends also on some other characteristics
like effective diffusion or shape of the potential. In this work
we use simulations to investigate the velocity correlation function in the
inertia Brownian ratchet. The connection between its behavior and the
optimal transport conditions is presented.
DY 46.16 Do 16:00 Poster D
Dynamics and interaction of dissipative solitons — •Hendrik
U. Bödeker 1 , Andreas W. Liehr 1 , Till D. Frank 2 , Rudolf
Friedrich 2 , Ulf-Hendrik Hansen 1 , and Hans-Georg Purwins 1
— 1 Westfälische Wilhelms-Universität Münster, Institut für Angewandte
Physik, Corrensstr. 2/4, 48149 Münster — 2 Westfälische Wilhelms-
Universität Münster, Institut für Theoretische Physik, Wilhelm-Klemm-
Str. 9, 48149 Münster
We present new results concerning the investigation of the dynamics
and the interaction of dissipative solitons occurring as current filaments
in a planar DC gas-discharge system with high-ohmic barrier. The dissipative
solitons exhibit interesting particle-like properties like generation
and annihilation, scattering, and formation of molecules. Processes in
which the number of solitons stays preserved can be understood by analyzing
the dynamics using means of stochastic data analysis. In this way,
both intrinsically standing and propagating solitons can be found, corresponding
to Brownian and active Brownian particles [1]. In addition,
a distance-dependant interaction law between mutually interacting dissipative
solitons can be determined, quantitatively explaining the experimentally
observed interaction phenomena. Generation and annihilation
processes taking place on a short time scale can be observed using fast
cameras, revealing different basic scenarios.
[1] H. U. Bödeker, M. C. Röttger, A. W. Liehr, T. D. Frank, R. Friedrich
and H.-G. Purwins, Noise-covered drift bifurcation of dissipative solitons in a
planar gas-discharge system, PRE 67 (2003) 056220.
DY 46.17 Do 16:00 Poster D
Characterisation of atrial fibrillation by analysis of ECG
records — •Th. Hennig 1 , A. Heinen 2 , St. Heinrichs 2 , D. Jäger 3 ,
and Ph. Maass 1 — 1 Institut für Physik, Technische Universität Ilmenau,
Germany — 2 Fachbereich Physik, Universität Konstanz, Germany
— 3 Medizinische Klinik II – Kardiologie, Städtisches Krankenhaus
Friedrichshafen, 88048 Friedrichshafen
We investigate the heartbeat of patients with atrial fibrillation (AF),
which is a cardiac arrhythmia where the normal pacemaking by the sinus
node is dysfunctional. The analysis of AF mechanisms and characteristics
is an important task, since it allows one to decide for the right diagnosis
and to improve possible therapies. Because standard ECG records
taken in hospitals are influenced by many different processes, it is difficult
to extract information from the ECG, which is particularly sensitive
to AF. We present novel methods to tackle this problem by employing
time series analysis and modeling, where AF is described by a stationary
process of irregular electrical excitations and the ventricular excitations
result from certain properties of the AV node. Our techniques allow us to
identify physiological parameters that otherwise can only be determined
invasively.
DY 46.18 Do 16:00 Poster D
Stochastic resonance in colloidal systems — •Dusan Babic 1,2 ,
Carmen Schmitt 1 , Igor Poberaj 2 , and Clemens Bechinger 1
— 1 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57,
70550 Stuttgart — 2 Faculty of mathematics and physics, University of
Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
The concept of stochastic resonance (SR) has been used to describe
very different effects such as the periodic occurence of the ice ages, the
feeding behavior of paddlefish or human balance control and visual perception.
The essential feature of SR is that in nonlinear systems noise
can improve the detection of weak periodic signals.
Although characteristic features of SR have been observed in several
experiments, there are only few examples where the effect is studied on