331 research outputs found
Dynamical Solution of the On-Line Minority Game
We solve the dynamics of the on-line minority game, with general types of
decision noise, using generating functional techniques a la De Dominicis and
the temporal regularization procedure of Bedeaux et al. The result is a
macroscopic dynamical theory in the form of closed equations for correlation-
and response functions defined via an effective continuous-time single-trader
process, which are exact in both the ergodic and in the non-ergodic regime of
the minority game. Our solution also explains why, although one cannot formally
truncate the Kramers-Moyal expansion of the process after the Fokker-Planck
term, upon doing so one still finds the correct solution, that the previously
proposed diffusion matrices for the Fokker-Planck term are incomplete, and how
previously proposed approximations of the market volatility can be traced back
to ergodicity assumptions.Comment: 25 pages LaTeX, no figure
Random replicators with asymmetric couplings
Systems of interacting random replicators are studied using generating
functional techniques. While replica analyses of such models are limited to
systems with symmetric couplings, dynamical approaches as presented here allow
specifically to address cases with asymmetric interactions where there is no
Lyapunov function governing the dynamics. We here focus on replicator models
with Gaussian couplings of general symmetry between p>=2 species, and discuss
how an effective description of the dynamics can be derived in terms of a
single-species process. Upon making a fixed point ansatz persistent order
parameters in the ergodic stationary states can be extracted from this process,
and different types of phase transitions can be identified and related to each
other. We discuss the effects of asymmetry in the couplings on the order
parameters and the phase behaviour for p=2 and p=3. Numerical simulations
verify our theory. For the case of cubic interactions numerical experiments
indicate regimes in which only a finite number of species survives, even when
the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of
negatively correlated couplings added, figures adde
Dynamics of on-line Hebbian learning with structurally unrealizable restricted training sets
We present an exact solution for the dynamics of on-line Hebbian learning in
neural networks, with restricted and unrealizable training sets. In contrast to
other studies on learning with restricted training sets, unrealizability is
here caused by structural mismatch, rather than data noise: the teacher machine
is a perceptron with a reversed wedge-type transfer function, while the student
machine is a perceptron with a sigmoidal transfer function. We calculate the
glassy dynamics of the macroscopic performance measures, training error and
generalization error, and the (non-Gaussian) student field distribution. Our
results, which find excellent confirmation in numerical simulations, provide a
new benchmark test for general formalisms with which to study unrealizable
learning processes with restricted training sets.Comment: 7 pages including 3 figures, using IOP latex2e preprint class fil
Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information
We study the dynamics of the batch minority game, with random external
information, using generating functional techniques a la De Dominicis. The
relevant control parameter in this model is the ratio of the
number of possible values for the external information over the number
of trading agents. In the limit we calculate the location
of the phase transition (signaling the onset of anomalous response),
and solve the statics for exactly. The temporal correlations
in global market fluctuations turn out not to decay to zero for infinitely
widely separated times. For the stationary state is shown to
be non-unique. For we analyse our equations in leading order in
, and find asymptotic solutions with diverging volatility
\sigma=\order(\alpha^{-{1/2}}) (as regularly observed in simulations), but
also asymptotic solutions with vanishing volatility
\sigma=\order(\alpha^{{1/2}}). The former, however, are shown to emerge only
if the agents' initial strategy valuations are below a specific critical value.Comment: 15 pages, 6 figures, uses Revtex. Replaced an old version of
volatility graph that. Rephrased and updated some reference
Domain Dynamics of Magnetic Films with Perpendicular Anisotropy
We study the magnetic properties of nanoscale magnetic films with large
perpendicular anisotropy comparing polarization microscopy measurements on
Co_28Pt_72 alloy samples based on the magneto-optical Kerr effect with Monte
Carlo simulations of a corresponding micromagnetic model. We focus on the
understanding of the dynamics especially the temperature and field dependence
of the magnetisation reversal process. The experimental and simulational
results for hysteresis, the reversal mechanism, domain configurations during
the reversal, and the time dependence of the magnetisation are in very good
qualitative agreement. The results for the field and temperature dependence of
the domain wall velocity suggest that for thin films the hysteresis can be
described as a depinning transition of the domain walls rounded by thermal
activation for finite temperatures.Comment: 7 pages Latex, Postscript figures included, accepted for publication
in Phys.Rev.B, also availible at:
http://www.thp.Uni-Duisburg.DE/Publikationen/Publist_Us_R.htm
Dynamical and Stationary Properties of On-line Learning from Finite Training Sets
The dynamical and stationary properties of on-line learning from finite
training sets are analysed using the cavity method. For large input dimensions,
we derive equations for the macroscopic parameters, namely, the student-teacher
correlation, the student-student autocorrelation and the learning force
uctuation. This enables us to provide analytical solutions to Adaline learning
as a benchmark. Theoretical predictions of training errors in transient and
stationary states are obtained by a Monte Carlo sampling procedure.
Generalization and training errors are found to agree with simulations. The
physical origin of the critical learning rate is presented. Comparison with
batch learning is discussed throughout the paper.Comment: 30 pages, 4 figure
Stromal vascular fraction cells as biologic coating of mesh for hernia repair
11 p.Background. The interest in non-manipulated cells originating from adipose tissue has raised tremendously in the field of tissue engineering and regenerative medicine. The resulting stromal vascular fraction (SVF) cells have been successfully used in numerous clinical applications. The aim of this experimental work is, first to combine a macroporous synthetic mesh with SVF isolated using a mechanical disruption process, and to assess the effect of those cells on the early healing phase of hernia. Methods. Human SVF cells combined with fibrin were used to coat commercial titanized polypropylene meshes. In vitro, viability and growth of the SVF cells were assessed using live/dead staining and scanning electron microscopy. The influence of SVF cells on abdominal wall hernia healing was conducted on immunodeficient rats, with a focus on short-term vascularization and fibrogenesis. Results. Macroporous meshes were easily coated with SVF using a fibrin gel as temporary carrier. The in vitro experiments showed that the whole process including the isolation of human SVF cells and their coating on PP meshes did not impact on the SVF cells? viability and on their capacity to attach and to proliferate. In vivo, the SVF cells were well tolerated by the animals, and coating mesh with SVF resulted in a decrease degree of vascularity compared to control group at day 21. Conclusions. The utilization of SVF-coated mesh influences the level of angiogenesis during the early onset of tissue healing. Further long-term animal experiments are needed to confirm that this effect correlates with a more robust mesh integration compared to non-SVF-coated mesh.European Hernia Society Research GrantTU
On suitability of phase-field and algebraic volume-of-fluid OpenFOAM® solvers for gas-liquid microfluidic applications
A first-principles study of the vibrational properties of crystalline tetracene under pressure
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