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 $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha<\alpha_c$ the stationary state is shown to be non-unique. For $\alpha\to 0$ we analyse our equations in leading order in $\alpha$, 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