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

Multiscale approach to the electronic structure of doped semiconductor surfaces

The inclusion of the global effects of semiconductor doping poses a unique challenge for first-principles simulations, because the typically low concentration of dopants renders an explicit treatment intractable. Furthermore, the width of the space-charge region (SCR) at charged surfaces often exceeds realistic supercell dimensions. Here, we present a multiscale technique that fully addresses these difficulties. It is based on the introduction of a charged sheet, mimicking the SCR-related field, along with free charge which mimics the bulk charge reservoir, such that the system is neutral overall. These augment a slab comprising “pseudoatoms” possessing a fractional nuclear charge matching the bulk doping concentration. Self-consistency is reached by imposing charge conservation and Fermi level equilibration between the bulk, treated semiclassically, and the electronic states of the slab, which are treated quantum-mechanically. The method, called CREST—the charge-reservoir electrostatic sheet technique—can be used with standard electronic structure codes. We validate CREST using a simple tight-binding model, which allows for comparison of its results with calculations encompassing the full SCR explicitly. Specifically, we show that CREST successfully predicts scenarios spanning the range from no to full Fermi level pinning. We then employ it with density functional theory, obtaining insight into the doping dependence of the electronic structures of the metallic “clean-cleaved” Si(111) surface and its semiconducting (2×1) reconstructions

Theory of agent-based market models with controlled levels of greed and anxiety

We use generating functional analysis to study minority-game type market models with generalized strategy valuation updates that control the psychology of agents' actions. The agents' choice between trend following and contrarian trading, and their vigor in each, depends on the overall state of the market. Even in `fake history' models, the theory now involves an effective overall bid process (coupled to the effective agent process) which can exhibit profound remanence effects and new phase transitions. For some models the bid process can be solved directly, others require Maxwell-construction type approximations.Comment: 30 pages, 10 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

Market response to external events and interventions in spherical minority games

We solve the dynamics of large spherical Minority Games (MG) in the presence of non-negligible time dependent external contributions to the overall market bid. The latter represent the actions of market regulators, or other major natural or political events that impact on the market. In contrast to non-spherical MGs, the spherical formulation allows one to derive closed dynamical order parameter equations in explicit form and work out the market's response to such events fully analytically. We focus on a comparison between the response to stationary versus oscillating market interventions, and reveal profound and partially unexpected differences in terms of transition lines and the volatility.Comment: 14 pages LaTeX, 5 (composite) postscript figures, submitted to Journal of Physics

The impact of transmural multiprofessional simulation-based obstetric team training on perinatal outcome and quality of care in the Netherlands

Background Perinatal mortality and morbidity in the Netherlands is relatively high compared to other European countries. Our country has a unique system with an independent primary care providing care to low-risk pregnancies and a secondary/tertiary care responsible for high-risk pregnancies. About 65% of pregnant women in the Netherlands will be referred from primary to secondary care implicating multiple medical handovers. Dutch audits concluded that in the entire obstetric collaborative network process parameters could be improved. Studies have shown that obstetric team training improves perinatal outcome and that simulation-based obstetric team training implementing crew resource management (CRM) improves team performance. In addition, deliberate practice (DP) improves medical skills. The aim of this study is to analyse whether transmural multiprofessional simulation-based obstetric team training improves perinatal outcome. Methods/Design The study will be implemented in the south-eastern part of the Netherlands with an annual delivery rate of over 9,000. In this area secondary care is provided by four hospitals. Each hospital with referring primary care practices will form a cluster (study group). Within each cluster, teams will be formed of different care providers representing the obstetric collaborative network. CRM and elements of DP will be implemented in the training. To analyse the quality of care as perceived by patients, the Pregnancy and Childbirth Questionnaire (PCQ) will be used. Furthermore, self-reported collaboration between care providers will be assessed. Team performance will be measured by the Clinical Teamwork Scale (CTS). We employ a stepped-wedge trial design with a sequential roll-out of the trainings for the different study groups. Primary outcome will be perinatal mortality and/or admission to a NICU. Secondary outcome will be team performance, quality of care as perceived by patients, and collaboration among care providers. Conclusion The effect of transmural multiprofessional simulation-based obstetric team training on perinatal outcome has never been studied. We hypothesise that this training will improve perinatal outcome, team performance, and quality of care as perceived by patients and care providers

Influence of external information in the minority game

The influence of a fixed number of agents with the same fixed behavior on the dynamics of the minority game is studied. Alternatively, the system studied can be considered the minority game with a change in the comfort threshold away from half filling. Agents in the frustrated, non ergodic phase tend to overreact to the information provided by the fixed agents, leading not only to large fluctuations, but to deviations of the average occupancies from their optimal values. Agents which discount their impact on the market, or which use individual strategies reach equilibrium states, which, unlike in the absence of the external information provided by the fixed agents, do not give the highest payoff to the collective.Comment: 8 pages, 6 figure

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

Statistical Mechanics of Dilute Batch Minority Games with Random External Information

We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of ergodicity breaking in this model is different from the phase transition in the standard minority game and is characterised by the onset of long-term memory at finite integrated response. We demonstrate that finite memory appears at the AT-line obtained from the corresponding replica calculation, and compare the behaviour of the dilute model with the minority game with market impact correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added, figure added, typos correcte

Continuum time limit and stationary states of the Minority Game

We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such equations. In particular, i) we confirm that the stationary state properties are given by the ground state configurations of a disordered (soft) spin system; ii) we derive the full stationary state distribution; iii) we characterize the dependence on initial conditions in the symmetric phase and iv) we clarify the behavior of the system as a function of the learning rate. This leaves us with a complete and coherent picture of the collective behavior of the Minority Game. Strikingly we find that the temperature like parameter which is introduced in the choice behavior of individual agents turns out to play the role, at the collective level, of the inverse of a thermodynamic temperature.Comment: Revised version (several new results added). 12 pages, 5 figure