Dynamical quenching and annealing in self-organization multiagent models

We study the dynamics of a generalized Minority Game (GMG) and of the Bar Attendance Model (BAM) in which a number of agents self-organize to match an attendance that is fixed externally as a control parameter. We compare the usual dynamics used for the Minority Game with one for the BAM that makes a better use of the available information. We study the asymptotic states reached in both frameworks. We show that states that can be assimilated to either thermodynamic equilibrium or quenched configurations can appear in both models, but with different settings. We discuss the relevance of the parameter $G$ that measures the value of the prize for winning in units of the fine for losing. We also provide an annealing protocol by which the quenched configurations of the GMG can progressively be modified to reach an asymptotic equlibrium state that coincides with the one obtained with the BAM.Comment: around 20 pages, 10 figure

Glassy dynamics, metastability limit and crystal growth in a lattice spin model

We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour typical of fragile glasses. However, the supercooled phase loses stability at an effective spinodal temperature, and thanks to this the Kauzmann paradox is resolved. Below the spinodal the system enters an off-equilibrium regime corresponding to fast crystal nucleation followed by slow activated crystal growth. In this phase and in a time region which is longer the lower the temperature we observe a violation of the fluctuation-dissipation theorem analogous to structural glasses. Moreover, we show that in this system there is no qualitative difference between a locally stable glassy configuration and a highly disordered polycrystal

Dynamics of the Time Horizon Minority Game

We present exact analytic results for a new version of the Minority Game (MG) in which strategy performance is recorded over a finite time horizon. The dynamics of this Time Horizon Minority Game (THMG) exhibit many distinct features from the MG and depend strongly on whether the participants are fed real, or random, history strings. The THMG equations are equivalent to a Markov Chain, and yield exact analytic results for the volatility given a specific realization for the quenched strategy disorder.Comment: Latex file, 11 pages, 6 figure

Alterations in T1 of normal and reperfused infarcted myocardium after Gd-BOPTA versus GD-DTPA on inversion recovery EPI.

This study tested whether Gd-BOPTA/Dimeg or Gd-DTPA exerts greater relaxation enhancement for blood and reperfused infarcted myocardium. Relaxivity of Gd-BOPTA is increased by weak binding to serum albumin. Thirty-six rats were subjected to reperfused infarction before contrast (doses = 0.05, 0.1, and 0.2 mmol/kg). delta R1 was repeatedly measured over 30 min. Gd-BOPTA caused greater delta R1 for blood and myocardium than did Gd-DTPA; clearance of both agents from normal- and infarcted myocardium was similar to blood clearance; plots of delta R1 myocardium/delta R1 blood showed equilibrium phase contrast distribution. Fractional contrast agent distribution volumes were approximately 0.24 for both agents in normal myocardium, 0.98 and 1.6 for Gd-DTPA and Gd-BOPTA, respectively, in reperfused infarction. The high value for Gd-BOPTPA was ascribed to greater relaxivity in infarction versus blood. It was concluded that Gd-BOPTA/Dimeg causes a greater delta R1 than Gd-DTPA in regions which contain serum albumin

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

On the stationary points of the TAP free energy

In the context of the p-spin spherical model, we introduce a method for the computation of the number of stationary points of any nature (minima, saddles, etc.) of the TAP free energy. In doing this we clarify the ambiguities related to the approximations usually adopted in the standard calculations of the number of states in mean field spin glass models.Comment: 11 pages, 1 Postscript figure, plain Te

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles

Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids

The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of $|\nabla E|^2$ that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average energy increases linearly with saddle point index in agreement with previous results for bulk systems.Comment: 14 pages, 7 figure

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