1,094 research outputs found
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 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
Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry
The problem of measuring nontrivial static correlations in deeply supercooled
liquids made recently some progress thanks to the introduction of amorphous
boundary conditions, in which a set of free particles is subject to the effect
of a different set of particles frozen into their (low temperature) equilibrium
positions. In this way, one can study the crossover from nonergodic to ergodic
phase, as the size of the free region grows and the effect of the confinement
fades. Such crossover defines the so-called point-to-set correlation length,
which has been measured in a spherical geometry, or cavity. Here, we make
further progress in the study ofcorrelations under amorphous boundary
conditions by analyzing the equilibrium properties of a glass-forming liquid,
confined in a planar ("sandwich") geometry. The mobile particles are subject to
amorphous boundary conditions with the particles in the surrounding walls
frozen into their low temperature equilibrium configurations. Compared to the
cavity, the sandwich geometry has three main advantages: i) the width of the
sandwich is decoupled from its longitudinal size, making the thermodynamic
limit possible; ii) for very large width, the behaviour off a single wall can
be studied; iii) we can use "anti-parallel" boundary conditions to force a
domain wall and measure its excess energy. Our results confirm that amorphous
boundary conditions are indeed a very useful new tool inthe study of static
properties of glass-forming liquids, but also raise some warning about the fact
that not all correlation functions that can be calculated in this framework
give the same qualitative results.Comment: Submited to JCP special issue on the glass transisio
Continuous time dynamics of the Thermal Minority Game
We study the continuous time dynamics of the Thermal Minority Game. We find
that the dynamical equations of the model reduce to a set of stochastic
differential equations for an interacting disordered system with non-trivial
random diffusion. This is the simplest microscopic description which accounts
for all the features of the system. Within this framework, we study the phase
structure of the model and find that its macroscopic properties strongly depend
on the initial conditions.Comment: 4 pages, 4 figure
Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''
We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper
[Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that
the effects of the temperature in the Thermal Minority Game ``can be eliminated
by time rescaling'' and consequently the behaviour is ``independent of T'' has
no general validity.Comment: 1 page, 1 figur
Basins of attraction of metastable states of the spherical -spin model
We study the basins of attraction of metastable states in the spherical
-spin spin glass model, starting the relaxation dynamics at a given distance
from a thermalized condition. Weighting the initial condition with the
Boltzmann distribution we find a finite size for the basins. On the contrary, a
white weighting of the initial condition implies vanishing basins of
attraction. We make the corresponding of our results with the ones of a
recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps 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
Adaptive Boolean Networks and Minority Games with Time--Dependent Capacities
In this paper we consider a network of boolean agents that compete for a
limited resource. The agents play the so called Generalized Minority Game where
the capacity level is allowed to vary externally. We study the properties of
such a system for different values of the mean connectivity of the network,
and show that the system with K=2 shows a high degree of coordination for
relatively large variations of the capacity level.Comment: 4 pages, 4 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
A New Stochastic Strategy for the Minority Game
We present a variant of the Minority Game in which players who where
successful in the previous timestep stay with their decision, while the losers
change their decision with a probability . Analytical results for different
regimes of and the number of players are given and connections to
existing models are discussed. It is shown that for the average
loss is of the order of 1 and does not increase with as for
other known strategies.Comment: 4 pages, 3 figure
Generalized strategies in the Minority Game
We show analytically how the fluctuations (i.e. standard deviation) in the
Minority Game (MG) can be made to decrease below the random coin-toss limit if
the agents use more general behavioral strategies. This suppression of the
standard deviation results from a cancellation between the actions of a crowd,
in which agents act collectively and make the same decision, and an anticrowd
in which agents act collectively by making the opposite decision to the crowd.Comment: Revised manuscript: a few minor typos corrected. Results unaffecte
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