139 research outputs found
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
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
Topological Modes in Dual Lattice Models
Lattice gauge theory with gauge group is reconsidered in four
dimensions on a simplicial complex . One finds that the dual theory,
formulated on the dual block complex , contains topological modes
which are in correspondence with the cohomology group ,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
.Comment: 10 pages, DIAS 94-3
Final state interactions in the parton model and massive lepton pair production
We show that when final state interactions are added to the parton model (Drell-Yan) formula for massive lepton pair production, the cross sections decreases. Our proof rests on assumptions similar to those made by Landshoff and Polkinghorne and others. Thus, contrary to previous claims, this effect cannot help explain the discrepancy between the parton model predictions for this process and the NBL data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22275/1/0000714.pd
On Duality of Two-dimensional Ising Model on Finite Lattice
It is shown that the partition function of the 2d Ising model on the dual
finite lattice with periodical boundary conditions is expressed through some
specific combination of the partition functions of the model on the torus with
corresponding boundary conditions. The generalization of the duality relations
for the nonhomogeneous case is given. These relations are proved for the
weakly-nonhomogeneous distribution of the coupling constants for the finite
lattice of arbitrary sizes. Using the duality relations for the nonhomogeneous
Ising model, we obtain the duality relations for the two-point correlation
function on the torus, the 2d Ising model with magnetic fields applied to the
boundaries and the 2d Ising model with free, fixed and mixed boundary
conditions.Comment: 18 pages, LaTe
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
Self-Segregation vs. Clustering in the Evolutionary Minority Game
Complex adaptive systems have been the subject of much recent attention. It
is by now well-established that members (`agents') tend to self-segregate into
opposing groups characterized by extreme behavior. However, while different
social and biological systems manifest different payoffs, the study of such
adaptive systems has mostly been restricted to simple situations in which the
prize-to-fine ratio, , equals unity. In this Letter we explore the dynamics
of evolving populations with various different values of the ratio , and
demonstrate that extreme behavior is in fact {\it not} a generic feature of
adaptive systems. In particular, we show that ``confusion'' and
``indecisiveness'' take over in times of depression, in which case cautious
agents perform better than extreme ones.Comment: 4 pages, 4 figure
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