540 research outputs found
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
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
Generating functional analysis of Minority Games with real market histories
It is shown how the generating functional method of De Dominicis can be used
to solve the dynamics of the original version of the minority game (MG), in
which agents observe real as opposed to fake market histories. Here one again
finds exact closed equations for correlation and response functions, but now
these are defined in terms of two connected effective non-Markovian stochastic
processes: a single effective agent equation similar to that of the `fake'
history models, and a second effective equation for the overall market bid
itself (the latter is absent in `fake' history models). The result is an exact
theory, from which one can calculate from first principles both the persistent
observables in the MG and the distribution of history frequencies.Comment: 39 pages, 5 postscript figures, iop styl
Period-two cycles in a feed-forward layered neural network model with symmetric sequence processing
The effects of dominant sequential interactions are investigated in an
exactly solvable feed-forward layered neural network model of binary units and
patterns near saturation in which the interaction consists of a Hebbian part
and a symmetric sequential term. Phase diagrams of stationary states are
obtained and a new phase of cyclic correlated states of period two is found for
a weak Hebbian term, independently of the number of condensed patterns .Comment: 8 pages and 5 figure
Dynamical Replica Theory for Disordered Spin Systems
We present a new method to solve the dynamics of disordered spin systems on
finite time-scales. It involves a closed driven diffusion equation for the
joint spin-field distribution, with time-dependent coefficients described by a
dynamical replica theory which, in the case of detailed balance, incorporates
equilibrium replica theory as a stationary state. The theory is exact in
various limits. We apply our theory to both the symmetric- and the
non-symmetric Sherrington-Kirkpatrick spin-glass, and show that it describes
the (numerical) experiments very well.Comment: 7 pages RevTex, 4 figures, for PR
Multiplpe Choice Minority Game With Different Publicly Known Histories
In the standard Minority Game, players use historical minority choices as the
sole public information to pick one out of the two alternatives. However,
publishing historical minority choices is not the only way to present global
system information to players when more than two alternatives are available.
Thus, it is instructive to study the dynamics and cooperative behaviors of this
extended game as a function of the global information provided. We numerically
find that although the system dynamics depends on the kind of public
information given to the players, the degree of cooperation follows the same
trend as that of the standard Minority Game. We also explain most of our
findings by the crowd-anticrowd theory.Comment: Extensively revised, to appear in New J Phys, 7 pages with 4 figure
Finite Size Effects in Separable Recurrent Neural Networks
We perform a systematic analytical study of finite size effects in separable
recurrent neural network models with sequential dynamics, away from saturation.
We find two types of finite size effects: thermal fluctuations, and
disorder-induced `frozen' corrections to the mean-field laws. The finite size
effects are described by equations that correspond to a time-dependent
Ornstein-Uhlenbeck process. We show how the theory can be used to understand
and quantify various finite size phenomena in recurrent neural networks, with
and without detailed balance.Comment: 24 pages LaTex, with 4 postscript figures include
Generating functional analysis of minority games with inner product strategy definitions
We use generating functional methods to solve the so-called inner product
versions of the minority game (MG), with fake and/or real market histories, by
generalizing the theory developed recently for look-up table MGs with real
histories. The phase diagrams of the lookup table and inner product MG versions
are generally found to be identical, with the exception of inner product MGs
where histories are sampled linearly, which are found to be structurally
critical. However, we encounter interesting differences both in the theory
(where the role of the history frequency distribution in lookup table MGs is
taken over by the eigenvalue spectrum of a history covariance matrix in inner
product MGs) and in the static and dynamic phenomenology of the models. Our
theoretical predictions are supported by numerical simulations.Comment: 30 pages, 12 figures (some lower resolution to enable submission,
originals available upon request), submitted to Journal of Physics
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