5,376 research outputs found
A Dynamic Game Model of Collective Choice in Multi-Agent Systems
Inspired by successful biological collective decision mechanisms such as
honey bees searching for a new colony or the collective navigation of fish
schools, we consider a mean field games (MFG)-like scenario where a large
number of agents have to make a choice among a set of different potential
target destinations. Each individual both influences and is influenced by the
group's decision, as well as the mean trajectory of all the agents. The model
can be interpreted as a stylized version of opinion crystallization in an
election for example. The agents' biases are dictated first by their initial
spatial position and, in a subsequent generalization of the model, by a
combination of initial position and a priori individual preference. The agents
have linear dynamics and are coupled through a modified form of quadratic cost.
Fixed point based finite population equilibrium conditions are identified and
associated existence conditions are established. In general multiple equilibria
may exist and the agents need to know all initial conditions to compute them
precisely. However, as the number of agents increases sufficiently, we show
that 1) the computed fixed point equilibria qualify as epsilon Nash equilibria,
2) agents no longer require all initial conditions to compute the equilibria
but rather can do so based on a representative probability distribution of
these conditions now viewed as random variables. Numerical results are
reported
Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems
A transfer matrix scaling technique is developed for randomly diluted
systems, and applied to the site-diluted Ising model on a square lattice in two
dimensions. For each allowed disorder configuration between two adjacent
columns, the contribution of the respective transfer matrix to the decay of
correlations is considered only as far as the ratio of its two largest
eigenvalues, allowing an economical calculation of a configuration-averaged
correlation length. Standard phenomenological-renormalisation procedures are
then used to analyse aspects of the phase boundary which are difficult to
assess accurately by alternative methods. For magnetic site concentration
close to , the extent of exponential behaviour of the curve
is clearly seen for over two decades of variation of . Close to the
pure-system limit, the exactly-known reduced slope is reproduced to a very good
approximation, though with non-monotonic convergence. The averaged correlation
lengths are inserted into the exponent-amplitude relationship predicted by
conformal invariance to hold at criticality. The resulting exponent
remains near the pure value (1/4) for all intermediate concentrations until it
crosses over to the percolation value at the threshold.Comment: RevTeX 3, 11 pages +5 figures, uuencoded, to appear in Phys. Rev. B
(1994), PUC/RJ preprin
A New Neural Architecture for Homing Missile Guidance
We present a new neural architecture which imbeds dynamic programming solutions to solve optimal target-intercept problems. They provide feedback guidance solutions, which are optimal with any initial conditions and time-to-go, for a 2D scenario. The method discussed in this study determines an optimal control law for a system by successively adapting two networks - an action and a critic network. This method determines the control law for an entire range of initial conditions; it simultaneously determines and adapts the neural networks to the optimal control policy for both linear and nonlinear systems. In addition, it is important to know that the form of control does not need to be known in order to use this metho
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