5,675 research outputs found
Covariant Coordinate Transformations on Noncommutative Space
We show how to define gauge-covariant coordinate transformations on a
noncommuting space. The construction uses the Seiberg-Witten equation and
generalizes similar results for commuting coordinates.Comment: 11 pages, LaTeX; email correspondence to [email protected]
Different hierarchy of avalanches observed in the Bak-Sneppen evolution model
We introduce a new quantity, average fitness, into the Bak-Sneppen evolution
model. Through the new quantity, a different hierarchy of avalanches is
observed. The gap equation, in terms of the average fitness, is presented to
describe the self-organization of the model. It is found that the critical
value of the average fitness can be exactly obtained. Based on the simulations,
two critical exponents, avalanche distribution and avalanche dimension, of the
new avalanches are given.Comment: 5 pages, 3 figure
Intelligent systems in the context of surrounding environment
We investigate the behavioral patterns of a population of agents, each controlled by a simple biologically motivated neural network model, when they are set in competition against each other in the Minority Model of Challet and Zhang. We explore the effects of changing agent characteristics, demonstrating that crowding behavior takes place among agents of similar memory, and show how this allows unique `rogue' agents with higher memory values to take advantage of a majority population. We also show that agents' analytic capability is largely determined by the size of the intermediary layer of neurons.
In the context of these results, we discuss the general nature of natural and artificial intelligence systems, and suggest intelligence only exists in the context of the surrounding environment (embodiment).
Source code for the programs used can be found at http://neuro.webdrake.net/
Sandpile model on a quenched substrate generated by kinetic self-avoiding trails
Kinetic self-avoiding trails are introduced and used to generate a substrate
of randomly quenched flow vectors. Sandpile model is studied on such a
substrate with asymmetric toppling matrices where the precise balance between
the net outflow of grains from a toppling site and the total inflow of grains
to the same site when all its neighbors topple once is maintained at all sites.
Within numerical accuracy this model behaves in the same way as the
multiscaling BTW model.Comment: Four pages, five figure
Percolation and depinning transitions in cut-and-paste models of adaptation
We show that a cut-and-paste model to mimic a trial-and-error process of adaptation displays two pairs of percolation and depinning transitions, one for persistence and the other for efficiency. The percolation transition signals the onset of a property and the depinning transition, the growth of the same property. Despite its simplicity, the cut-and-paste model is qualitatively the same as the Minority Game. A majority cut-and-paste model is also introduced, to mimic the spread of a trend. When both models are iterated, the majority model reaches a frozen state while the minority model converges towards an alternate state. We show that a transition from the frozen to the alternate state occurs in the limit of a non-adaptive system
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
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