93 research outputs found
Hierarchical Crossover and Probability Landscapes of Genetic Operators
The time evolution of a simple model for crossover is discussed. A variant of
this model with an improved exploration behavior in phase space is derived as a
subset of standard one- and multi-point crossover operations. This model is
solved analytically in the flat fitness case. Numerical simulations compare the
way of phase space exploration of different genetic operators. In the case of a
non-flat fitness landscape, numerical solutions of the evolution equations
point out ways to estimate premature convergence.Comment: 11 pages, uuencoded postcript fil
A Minimal Model for Tag-based Cooperation
Recently, Riolo et al. [R. L. Riolo et al., Nature 414, 441 (2001)] showed by
computer simulations that cooperation can arise without reciprocity when agents
donate only to partners who are sufficiently similar to themselves. One
striking outcome of their simulations was the observation that the number of
tolerant agents that support a wide range of players was not constant in time,
but showed characteristic fluctuations. The cause and robustness of these tides
of tolerance remained to be explored. Here we clarify the situation by solving
a minimal version of the model of Riolo et al. It allows us to identify a net
surplus of random changes from intolerant to tolerant agents as a necessary
mechanism that produces these oscillations of tolerance which segregate
different agents in time. This provides a new mechanism for maintaining
different agents, i.e. for creating biodiversity. In our model the transition
to the oscillating state is caused by a saddle node bifurcation. The frequency
of the oscillations increases linearly with the transition rate from tolerant
to intolerant agents.Comment: 8 pages, 9 figure
Parametric Feedback Resonance in Chaotic Systems
If one changes the control parameter of a chaotic system proportionally to the distance between an arbitrary point on the strange attractor and the actual trajectory, the lifetime τ of the most stable unstable periodic orbit in the vicinity of this point starts to diverge with a power law. The volume in parameter space where τ becomes infinite is finite and from its nonfractal boundaries one can determine directly the local Liapunov exponents. The experimental applicability of the method is demonstrated for two coupled diode resonators
Sierpinski signal generates 1 / f ␣ spectra
We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1 / f ␣ spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns
Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement
Difference control schemes for controlling unstable fixed points become
important if the exact position of the fixed point is unavailable or moving due
to drifting parameters. We propose a memory difference control method for
stabilization of a priori unknown unstable fixed points by introducing a memory
term. If the amplitude of the control applied in the previous time step is
added to the present control signal, fixed points with arbitrary Lyapunov
numbers can be controlled. This method is also extended to compensate arbitrary
time steps of measurement delay. We show that our method stabilizes orbits of
the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70,
056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205
Sierpinski signal generates spectra
We investigate the row sum of the binary pattern generated by the Sierpinski
automaton: Interpreted as a time series we calculate the power spectrum of this
Sierpinski signal analytically and obtain a unique rugged fine structure with
underlying power law decay with an exponent of approximately 1.15. Despite the
simplicity of the model, it can serve as a model for spectra in a
certain class of experimental and natural systems like catalytic reactions and
mollusc patterns.Comment: 4 pages (4 figs included). Accepted for publication in Physical
Review
Corticothalamic projections control synchronization in locally coupled bistable thalamic oscillators
Thalamic circuits are able to generate state-dependent oscillations of
different frequencies and degrees of synchronization. However, only little is
known how synchronous oscillations, like spindle oscillations in the thalamus,
are organized in the intact brain. Experimental findings suggest that the
simultaneous occurrence of spindle oscillations over widespread territories of
the thalamus is due to the corticothalamic projections, as the synchrony is
lost in the decorticated thalamus. Here we study the influence of
corticothalamic projections on the synchrony in a thalamic network, and uncover
the underlying control mechanism, leading to a control method which is
applicable in wide range of stochastic driven excitable units.Comment: 4 pages with 4 figures (Color online on p.3-4) include
Stochastic gain in population dynamics
We introduce an extension of the usual replicator dynamics to adaptive
learning rates. We show that a population with a dynamic learning rate can gain
an increased average payoff in transient phases and can also exploit external
noise, leading the system away from the Nash equilibrium, in a reasonance-like
fashion. The payoff versus noise curve resembles the signal to noise ratio
curve in stochastic resonance. Seen in this broad context, we introduce another
mechanism that exploits fluctuations in order to improve properties of the
system. Such a mechanism could be of particular interest in economic systems.Comment: accepted for publication in Phys. Rev. Let
The role of inhibitory feedback for information processing in thalamocortical circuits
The information transfer in the thalamus is blocked dynamically during sleep,
in conjunction with the occurence of spindle waves. As the theoretical
understanding of the mechanism remains incomplete, we analyze two modeling
approaches for a recent experiment by Le Masson {\sl et al}. on the
thalamocortical loop. In a first step, we use a conductance-based neuron model
to reproduce the experiment computationally. In a second step, we model the
same system by using an extended Hindmarsh-Rose model, and compare the results
with the conductance-based model. In the framework of both models, we
investigate the influence of inhibitory feedback on the information transfer in
a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose
neuron model, which is computationally less costly and thus siutable for
large-scale simulations, reproduces the experiment better than the
conductance-based model. Further, in agreement with the experiment of Le Masson
{\sl et al}., inhibitory feedback leads to stable self-sustained oscillations
which mask the incoming input, and thereby reduce the information transfer
significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review
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