25,502 research outputs found
Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs
We study two of the simple rules on finite graphs under the death-birth
updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman
and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio
cutoff point for the magnitude of fixation probabilities of the underlying
evolutionary game between cooperators and defectors. We view the Markov chains
associated with the two updating mechanisms as voter model perturbations. Then
we present a first-order approximation for fixation probabilities of general
voter model perturbations on finite graphs subject to small perturbation in
terms of the voter model fixation probabilities. In the context of regular
graphs, we obtain algebraically explicit first-order approximations for the
fixation probabilities of cooperators distributed as certain uniform
distributions. These approximations lead to a rigorous proof that both of the
rules of Ohtsuki et al. are valid and are sharp.Comment: Published in at http://dx.doi.org/10.1214/12-AAP849 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stochastic Schr\"odinger Equation for a Non-Markovian Dissipative Qubit-Qutrit System
We investigate the non-Markovian quantum dynamics of a hybrid open system
consisting of one qubit and one qutrit by employing a stochastic
Schr\"{o}dinger equation to generate diffusive quantum trajectories. We have
established an exact quantum state diffusion (QSD) equation for the dissipative
qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an
important application, the non-Markovian QSD equation is employed to simulate
the entanglement decay and generation measured by negativity. Finally, some
steady state properties of the hybrid system are also discussed.Comment: EPL in pres
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