Discrete solitons in coupled active lasing cavities

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and grey cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by the discrete diffraction and are stable when the bistability of homogenous states is absent.Comment: 3 pages, 3 figures, accepted to Optics Letters (October 2012

Dictators and Their Viziers: Agency Problems in Dictatorships

The possibility of treason by a close associate has been a nightmare of most dictators throughout history. Better informed viziers are also better able to discriminate among potential plotters, and this makes them more risky subordinates for the dictator. To avoid this, dictators, especially which are weak and vulnerable, sacri.ce the competence of their agents, hiring mediocre but loyal subordinates. One reason why democracies generally witness more talented people in the government is the dictator.s inability to commit to the optimal (less than the capital) punishment for those who unsuccessfully plotted to remove him from power. Furthermore, any use of incentive schemes by a dictator is limited by the fact that rewards are conditional on dictator.s own willingness to keep his promises, while punishments are conditional on dictator.s own survival. We model a principalagent game between a dictator and his (probably, few) viziers both in static and dynamic perspectives. The dynamic model allows us to focus on the succession problem the insecure dictators face.http://deepblue.lib.umich.edu/bitstream/2027.42/40121/3/wp735.pd

Dictators and Their Viziers: Agency Problems in Dictatorships

The possibility of treason by a close associate has been a nightmare of most dictators throughout history. Better informed viziers are also better able to discriminate among potential plotters, and this makes them more risky subordinates for the dictator. To avoid this, dictators, especially those which are weak and vulnerable, sacrifice the competence of their agents, hiring mediocre but loyal subordinates. However, any use of incentive schemes by a dictator is limited by the fact that all punishments are conditional on the dictator’s own survival, and a dictator is typically unable to commit to the optimal (i.e., less than capital) punishment for those who unsuccessfully plotted against him. We endogenize loyalty and competence in a principal-agent game between a dictator and his (probably, few) viziers in both static and dynamic settings. The dynamic model allows us to focus on the succession problem that insecure dictators face.Dictatorship, Loyalty and Competence, Positive Political Theory, Principal-Agent, Non-democratic Succession

Morse coding for a Fuchsian group of a finite covolume

We consider the Morse coding of the geodesic flow on the hyperbolic plane $H$ with respect to a Dirichlet fundamental domain $D$ of a Fuchsian group $\Gamma$. The main theorem states that the codes of all the generic geodesics constitute a $k$-step topological Markov chain, if and only if the fundamental domain $D$ is an ideal polygon (i.e. has all of its vertices on the absolute).Comment: 11 pages, 4 figure