Emergence of order in selection-mutation dynamics

We characterize the time evolution of a d-dimensional probability distribution by the value of its final entropy. If it is near the maximally-possible value we call the evolution mixing, if it is near zero we say it is purifying. The evolution is determined by the simplest non-linear equation and contains a d times d matrix as input. Since we are not interested in a particular evolution but in the general features of evolutions of this type, we take the matrix elements as uniformly-distributed random numbers between zero and some specified upper bound. Computer simulations show how the final entropies are distributed over this field of random numbers. The result is that the distribution crowds at the maximum entropy, if the upper bound is unity. If we restrict the dynamical matrices to certain regions in matrix space, for instance to diagonal or triangular matrices, then the entropy distribution is maximal near zero, and the dynamics typically becomes purifying.Comment: 8 pages, 8 figure

Modeling the X-ray Contribution of X-ray Binary Jets

Astrophysical jets exist in both XRBs and AGN, and seem to share common features, particularly in the radio. While AGN jets are known to emit X-rays, the situation for XRB jets is not so clear. Radio jets have been resolved in several XRBs in the low/hard state, establishing that some form of outflow is routinely present in this state. Interestingly, the flat-to-inverted radio synchrotron emission associated with these outflows strongly correlates with the X-ray emission in several sources, suggesting that the jet plasma plays a role at higher frequencies. In this same state, there is increasing evidence for a turnover in the IR/optical where the flat-to-inverted spectrum seems to connect to an optically thin component extending into the X-rays. We discuss how jet synchrotron emission is likely to contribute to the X-rays, in addition to inverse Compton up-scattering, providing a natural explanation for these correlations and the turnover in the IR/optical band. We present model parameters for fits to several sources, and address some common misconceptions about the jet model.Comment: 4 pages, 1 Table, conference proceedings for "The Physics of Relativistic Jets in the Chandra and XMM Era, Bologna, 2002", Eds. G. Brunetti, D. E. Harris, R. M. Sambruna & G. Sett

Coevolution of dynamical states and interactions in dynamic networks

We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the outcome of the game. As an example we consider a model of cooperation, where the adaptation is shown to facilitate the formation of a hierarchical interaction network that sustains a highly cooperative stationary state. The resulting network has the characteristics of a small world network when a mechanism of local neighbor selection is introduced in the adaptive network dynamics. The highly connected nodes in the hierarchical structure of the network play a leading role in the stability of the network. Perturbations acting on the state of these special nodes trigger global avalanches leading to complete network reorganization.Comment: 4 pages, 5 figures, for related material visit http:www.imedea.uib.es/physdept

Topological enslavement in evolutionary games on correlated multiplex networks

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions

Disordered Environments in Spatial Games

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at $\rho^*$, separating a region with spatial chaos from one with localized, stable groups of cooperators.Comment: 6 pages, 5 figure

Parity Doubling and SU(2)_L x SU(2)_R Restoration in the Hadron Spectrum

We construct the most general nonlinear representation of chiral SU(2)_L x SU(2)_R broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses.Comment: 4 pages, 1 figure; v3: Note added to clarify implications for hadrons that do not couple to pions: Chiral symmetry can be realized linearly on such states, leading to parity doubling. To the extent that they are parity doubled, these hadrons must decouple from pions, a striking prediction that can be tested experimentally. This applies to the work of L. Glozman and collaborator

The supermassive black hole in NGC4486a detected with SINFONI at the VLT

The near-infrared integral field spectrograph SINFONI at the ESO VLT opens a new window for the study of central supermassive black holes. With a near-IR spatial resolution similar to HST optical and the ability to penetrate dust it provides the possibility to explore the low-mass end of the M-sigma relation (sigma<120km/s) where so far very few black hole masses were measured with stellar dynamics. With SINFONI we observed the central region of the low-luminosity elliptical galaxy NGC4486a at a spatial resolution of ~0.1arcsec in the K band. The stellar kinematics was measured with a maximum penalised likelihood method considering the region around the CO absorption band heads. We determined a black hole mass of M_BH=1.25^{+0.75}_{-0.79} x 10^7 M_sun (90% C.L.) using the Schwarzschild orbit superposition method including the full 2-dimensional spatial information. This mass agrees with the predictions of the M-sigma relation, strengthening its validity at the lower sigma end.Comment: 7 pages, 7 figures. Accepted by MNRA

Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything

Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's strategy, or else to set the ratio between a ZD player's and their opponent's expected payoff. Here we show that while ZD strategies are weakly dominant, they are not evolutionarily stable and will instead evolve into less coercive strategies. We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition.Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature Communications requirements. To appear in Nature Communication