On evolutionary ray-projection dynamics

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner

Generalized projection dynamics in evolutionary game theory

We introduce the ray-projection dynamics in evolutionary game\ud theory by employing a ray projection of the relative �tness (vector)\ud function both locally and globally. By global (local) ray projection we\ud mean a projection of the vector (close to the unit simplex) unto the unit\ud simplex along a ray through the origin. For these dynamics, we prove\ud that every interior evolutionarily stable strategy is an asymptotically\ud stable �xed point, and that every strict equilibrium is an evolutionarily\ud stable state and an evolutionarily stable equilibrium.\ud Then, we employ these projections on a set of functions related to\ud the relative �tness function which yields a class containing e.g., best-\ud response, logit, replicator, and Brown-Von-Neumann dynamics

Attractive evolutionary equilibria

We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary dynamics. For instance, each attractive evolutionarily stable strategy is an attractive evolutionarily stable equilibrium for certain barycentric ray-projection dynamics, and vice versa

Cosmic Ray Acceleration at the Forward Shock in Tycho's Supernova Remnant: Evidence from Chandra X-ray Observations

We present evidence for cosmic ray acceleration at the forward shock in Tycho's supernova remnant (SNR) from three X-ray observables: (1) the proximity of the contact discontinuity to the forward shock, or blast wave, (2) the morphology of the emission from the rim of Tycho, and (3) the spectral nature of the rim emission. We determine the locations of the blast wave (BW), contact discontinuity (CD), and reverse shock (RS) around the rim of Tycho's supernova remnant using a principal component analysis and other methods applied to new Chandra data. The azimuthal-angle-averaged radius of the BW is 251". For the CD and RS we find average radii of 241" and 183", respectively. Taking account of projection effects, we find ratios of 1:0.93:0.70 (BW:CD:RS). We show these values to be inconsistent with adiabatic hydrodynamical models of SNR evolution. The CD:BW ratio can be explained if cosmic ray acceleration of ions is occurring at the forward shock. The RS:BW ratio, as well as the strong Fe Ka emission from the Tycho ejecta, imply that the RS is not accelerating cosmic rays. We also extract radial profiles from ~34% of the rim of Tycho and compare them to models of surface brightness profiles behind the BW for a purely thermal plasma with an adiabatic shock. The observed morphology of the rim is much more strongly peaked than predicted by the model, indicating that such thermal emission is implausible here. Spectral analysis also implies that the rim emission is non-thermal in nature, lending further support to the idea that Tycho's forward shock is accelerating cosmic rays.Comment: 39 pages, 10 figures, accepted by Ap

On the Characteristic Isolation of Compact Subgroups within Loose Groups of Galaxies

We have explored the hypothesis that compact subgroups lying within dense environments as loose groups of galaxies, at a certain stage of their evolutionary history, could be influenced by the action of the tidal field induced by the gravitational potential of the whole system. We argue that empty rings observed in projection around many compact subgroups of galaxies embedded in larger hosts originate around the spherical surface drawn by the tidal radius where the internal binding force of the compact subgroup balances the external tidal force of the whole system. This effect would torn apart member galaxies situated in this region determining a marked isolation of the subgroups from the rest of the host groups. If so, subsequent evolution of these subgroups should not be affected by external influences as the infall of new surrounding galaxies on them. Following this idea we have developed a statistical method of investigation and performed an application to show evidences of such effect studying a loose group of galaxies hosting a compact group in its central region. The system UZC 578 / HCG 68 seems to be a fair example of such hypothesized process.Comment: 12 pages, match version accepted for publication in TOAJ, corrected typo

A correspondence between solution-state dynamics of an individual protein and the sequence and conformational diversity of its family.

Conformational ensembles are increasingly recognized as a useful representation to describe fundamental relationships between protein structure, dynamics and function. Here we present an ensemble of ubiquitin in solution that is created by sampling conformational space without experimental information using "Backrub" motions inspired by alternative conformations observed in sub-Angstrom resolution crystal structures. Backrub-generated structures are then selected to produce an ensemble that optimizes agreement with nuclear magnetic resonance (NMR) Residual Dipolar Couplings (RDCs). Using this ensemble, we probe two proposed relationships between properties of protein ensembles: (i) a link between native-state dynamics and the conformational heterogeneity observed in crystal structures, and (ii) a relation between dynamics of an individual protein and the conformational variability explored by its natural family. We show that the Backrub motional mechanism can simultaneously explore protein native-state dynamics measured by RDCs, encompass the conformational variability present in ubiquitin complex structures and facilitate sampling of conformational and sequence variability matching those occurring in the ubiquitin protein family. Our results thus support an overall relation between protein dynamics and conformational changes enabling sequence changes in evolution. More practically, the presented method can be applied to improve protein design predictions by accounting for intrinsic native-state dynamics

Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

The Origin And Loss Of Periodic Patterning In The Turtle Shell

The origin of the turtle shell over 200 million years ago greatly modified the amniote body plan, and the morphological plasticity of the shell has promoted the adaptive radiation of turtles. The shell, comprising a dorsal carapace and a ventral plastron, is a layered structure formed by basal endochondral axial skeletal elements (ribs, vertebrae) and plates of bone, which are overlain by keratinous ectodermal scutes. Studies of turtle development have mostly focused on the bones of the shell; however, the genetic regulation of the epidermal scutes has not been investigated. Here, we show that scutes develop from an array of patterned placodes and that these placodes are absent from a soft-shelled turtle in which scutes were lost secondarily. Experimentally inhibiting Shh, Bmp or Fgf signaling results in the disruption of the placodal pattern. Finally, a computational model is used to show how two coupled reaction-diffusion systems reproduce both natural and abnormal variation in turtle scutes. Taken together, these placodal signaling centers are likely to represent developmental modules that are responsible for the evolution of scutes in turtles, and the regulation of these centers has allowed for the diversification of the turtle shell