Rare Variant of Vastus Medialis Detected in vivo by Ultrasound and Confirmed by High-resolution MRI.

[Purpose] This report describes an unusual incidental finding during ultrasound investigation of the vastus medialis muscle. Volunteers underwent ultrasound scanning as part of an on-going investigation into the architecture of the vastus medialis muscle. [Subjects and Methods] The distal thighs of forty-one subjects were scanned using the Philips iU22 US system. An unusual muscle morphology was detected bilaterally in one subject, who then underwent a 3T Magnetic Resonance Imaging (MRI) scan in order to further investigate the muscle morphology. The subject in question was a 32 year-old female who suffers from recurrent bilateral patellar dislocations. [Results] The MRI scan confirmed the ultrasound findings, and indicated the presence of the vastus medialis in two layers, with the VML continuing deep, separate from the VMO. [Conclusion] Although this rare variant has been been reported in previous cadaveric studies, we believe this to be the first report in the literature of this morphology in vivo. The biomechanical implications of this muscle arrangement are unknown, but it may not be without significance that this individual suffers from recurrent patellar dislocations

Holonomies of Intersecting Branes

We discuss the geometry of string and M-theory gauge fields in Deligne cohomology. In particular, we show how requiring string structure (or loop space Spin-C structure) on the five-brane leads to topological conditions on the flux in the relative Deligne cohomology of the bulk - brain pair.Comment: 8 pages, LaTeX, talk given in the RTN Workshop "The quantum structure of spacetime and the geometric nature of fundamental interactions," (Kolymbari, Greece, September 2004

An Application of Evolutionary Game Theory to Social Dilemmas: The Traveler's Dilemma and the Minimum Effort Coordination Game

The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games

Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point (N>3) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.Comment: 14 pages, LaTeX, version to be publishe

Global anomalies in M-theory

We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the boundary. We then consider M-theory configurations that include a five-brane. In this case, diffeomorphisms of the eleven-manifold induce diffeomorphisms of the five-brane world-volume and gauge transformations on its normal bundle. These transformations are also potentially anomalous. In both of these cases, it has previously been shown that the perturbative anomalies, i.e. the anomalies under transformations that can be continuously connected to the identity, cancel. We extend this analysis to global anomalies, i.e. anomalies under transformations in other components of the group of gauge transformations and diffeomorphisms. These anomalies are given by certain topological invariants, that we explicitly construct.Comment: 14 pages, harvma

Co-evolution of strategy and structure in complex networks with dynamical linking

Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. We provide analytic results for the limiting cases where linking dynamics is much faster than evolutionary dynamics and vice-versa, and show how the individual capacity of forming new links or severing inconvenient ones maps into the problem of strategy evolution in a well-mixed population under a different game. For intermediate ranges, we investigate numerically the detailed interplay determined by these two time-scales and show that the scope of validity of the analytical results extends to a much wider ratio of time scales than expected

Evolutionary Dynamics of Bertrand Duopoly

Duopolies are one of the simplest economic situations where interactions between firms determine market behavior. The standard model of a price-setting duopoly is the Bertrand model, which has the unique solution that both firms set their prices equal to their costs-a paradoxical result where both firms obtain zero profit, which is generally not observed in real market duopolies. Here we propose a new game theory model for a price-setting duopoly, which we show resolves the paradoxical behavior of the Bertrand model and provides a consistent general model for duopolies

Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive systems. For well-mixed systems where interactions result in fitness reductions of the losers exceeding fitness gains of the winners, classical theory predicts that two strategies go extinct. The effects of spatial heterogeneity and dispersal rates on this outcome are analyzed using a general framework for evolutionary games in patchy landscapes. The analysis reveals that coexistence is determined by the rates at which dominant strategies invade a landscape occupied by the subordinate strategy (e.g. rock invades a landscape occupied by scissors) and the rates at which subordinate strategies get excluded in a landscape occupied by the dominant strategy (e.g. scissor gets excluded in a landscape occupied by rock). These invasion and exclusion rates correspond to eigenvalues of the linearized dynamics near single strategy equilibria. Coexistence occurs when the product of the invasion rates exceeds the product of the exclusion rates. Provided there is sufficient spatial variation in payoffs, the analysis identifies a critical dispersal rate $d^*$ required for regional persistence. For dispersal rates below $d^*$, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally. For dispersal rates above $d^*$, the product of the exclusion rates exceed the product of the invasion rates and the strategies are extinction prone. These results highlight the delicate interplay between spatial heterogeneity and dispersal in mediating long-term outcomes for evolutionary games.Comment: 31pages, 5 figure

Gribov Copies and Smeared Correlation Functions in Lattice QCD

We study the influence of Gribov copies in the Coulomb gauge on the smeared hadronic correlation functions that are involved in the determination of the B meson decay constant. We find that the residual gauge freedom associated to Gribov copies induces observable noise effects, though at the level of numerical accuracy of our simulation these effects are not relevant to the final determination of f_B. Our results indicate that such effects may become important on bigger lattices.Comment: 12pgs., preprint n. 892, June 24, 1992, Dipartimento di Fisica Univ. of Rome "La Sapienza