Shadows and Twisted Variables

We explain how a new type of fields called shadows and the use of twisted variables allow for a better description of Yang-Mills supersymmetric theories. (Based on lectures given in Cargese, June 2006.)Comment: Cargese Jun 200

Optimization of TFRC loss history initialization

This letter deals with the initialization of the loss history structure in the TFRC (TCP-Friendly Rate Control) mechanism. This initialization occurs after the detection of the first loss event after every slowstart phase. The loss history is crucial for the algorithm since it returns the packet loss rate estimation. This estimation is used in the TFRC equation to compute the sending rate. In this letter, we propose a new method to compute the packet loss rate which is more computationally efficient and remains as accurate as the classical commonly used method. The motivation of this work is to reduce the computation time and formulate a unified computation scheme. This method is based on the Newton’s algorithm issued from numerical analysis of the TCP throughput equation. This proposal is evaluated analytically and the results show a significant improvement in terms of the computation time

Twisted Superspace

We formulate the ten-dimensional super-Yang-Mills theory in a twisted superspace with 8+1 supercharges. Its constraints do not imply the equations of motion and we solve them. As a preliminary step for a complete formulation in a twisted superspace, we give a superspace path-integral formulation of the N=2, d=4 super-Yang-Mills theory without matter. The action is the sum of a Chern--Simons term depending on a super-connection plus a BF-like term. The integration over the superfield B implements the twisted superspace constraints on the super-gauge field, and the Chern-Simons action reduces to the known action in components

From calls to communities: a model for time varying social networks

Social interactions vary in time and appear to be driven by intrinsic mechanisms, which in turn shape the emerging structure of the social network. Large-scale empirical observations of social interaction structure have become possible only recently, and modelling their dynamics is an actual challenge. Here we propose a temporal network model which builds on the framework of activity-driven time-varying networks with memory. The model also integrates key mechanisms that drive the formation of social ties - social reinforcement, focal closure and cyclic closure, which have been shown to give rise to community structure and the global connectedness of the network. We compare the proposed model with a real-world time-varying network of mobile phone communication and show that they share several characteristics from heterogeneous degrees and weights to rich community structure. Further, the strong and weak ties that emerge from the model follow similar weight-topology correlations as real-world social networks, including the role of weak ties.Comment: 10 pages, 5 figure

Propagation of seismic waves through a spatio-temporally fluctuating medium: Homogenization

Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally stationary medium is almost universally invoked. However, the Sun is in a constant state of evolution, on a broad range of spatio-temporal scales. At the zero wavelength limit, i.e., when the wavelength is much shorter than the scale over which the medium varies, the WKBJ (ray) approximation may be applied. Here, we address the other asymptotic end of the spectrum, the infinite wavelength limit, using the technique of homogenization. We apply homogenization to scenarios where waves are propagating through rapidly varying media (spatially and temporally), and derive effective models for the media. One consequence is that a scalar sound speed becomes a tensorial wavespeed in the effective model and anisotropies can be induced depending on the nature of the perturbation. The second term in this asymptotic two-scale expansion, the so-called corrector, contains contributions due to higher-order scattering, leading to the decoherence of the wavefield. This decoherence may be causally linked to the observed wave attenuation in the Sun. Although the examples we consider here consist of periodic arrays of perturbations to the background, homogenization may be extended to ergodic and stationary random media. This method may have broad implications for the manner in which we interpret seismic measurements in the Sun and for modeling the effects of granulation on the scattering of waves and distortion of normal-mode eigenfunctions.Comment: 17 pages, 6 figures, in press, Ap