Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem

In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its demand to obtain polynomial equations. In this work, we propose a method to derive the polynomial equations using source-to-sink path gains as the variables. In the path gain formulation, we show that linear and quadratic equations suffice; therefore, network coding becomes equivalent to a system of polynomial equations of maximum degree 2. We present algorithms for generating the equations in the path gains and for converting path gain solutions to edge-to-edge gain solutions. Because of the low degree, simplification is readily possible for the system of equations obtained using path gains. Using small-sized network coding problems, we show that the path gain approach results in simpler equations and determines solvability of the problem in certain cases. On a larger network (with 87 nodes and 161 edges), we show how the path gain approach continues to provide deterministic solutions to some network coding problems.Comment: 12 pages, 6 figures. Accepted for publication in IEEE Transactions on Information Theory (May 2010

Cosmic Microwave Background Polarization Signals from Tangled Magnetic Fields

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). For fields which redshift to a present value of $B_0 = 3\times 10^{-9}$ Gauss, these vector modes are shown to generate polarization anisotropies of order $0.1\mu K - 4 \mu K$ on small angular scales ($500 < l < 2000$), assuming delta function or a power law spectra with $n=-1$. About 200 times larger signals result for $n=2$ spectra. Unlike inflation generated, scalar modes, these signals are dominated by the odd parity, B-type polarization, which could help in their detection.Comment: 4 pages, Revtex, matches version to be published in Phys. Rev. Let

Bilevel shared control for teleoperators

A shared system is disclosed for robot control including integration of the human and autonomous input modalities for an improved control. Autonomously planned motion trajectories are modified by a teleoperator to track unmodelled target motions, while nominal teleoperator motions are modified through compliance to accommodate geometric errors autonomously in the latter. A hierarchical shared system intelligently shares control over a remote robot between the autonomous and teleoperative portions of an overall control system. Architecture is hierarchical, and consists of two levels. The top level represents the task level, while the bottom, the execution level. In space applications, the performance of pure teleoperation systems depend significantly on the communication time delays between the local and the remote sites. Selection/mixing matrices are provided with entries which reflect how each input's signals modality is weighted. The shared control minimizes the detrimental effects caused by these time delays between earth and space

Is Africa Integrated in the Global Economy?

The popular impression that Africa has not integrated into world trade, as suggested by the evolution in simple indicators, has been called into question recently by more formal analysis. This paper refines and generalizes this analysis and lends support to the popular view of disintegration, but only for countries in Francophone Africa. These countries are currently underexploiting their trading opportunities and have witnessed disintegration over time, a trend that is most pronounced in their trade with technologically advanced countries. There is some evidence, on the other hand, that countries in Anglophone Africa are reversing the trend of disintegration, particularly in their trade with advanced countries. Copyright 2003, International Monetary Fund

The generation of helical magnetic field in a viable scenario of Inflationary Magnetogenesis

We study the generation of helical magnetic fields in a model of inflationary magnetogenesis which is free from the strong coupling and back-reaction problems. To generate helical magnetic fields, we add an $f^2 \tilde{F}^{\mu\nu} F_{\mu\nu}$ term to the lagrangian of Ratra model. The strong coupling and back-reaction problems are avoided if we take a particular behaviour of coupling function $f$, in which $f$ increases during inflation and decreases post inflation to reheating. The generated magnetic field is fully helical and has a blue spectrum, $d\rho_B/d\ln k \propto k^4$. This spectrum is obtained when coupling function $f\propto a^2$ during inflation. The scale of reheating in our model has to be lower than $4000$ GeV to avoid back-reaction post inflation. The generated magnetic field spectrum satisfies the $\gamma$-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are $\sim 4 \times 10^{-11}$ G and $70$ kpc respectively, if reheating takes place at 100 GeV. For reheating at the QCD scales of $150$ MeV, the field strength increases to $\sim$ nano gauss, with coherence scale of $0.6$ Mpc.Comment: 11 pages, Submitted to PR

A Vishniac type contribution to the polarisation of the CMBR?

Radiation which has a quadrupole component of anisotropy, can get polarized by Thomson scattering from charged particles. In the cosmological context, the microwave background photons develop significant quadrupole anisotropy as they free stream away from the the epoch of standard recombination. Reionization in the post recombination era can provide free electrons to Thomson scatter the incident anisotropic $CMBR$ photons. We compute the resulting polarisation anisotropy on small (arc-minute) angular scales. We look for significant non-linear contributions, as in the case of Vishniac effect in temperature anisotropy, due to the coupling of small-scale electron density fluctuations, at the new last scattering surface, and the temperature quadrupole. We show that, while, in cold dark matter type models, this does not lead to very significant signals ($\sim 0.02 - 0.04 \mu K$), a larger small angular scale polarization anisotropy, ($\sim 0.1 - 0.5\mu K$), can result in isocurvature type models.Comment: 13 pages, Revtex, no figure