Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios

An asymmetrical synchrotron model for knots in the 3C 273 jet

To interpret the emission of knots in the 3C 273 jet from radio to X-rays, we propose a synchrotron model in which, owing to the shock compression effect, the injection spectra from a shock into the upstream and downstream emission regions are asymmetric. Our model could well explain the spectral energy distributions of knots in the 3C 273 jet, and predictions regarding the knots spectra could be tested by future observations.Comment: 9 pages, 1 figure, 1 table, new version accepted for publication in Ap

A Non-Mainstream Viewpoint on Apparent Superluminal Phenomena in AGN Jet

The group velocity of light in material around the AGN jet is acquiescently one (c as a unit), but this is only a hypothesis. Here, we re-derive apparent superluminal and Doppler formulas for the general case (it is assumed that the group velocity of light in the uniform and isotropic medium around a jet (a beaming model) is not necessarily equal to one, e.g., Araudo et al. (2010) thought that there may be dense clouds around AGN jet base), and show that the group velocity of light close to one could seriously affect apparent superluminal phenomena and Doppler effect in the AGN jet (when the viewing angle and Lorentz factor take some appropriate values).Comment: 4 pages, 2 figures, new version accepted for publication in Journal of Astrophysics and Astronom

Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.Comment: 22 pages, 11 figures, 2 table

An hourglass model for the flare of HST-1 in M87

To explain the multi-wavelength light curves (from radio to X-ray) of HST-1 in the M87 jet, we propose an hourglass model that is a modified two-zone system of Tavecchio & Ghisellini (hereafter TG08): a slow hourglass-shaped or Laval nozzle-shaped layer connected by two revolving exponential surfaces surrounding a fast spine, through which plasma blobs flow. Based on the conservation of magnetic flux, the magnetic field changes along the axis of the hourglass. We adopt the result of TG08---the high-energy emission from GeV to TeV can be produced through inverse Compton by the two-zone system, and the photons from radio to X-ray are mainly radiated by the fast inner zone system. Here, we only discuss the light curves of the fast inner blob from radio to X-ray. When a compressible blob travels down the axis of the first bulb in the hourglass, because of magnetic flux conservation, its cross section experiences an adiabatic compression process, which results in particle acceleration and the brightening of HST-1. When the blob moves into the second bulb of the hourglass, because of magnetic flux conservation, the dimming of the knot occurs along with an adiabatic expansion of its cross section. A similar broken exponential function could fit the TeV peaks in M87, which may imply a correlation between the TeV flares of M87 and the light curves from radio to X-ray in HST-1. The Very Large Array (VLA) 22 GHz radio light curve of HST-1 verifies our prediction based on the model fit to the main peak of the VLA 15 GHz radio light curve.Comment: 14 pages, 2 figures, accepted for publication in A

Optically-Nonactive Assorted Helices Array with Interchangeable Magnetic/Electric Resonance

We report here the designing of optically-nonactive metamaterial by assembling metallic helices with different chirality. With linearly polarized incident light, pure electric or magnetic resonance can be selectively realized, which leads to negative permittivity or negative permeability accordingly. Further, we show that pure electric or magnetic resonance can be interchanged at the same frequency band by merely changing the polarization of incident light for 90 degrees. This design demonstrates a unique approach to construct metamaterial.Comment: 15 pages, 4 figure

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page