Purging of untrustworthy recommendations from a grid

In grid computing, trust has massive significance. There is lot of research to propose various models in providing trusted resource sharing mechanisms. The trust is a belief or perception that various researchers have tried to correlate with some computational model. Trust on any entity can be direct or indirect. Direct trust is the impact of either first impression over the entity or acquired during some direct interaction. Indirect trust is the trust may be due to either reputation gained or recommendations received from various recommenders of a particular domain in a grid or any other domain outside that grid or outside that grid itself. Unfortunately, malicious indirect trust leads to the misuse of valuable resources of the grid. This paper proposes the mechanism of identifying and purging the untrustworthy recommendations in the grid environment. Through the obtained results, we show the way of purging of untrustworthy entities.Comment: 8 pages, 4 figures, 1 table published by IJNGN journal; International Journal of Next-Generation Networks (IJNGN) Vol.3, No.4, December 201

Alias-free, real coefficient m-band QMF banks for arbitrary m

Based on a generalized framework for alias free QMF banks, a theory is developed for the design of uniform QMF banks with real-coefficient analysis filters, such that aliasing can be completely canceled by appropriate choice of real-coefficient synthesis filters. These results are then applied for the derivation of closed-form expressions for the synthesis filters (both FIR and IIR), that ensure cancelation of aliasing for a given set of analysis filters. The results do not involve the inversion of the alias-component (AC) matrix

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

Homoclinic bifurcations in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in low-Prandtl-number ($0 \leq Pr \leq 0.025$) Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis. We have performed simulations with \textit{stress-free} top and bottom boundaries for several values of Taylor number ($5 \leq Ta \leq 50$) near the instability onset. We observe a single homoclinic ungluing bifurcation, marked by the spontaneous breaking of a larger limit cycle into two limit cycles with the variation of the reduced Rayleigh number $r$ for smaller values of $Ta (< 25)$. A pair of homoclinic bifurcations, instead of one bifurcation, is observed with variation of $r$ for slightly higher values of $Ta$ ($25 \leq Ta \leq 50$) in the same fluid dynamical system. The variation of the bifurcation threshold with $Ta$ is also investigated. We have also constructed a low-dimensional model which qualitatively captures the dynamics of the system near the homoclinic bifurcations for low rotation rates. The model is used to study the unfolding of bifurcations and the variation of the homoclinic bifurcation threshold with $Pr$.Comment: 6 pages, 7 figures, 1 tabl

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Erasing Distinguishability Using Quantum Frequency Up-Conversion

The frequency distinguishability of two single photons was successfully erased using single photon frequency up-conversion. A frequency non-degenerate photon pair generated via spontaneous four-wave mixing in a dispersion shifted fiber was used to emulate two telecom-band single photons that were in the same temporal mode but in different frequency modes. The frequencies of these photons were converted to the same frequency by using the sum frequency generation process in periodically poled lithium niobate waveguides, while maintaining their temporal indistinguishability. As a result, the two converted photons exhibited a non-classical dip in a Hong-Ou-Mandel quantum interference experiment. The present scheme will add flexibility to networking quantum information systems that use photons with various wavelengths.Comment: 4 pages, 5 figure

Analytic Light-Curves of Gamma-Ray Burst Afterglows: Homogeneous versus Wind External Media

Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies, and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and for a wind ejected by the GRB progenitor. We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at sub-millimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton scatterings on the electron cooling, a new possible time-dependence of the cooling break is identified. The signature of the up-scattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a pre-ejected wind, as a temporary mild flattening of the afterglow decay. The up-scattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting few hours after the main event.Comment: 11 pages, to be published in the ApJ, vol 54

On Rational Sets in Euclidean Spaces and Spheres

IFor a positive rational $l$, we define the concept of an $l$-elliptic and an $l$-hyperbolic rational set in a metric space. In this article we examine the existence of (i) dense and (ii) infinite $l$-hyperbolic and $l$-ellitpic rationals subsets of the real line and unit circle. For the case of a circle, we prove that the existence of such sets depends on the positivity of ranks of certain associated elliptic curves. We also determine the closures of such sets which are maximal in case they are not dense. In higher dimensions, we show the existence of $l$-ellitpic and $l$-hyperbolic rational infinite sets in unit spheres and Euclidean spaces for certain values of $l$ which satisfy a weaker condition regarding the existence of elements of order more than two, than the positivity of the ranks of the same associated elliptic curves. We also determine their closures. A subset $T$ of the $k$-dimensional unit sphere $S^k$ has an antipodal pair if both $x,-x\in T$ for some $x\in S^k$. In this article, we prove that there does not exist a dense rational set $T\subset S^2$ which has an antipodal pair by assuming Bombieri-Lang Conjecture for surfaces of general type. We actually show that the existence of such a dense rational set in $S^k$ is equivalent to the existence of a dense $2$-hyperbolic rational set in $S^k$ which is further equivalent to the existence of a dense 1-elliptic rational set in the Euclidean space $\mathbb{R}^k$.Comment: 20 page