On the Multivariate Gamma-Gamma (ΓΓ) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.

Projected equations of motion approach to hybrid quantum/classical dynamics in dielectric-metal composites

We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

A Modified Pole-Zero Technique for the Synthesis of Waveguide Leaky-Wave Antennas Loaded With Dipole-Based FSS

An extension of the pole-zero matching method proposed by Stefano Maci et al. for the analysis of electromagnetic bandgap (EBG) structures composed by lossless dipole-based frequency selective surfaces (FSS) printed on stratified dielectric media, is presented in this paper. With this novel expansion, the dipoles length appears as a variable in the analytical dispersion equation. Thus, modal dispersion curves as a function of the dipoles length can be easily obtained with the only restriction of single Floquet mode propagation. These geometry-dispersion curves are essential for the efficient analysis and design of practical EBG structures, such as waveguides loaded with artificial magnetic conductors (AMC) for miniaturization, or leaky-wave antennas (LWA) using partially reflective surfaces (PRS). These two practical examples are examined in this paper. Results are compared with full-wave 2D and 3D simulations showing excellent agreement, thus validating the proposed technique and illustrating its utility for practical designs.

On generating set index functions for randomized caches

Caches hide the growing latency of accesses to the main memory from the processor by storing the most recently used data on-chip. To limit the search time through the caches, they are organized in a direct mapped or set-associative way. Such an organization introduces many conflict misses that hamper performance. This paper studies randomizing set index functions, a technique to place the data in the cache in such a way that conflict misses are avoided. The performance of such a randomized cache strongly depends on the randomization function. This paper discusses a methodology to generate randomization functions that perform well over a broad range of benchmarks. The methodology uses profiling information to predict the conflict miss rate of randomization functions. Then, using this information, a search algorithm finds the best randomization function. Due to implementation issues, it is preferable to use a randomization function that is extremely simple and can be evaluated in little time. For these reasons, we use randomization functions where each randomized address bit is computed as the XOR of a subset of the original address bits. These functions are chosen such that they operate on as few address bits as possible and have few inputs to each XOR. This paper shows that to index a 2(m)-set cache, it suffices to randomize m+2 or m+3 address bits and to limit the number of inputs to each XOR to 2 bits to obtain the full potential of randomization. Furthermore, it is shown that the randomization function that we generate for one set of benchmarks also works well for an entirely different set of benchmarks. Using the described methodology, it is possible to reduce the implementation cost of randomization functions with only an insignificant loss in conflict reduction.

A test for psychometric function shift

A nonparametric, small-sample-size test for the homogeneity of two psychometric functions against the left- and right-shift alternatives has been developed. The test is designed to determine whether it is safe to amalgamate psychometric functions obtained in different experimental sessions. The sum of the lower and upper p-values of the exact (conditional) Fisher test for several 2 × 2 contingency tables (one for each point of the psychometric function) is employed as the test statistic. The probability distribution of the statistic under the null (homogeneity) hypothesis is evaluated to obtain corresponding p-values. Power functions of the test have been computed by randomly generating samples from Weibull psychometric functions. The test is free of any assumptions about the shape of the psychometric function; it requires only that all observations are statistically independent. © 2011 Psychonomic Society, Inc.

Realizing a high magnetic moment in Gd/Cr/FeCo: The role of the rare earth

The search for materials or systems exhibiting a high magnetic saturation has been of longstanding importance. It has been suggested that increased saturation could be achieved by coupling a transition metal via a spacer to a rare earth. We report Gd/Cr/Fe₇₀Co₃₀ multilayer stacks and find reduced yet modulating magnetic moment as a function of Cr thickness. Through a micro structural analysis the lowered moment is indicated by the nucleation of the ultrathin Gd films into an fcc phase. We discuss the possible solution in terms of quasi-perfect lattice match seed material to promote growth of hcp Gd.