Spectral Efficiency of Channel-Aware Schedulers in Non-identical Composite Links with Interference

Accurate system planning and performance evaluation requires knowledge of the joint impact of scheduling, interference, and fading. However, current analyses either require costly numerical simulations or make simplifying assumptions that limit the applicability of the results. In this paper, we derive analytical expressions for the spectral efficiency of cellular systems that use either the channel-unaware but fair round robin scheduler or the greedy, channel-aware but unfair maximum signal to interference ratio scheduler. As is the case in real deployments, non-identical co-channel interference at each user, both Rayleigh fading and lognormal shadowing, and limited modulation constellation sizes are accounted for in the analysis. We show that using a simple moment generating function-based lognormal approximation technique and an accurate Gaussian-Q function approximation leads to results that match simulations well. These results are more accurate than erstwhile results that instead used the moment-matching Fenton-Wilkinson approximation method and bounds on the Q function. The spectral efficiency of cellular systems is strongly influenced by the channel scheduler and the small constellation size that is typically used in third generation cellular systems.

Electron transfer statistics and thermal fluctuations in molecular junctions

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects. (C) 2015 AIP Publishing LLC.

Full current statistics for a disordered open exclusion process

We consider the nonabelian sandpile model defined on directed trees by Ayyer et al. (2015 Commun. Math. Phys. 335 1065). and restrict it to the special case of a one-dimensional lattice of n sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.

Some central limit theorems for doubly restricted partitions

Let P_{K, L}(N) be the number of unordered partitions of a positive integer N into K or fewer positive integer parts, each part not exceeding L. A distribution of the form

Ʃ/N≤x P_K,L(N)

is considered first. For any fixed K, this distribution approaches a piecewise polynomial function as L increases to infinity. As both K and L approach infinity, this distribution is asymptotically normal. These results are proved by studying the convergence of the characteristic function.

The main result is the asymptotic behavior of P_K,K(N) itself, for certain large K and N. This is obtained by studying a contour integral of the generating function taken along the unit circle. The bulk of the estimate comes from integrating along a small arc near the point 1. Diophantine approximation is used to show that the integral along the rest of the circle is much smaller.

压缩函数局部平衡度与Hash函数平衡度的关系研究

主要探讨了基于MD方式构造hash函数时平衡度的保持问题，说明了压缩函数满足何种条件时hash函数能够取得最好的平衡度，提出了局部平衡度的概念，并利用此概念解决了压缩函数局部平衡度与hash函数平衡度的关系问题．这对于未来的hash函数的设计有非常重要的意义．

Range-based attacks on links in random scale-free networks

Range and load play key roles in the problem of attacks on links in random scale-free (RSF) networks. In this paper we obtain the approximate relation between range and load in RSF networks by the generating function theory, and then give an estimation about the impact of attacks on the efficiency of the network. The results show that short-range attacks are more destructive for RSF networks, and are confirmed numerically.

Enhancing robustness and immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q(c) for networks containing arbitrary order cycles. For three-cycles, the dependence of q(c) on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

Calculation of the multimode Franck-Condon factors based on the coherent state method

The equivalence of two ways for the calculation of overlap integrals, i.e. the Sharp Rosenstock generating function method and the Doktorov coherent state method, has been proved. On the basis of the generating function of the overlap integrals, a new closed form expression for the Franck - Condon integrals for overlap multidimensional harmonic oscillators has been exactly derived. In addition, some useful analytical expressions for the calculations of the multimode Franck - Condon factors have been given.

Ergodic Capacity of Cognitive TAS/GSC Relaying in Nakagami-m Fading Channels

We examine the impact of transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decode-and-forward (DF) relaying in Nakagami-m fading channels. We select a single transmit antenna at the secondary transmitter which maximizes the receive signal-to-noise ratio (SNR) and combine a subset of receive antennas with the largest SNRs at the secondary receiver. In an effort to assess the performance, we first derive the probability density function and cumulative distribution function of the end-to-end SNR using the moment generating function. We then derive new exact closed-form expression for the ergodic capacity. More importantly, by deriving the asymptotic expression for the high SNR approximation of the ergodic capacity, we gather deep insights into the high SNR slope and the power offset. Our results show that the high SNR slope is 1/2 under the proportional interference power constraint. Under the fixed interference power constraint, the high SNR slope is zero.

Human body shadowing in cellular device-to-device communications: channel modeling using the shadowed κ−μ fading model

Using device-to-device communications as an underlay for cellular communications will provide an exciting opportunity to increase network capacity as well as improving spectral efficiency. The unique geometry of device-to-device links, where user equipment is often held or carried at low elevation and in close proximity to the human body, will mean that they are particularly susceptible to shadowing events caused not only by the local environment but also by the user's body. In this paper, the shadowed κ - μ fading model is proposed, which is capable of characterizing shadowed fading in wireless communication channels. In this model, the statistics of the received signal are manifested by the clustering of multipath components. Within each of these clusters, a dominant signal component with arbitrary power may exist. The resultant dominant signal component, which is formed by the phasor addition of these leading contributions, is assumed to follow a Nakagami- m distribution. The probability density function, moments, and the moment-generating function are also derived. The new model is then applied to device-to-device links operating at 868 MHz in an outdoor urban environment. It was found that shadowing of the resultant dominant component can vary significantly depending upon the position of the user equipment relative to the body and the link geometry. Overall, the shadowed κ - μ fading model is shown to provide a good fit to the field data as well as providing a useful insight into the characteristics of the received signal.

Generalized Selection Combining for Cognitive Relay Networks over Nakagami-m Fading

We consider transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decodeand-forward (DF) relaying in Nakagami-m fading channels. In an effort to assess the performance, the probability density function and the cumulative distribution function of the endto-end SNR are derived using the moment generating function, from which new exact closed-form expressions for the outage probability and the symbol error rate are derived. We then derive a new closed-form expression for the ergodic capacity. More importantly, by deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, we establish new design insights under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interference power constraint. Several pivotal conclusions are reached. For the first scenario, the full diversity order of the
outage probability and the symbol error rate is achieved, and the high SNR slope of the ergodic capacity is 1/2. For the second scenario, the diversity order of the outage probability and the symbol error rate is zero with error floors, and the high SNR slope of the ergodic capacity is zero with capacity ceiling.

Shadowed Fading in Indoor Off-Body Communications Channels: A Statistical Characterization using the κ – μ / Gamma Composite Fading Model

This paper investigates the characteristics of the shadowed fading observed in off-body communications channels at 5.8 GHz. This is realized with the aid of the $\kappa-\mu$ / gamma composite fading model which assumes that the transmitted signal undergoes $\kappa-\mu$ fading which is subject to \emph{multiplicative} shadowing. Based on this, the total power of the multipath components, including both the dominant and scattered components, is subject to non-negligible variations that follow the gamma distribution. For this model, we present an integral form of the probability density function (PDF) as well as important analytic expressions for the PDF, cumulative distribution function, moments and moment generating function. In the case of indoor off-body communications, the corresponding measurements were carried out in the context of four explicit individual scenarios namely: line of sight (LOS) and non-LOS (NLOS) walking, rotational and random movements. The measurements were repeated within three different indoor environments and considered three different hypothetical body worn node locations. With the aid of these results, the parameters for the $\kappa-\mu$ / gamma composite fading model were estimated and analyzed extensively. Interestingly, for the majority of the indoor environments and movement scenarios, the parameter estimates suggested that dominant signal components existed even when the direct signal path was obscured by the test subject's body. Additionally, it is shown that the $\kappa-\mu$ / gamma composite fading model provides an adequate fit to the fading effects involved in off-body communications channels. Using the Kullback-Leibler divergence, we have also compared our results with another recently proposed shadowed fading model, namely the $\kappa-\mu$ / lognormal LOS shadowed fading model. It was found that the $\kappa-\mu$ / gamma composite fading model provided a better fit for the majority of the scenarios considered in this study.

Polinómios de Appell multidimensionais e sua representação matricial

Nesta dissertação é apresentada uma abordagem a polinómios de Appell multidimensionais dando-se especial relevância à estrutura da sua função geradora. Esta estrutura, conjugada com uma escolha adequada de ordenação dos monómios que figuram nos polinómios, confere um carácter unificador à abordagem e possibilita uma representação matricial de polinómios de Appell por meio de matrizes particionadas em blocos. Tais matrizes são construídas a partir de uma matriz de estrutura simples, designada matriz de criação, subdiagonal e cujas entradas não nulas são os sucessivos números naturais. A exponencial desta matriz é a conhecida matriz de Pascal, triangular inferior, onde figuram os números binomiais que fazem parte integrante dos coeficientes dos polinómios de Appell. Finalmente, aplica-se a abordagem apresentada a polinómios de Appell definidos no contexto da Análise de Clifford.

Relações petrogénicas entre o complexo gnáissico migmático e o granito de Banabuiú (Nordeste do Brasil)

A região de Banabuiú situa-se no Domínio Ceará Central, na porção setentrional da Província Borborema, um dos cinturões orogénicos formados durante o evento Brasiliano/Pan-Africano no final do Neoproterozóico. As duas unidades litológicas principais presentes na área são: o complexo gnáissicomigmatítico (metapelitos e metagrauvaques) e granitóides brasilianos. Para além das formações paraderivadas, no substrato da região também foi identificado um conjunto de rochas ortoderivadas, até então não individualizado na cartografia existente. Tanto a sequência paraderivada, como os materiais ortoderivados, foram intensamente afectados por metamorfismo regional da fácies granulítica durante a Orogenia Brasiliana, que atingiu as condições de fusão parcial, gerando migmatitos com um amplo espectro de morfologias. Estes migmatitos apresentam estruturas dominantemente estromáticas, embora localmente se tenham identificado também corpos irregulares de diatexitos de tipo“schlieren”, “schollen” e “maciço (s.s)”, indicando que o processo de migmatização culminou com a produção de maiores quantidades de fundido. Em termos tectónicos, o basamento da região regista os efeitos de três fases de deformação, embora as estruturas concordantes à D3 sejam dominantes e obliterem, em muitos casos, as anisotropias anteriores. A maior parte dos fundidos anatécticos parece ter sido produzida durante tectónica transcorrente D3. No entanto, as condições metamórficas para o início da fusão parcial parece ter sido atingidas antes, durante a D2, já que também existem leucossomas, embora em proporções reduzidas, associados com as estruturas desta fase. A grande quantidade de volumes de leucossomas / veios leucocráticos encontrados na região, está relacionada com a actuação da zona de cisalhamento de Orós e parece corresponder a fundidos anatécticos gerados em níveis mais profundos que foram injectados nas sequências orto- e para-derivadas, devido a notória escassez de leucossomas “in situ” nestas rochas. A presença de fluidos aquosos injectados no complexo migmatítico de Banabuiú terá proporcionado a re-hidratação e retrogradação das rochas hospedeiras, evidenciada, essencialmente, pela presença de moscovite tardia, amplamente distribuída nos metassedimentos e ortognaisses, sobretudo nas zonas próximas aos leucossomas e veios leucocráticos. Dados isotópicos apontam que as rochas da região de Banabuiú apresentam valores fortemente negativos de εNdt e positivos de εSrt sugerindo um significativo envolvimento de materiais supracrustais do grupo Acopiara na formação do complexo migmatítico e na petrogénese do maciço granítico de Banabuiú e o marcado fraccionamento isotópico Sm-Nd observado nalguns dos leucossomas analisados indica que os líquidos anatécticos que lhes deram origem resultaram de processos de fusão em desequilíbrio, em condições anidras, e foram rapidamente extraídos da área-fonte, comprovando o carácter alóctone dos veios leucocráticos intercalados nos ortognaisses e paragnaisses de Banabuiú.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.