of its ideal counterpart: where Id n v denotes n V ϫ n V identity. By this condition the reconstruction matrix F is generally not yet entirely determined. It leaves n C n K -n V degrees of freedom per voxel, which may be utilized for SNR optimization. To that end each diagonal element of the image noise

jk be the proportion of all paths linking actors j and k which pass through actor i. The betweenness of actor i is defined as the sum of all b jk where i, j, and k are distinct. It is normalized by dividing by the maximum betweenness in an n-actor network. II. Sample and Data Data for our analysis

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that jf(x) 0 f(y)j 2 if d(x; y) = 1 and jf(x) 0 f(y)j 1 if d(x; y) = 2. The L(2; 1)-labeling number (G) of G is the smallest number k such that G has a L(2; 1)-labeling

latency. We study these mechanisms in an implementation called Collection Tree Protocol (CTP) and evaluate their contributions to its performance. We evaluate CTP on 12 different testbeds ranging in size from 20–310 nodes and comprising 7 hardware platforms, on 6 different link layers, and on interference

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Parametric max-stable processes are increasingly used to model spatial extremes. Since the dependence structure is specified for block maxima, the data used for inference are block maxima from all sites. To improve the estimation efficiency, we propose a two-step approach with composite likelihood that utilizes site-wise daily records in addition to block maxima. Besides the parameter estimation, there is no formal model checking and diagnosis method for spatial extremes modeling yet. Model diagnosis in practice has been informal and mostly based on visual checking tools such as residual plot and quantile-quantile plot. We proposed a goodness-of-fit test for max-stable processes based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function. The proposed two-step procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal pa-rameters with an independence Likelihood by ignoring the spatial dependence. Given ithe marginal parameter estimates, the second step estimates the dependence parameters

, and we can say the Campbell bandwidth is the minimum average bandwidth for en-coding the process across all possible distortion levels. IX. CONCLUSION We have presented two new derivations of the coefficient rate in-troduced by Campbell. One derivation solidifies its interpretation as a coefficient rate, and shows that the spectral entropy of a random process is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band that contains most of the energy. The second derivation implies that the number of samples of a particular component should be proportional to the variance of that component. We discussed the implications of the latter result for realization-adap-tive source coding and provided a connection with the familiar reverse water-filling result from rate distortion theory. From the coefficient rate, we defined a quantity called the Campbell bandwidth of a random process, and we contrasted Fourier bandwidth, Shannon bandwidth, and Campbell bandwidth. ACKNOWLEDGMENT The authors are indebted to the referees for their constructive com-ments and insights.

Abstract—We investigate achievable degrees of freedom (DoF) for a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with L clusters andK users per cluster. Each user is equipped with M antennas and the relay with N antennas. We assume a new data exchange model, termed clustered

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I would like to thank my parents for always believing in me. I would also like to thank my supervisors Richard Lindner and Johannes Buchmann for their useful comments and suggestions on how to improve the queality of the thesis. Not on last place I would like to thank Vadim Lyubashevsky and Luis Carlos Coronado Garcia for their kindness and readiness to answer my questions. Warranty I hereby warrant that the content of this thesis is the direct result of my own work and that any use made in it of published or unpublished material is fully and correctly referenced. I also warrant that the presented work has