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In this paper, we turn the interpolation problem of coarsely-sampled data into a denoising problem. From this point of view, we illustrate the benefit of random sampling at sub-Nyquist rate over regular sampling at the same rate. We show that, using nonlinear sparsity promoting optimization, coarse random sampling may actually lead to significantly better wavefield reconstruction than equivalent regularly sampled data.

Pseudorandom number generator‘s statistical features were analyzed in this work. Pseudorandom numbers are applied in many fields, that‘s why it‘s important for them to satisfy following requirements: • to have uniform distribution, • to be uncorrelated. Hypothesis that random numbers are distributed uniformly is checked by Pearson test. Hypothesis that autocorrelation function is equal to zero is checked by Box Ljung test. During investigation it was noticed, that in all ways generated random numbers didn’t have uniform distribution, except linear congriuential generator. Applying different transformations was set, that for combinations v1-v8 when using parabola, transformed random numbers had uniform distribution. Arcsine was the best transformation for nonlinear congriuential generator. While testing hypothesis about autocorrelation function’s equality to zero was noticed, that zero hypothesis rejection or not depends on: • random numbers generation algorithm, • generated sample size, The best generator, which satisfied requirements, is linear congriuential generator, but it is not suitable, because it is too predictable. Nonlinear congruential generator is chosen as the best one, because its statistical features are closest to the linear generator.

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No description available.

Algorithms to generate walks (chains of unit-length, freely-jointed segments) and polygons (closed walks) in spherical confinements have been developed in the last few years. These algorithms generate polygons inside spherical confinement based on their mathematically derived probability distributions. The generated polygons do not occupy any volume { although that would be useful for some applications. This thesis investigates how to generate walks and polygons which occupy some volume in spherical confinement. More specifically, in this thesis, existing methods described in the literature have been studied and implemented to generate walks and polygons in confinement. Additionally, these methods were adapted to design, develop, and implement an algorithm which generates walks and polygons in confinement with thick segments, that is, segments which occupy volume. Data is collected by generating walks and polygons of different lengths with and without thickness inside the spherical confinements of various radii to compare walks and polygons with thickness with those generated without thickness. The analysis of the collected data shows that a. the newly developed algorithm indeed generates polygons which are thicker than those generated with the volumeless algorithm; and b. the newly developed algorithm generates polygons which are different from the polygons generated by the volumeless algorithm. The analysis also includes an assessment of the computational cost of generating thick polygons.

In this dissertation, analysis and design of the efficient Medium Access Control (MAC) sub-layer schemes are considered for Vehicular Ad hoc Networks (VANE~s). The contributions of this study are three-fold. First, an analytical model based on Markov chain is developed in order to investigate the performance of the MAC sub-layer of the IEEE 802.11p for vehicular communications. The results indicate that single channel MAC sub-layers may not be adequate for the future Intelligent Transportation Systems (ITS). The analytical model is validated with the results from simulation-based analysis. Performance analysis based on simulations is given on MAC metrics such as throughput, access delay, packet delivery. Second, a multi-channel MAC protocol is proposed and comprehensively analyzed in terms of channel utilizing and Quality of service (QoS) differentiation for dense VANETs. It is demonstrated that the proposed scheme, namely Asynchronous Multichannel MAC with Distributed TDMA (AMCMACD), improves the system performance in terms of throughput, packet delivery rate, collision rate on service channels, load balancing, and service differentiation for dense vehicular networks. Third, to cope with the interference from contention with neighbours within two hops in large-scale networks, a Large-scale Asynchronous Multichannel MAC (LS-AMCMAC) is proposed. The proposed scheme outperforms other benchmark multichannel MAC schemes in large-scale networks, in terms of throughput, channel utilization, dissemination of emergency messages, and the collision rates on control and service channels.

This thesis contains four chapters. Each chapter constitutes an empirical exercise in which I apply econometric ideas on studying the dynamics of large cross sections of data (Random Fields). Three of them concern the empirics of convergence and the fourth analyses business cycle fluctuations. The first, "Notes on Convergence Empirics: Some Calculations for Spanish Regions," describes the econometric methods for studying the dynamics of the distributions and how to characterise convergence in this framework, explains why the standard cross-section regression analysis is misleading when testing for convergence and then performs some calculations for regions in Spain. The second chapter, "Dynamics of the Income Distribution Across OECD Countries", considers its baseline hypotheses to be those generated by the Solow growth model. Using sequential conditioning, it studies whether the convergence hypothesis implications can be shown to hold for the OECD economies. It finds that neither absolute nor conditional convergence, in the sense of economies approaching the OECD average, has taken place. The third chapter, "Cross Sectional Firm Dynamics: Theory and Empirical Results", extends ideas of distribution dynamics to a discrete choice setting, and extends the reasoning of Galton's Fallacy to the logit model. It provides evidence of the tendency of firm sizes to converge for the US chemicals sector by analysing dynamically evolving cross-section distributions. Finally, the fourth chapter, "Unemployment in Europe and Regional Labour Fluctuations" applies distribution dynamics ideas to a business cycle setting. It analyses the dynamics of employment for 51 European regions from 1960 to 1990, addressing the issue of whether regional shocks have aggregate effects on unemployment or the opposite. It uses a model for non-stationary evolving distributions to identify idiosyncratic and aggregate disturbances.

In this paper we consider optimum design of experiments for correlated observations. We approximate the error component of the process by an eigenvector expansion of the corresponding covariance function. Furthermore we study the limit behavior of an additional white noise as a regularization tool. The approach is illustrated by some typical examples. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Model selection is an important part of classification. In this thesis we study the two classification models logistic regression and random forest. They are compared and evaluated based on prediction accuracy and metadata analysis. The models were trained on 25 diverse datasets. We calculated the prediction accuracy of both models using RapidMiner. We also collected metadata for the datasets concerning number of observations, number of predictor variables and number of classes in the response variable.     There is a correlation between performance of logistic regression and random forest with significant correlation of 0.60 and confidence interval [0.29 0.79]. The models appear to perform similarly across the datasets with performance more influenced by choice of dataset rather than model selection.     Random forest with an average prediction accuracy of 81.66% performed better on these datasets than logistic regression with an average prediction accuracy of 73.07%. The difference is however not statistically significant with a p-value of 0.088 for Student's t-test.     Multiple linear regression analysis reveals none of the analysed metadata have a significant linear relationship with logistic regression performance. The regression of logistic regression performance on metadata has a p-value of 0.66. We get similar results with random forest performance. The regression of random forest performance on metadata has a p-value of 0.89. None of the analysed metadata have a significant linear relationship with random forest performance.     We conclude that the prediction accuracies of logistic regression and random forest are correlated. Random forest performed slightly better on the studied datasets but the difference is not statistically significant. The studied metadata does not appear to have a significant effect on prediction accuracy of either model.