abstract: Limited spectral access motivates technologies that adapt to diminishing resources and increasingly cluttered environments. A joint positioning-communications system is designed and implemented on \acf{COTS} hardware. This system enables simultaneous positioning of, and communications between, nodes in a distributed network of base-stations and unmanned aerial systems (UASs). This technology offers extreme ranging precision ($<$ 5 cm) with minimal bandwidth (10 MHz), a secure communications link to protect against cyberattacks, a small form factor that enables integration into numerous platforms, and minimal resource consumption which supports high-density networks. The positioning and communications tasks are performed simultaneously with a single, co-use waveform, which efficiently utilizes limited resources and supports higher user densities. The positioning task uses a cooperative, point-to-point synchronization protocol to estimate the relative position and orientation of all users within the network. The communications task distributes positioning information between users and secures the positioning task against cyberattacks. This high-performance system is enabled by advanced time-of-arrival estimation techniques and a modern phase-accurate distributed coherence synchronization algorithm. This technology may be installed in ground-stations, ground vehicles, unmanned aerial systems, and airborne vehicles, enabling a highly-mobile, re-configurable network with numerous applications. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

Dans cette thèse, nous nous intéressons aux méthodes dites récursives qui permettent une mise à jour des estimations séquentielles de données spatiales ou spatio-temporelles et qui ne nécessitent pas un stockage permanent de toutes les données. Traiter et analyser des flux des données, Data Stream, de façon effective et efficace constitue un défi actif en statistique. En effet, dans beaucoup de domaines d'applications, des décisions doivent être prises à un temps donné à la réception d'une certaine quantité de données et mises à jour une fois de nouvelles données disponibles à une autre date. Nous proposons et étudions ainsi des estimateurs à noyau de la fonction de densité de probabilité et la fonction de régression de flux de données spatiales ou spatio-temporelles. Plus précisément, nous adaptons les estimateurs à noyau classiques de Parzen-Rosenblatt et Nadaraya-Watson. Pour cela, nous combinons la méthodologie sur les estimateurs récursifs de la densité et de la régression et celle d'une distribution de nature spatiale ou spatio-temporelle. Nous donnons des applications et des études numériques des estimateurs proposés. La spécificité des méthodes étudiées réside sur le fait que les estimations prennent en compte la structure de dépendance spatiale des données considérées, ce qui est loin d'être trivial. Cette thèse s'inscrit donc dans le contexte de la statistique spatiale non-paramétrique et ses applications. Elle y apporte trois contributions principales qui reposent sur l'étude des estimateurs non-paramétriques récursifs dans un cadre spatial/spatio-temporel et s'articule autour des l'estimation récursive à noyau de la densité dans un cadre spatial, l'estimation récursive à noyau de la densité dans un cadre spatio-temporel, et l'estimation récursive à noyau de la régression dans un cadre spatial. / In this thesis, we are interested in recursive methods that allow to update sequentially estimates in a context of spatial or spatial-temporal data and that do not need a permanent storage of all data. Process and analyze Data Stream, effectively and effciently is an active challenge in statistics. In fact, in many areas, decisions should be taken at a given time at the reception of a certain amount of data and updated once new data are available at another date. We propose and study kernel estimators of the probability density function and the regression function of spatial or spatial-temporal data-stream. Specifically, we adapt the classical kernel estimators of Parzen-Rosenblatt and Nadaraya-Watson. For this, we combine the methodology of recursive estimators of density and regression and that of a distribution of spatial or spatio-temporal data. We provide applications and numerical studies of the proposed estimators. The specifcity of the methods studied resides in the fact that the estimates take into account the spatial dependence structure of the relevant data, which is far from trivial. This thesis is therefore in the context of non-parametric spatial statistics and its applications. This work makes three major contributions. which are based on the study of non-parametric estimators in a recursive spatial/space-time and revolves around the recursive kernel density estimate in a spatial context, the recursive kernel density estimate in a space-time and recursive kernel regression estimate in space.

The presented thesis is focused on the GMRES convergence analysis. The basic principles of CG, MINRES and GMRES are briefly explained. The thesis summarizes some known convergence results of these methods. The known characterizations of the matrices and the right hand sides gen- erating the same Krylov residual spaces are summarized. Connections and the differences between the different points of view on GMRES convergence analysis are shown. We expect that if the convergence curve of GMRES applied to the nonnormal matrix and the right hand side seems to be de- termined by the eigenvalues of the matrix then exists a matrix that is close to normal and has the same spectrum as the matrix and for the right hand side has the same GMRES convergence curve (We assume that the initial approximation 0 = 0). Several numerical experiments are done to examine this assumption. This thesis describes an unpublished result of Gérard Meu- rant which is the formula for the norm of the -th error of GMRES applied to the matrix and right hand side and its derivation. The upper estimate of the -th GMRES error is derived. This estimate is minimized via spectrum.

Bibliografický záznam LABANTOVÁ, Zuzana. Mediální konvergence v prostředí internetu. Praha, 2011. 126 s. Diplomová práce (Mgr.) Univerzita Karlova, Fakulta sociálních věd, Institut komunikačních studií a žurnalistiky. Katedra mediálních studií. Vedoucí diplomové práce Mgr. Jaroslav Švelch Abstract Media convergence - continuous merging of media determined by new technologies development - is one of the most significant phenomenons nowadays. The theoretical portion of this thesis describes technological, economical and content aspects of convergence. It is emphasizing Henry Jenkins's definition, which characterizes convergence as change in audience behavior, their active media content consumption. This contrast between passive audience of old traditional media and active audience of convergence media is a premise of following empirical portion of the thesis. It aims to assign socio- demographic characteristics to these contradictory descriptions. Audience of MF DNES, Rádio Impuls and TV Nova are elected as representatives of traditional audience and their profile is compared with iDnes.cz, Impuls.cz and nova.cz users characteristics. Methodologically, the thesis uses a quantitative analyze of dates gained from continuous big media researches realized in the Czech Republic. The thesis focuses also on these...

Die ökonomische Wachstumsliteratur ging lange Zeit davon aus, dass die absolute Konvergenz zwischen Ländern (und Regionen) ein Naturgesetz ist. Mittlerweile weiß man, dass die Länder eher einer Clubkonvergenz, die Pro-Kopf- Einkommen also eher einer Polarisierung unterliegen. Neben einer theoretischen Beschreibung der beiden Ansätze erläutert der Beitrag einige ausgewählte Erklärungsansätze für das Phänomen der Clubkonvergenz. Außerdem wird die empirische Einkommensverteilung in den Regionen der EU dargestellt. / In its beginnings, growth literature viewed absolute convergence between countries (and regions) as a kind of natural law. In the meantime, however, it is known that countries follow rather club convergence, which means that per capita incomes polarise. The two concepts will first be defined. Thereafter, selected approaches seeking an explanation for this phenomenon are presented. The article closes with an analysis of the empirical distribution of incomes across the regions of the EU.

This paper tests the regional convergence of GDP per capita across 27 Chinese provinces during the period 1961-2018 with considering the spatial interactions. First, this study only finds a slight divergence over the entire period. Furthermore, the flowing research of this paper divides the overall time span into three sub-period based on two major economic policies, namely the “Open Door Policy” and the “Western Development Strategy”. During the period 1961-1977, which is regarded as a phase of planned economy, this paper finds the evidence of regional convergence. Moreover, the results indicate a slight divergence in GDP per capita during the period 1978-1999, proving that the “Open Door Policy” intensifies regional gaps of China. Finally, this study verifies the role of the “Western Development Strategy” in reducing regional differences since a convergence is found during the last period 2000-2018. The outcomes of this research reveal a strong relationship between economic policies and regional convergence, and thus the transition of policies should be considered when investigating the economic convergence. Furthermore, this research also verifies the importance of spatial effects in the process of convergence or divergence. The results are likely to be biased if the spatial dependence is neglected.

The fractional Laplacian is a promising mathematical tool due to its ability to capture the anomalous diffusion and model the complex physical phenomenon with long-range interaction, such as fractional quantum mechanics, image processing, jump process, etc. One of the important applications of fractional Laplacian is a turbulence intermittency model of fractional Navier-Stokes equation which is derived from Boltzmann's theory. However, the efficient computation of this model on bounded domains is challenging as highly accurate and efficient numerical methods are not yet available. The bottleneck for efficient computation lies in the low accuracy and high computational cost of discretizing the fractional Laplacian operator. Although many state-of-the-art numerical methods have been proposed and some progress has been made for the existing numerical methods to achieve quasi-optimal complexity, some issues are still fully unresolved: i) Due to nonlocal nature of the fractional Laplacian, the implementation of the algorithm is still complicated and the computational cost for preparation of algorithms is still high, e.g., as pointed out by Acosta et al \cite{AcostaBB17} 'Over 99\% of the CPU time is devoted to assembly routine' for finite element method; ii) Due to the intrinsic singularity of the fractional Laplacian, the convergence orders in the literature are still unsatisfactory for many applications including turbulence intermittency simulations. To reduce the complexity and computational cost, we consider two numerical methods, finite difference and spectral method with quasi-linear complexity, which are summarized as follows. We develop spectral Galerkin methods to accurately solve the fractional advection-diffusion-reaction equations and apply the method to fractional Navier-Stokes equations. In spectral methods on a ball, the evaluation of fractional Laplacian operator can be straightforward thanks to the pseudo-eigen relation. For general smooth computational domains, we propose the use of spectral methods enriched by singular functions which characterize the inherent boundary singularity of the fractional Laplacian. We develop a simple and easy-to-implement fractional centered difference approximation to the fractional Laplacian on a uniform mesh using generating functions. The weights or coefficients of the fractional centered formula can be readily computed using the fast Fourier transform. Together with singularity subtraction, we propose high-order finite difference methods without any graded mesh. With the use of the presented results, it may be possible to solve fractional Navier-Stokes equations, fractional quantum Schrodinger equations, and stochastic fractional equations with high accuracy. All numerical simulations will be accompanied by stability and convergence analysis.

In this paper we will investigate the connection between a random walk and a continuous time stochastic process. Donsker's Theorem states that a random walk under certain conditions will converge to a Wiener process. We will provide a detailed proof of this theorem which will be used to prove that a geometric random walk converges to a geometric Brownian motion.

Thesis: M.S., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1980 / Bibliography: leaves 85-87. / by Frances Annette Habib. / M.S. / M.S. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

<p>We study decentralized multiagent optimization over networks modeled as undirected</p> <p>graphs. The optimization problem consists of minimizing a (non convex) smooth function</p> <p>plus a convex extended-value function, which enforces constraints or extra structure on the</p> <p>solution (e.g., sparsity, low-rank). We further assume that the objective function satisfies the</p> <p>Kurdyka- Lojasiewicz (KL) property, with exponent in [0, 1). The KL property is satisfied</p> <p>by several (non convex) functions of practical interest, e.g., arising from machine learning</p> <p>applications; in the centralized setting, it permits to achieve strong convergence guarantees.</p> <p>Here we establish a first convergence result of the same type for distributed algorithms,</p> <p>specifically the distributed gradient-tracking based algorithm SONATA, first proposed in</p> <p>[ 1 ]. When exponent is in (0, 1/2], the sequence generated by SONATA is proved to converge to a</p> <p>stationary solution of the problem at an R-linear rate whereas sublinear rate is certified</p> <p>when KL exponent is in (1/2, 1). This matches the convergence behaviour of centralized proximal-gradient</p> <p>algorithms. Numerical results validate our theoretical findings.</p>