The thesis deals with natural disasters from the statistical point of view and treats them as extremal observations. Basics of classical extreme value theory will be summarized and new approach based on maximum entropy principle will be proposed. Both methods will be used in order to analyze real discharge data observed at the river Vltava.

Multiple-input-multiple-output (MIMO) systems of current LTE releases are capable of adaptation in the azimuth only. More recently, the trend is to enhance the system performance by exploiting the channel's degrees of freedom in the elevation through the dynamic adaptation of the vertical antenna beam pattern. This necessitates the derivation and characterization of three-dimensional (3D) channels. Over the years, channel models have evolved to address the challenges of wireless communication technologies. In parallel to theoretical studies on channel modeling, many standardized channel models like COST-based models, 3GPP SCM, WINNER, ITU have emerged that act as references for industries and telecommunication companies to assess system-level and link-level performances of advanced signal processing techniques over real-like channels. Given the existing channels are only two dimensional (2D) in nature; a large effort in channel modeling is needed to study the impact of the channel component in the elevation direction. The first part of this work sheds light on the current 3GPP activity around 3D channel modeling and beamforming, an aspect that to our knowledge has not been extensively covered by a research publication. The standardized MIMO channel model is presented, that incorporates both the propagation effects of the environment and the radio effects of the antennas. In order to facilitate future studies on the use of 3D beamforming, the main features of the proposed 3D channel model are discussed. A brief overview of the future 3GPP 3D channel model being outlined for the next generation of wireless networks is also provided. In the subsequent part of this work, we present an information-theoretic channel model for MIMO systems that supports the elevation dimension. The model is based on the principle of maximum entropy, which enables us to determine the distribution of the channel matrix consistent with the prior information on the angles of departure and angles of arrival of the propagation paths. Based on this model, an analytical expression for the cumulative density function (CDF) of the mutual information (MI) for systems with a single receive and finite number of transmit antennas in the general signal-to-interference-plus-noise-ratio (SINR) regime is provided. The result is extended to systems with multiple receive antennas in the low SINR regime. A Gaussian approximation to the asymptotic behavior of the MI distribution is derived for the large number of transmit antennas and paths regime. Simulation results study the performance gains realizable through meticulous selection of the transmit antenna down tilt angles, confirming the potential of elevation beamforming to enhance system performance. The results validate the proposed analytical expressions and elucidate the dependence of system performance on azimuth and elevation angular spreads and antenna patterns. We believe that the derived expressions will help evaluate the performance of 3D 5G massive MIMO systems in the future.

Nous avons travaillé sur le développement d’un instrument de mesure de la luminescence induite par un faisceau d’ions lourds (nucléons  12) et d’énergie de l’ordre du MeV/nucléons. Basé sur une méthode de comptage de photons uniques obtenus par coïncidences, le dispositif permet d’obtenir sur 16 voies à la fois un spectre en énergie dans le domaine proche UV-visible-proche IR (185-920 nm) et la réponse temporelle sur la gamme ns-µs, avec un échantillonnage de 100 ps. Des mesures en température peuvent être réalisées depuis la température ambiante jusqu’à 30K.Ce travail met particulièrement l’accent sur les méthodes d’extraction des données : Une fois montrée la nécessité de déconvoluer les signaux, on s’intéresse dans un premier temps à évaluer différents profils instrumentaux modélisés et reconstruit à partir de mesures. A cet effet, un travail de caractérisation temporelle de chaque constituant du dispositif est mené. Puis ces profils instrumentaux sont utilisés dans deux méthodes de déconvolution par moindres carrés d’abord puis par maximum d’entropie ensuite.Deux matériaux types sont testés : Le Titanate de Strontium pour l’étude de la dynamique de l’excitation électronique, et un scintillateur plastique commercial, le BC400, pour l’étude du vieillissement et de la baisse des performances en fonction de la fluence. Dans les deux cas on a pu mettre en évidence la présence d’une composante ultra rapide de constante de temps subnanoseconde. / We developed an instrument for measuring the luminescence induced by a heavy ion beam (nucleons  12) and energy in the range of MeV / nucleon. Based on a single photon counting method obtained by coincidences, the device can provide in the same run a 16-channel energy spectrum in the UV-visible- IR region (185-920 nm) and a time-resolved response in the range of ns up to µs for each channel. Temperature measurements can be performed from room temperature down to 30K.This work places particular emphasis on data extraction methods: Once the need to deconvolve the signals demonstrated the evaluation of different instrument profiles (simulated and reconstructed from measurements) leads to a systematic temporal characterization of each component of the device. Then, these instrumental profiles are used in two deconvolution methods: least squares first followed by maximum entropy method.Two typical materials are tested: the Strontium Titanate for the study of the dynamics of the electronic excitation, and a commercial scintillator, the BC400, for the study of the aging and the decrease of performances with fluence. In both cases, we have been able to highlight the presence of an ultrafast component of subnanosecond time constant.

In the light of the ongoing loss of biodiversity at the global scale, monitoring grasslands is nowadays of utmost importance considering their functional relevance in terms of the ecosystem services that they provide. Here, guidelines of the European Union like the Fauna-Flora-Habitat Directive and the European Agricultural fund for Rural Development with its HNV indicators are crucial. Indeed, they form the legal framework for nature conservation and define grasslands as one of their conservation targets, whose status needs to be assessed and reported by all member states on a regular basis. In the light of these reporting requirements, the need for a harmonised and thorough grassland monitoring is highly demanding since most member states are still currently adopting intensive field surveys or photointerpretation with differing levels of detail for mapping habitat distribution. To this purpose, a cost-effective solution is offered by Earth Observation data for which specific grassland monitoring methodologies shall be then implemented which are capable of processing multitemporal acquisitions collected throughout the entire growing season. Although optical data are most suited for characterising vegetation in terms of spectral information content, they are actually subject to weather conditions (especially cloud coverage), which hinder the possibility of collecting enough information over the full phenological cycle. Furthermore, so far only few studies started employing high and very high resolution optical time series for grassland habitat monitoring since they have become available e.g., from the RapidEye satellites, only in the recent past. To overcome this limitation, SAR systems can be employed which provide imagery independent from weather or daytime conditions, hence enabling vegetation analysis by means of complete time series. Compared to optical data, radar imagery is less affected by the physical-chemical characteristics of the surface, but rather it is sensitive to structural features like geometry and roughness. However, in this context presently only very few techniques have been implemented, which are anyhow not suitable to be employed in an operational framework. Furthermore, to address the classification task, supervised approaches (which require in situ information for all the land-cover classes present in the study area) represent the most accurate methodological solution; nevertheless, collecting an exhaustive ground truth is generally expensive both in terms of time and economic costs and is not even feasible when the test site is remote. However, in many applications the end-users are generally only interested in very few specific targeted land-cover classes which, for instance, have high ecological value or are associated with support actions, subsidies or benefits from national or international institutions. The categorisation of specific grasslands and habitat types as those addressed in this thesis falls within such category of problems, which is defined in the literature as targeted land-cover classification. In this framework, a robust and effective targeted classification system for the automatic identification of grassland types by means of multi-temporal and multi-polarised SAR data has been developed within this thesis. In particular, the proposed system is composed of three main blocks: the preprocessing of the SAR image time series including the Kennaugh decomposition, the feature extraction including multi-temporal filtering and texture analysis, and the hierarchical targeted classification, which consist of two phases where first a one-class classifier is employed to outline the merger of all the grassland types of interest considered as a single information class and then a multi-class classifier is applied for discriminating the specific targeted classes within the areas identified as positive by the one-class classifier. To evaluate the capabilities of the proposed methodology, several experimental trials have been carried out over two test sites located in Southern Bavaria (Germany) and Mecklenburg Western-Pomerania (Germany) for which six diverse datasets have been derived from multitemporal series of dualpol TerraSAR-X as well as dual-/quadpol Radarsat-2 images. Four among the Natura 2000 habitat types of the Fauna-Flora-Habitat Directive as well all High Nature Value grassland types have been considered as targeted classes for this study. Overall, the proposed system proved to be robust and confirmed the effectiveness of employing multitemporal and multi-polarisation VHR SAR data for discriminating habitat types and High Nature Value grassland types, exhibiting high potential for future employment even at larger scales. In particular, it could be demonstrated that the proposed hierarchical targeted classification approach outperforms the available state-of-the-art methods and has a clear advantage with respect to the standard approaches in terms of robustness, reliability and transferability.

In this study the maximum entropy formalism [JAYN 57] is suggested as an alternative theory for general queueing systems of computer performance analysis. The motivation is to overcome some of the problems arising in this field and to extend the scope of the results derived in the context of Markovian queueing theory. For the M/G/l model a unique maximum entropy solution., satisfying locALl balance is derived independent of any assumptions about the service time distribution. However, it is shown that this solution is identical to the steady state solution of the underlying Marko-v process when the service time distribution is of the generalised exponential (CE) type. (The GE-type distribution is a mixture of an exponential term and a unit impulse function at the origin). For the G/M/1 the maximum entropy solution is identical in form to that of the underlying Markov process, but a GE-type distribution still produces the maximum overall similar distributions. For the GIG11 model there are three main achievements: first, the spectral methods are extended to give exaft formulae for the average number of customers in the system for any G/G/l with rational Laplace transform. Previously, these results are obtainable only through simulation and approximation methods. (ii) secondly, a maximum entropy model is developed and used to obtain unique solutions for some types of the G/G/l. It is also discussed how these solutions can be related to the corresponding stochastic processes. (iii) the importance of the G/GE/l and the GE/GE/l for the analysis of general networks is discussed and some flow processes for these systems are characterised. For general queueing networks it is shown that the maximum entropy solution is a product of the maximum entropy solutions of the individual nodes. Accordingly, existing computational algorithms are extended to cover general networks with FCFS disciplines. Some implementations are suggested and a flow algorithm is derived. Finally, these results are iised to improve existing aggregation methods. In addition, the study includes a number of examples, comparisons, surveys, useful comments and conclusions.

Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made. / Algerian government

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Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Neste trabalho, fazemos um estudo das correntes e das medidas transversas invariantes por holonomia, e mostraremos o resultado de D. Sullivan [23] sobre a correspondência biunívoca entre estes dois objetos. Em particular mostraremos um resultado conhecido de J. Plante [17] sobre a existência de medidas transversas invariantes sob a hipótese de crescimento sub-exponencial. Apresentamos também, o resultado devido a Ruelle-Sullivan [19] de que a medida de máxima entropia de um difeomorfismo topologicamente mixing pode-se expressar como o produto de duas medidas transversas invariantes para as folheações estáveis e instáveis. Por último, mostramos que os difeomorfismos de Anosov topologicamente mixing, que preservam a orientação das folhas estáveis e folhas instáveis induzem elementos da cohomologia de DeRham / In this work, we make a study of currents and holonomy invariant transverse measure, and we will show the result of D. Sullivan [23] about the biunivocal correspondence between these two objects. In particular we show a known result of J. Plante [17] about the existence of invariant transverse measures under the hypothesis of sub-exponential growth. Also we will present, the result due to Ruelle-Sullivan [19] that the maximum entropy measure of a diffeomorphism topologically mixing can be expressed as the product of two invariant transverse measures for stable and unstable foliations. Finally, we show that the Anosov diffeomorphisms topologically mixing, which preserve the orientation of the leaves stable and unstable induce elements DeRham cohomology

Esta tese apresenta um desenvolvimento do fator de atrito (f) para escoamentos incompressíveis. O desenvolvimento é baseado no modelo clássico de Colebrook-White e no recente modelo da Entropia Máxima. Este desenvolvimento pode ser considerado como um modelo conceitual, porém não completamente, por causa do relacionamento entre o número de Reynolds (Re) e o parâmetro de entropia (M) determinado através de ajustes numéricos realizados com bons dados experimentais. Quatro algoritmos de cálculo foram criados para simplificar a aplicação do modelo, evidenciando sua eficácia e a eficiência. / This thesis presents a development of friction factor (f) for incompressible pipe flow calculation. The development is based on the classical Colebrook-White model and on the recent maximum entropy model. The development cam be considered as a conceptual one, but not completely, because the relationship that links the Reynolds number (Re) to the entropy parameter (M) was determined by numerical fitting on accurate but experimental data. Four calculation algorithms were produced to simplify the model applications, evidencing efficiency and effectiveness.