This thesis examines the co-occurrence of wintertime low temperature extremes (cold spells) over North America and wet or windy extremes over Europe. Prolonged (≅ 5 days) North American cold spells can be associated with both upstream and downstream anomalous large-scale atmospheric flows, the latter modulating extreme weather occurrences over Europe. The approximate co-occurrence of European wet or windy extremes with North American cold spells is temporally and spatially dependent on the location of cold spells. We identify three broad regional clusters of cold spells:  Central Canada: cold spells are predominantly preceded by Iberian precipitation extremes. Eastern United States: occurrences of both wind and precipitation extremes in Iberia before and after the cold spell. East Canada: cold spells are predominantly followed by wind extremes over the British Isles and Northern Europe. We show that cold spells over these three regions are associated with distinct storm track and jet stream anomalies over the North Atlantic. Iberia experiences a higher number of extratropical cyclones during Central Canada cold spells due to an equatorward displacement of the jet. However, the propagation of extratropical cyclones over Europe is limited due to a Scandinavian block-type configuration over Northern Europe. Eastern United States cold spells show a similar configuration to Central Canada. However, this configuration does not show the Scandinavian block-type feature, resulting in a higher number of extratropical cyclones affecting Iberia and Southern Europe. Eastern Canada cold spells are associated with an extended and accelerated jet over Northern Europe. As a result, the UK, France and Northern Europe experience more intense extratropical cyclones on average, with the accelerated jet resulting in stronger extratropical cyclones throughout the North Atlantic in general. These results evidence the existence of a systematic statistical and dynamical connection between North American cold spells and European wet or windy extremes.

Risk assessment for natural hazards and financial extreme events requires the statistical analysis of extreme events, often beyond observed levels. The characterization and extrapolation of the probability of rare events rely on assumptions about the extremal dependence type and about the specific structure of statistical models. In this thesis, we develop models with flexible tail dependence structures, in order to provide a reliable estimation of tail characteristics and risk measures. From a methodological perspective, this thesis makes the following novel developments. 1) We propose new copula-based models for multivariate and spatial extremes with flexible tail dependence structures, which are parsimonious and able to bridge smoothly asymptotic dependence and asymptotic independence classes, in both the upper and the lower tails; 2) Moreover, aiming at describing more general dependence structures using graphs, we propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC) under the framework of regular variation to learn complex extremal network structures; 3) Finally, we develop a semi-parametric neural-network-based regression model to identify spatial causal effects at all quantile levels (including low and high quantiles). Overall, we make novel contributions to creating new flexible extremal dependence models, developing and implementing novel Bayesian computation algorithms, and taking advantage of machine learning and causal inference principles for modeling extremes. Our novel methodologies are illustrated by a range of applications to financial, climatic, and health data. Specifically, we apply our bivariate copula model to the historical closing prices of five leading cryptocurrencies and estimate the extremal dependence evolution over time, and we use the PTCC to learn the extreme risk network of historical global currency exchange data. Moreover, our multivariate spatial factor copula model is applied to study the upper and lower extremal dependence structures of the daily maximum and minimum air temperature from the state of Alabama in the southeastern United States; and we also apply the PTCC in extreme river discharge network learning for the Upper Danube basin. Finally, we apply the causal spatial quantile regression model in quantifying spatial quantile treatment effects of maternal smoking on extreme low birth weight of newborns in North Carolina, United States.

This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, including practical knowledges.

Al-Wasatiyya - The Middle Path as theological program in Southern European (Bosnian) and Southeast Asian (Malaysian) contexts. This study examines the neglected phenomenon of al-wasitiyyah and how it relates to an Islamic theological context. This study focuses on the religious aspect of al-wasatiyyah, specifically in beliefs, actions, rituals and ethics perspective, social and interpersonal relationships. The main purpose of this study is to describe, clarify and critically examine the phenomenon of al-wasatiyya as a theological program, and practices in Europe, namely in Bosnia and Herzegovina and Southeast Asia, Malaysia. The material for the investigation consists of some relevant literature, scientific articles, and open-ended interviews with prominent researchers in al-wasatiyya from the chosen countries of research. The methodology used in the study is a qualitative textual analysis of the open individual interviews. The analysis and its results provide us with specific answers to the following question: how the concept of al-wasatiyya can be understood in an Islamic theological context, and then displays its scale, interpretations and practices. There are similarities as well as differences between the Southern European and Southeast Asian perspectives on the field of al-wasatiyya. Lastly, the critical objections against al-wasatiyya are examined, and ultimately the results of the study are compared to previous research on the field.  The results show that the neglected phenomenon of al-wasatiyya returned back to the Islamic discourse in the early 2000s, especially after the tragic events of 9/11 in the US. Thus, the result of the study indicates that al-wasatiyya occurs as a reaction to extremism and radicalism in Islam. Finally, the results of the study demonstrate that the concept of al-wasatiyya, except for religious purposes, can be used as well in other areas and socio-political systems in the contemporary world.

The central issue of this thesis is investigating the eventuality of systemic break- downs in the international financial system through examining systemic depen- dence between bank and insurance sectors. Standard models of systemic risk often use correlation of stock returns to evaluate the magnitude of intercon- nectedness between financial institutions. One of the main drawbacks of this approach is that it is oriented towards observations occurring along the central part of the distribution and it does not capture the dependence structure of outlying observations. To account for that, we use methodology which builds on the Extreme Value Theory and is solely focused on capturing dependence in extremes. The analysis is performed using the data on stock prices of the EU largest banks and insurance companies. We study dependencies in the pre- crisis and post-crisis period. The objective is to discover which sector poses a higher systemic threat to the international financial stability. Also, we try to find empirical evidence about an increase in interconnections in recent post- crisis years. We find that in both examined periods systemic dependence in the banking sector is higher than in the insurance sector. Our results also in- dicate that extremal interconnections in the respective sectors increased,...

Global warming is affecting the Earth climate year by year, the biggest difference being observable in increasing temperatures in the World Ocean. Following the long- term global ocean warming trend, average sea surface temperatures across the global tropics and subtropics have increased by 0.4–1◦C in the last 40 years. These rates become even higher in semi-enclosed southern seas, such as the Red Sea, threaten- ing the survival of thermal-sensitive species. As average sea surface temperatures are projected to continue to rise, careful study of future developments of extreme temper- atures is paramount for the sustainability of marine ecosystem and biodiversity. In this thesis, we use Extreme-Value Theory to study sea surface temperature extremes from a gridded dataset comprising 16703 locations over the Red Sea. The data were provided by Operational SST and Sea Ice Analysis (OSTIA), a satellite-based data system designed for numerical weather prediction. After pre-processing the data to account for seasonality and global trends, we analyze the marginal distribution of ex- tremes, defined as observations exceeding a high spatially varying threshold, using the Generalized Pareto distribution. This model allows us to extrapolate beyond the ob- served data to compute the 100-year return levels over the entire Red Sea, confirming the increasing trend of extreme temperatures. To understand the dynamics govern- ing the dependence of extreme temperatures in the Red Sea, we propose a flexible local approach based on R-Pareto processes, which extend the univariate Generalized Pareto distribution to the spatial setting. Assuming that the sea surface temperature varies smoothly over space, we perform inference based on the gradient score method over small regional neighborhoods, in which the data are assumed to be stationary in space. This approach allows us to capture spatial non-stationarity, and to reduce the overall computational cost by taking advantage of distributed computing resources. Our results reveal an interesting extremal spatial dependence structure: in particular, from our estimated model, we conclude that significant extremal dependence prevails for distances up to about 2500 km, which roughly corresponds to the Red Sea length.

Malgré des conditions sèches qui prédominent depuis les années 1970, l’Afrique de l’Ouest a subi au cours des deux dernières décennies des épisodes d’inondations sévères qui ont provoqué de nombreux décès et dommages socio-économiques. L’émergence de ce nouveau problème montre une nouvelle facette de la sensibilité de cette région aux changements hydro-climatiques, appelant à une meilleure caractérisation de l’aléa inondation, des processus qui le génèrent, ainsi que la mise en place de méthodes permettant de projeter les évolutions futures de cet aléa pour mieux s’en prémunir.Dans ce contexte, la thèse cherche à répondre à trois questions principales :1) L’augmentation des dommages liés aux inondations s’est-elle accompagnée d’une intensification des crues extrêmes en Afrique de l’Ouest?2) Comment modéliser les orages de mousson, premier facteur de génération du ruissellement, afin d’explorer l’impact de leurs caractéristiques sur les crues?3) Compte tenu des changements climatiques à l’œuvre dans la région, à quelles tendances hydro-climatiques peut-on s’attendre dans le futur ?Dans un premier temps, on évalue l’évolution des crues en Afrique de l’Ouest au cours des soixante dernières années en utilisant de méthodes basées sur la théorie de valeurs extrêmes. Les résultats montrent une augmentation forte des événements hydrologiques extrêmes depuis les années 1970s dans les sous-bassins Sahéliens du fleuve Niger et depuis les années 1980s dans les sous-bassins soudano-guinéens du fleuve Sénégal. Les niveaux de retour calculés à partir des modèles non-stationnaires dépassent ceux qui ont été calculés avec un modèle stationnaire avec plus de 95% de certitude pour les périodes de retour les plus courtes (<10 ans).On présente ensuite des développements récents apportés à un simulateur stochastique d’orages de mousson à meso-échelle (StochaStorm). Ils incluent: une modélisation de l’occurrence de ces orages, la représentation explicite des valeurs de pluie extrêmes et une amélioration du schéma temporel d’intensité infra-événementielle. Implémenté et évalué à partir des donnés haute-résolution de l’observatoire AMMA-CATCH, le générateur montrent de très bonnes capacités à reproduire les propriétés des orages, confirmant son potentiel pour des études d’impact hydrologique.Enfin, une chaîne de modélisation est élaborée afin de proposer des projections hydrologiques pour le futur sur un bassin sahélien de meso-échelle (Dargol, 7000 km²). L’originalité de cette chaîne provient de la prise en compte du continuum d’échelles entre climat global et impact local à travers la représentation du régime des pluies à l’échelle des orages de mousson, dont les propriétés d’occurrence et d’intensité ont des impacts majeurs sur la réponse hydrologique. La chaîne de modélisation inclut le modèle climatique CP4-Africa, unique modèle à convection explicite fournissant des simulations de long terme en Afrique ; une méthode de débiaisage statistique; le simulateur Stochastorm ; et un modèle pluie-débit spécifiquement adapté aux processus hydrologique sahéliens. La chaine est évaluée sur une période de contrôle 1997-2006 puis utilisée pour des projections futures montrant une hausse par un facteur 1,5 des débits maximum annuels et un doublement des volumes moyens annuels à l’horizon 2100.Les résultats ont des implications majeures notamment pour l’ingénierie hydrologique. Les méthodes actuellement utilisées pour appréhender les risques hydrologiques dans la région ne prennent pas en compte la non-stationnarité hydro-climatique risquant de sous-évaluer l’aléa hydrologique et sous-dimensionner les ouvrages hydrauliques utilisés pour s’en protéger. La thèse suggère aussi quelques pistes afin mieux définir les trajectoires hydrologiques passées et futures en incluant, au-delà des précipitations, les changements sociétaux et environnementaux, leurs interactions et rétroactions dans les approches de modélisation. / The semi-arid regions of West Africa are known for their dry conditions which have predominated since the 1970s. In recent years, however, West Africa has witnessed a series of severe flooding events which caused widespread fatalities and socioeconomic damages. The emergence of this new problem demonstrates the sensitivity of the region to changes in the hydroclimatic system and calls for an improved characterization of flood hazard and the mechanisms that generate it. It also signals the need to develop projections for how flood hazard may evolve in the future in order to inform appropriate adaptation measures.In this context, the following PhD thesis seeks to answer three main questions:1) Is there a significant trend in extreme streamflow in West Africa, or are the documented flooding events isolated incidences?2) How can one model mesoscale convective systems, the primary driver of runoff in the region, in order to explore the properties of precipitation that drive streamflow?3) Based on potential climate change in the region, what trends might be observed in streamflow in the future?First, changes in extreme hydrological events West Africa over the past 60 years are evaluated by applying non-stationary methods based on extreme value theory. Results show a strong increasing trend in extreme hydrological events since the 1970s in the Sahelian Niger River basin and since the 1980s in the Sudano-Guinean catchments in the Senegal River basin. Return levels calculated from non-stationary models are determined to exceed those calculated from a stationary model with over 95% certainty for shorter return periods (<10 years).Next, recent developments are presented for a stochastic precipitation simulator (Stochastorm) designed for modeling mesoscale convective storms, the main rainfall source in the Sahel. Developments include a model for storm occurrence, the explicit representation of extreme rainfall values, and an improvement in the modeling of sub-event intensities. Using high-resolution data from the AMMA-CATCH observatory, simulation outputs were confirmed to realistically represent key characteristics of MCSs, showing the simulator’s potential for use in impact studies.Finally, a modeling chain for producing future hydrological projections is developed and implemented in a Sahelian river basin (Dargol, 7000km2). The chain is original as it is the first attempt in West Africa to encompass the continuum of scales from global climate to convective storms, whose properties have major impacts on hydrological response and as a result local flood risk. The modeling chain components include the convection-permitting regional climate model (RCM) CP4-Africa, the only RCM (to date) explicitly resolving convection and providing long-term simulations in Africa; a bias correction approach; the stochastic precipitation generator Stochastorm; and a rainfall-runoff model specifically developed for Sahelian hydrological processes. The modeling chain is evaluated for a control period (1997-2006) then for future projections (ten years at the end of the 21st century). Hydrological projections show that peak annual flow may become 1.5-2 times greater and streamflow volumes may double or triple on average near the end of the 21st century compared to 1997-2006 in response to projected changes in precipitation.The results raise critical issues notably for hydrological engineering. Current methods used to evaluate flood risk in the region do not take non-stationarity into account, leading to a major risk of underestimating potential floods and undersizing the hydraulic infrastructure designed for protecting against them. It is also suggested to not only consider rainfall changes but also societal and environmental changes, interactions, and feedbacks in order to better attribute past hydrological hazards and their future trajectories to related causes.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Ao analisar a Educação Básica nos dias atuais, observa-se que no Ensino Médio o estudo dos problemas sobre máximos e mínimos é realizado de forma limitada e superficial, resumindo-se basicamente a algumas aplicações de funções quadráticas. A resolução de problemas de otimização de índole geométrica constitui um campo fértil para trabalhar a formação matemática dos alunos nesse nível e contribuir com o aperfeiçoamento da qualidade do ensino da Matemática. Esta categoria de problemas pode ser de utilidade na preparação de alunos para as Olimpíadas de Matemática. Este trabalho aborda o estudo e descrição de métodos de solução de problemas de otimização em geometria euclidana, apresentando uma catalogação devida a Andreescu, junto a vários exemplos resolvidos. / Looking over the Basic Education nowadays, it becomes aware that in high school the study of maxima and minimas problems is carry out in a limited and superficial way. In general, the resolution of these problems lessened to some application of quadratic functions. However, Geometric optimizations problems may be a fecund area to contribute for improving the quality of math education at this level and to develop the mathematical mind of students. That category of problems is also useful for training students for the Math Olympics. This masters dissertation deals with the study of resolutions methods of optimization problems in Euclidean Plane Geometry, presenting a cataloging, according to Andreescu, and some several solved illustrative examples.

[pt] Quando ocorre algum tipo de falta em uma Linha de Transmissão (LT), sua localização exata é essencial para uma rápida recomposição do Sistema Elétrico. Métodos que utilizam tensão e corrente de apenas um terminal contêm simplificações que podem acarretar erros. Esta dissertação investiga a aplicação de Redes Neurais Artificiais (RNA) na obtenção de uma nova forma de identificar o tipo do curto- circuito e determinar a sua localização, utilizando dados obtidos em somente um terminal. O trabalho consiste de 4 partes principais: estudo bibliográfico da área de Redes Neurais; simulações de faltas para a obtenção de padrões; definição e implementação dos modelos de Redes Neurais para identificação e localização da falta; e estudos de casos. Na fase do estudo bibliográfico sobre RNA, foi verificado que as topologias de redes mais usuais são as Feed Forward, que podem ter uma ou mais camadas de Elementos Processadores (EP), sendo as redes com múltiplas camadas (Multi-Layer) a configuração mais completa. Para treinamento da rede, o algoritmo de aprendizado mais utilizado é o Back Propagation. Como fruto deste estudo bibliográfico é apresentado neste trabalho um resumo sobre RNA. Nas simulações de faltas para obtenção dos padrões de treinamento e teste, foi utilizado um sistema automático que, através da combinação de vários parâmetros do sistema elétrico, gera situações diferentes de falta. Este sistema utiliza como base o programa Alternative Transient Program -ATP. Neste trabalho o sistema elétrico está representado por uma LT de 345 KV, com fontes equivalentes representando um sistema real de Furnas Centrais Elétricas. Todos o sinais de tensão e corrente utilizados são representados por fasores de 60 Hz, obtidos através da Transformada Discreta de Fourier (TDF). Os modelos de RNAs para identificação e localização de falta foram implementados com sub-rotinas de redes neurais do programa MATLAB ver. 6.0, representados por Redes Perceptron Multicamadas (Multi Layer Perceptron), treinadas com algoritmo Back Propagation com taxa de aprendizado adaptativa e o termo momentum fixo. Um modelo único de RNA identifica quais as fases (A, B, C e T) envolvidas, classificando o tipo de falta, que pode ser: Monofásica; Bifásica; Bifásica-Terra ou Trifásica. Para a localização da falta, foram definidas 4 arquiteturas de RNA, uma para cada tipo de falta. A ativação de cada topologia de RNA para localização é definida em função do tipo de falta classificada no modelo de identificação com RNA. Na etapa de estudo de casos testou-se o desempenho de cada modelo de RNA utilizando casos de testes em outras situações de falta, diferentes dos conjuntos de treinamento. A RNA de identificação de falta foi avaliada para situações de faltas envolvendo outras LTs, com diferentes níveis de tensão. Os resultados das 4 RNAs de localização da falta foram comparados com os resultados obtidos utilizando o método tradicional, tanto para os casos simulados quanto para algumas situações reais de falta. A utilização de RNAs para a identificação e a localização de falta mostrouse bastante eficiente para os casos analisados, comprovando a aplicabilidade das redes neurais nesse problema. / [en] When a kind of fault occurs in a Transmission Line, its exact location is essential for a fast reclosing of the Electric System. Methods that use voltages and currents from only one terminal contain simplifications that can to cause mistakes. This paper presents an investigation about application of Artificial Neural Network (ANN) obtaining a new way of identification for the type of the short circuit and its location, using data obtained only in one terminal. The work consists on the following 4 main parts: bibliographical study of Neural Network`s area; simulations of faults in order to obtain of patterns; definition and implementation of Neural Network`s models for identification and location of the fault; and studies of cases. In the bibliographical study step on ANN, it was verified that the topologies for the more usual nets are Feed-

Title: Frequency analysis of precipitation amounts Author: Mgr. Zuzana Rulfová Department: Department of Atmospheric Physics Supervisor: RNDr. Jan Kyselý, Ph.D., Institute of Atmospheric Physics CAS Abstract: This thesis deals with analysing characteristics of mean and extreme precipitation in observations and regional climate models (RCMs) with respect to their convective and stratiform origin. An algorithm for subdivision of precipitation amounts into predominantly convective and stratiform using station weather data is proposed and evaluated. The time series of convective and stratiform precipitation from the Czech Republic over 1982-2010 are used for analysing basic climatological characteristics of precipitation, including extremes, and evaluating RCMs from the ENSEMBLES project. Projected changes of convective and stratiform precipitation in Central Europe (the Czech Republic) are analysed using data from RCM simulations from the EURO-CORDEX project. The last part of the thesis introduces a new statistical model for analysing precipitation extremes. This model takes advantage from knowledge of origin of precipitation extremes. In future climate we could expect more convective and stratiform precipitation amounts in all seasons except summer, when climate models project decline in amounts of stratiform...