Des procédures de classement sont largement utilisées pour décrire les phénomènes observés dans de nombreux domaines des sciences sociales et naturelles, par exemple la sociologie, l’économie, la linguistique, la démographie, la physique, la biologie, etc.Dans cette thèse, nous nous sommes attachés à l’étude des propriétés de classement et des dynamiques sous-jacentes intégrées dans les systèmes complexes. En particulier,nous nous sommes concentrés sur les classements par score ou par prix dans les systèmes sportifs et les classements d’utilisation des mots ou caractères dans les langues humaines. Le but est de comprendre les mécanismes sous-jacents à ces questions en utilisant les méthodes de la physique statistique, de la statistique bayésienne et de la modélisation multi-agents. Les résultats concrets concernent les aspects suivants.Nous avons tout d’abord traité une étude sur les classements par score/prix dans les systèmes sportifs et analysé 40 échantillons de données dans 12 disciplines sportives différentes. Nous avons trouvé des similitudes frappantes dans différents sports, à savoir le fait que la répartition des résultats/prix suit les lois puissance universelles.Nous avons également montré que le principe de Pareto est largement respecté dans de nombreux systèmes sociaux: ainsi 20% des joueurs accumulent 80% des scores et de l’argent. Les données concernant les matchs de tennis en individuels nous ont révélé que lorsque deux joueurs s’affrontent, la probabilité que le joueur de rang supérieur gagne est liée à la différence de rang des deux adversaires. Afin de comprendre les origines de la mise à l’échelle universelle, nous avons proposé un modèle multi-agents,qui peut simuler les matchs de joueurs à travers différentes compétitions. Les résultats de nos simulations sont cohérents avec les résultats empiriques. L’extension du domaine d’étude de la simulation indique que le modèle est assez robuste par rapport aux modifications de certains paramètres. La loi de Zipf est le comportement le plus régulièrement observé dans la linguistique statistique. Elle a dès lors servi de prototype pour les relations entre rang d’apparitions et fréquence d’apparitions (relations rang-fréquence dans la suite du texte) et les lois d’échelle dans les sciences naturelles. Nous avons étudié plusieurs textes, précisé le domaine de validité de la loi de Zipf, et trouvé que la plage de validité augmente lors du mélange de différents textes. Basé sur l’analyse sémantique latente, nous avons proposé un modèle probabiliste, dans lequel nous avons supposé que les mots sont ajoutés au texte avec des probabilités aléatoires, tandis que leur densité a priori est liée, via la statistique bayésienne, aux caractéristiques générales du lexique mental de l’auteur de ce même texte. Notre modèle explique la loi de Zipf ainsi que ses limites de validité, et la généralise aux hautes et basses fréquences et au hapax legomena.Dans une autre étude, nous avons précisé les relations rang-fréquence pour les caractères chinois. Nous avons choisi d’étudier des textes courts en premier, car pour le bien de l’analyse rang fréquence, les longs textes ne sont que des mélanges de textes plus courts, thématiquement homogènes. Nos résultats ont montré que la loi de Zipf appliqués aux caractères chinois tient parfaitement pour des textes assez courts (quelques milliers de caractères différents). Le même domaine de validité est observé pour les textes courts anglais. Nous avons soutenu que les longs textes chinois montrent une structure hiérarchique à deux couches: des caractères dont la fréquence d’apparition suit une loi puissance (première couche) et des caractères dont l’apparition suit une loi exponentielle (deuxième couche)... / Ranking procedures are widely used to describe the phenomena in many differentfields of social and natural sciences, e.g., sociology, economics, linguistics, demography,physics, biology, etc. In this dissertation, we dedicated to study the ranking propertiesand underlying dynamics embedded in complex systems. In particular, we focused onthe scores/prizes ranking in sports systems and the words/characters usage ranking inhuman languages. The aim is to understand the mechanisms behind these issues byusing the methods of statistical physics, Bayesian statistics and agent-based modeling.The concrete results concern the following aspects.We took up an interesting topic on the scores/prizes ranking in sports systems, andanalyzed 40 data samples in 12 different sports fields. We found the striking similaritiesin different sports, i.e., the distributions of scores/prizes follow the universal powerlaws. We also showed that the data yielded the Pareto principle extensively observedin many social systems: 20% of the players accumulate 80% of the scores and money.For the tennis head-to-head data, we revealed that when two players compete, theprobability that the higher-ranked player will win is related to the rank difference ofthe two opponents. In order to understand the origins of the universal scaling, weproposed an agent-based model, which can simulate the competitions of players indifferent matches, and results from our simulations are consistent with the empiricalfindings. Extensive simulation studies indicate that the model is quite robust withrespect to the modifications of some parameters.Zipf’s law is the major regularity of statistical linguistics that served as a prototypefor the rank-frequency relations and scaling laws in natural sciences. We investigatedseveral English texts, clarified the valid range of Zipf’s law, and found this valid rangeincreases upon mixing different texts. Based on the latent semantic analysis, we proposeda probabilistic model, in which we assumed that the words are drawn into thetext with random probabilities, while their apriori density relates, via Bayesian statistics,to the general features of mental lexicon of the author who produced the text. Ourmodel explained the Zipf’s law together with the limits of its validity, its generalizationto high and low frequencies and hapax legomena. In another work, we specified the rank-frequency relations for Chinese characters. We chose to study the short texts first, since for the sake of the rank-frequency analysis,long texts are just mixtures of shorter, thematically homogenous pieces. Our resultsshowed that the Zipf’s law for Chinese characters perfectly holds for sufficiently shorttexts (few thousand different characters), and the scenario of its validity is similar tothat for short English texts. We argued long Chinese texts display a two-layer, hierarchicstructure: power-law rank-frequency characters (first layer) and the exponentialones (second layer). The previous results on the invalidity of the Zipf’s law for longtexts are accounted for by showing that in between of the Zipfian range and the regionof very rare characters (hapax legomena) there emerges a range of ranks, wherethe rank-frequency relation is approximately exponential. From comparative analysisof rank-frequency relations for Chinese and English, we suggested the characters playfor Chinese writers the same role as the words for those writing within alphabeticalsystems.

Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1

Um eine Entscheidung zu treffen, muss Information interpretiert und in eine Handlung übersetzt werden. Dafür wird die a priori Wahrscheinlichkeit bezüglich der Entscheidungsalternativen in den Prozess der Entscheidungsfindung integriert und löst Mechanismen der Handlungsvorbereitung aus. In der vorliegenden Dissertation habe ich untersucht, welche Vorbereitungsprozesse aufgrund von wahrscheinlichkeitsbasierter Vorinformation stattfinden und welche Gehirnareale mit der Integration dieser Information assoziiert sind. Um diese Fragen zu beantworten, habe ich eine Verhaltensstudie, eine Studie mit Ableitung des Elektroenzephalogramms (EEG) und eine Studie mittels der funktionellen Magnetresonanztomographie (fMRT) mit simultaner Ableitung des EEGs durchgeführt. Die Versuchspersonen bearbeiteten währenddessen eine Zahlenvergleichsaufgabe mit einem Hinweisreiz, der Wahrscheinlichkeitsinformation bezüglich der erforderlichen Antwort enthielt. Die Reaktionszeit wurde durch die wahrscheinlichkeitsbasierte Vorinformation des Hinweisreizes parametrisch moduliert (Studie 1). Daraus lässt sich schlussfolgern, dass Vorbereitungsprozesse in Abhängigkeit der Wahrscheinlichkeitsinformation stattfinden. Die EEG Studie (Studie 2) ergab einen parametrischen Effekt von Wahrscheinlichkeitsinformation auf die Amplitude der Contingent Negative Variation (CNV), einer EEG-Komponente, die Vorbereitungsprozesse auf prämotorischer Ebene reflektiert. Darüber hinaus fand sich mittels einer Dipolquellenanalyse ein Dipol im anterioren Cingulum (ACC), dessen Aktivität ebenfalls durch die Wahrscheinlichkeitsinformation parametrisch moduliert war. Diese Ergebnisse lassen auf prämotorische Vorbereitungsprozesse aufgrund von Wahrscheinlichkeitsinformation schließen. In den fMRT-Ergebnissen zeigte sich eine parametrisch modulierte neuronale Aktivierung im posterioren Teil des medial-frontalen Kortex (pMFC), die auf eine Kontrollfunktion zur Handlungsanpassung dieses Areals zurückgeführt werden kann (Studie 3a). Um dynamische Fluktuationen der Wahrscheinlichkeitsverarbeitung zu untersuchen, wurde die CNV Amplitude der Einzeltrials in das Modell der fMRT-Analyse integriert (Studie 3b). Die CNV Amplitude korrelierte mit der neuronalen Aktivität in einem Netzwerk, bestehend aus frontalen, parietalen und striatalen Arealen, das mit allgemeiner wahrscheinlichkeitsunabhängiger Handlungsvorbereitung im Zusammenhang steht. Dagegen zeigten sich im dorsolateralen Präfrontalkortex (DLPFC), im inferioren frontalen Gyrus (IPG) und im inferioren Parietallappen (IPL) Aktivierungen, die sich auf die dynamische Integration von Wahrscheinlichkeitsinformation zurückführen lassen. / To prepare actions in advance, prior information about the probability of decision alternatives is integrated into the decision-making process. In the present dissertation, I investigated preparatory processes elicited by prior probability (PP) and the neural basis of PP processing. In three studies, I collected behavioral data and, furthermore, recorded electroencephalographic (EEG) data separately as well as simultaneously with functional magnetic resonance imaging (fMRI). While applying these methods, participants had to perform a number comparison task with a precue delivering PP about a subsequent response-demanding stimulus. The probability precue elicited the preparation of the response, as shown by the parametrical modulation of response time (RT) depending on PP (Study 1). The EEG study (Study 2) revealed a parametrical effect of PP on the contingent negative variation (CNV) during the foreperiod, which is an indicator for premotor response preparation. Furthermore, a dipole was located in the anterior cingulate cortex (ACC) with its activity parametrically modulated by PP. These EEG results suggest that PP influences premotor response preparation in a parametrical fashion. An analysis of fMRI data showed that neural activity in the posterior medial frontal cortex (pMFC) increased with increasing PP (Study 3a), which is attributed to a monitoring function of this region with respect to behavioral adjustment and initiation of response preparation depending on the PP. By applying an EEG-informed fMRI analysis (Study 3b), I focused on trial-to-trial fluctuations in PP processing and general response preparation as represented by the single-trial CNV amplitude. I found that the CNV amplitude was correlated with neural activity in a network consisting of frontal, parietal, and striatal regions reflecting general preparatory processes independently of PP. Parts of the network, namely, the dorsolateral prefrontal cortex (DLPFC), the inferior frontal gyrus (IFG), and the inferior parietal lobule (IPL), showed activations, which exclusively represented the contributions of PP to the CNV amplitude fluctuations. These results suggest that PP elicits premotor response preparation and activates the pMFC parametrically signaling the need for behavioral adjustment. In contrast, DLPFC, IFG, and IPL are involved in dynamically fluctuating PP processing mechanisms.

Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuições a priori de Jeffreys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposição de heteoscedasticidade. Mostramos que a distribuição a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori é própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber é desenvolvida com a finalidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais é utilizado para o ajuste do modelo proposto. / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Jeffreys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Jeffreys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models.

A Tomografia por Impedância Elétrica tem como objetivo estimar a distribuição de impedância elétrica dentro de uma região a partir de medidas de potencial elétrico coletadas apenas em seu contorno externo quando corrente elétrica é imposta neste mesmo contorno. Uma das aplicações para esta tecnologia é o monitoramento das condições pulmonares de pacientes em Unidades de Tratamento Intensivo. Dentre vários algoritmos, destacam-se os filtros de Kalman que abordam o problema de estimação sob o ponto de vista probabilístico, procurando encontrar a distribuição de probabilidade do estado condicionada à realização das medidas. Para que estes filtros possam ser utilizados, um modelo de evolução temporal do sistema sendo observado deve ser adotado. Esta tese propõe o uso de um modelo de evolução para a variação de volume de ar nos pulmões durante a respiração de um paciente sob ventilação artificial. Este modelo é utilizado no unscented Kalman filter, uma extensão não linear do filtro de Kalman. Tal modelo é ajustado em paralelo à estimação do estado, utilizando um esquema dual de estimação. Um algoritmo de segmentação de imagem é proposto para identificar as regiões pulmonares nas imagens estimadas e assim utilizar o modelo de evolução. Com o intuito de melhorar as estimativas, o método do erro de aproximação é utilizado no modelo de observação para mitigar os erros de modelagem e informação a priori é adicionada na solução do problema inverso mal-posto. O método é avaliado através de simulações numéricas e ensaio experimental coletado em um voluntário. Os resultados mostram que o método proposto melhora as estimativas feitas pelo filtro de Kalman, propiciando a visualização de imagens absolutas, dinâmicas e com bom nível de contraste entre os tecidos e órgãos internos. / Electrical impedance tomography estimates the electrical impedance distribution within a region given a set of electrical potential measurements acquired along its boundary at the same time that electrical currents are imposed on the same boundary. One of the applications of this technology is lung monitoring of patients in Intensive Care Units. One class of algorithms employed for the estimation are the Kalman filters which deal with the estimation problem in a probabilistic framework, looking for the probability density function of the state conditioned to the acquired measurements. In order to use such filters, an evolution models of the system must be employed. This thesis proposes an evolution model of the variation of air in the lungs of patients under artificial ventilation. This model is used on the Unscented Kalman Filter, a nonlinear extension of the Kalman filter. This model is adjusted in parallel to the state estimation, in a dual estimation scheme. An image segmentation algorithm is proposed for identifying the lungs in the images. In order to improve the estimate, the approximation error method is employed for mitigating the observation model errors and prior information is added for the solution of the ill-posed inverse problem. The method is evaluated with numerical simulations and with experimental data of a volunteer. The results show that the proposed method increases the quality of the estimates, allowing the visualization of absolute and dynamic images, with good level of contrast between the tissues and internal organs.

In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boundary data. We take the two steps approximation approach i.e. using high-order in time DGFEM; the discretisation approach in time introduced by D Schötzau (PhD thesis, Swiss Federal institute of technology, Zürich, 1999) to fi rst obtain the semidiscrete scheme and then conformal spatial discretisation to obtain the fully-discrete formulation. We have shown solvability, unconditional stability and conditional a priori error estimates within our abstract framework for the fully discretized problem. The skew-symmetric spatial forms arising in our abstract framework for the semi- and fully-discrete schemes do not full ll the underlying assumptions in D. Schötzau's work. But the semi-discrete and fully discrete forms satisfy an Inf-sup condition, essential for our proofs; in this sense our approach is also a generalisation of D. Schötzau's work. All estimates are given in a norm in space and time which is weaker than the Hilbert norm belonging to our abstract function spaces, a typical complication in evolution problems. To the best of the author's knowledge, with the approximation approach we used, these stability and a priori error estimates with their abstract structure have not been shown before for the abstract variational formulation used in this thesis. Finally we apply our abstract framework to the acoustic and an elasto-dynamic linear equations with non-homogeneous Dirichlet boundary data.

History is descriptive. Epistemology is conceived as normative. It appears, then, that a historical approach to epistemology, like historical epistemology, might not be epistemically normative. In our context here, epistemology is not a systematic theory of knowledge, truth, or justification. In this thesis I approach epistemic justification through the vantage point of practice of science. Practice is about reasoning. Reasoning, conceived as the human propensity to order perceptions, beliefs, memories, etc., in ways that permit us to have understanding, is not only about thinking. Reasoning has to do with our actions, too: In the ordering of reasoning we take into account the desires of ourselves and others. Reasoning has to do with tinkering with stuff, physical or abstract. Practice is primarily about skills. Practices are not mere groping. They have a form. Performing according to a practice is an activity with a lot of plasticity. The skilled performer retains the form of the practice in many different situations. Finally, practices are not static in time. Practices develop. People try new things, some of which may work out, others not. The technology involved in how to go about doing things in a particular practice changes, and the concepts concerning understanding what one is doing also may change. This is the point where history enters the picture. In this thesis I explore the interactions between history, reasoning, and skills from the viewpoint of a particular type of epistemic justification: a priori justification. An a priori justified proposition is a proposition which is evident independent of experience. Such propositions are self-evident. We will make sense of a priori justification in a context of regarding science as practice, so that we will be able to demonstrate that the latter accommodates the normative character of science.

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本論文乃是討論法國人類學家李維斯陀的著作《結構人類學》一對於文化人類學以及民族學研究的重要意義，並說明《結構人類學》所代表的結構主義方法對於文化人類學與民族學的衝擊，並就由《c人類學》一書所引發的一連串法國學術界之討論，進行一屬於法國當代結構研究方法之變化改動上的描寫，這段學術上的重要變化正是自1958年到1969年之間的法國學術發展，而其發展的過程乃是自《結構人類學》1958年出版到《考古知識學》1969年出版為最高點的發展，這其中的結構主義的研究方法，乃由結構走向後結構，或說由結構轉變為差異思想，在《考古知識學》上則其傅柯於1966年自身的《詞與物》一作品之討論，而以“知識型”為方法來研究對傳統的一切文化、人文研究的項目之方法提出修正，這其間的過程，歷經三位學者，分別是：李維斯陀、傅柯、德希達，而三者作品皆集中在1958年到1969年出版於法國學術界本論文即是對於此方法的變革過程，為就三者的主要作品作一理論的分析，以對民族學、民族史的研究方法有直接的幫助。