Cette thèse a été réalisée au sein de l’entreprise Invivoo. L’objectif principal était de trouver des stratégies d’investissement : avoir un gain important et un risque faible. Les travaux de recherche ont été principalement portés par ce dernier point. Dans ce sens, nous avons voulu généraliser un modèle fidèle à la réalité des marchés financiers, que ce soit pour des données à basse comme à haute fréquence et, à très haute fréquence, variation par variation. / No English summary available.

Cette thèse est consacrée à l'étude de solutions globales et régulières de certaines EDP hamiltoniennes, du point de vue de la croissance de leurs normes de Sobolev. Un tel phénomène traduit une modification de la répartition de l'énergie dans l'espace des fréquences, appelée parfois "turbulence faible". On étudie d'abord une équation d'évolution non-linéaire où intervient un laplacien fractionnaire, et l'on prouve des estimées a priori sur la vitesse de croissance des normes de Sobolev. On introduit ensuite une équation où de telles estimées sont optimales : une équation de Szegő, intégrable, avec une non-linéarité quadratique, et où certaines solutions régulières croissent à vitesse exponentielle tout en restant bornées dans l'espace d'énergie. On classifie les ondes progressives de cette équation de Szegő quadratique, et l'on met en évidence l'instabilité d'une partie d'entre elles. Enfin, on exhibe pour cette équation une hiérarchie de lois de conservation, qui permet d'étudier plus précisément les solutions rationnelles turbulentes. / In this thesis we study global smooth solutions of certain Hamiltonian PDEs, in order to capture the possible growth of their Sobolev norms. Such a phenomenon is typical for what is sometimes called "weak turbulence" : a change in the distribution of energy between Fourier modes. We first study a nonlinear evolution equation involving a fractional Laplacian, and we prove a priori estimates on the growth of Sobolev norms. We then introduce an equation where these estimates turn out to be optimal : an integrable Szegő equation with a quadratic nonlinearity, which admits exponentially growing smooth solutions that remain bounded in the energy space. We classify the traveling wave solutions of this quadratic Szegő equation, and show that some of them are unstable. Eventually we find a hierarchy of conservation laws for this equation, which leads us into a deeper study of rational turbulent solutions.

The field of urban hydrology is in need of high temporal resolution data series in order to effectively model and analyse existing and future trends in extreme precipitation. When high resolution data sets are, for any number of reasons, not available for a given location, the technique of disaggregation using a random cascade model can be applied. Previous studies have demonstrated the relevance of random cascades in the context of rainfall data disaggregation with temporal resolutions usually down to 1 hour. In this study, an attempt at disaggregation to a resolution of 1 minute was made. Using newly disaggregated rainfall data for different regions in Sweden, the possibility of clustering rain events into separate regional hyetographs was investigated. The random cascade model was calibrated using existing municipal rainfall data with a temporal resolution of 1 minute, in order to disaggregate continuous 15 minutes data series provided by the Swedish Meteorological and Hydrological Institute (SMHI). The disaggregation process was then performed in multiple stochastic realisations, in order to correct the uncertainties inherent to the random cascade model. The disaggregation results were assessed by comparing them with calibration data: two main rainfall parameters, EV and ED, were analysed by determining their behaviours and distribution. The possibility of transfering calibration parameters from one station to another was also assessed in a similar manner, again by studying EV & ED for different scenarios. Finally, hyetographs were clustered, compared and contrasted, in order to ascertain previously theorized differences between regions. This research showed the feasibility of applying a random cascade model to very high temporal resolutions in Sweden, while replicating rainfall characteristics from the calibration data quite well. The analysis of the spatial transferability of calibration parameters yielded inconclusive results, as rainfall characteristics were preserved in some cases but failed in others. Lastly, distinct regional differences in hyetographs were noted, but no clear conclusions could be drawn owing to the delimitations of this study. / Inom småskalig hydrologisk modellering finns det idag ett behov av dataserier med hög tidsupplösning för att effektivt kunna modellera och analysera både aktuella och kommande trender hos extrema regnhändelser. När högupplösta dataserier är otillgängliga vid en önskad mätplats kan disaggregering med hjälp av en slumpmässig kaskadmodell tillämpas. Tidigare forskning har visat att kaskadmodeller är användbara för disaggregering av regndata med en tidsupplösning av 1 timme. I denna studie disaggregerades dataserier med syftet att uppnå en tidsupplösningav av 1 minut. För att kunna analysera eventuella skillnader mellan regioner klustrades även hyetografer med de framtagna dataserierna. Den slumpmässiga kaskadmodellen kalibrerades med befintlig kommunal data med en tidsupplösning på 1 minut, för att sedan kunna disaggregera 15 minuters data från SMHIs databaser. Disaggregeringen genomfördes i ett antal olika stokastiska realisationer för att kunna ta hänsyn till, och korrigera, de inneboende osäkerheterna i den slumpmässiga kaskadmodellen. Disaggregeringsresultaten bedömdes genom en jämförelse med kalibreringsdata: två regnegenskaper, regnvaraktighet (ED) och regnvolym (EV), analyserades för att kunna bestämma derasfördelningar och beteenden. Kalibreringsparametrarnas överförbarhet analyserades också med hjälp av ED & EV för olika scenarier. Slutligen klustrades hyetografer för att fastställa potentiella skillnader mellan regioner. Studien påvisade möjligheten att använda en slumpmässig kaskadmodell till höga tidsupplösningar i Sverige. Modellen lyckades återskapa regnegenskaper från kalibreringsdata vid disaggregeringen. Möjligheten att överföra kalibreringsparametrar från en station till en annan visade sig dock inte vara helt övertygande: regnegenskaper återskapades endast i vissa fall, men inte i samtliga. Slutligen konstaterades regionala skillnader i hyetografer, men tydliga slutsatser kunde inte dras på grund av underliggande begränsningar med studien.

Tato disertační práce se zabývá problematikou zpracování vysokofrekvenčních časových řad. Zaměřuje se na návrh algoritmů a metod pro podporu predikce těchto dat. Výsledkem je model pro podporu řízení rozhodovacího procesu implementovaný do platformy pro komplexní zpracování dat. Model navrhuje způsob formalizace množiny podnikových pravidel, které popisují rozhodovací proces. Navržený model musí vyhovovat splnění požadavků na robustnost, rozšiřitelnost, zpracování v reálném čase a požadavkům ekonometriky. Práce shrnuje současné poznatky a metodologie pro zpracování vysokofrekvenčních finančních dat, jejichž zdrojem jsou nejčastěji burzy. První část práce se věnuje popisu základních principů a přístupů používaných pro zpracování vysokofrekvenčních časových dat v současné době. Další část se věnuje popisu podnikových pravidel, rozhodovacího procesu a komplexní platformy pro zpracování vysokofrekvenčních dat a samotnému zpracování dat pomocí zvolené komplexní platformy. Důraz je kladen na výběr a úpravu množiny pravidel, které řídí rozhodovací proces. Navržený model popisuje množinu pravidel pomocí maticové gramatiky. Tato gramatika spadá do oblasti gramatik s řízeným přepisováním a pomocí definovaných matic umožňuje ovlivnit zpracování dat.

The diploma thesis deals with the evaluation of the lifetimes of smooth and notched specimens. The comparison of their lifetimes is focused on the case of high-frequency cyclic loading in the area of high-cycle and gigacycle fatigue of materials. The theory of critical distances is used to evaluate and recalculate the life curves of the notched specimens. The effect of the notch is quantified using the Line method. The critical length parameter is determined so that the life curve of the notched specimens corresponds to the curve measured on smooth specimens. The result is the dependence of the critical length parameter on the number of cycles to fracture. Knowledge of critical length parameters can be used to determine the lifetime of notched specimens as well as real notched components using the results of fatigue tests of smooth specimens.

Diese Arbeit untersucht Inferenz für Streuungsparameter bedingter Gaußprozesse anhand diskreter verrauschter Beobachtungen in einem Hochfrequenz-Setting. Unser Ziel dabei ist es, eine asymptotische Charakterisierung von effizienter Schätzung in einem allgemeine Gaußschen Rahmen zu finden. Für ein parametrisches Fundamentalmodell wird ein Hájek-Le Cam-Faltungssatz hergeleitet, welcher eine exakte asymptotische untere Schranke für Schätzmethoden liefert. Dazu passende obere Schranken werden konstruiert und die Bedeutung des Satzes wird verdeutlicht anhand zahlreicher Beispiele wie der (fraktionellen) Brownschen Bewegung, dem Ornstein-Uhlenbeck-Prozess oder integrierten Prozessen. Die Herleitung der Effizienzresultate basiert auf asymptotischen Äquivalenzen und kann für verschiedene Verallgemeinerungen des parametrischen Fundamentalmodells verwendet werden. Als eine solche Erweiterung betrachten wir das Schätzen der quadrierten Kovariation eines stetigen Martingals anhand verrauschter asynchroner Beobachtungen, welches ein fundamentales Schätzproblem in der Öknometrie ist. Für dieses Modell erhalten wir einen semi-parametrischen Faltungssatz, welcher bisherige Resultate im Sinne von Multidimensionalität, Asynchronität und Annahmen verallgemeinert. Basierend auf den vorhergehenden Herleitungen entwickeln wir einen statistischen Test für den Hurst-Parameter einer fraktionellen Brownschen Bewegung. Ein Score- und ein Likelihood-Quotienten-Test werden implementiert sowie analysiert und erste empirische Eindrücke vermittelt. / This work studies inference on scaling parameters of a conditionally Gaussian process under discrete noisy observations in a high-frequency regime. Our aim is to find an asymptotic characterisation of efficient estimation for a general Gaussian framework. For a parametric basic case model a Hájek-Le Cam convolution theorem is derived, yielding an exact asymptotic lower bound for estimators. Matching upper bounds are constructed and the importance of the theorem is illustrated by various examples of interest such as the (fractional) Brownian motion, the Ornstein-Uhlenbeck process or integrated processes. The derivation of the efficiency result is based on asymptotic equivalences and can be employed for several generalisations of the parametric basic case model. As such an extension we consider estimation of the quadratic covariation of a continuous martingale from noisy asynchronous observations, which is a fundamental estimation problem in econometrics. For this model, a semi-parametric convolution theorem is obtained which generalises existing results in terms of multidimensionality, asynchronicity and assumptions. Based on the previous derivations, we develop statistical tests on the Hurst parameter of a fractional Brownian motion. A score test and a likelihood ratio type test are implemented as well as analysed and first empirical impressions are given.

This work deals with the analog multipliers, mainly of the voltage multipliers. Also the modifications of current output will appear here. The first part is devoted to a choice several multipliers and a description of their functions, the possible involvement and introduction of the most important catalog values. The next section deals with the simple application that contains at least one of the multipliers. Next was the implementation of selected applications and measure their actual performance parameters. Results are then compared with computer simulations. As final step is done of tolerance and sensitivity analysis of simulated configurations of circuits.

This thesis deals with the analysis of high-frequency ECG, namely by parameters for the determination of cardiac asynchrony from the amplitude envelopes ultra-high-frequency ECG. In the theoretical part is described the conventional and high-frequency ECG, procedure of their scanning and parameters of the acquired record. Also is described the electrical conduction system of the heart and its blockade. This issue is followed by chapters about cardiac asynchrony and its treatments by biventricular pacemaker – resynchronization therapy. The chapter about resynchronization includes a description of the methods used for the indication for therapy based on conventional and high-frequency ECG. In the practical part are proposed new parameters for determining heart asynchrony from high-frequency ECG, programmed their detection in environment MATLAB and described realization of detection and obtained results. In the last part of thesis is described statistical evaluation of data and is decided about suitability of use the proposed parameters.

The goal of this thesis is to detect pacing pulses in ultra high-frequency ECG so as to remove these pacing pulses. It makes evaluation of higher frequency components of QRS complex possible. This evaluation is impossible while pacing pulses are present. Chosen issue is solved using heuristic algorithm. Algorithm uses spacing of signal by line in the area which is not influenced by pacing pulses. Subsequently this line is made longer and using differences between line and signal (or another rules) edges of pacing pulses are detected. The top of the stimulation tip is detected by thresholding envelope of original signal´s first difference. More algorithms are tested in this thesis. Several methods of removing pacing pulses are suggested in thesis. Envelopes of high-frequency components are created. Envelopes are analyzed subsequently and suggested methods of removing pacing pulses are compared on the basis of these analysis. Finally the detection efficiency is evaluated.

The subject of this doctoral thesis is the study of dielectric properties of a binary composite made up of a polymer matrix and metallic filler. Properties of such composites have been extensively examined in the past and they turned out to depend on temperature, frequency and in particular on filler concentration. The objective of this work was first to experimentally establish and second to describe quantitatively the effect of the size of metallic particles on the properties of the composite concerned, yet at the same filler concentration. This study was carried out on the model system ethylene-vinylacetate copolymer – nickel. The acquisition of experimental results required extensive measurements in a wide frequency and temperature interval, as well as a manufacture and preparation of a large set of samples with different concentrations and Ni filler sizes. Measurements were in part carried out at the Centre for Electronic Correlations and Magnetism, Institute of Experimental Physics V of the University of Augsburg (Germany) and, after the installation of a new cryogenic system, at the Department of Physics at FEEC, BUT Brno. Measurements were performed on a number of meters (Alpha-Analyzer of Novocontrol, HP4284A and HP4285A of Hewlett Packard and E4991A of Agilent) in the frequency range 1 Hz – 1 MHz and in the temperature interval 10 K – 300 K. The nickel concentration in systems studied varied from 0 % to 75 % and nickel particles were of a spherical shape with diameters between 35 and 115 m. The measurement results have shown that in the above frequency and temperature window just a single relaxation and a single conductivity mechanism occur. It was also proved that the frequency dependence of complex permittivity is for different Ni particle sizes at the same concentration different. These results have been quantified and a simple mathematical formula based on the Lichtenecker mixture rule has been proposed for their description. The physical origin of the effect of particle size at the same total nickel concentration is sought in different surface areas of internal interfaces between nickel and polymer in the composite