Orientador: Hugo Enrique Hernandez Figueroa / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-14T12:30:52Z (GMT). No. of bitstreams: 1 Paixao_OswaldoPedreira_D.pdf: 3002384 bytes, checksum: f5a0e8e8022dabd36cfce9ffdb839f9b (MD5) Previous issue date: 2009 / Resumo: Este trabalho, tem como objetivo o desenvolvimento de novas técnicas, para análise de regime permanente não-autonoma de circuitos de alta-velocidade não-lineares em grande-escala. Para tal, é proposto um novo método do balanço harmônico (BH) fundamentado em uma eficiente metodologia de decomposição multi-níveis, que subdivide um circuito não-linear em grande escala em uma estrutura hierarquica de super-redes (SuRs) esparsamente interconectadas. Mais precisamente, em cada nível de hierarquia, o circuito é composto por SuRs intermediárias, SuRs de fundo, e redes de conexão (RCs). As SuRs de fundo são decompostas em um aglomerado de subredes não-lineares (SRNs) correspondendo a dispositivos semicondutores, que por sua vez, estão envolvidos por uma sub-rede linear (SRL). A equação de estado e de sonda das SuRs de fundo foram obtidas utilizando uma nova metodologia que combina a formulação de espaço de estado (FEE) para as SRNs com a formulação nodal modificada (FNM) para a SRL. Esta metodologia FEE/FNM produz um sistema quadrado de equações com menor tamanho possível. Para realização das conversões do sinal entre os domínios do tempo e da frequência, foram discutidas e implementadas diferentes transformadas de Fourier discreta (TFDs), para operação em regime multi-tons, incluindo sinais com modulação digital. A equação determinante do BH multi-níveis do circuito assume uma estrutura hierarquica do tipo bloco diagonal com borda , que pode ser eficientemente resolvida utilizando técnicas de processamento paralelo. A matriz jacobiana de cada SuR de fundo é processada utilizando eficientes técnicas de matrizes esparsas, junto com o conceito de espectro de derivada. Para a solução da equação determinante, foram utilizados os métodos de Newton e do tensor para problemas de pequena- e média-escala, e os métodos de Newton inexato e do tensor inexato para problemas em grande-escala. A globalização via pesquisa-em-linha com retrocedimento, foi adotada para nestes solucionadores não-lineares. Entretanto, para o método do tensor e do tensor inexato, também foi adotada a técnica de pesquisa-em-linha curvilinear. Nos métodos inexatos, técnicas de pré-condicionamento foram utilizadas, para aumentar a eficiência e a robustez do solucionador linear iterativo em subespaço de Krylov (GMRES, GMRES-Bt e TGMRES-Bt). Finalmente, a formulação proposta foi validada e a eficiência do método do tensor e do tensor inexato comparada com o método de Newton e de Newton inexato, para diferentes topologias de circuitos utilizando diodos, FETs e HBTs, e operando sob diferentes regimes de excitação multi-tons. / Abstract: This work deals with the development of new techniques for nonautonomous nonlinear steady-state analysis of high-speed large-scale integrated circuits. To this end, it is proposed a novel harmonic balance (HB) method fundamented on a efficient multi-level decomposition methodology, that divides a large-scale circuit into hierarchical structure of sparsely interconnected supernetworks (SuNs). More precisely, the circuit is composed by intermediary SuRs, bottom SuRs and connection networks (CNs). The bottom SuNs are decomposed into a cluster of nonlinear subnetworks (NSNs) corresponding to the opto-electronic semiconductor devices, which in turn, are embedded by a linear subnetwork (LSN). Multi-port elements can be included in the LSN, in order to use measured data or results from electromagnetic analysis of structures with complex geometries. The formulation of the bottom SuN state and probe equations uses an improved table-oriented statespace formulation (SSF), that produces a square system with the lowest possible size, which is equal to the number of nonlinear state-variables (branch voltages and currents) that act as argument of the fuctions representing the semiconductor devices nonlinearities. The SSF is compared with the classical modified nodal formulation (MNF). For dealing with signal timefrequency conversions, discrete Fourier transform (DFT) techniques for different multi-tone regimes are discussed, including complex digitally modulated signals. The multi-level HB determining equation of the circuit assumes a hierarchical block bordered structure that can be efficiently tackled by parallel processing techniques. The HB jacobian matrix is handled using efficient sparse matrix techniques with a proper definition of the derivatives spectra. For the solution of a large-size HB problem, we investigated the applications of inexact tensor method based on Krylov-subspace techniques. Preconditioning are used to improve the robustness of the iterative tensor solver. To determine the circuit DC regime, we employ the tensor method. We adopted the backtracking linesearch technique as a globalisation strategy. However, for the tensor method, in particular, a curvilinear linesearch was also implemented. Finally, the formulation was validated and, the tensor and inexact tensor method efficiency was compared with the Newton and inexact Newton method, respectively, for several different circuits using diodos, FETs and HBTs, and operating under different multi-tone regimes. / Doutorado / Engenharia de Telecomunicações / Doutor em Engenharia Elétrica

Le but de notre étude était de valider un indicateur de la qualité de l’environnement, parmi trois approches : des mesures morphologiques de juvéniles de poissons ; la quantification de l’asymétrie fluctuante de leurs otolithes ; l’analyse de la forme de leurs otolithes. Les résultats in aquaria sur Dicentrarchus labrax ont montré une absence d’effet de mono contaminations par des polluants classiques comme le phosphore ou le zinc, à des concentrations correspondant à celles in situ en zones fortement anthropisées. Des concentrations plus élevées de zinc ont toutefois induit une modification de la forme des otolithes en plus d’un effet négatif sur la taille et le poids. Par nos prélèvement in situ sur trois ans d’Oblada melanura, nous avons mis en évidence de manière reproductible que, comparativement à des sites préservés et des arrivées de petits cours d’eau, des ports de plaisance de taille moyenne ont un effet négatif sur la longueur standard des juvéniles et induisent une modification de la forme de leurs otolithes. De l’ensemble de nos résultats nous pouvons déduire que tailles et poids sont facilement mesurables mais présentent des variabilités dans leurs réponses. La mesure de l’asymétrie des otolithes de juvéniles ne semble pas adaptée à une utilisation en bioindication. Au contraire, l’analyse de formes des sagittae de juvéniles paraît adaptée pour suivre des modifications de l’environnement pour des poissons de deux familles différentes, Moronidés et Sparidés. Cette analyse semble un outil prometteur en bioindication, applicable pour les gestionnaires de l’environnement. / The aim of our study was to validate the most suitable environmental indicator among three approaches: morphological measurements of fish juveniles; quantification of the fluctuating asymmetry of their otoliths; analysis of their otolith shape. In aquaria, results for Dicentrarchus labrax have shown that mono-contamination by classical pollutants, such as phosphorus or zinc, has no effect for concentrations corresponding to those measured in highly anthropized environments. Nevertheless, higher zinc concentrations induce otolith shape alterations in addition to their negative impact on fish size and weight. On the basis of our three-year in situ Oblada melanura samplings, we have demonstrated that, in a replicable manner, compared to preserved areas and small waterway mouths, mid-size recreational harbours negatively impact juvenile standard length and also alter otolith shape. By comparison with in aquaria results, these alterations are consistent with a synergy of disturbance sources which taken independently do not have any impact. Taking into account all our results, we deduce that size and weight are easy to measure but show response variability. Measurement of fish juvenile otoliths' fluctuating asymmetry does not seem to be suitable for use in bioindication. Conversely, fish juvenile sagittae shape analysis is well-suited to surveys of environmental modifications, for fishes from two different families, Moronidae and Sparidae. This analysis seems to be a promising tool for bioindication, with a practical application for environmental managers.

The on-line condition monitoring of turbomachinery blades is of utmost importance to ensure the long term health and availability of such machines and as such has been an area of study since the late 1960s. As a result a number of on-line blade vibration measurement techniques are available, each with its own associated advantages and shortcomings. In general, on-blade sensor measurement techniques suffer from sensor lifespan, whereas non-contact techniques usually have measurement bandwidth limitations. One non-contact measurement technique that yields improvements in the area of measurement bandwidth is laser Doppler vibrometry. This thesis presents results and findings from utilizing laser Doppler vibrometry in an Eulerian fashion (i.e. a fixed reference frame) to measure on-line blade vibrations in axial-flow turbomachinery. With this measurement approach, the laser beam is focussed at a fixed point in space and measurements are available for the periods during which each blade sweeps through the beam. The characteristics of the measurement technique are studied analytically with an Euler-Bernoulli cantilever beam and experimental verification is performed. An approach for the numerical simulation of the measurement technique is then presented. Associated with the presented measurement technique are the short periods during which each blade is exposed to the laser beam. This characteristic yields traditional frequency domain signal processing techniques unsuitable for providing useful blade health indicators. To obtain frequency domain information from such short signals, it is necessary to employ non-standard signal processing techniques such as non-harmonic Fourier analysis. Results from experimental testing on a single-blade test rotor at a single rotor speed are presented in the form of phase angle trends obtained with non-harmonic Fourier analysis. Considering the maximum of absolute unwrapped phase angle trends around various reference frequencies, good indicators of blade health deterioration were obtained. These indicators were verified numerically. To extend the application of this condition monitoring approach, measurements were repeated on a five-blade test rotor at four different rotor speeds. Various damage cases were considered as well as different ELDV measurement positions. Using statistical parameters of the abovementioned indicators as well as time domain parameters, it is shown that with this condition monitoring approach, blade damage can successfully be identified and quantified with the aid of artificial neural networks. / Thesis (PhD)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

Data gathering is a constant in human history with ever increasing amounts in quantity and dimensionality. To get a feel for the data, make it interpretable, or find underlying laws it is necessary to fit a function to the finite and possibly noisy data. In this thesis we focus on a method achieving this, namely least squares approximation. Its discovery dates back to around 1800 and it has since then proven to be an indispensable tool which is efficient and has the capability to achieve optimal error when used right. Crucial for the least squares method are the ansatz functions and the sampling points. To discuss them, we gather tools from probability theory, frame subsampling, and $L_2$-Marcinkiewicz-Zygmund inequalities. With that we give results in the worst-case or minmax setting, when a set of points is sought for approximating a class of functions, which we model as a generic reproducing kernel Hilbert space. Further, we give error bounds in the statistical learning setting for approximating individual functions from possibly noisy samples. Here, we include the covariate-shift setting as a subfield of transfer learning. In a natural way a parameter choice question arises for balancing over- and underfitting effect. We tackle this by using the cross-validation score, for which we show a fast way of computing as well as prove the goodness thereof.:1 Introduction 2 Least squares approximation 3 Reproducing kernel Hilbert spaces (RKHS) 4 Concentration inequalities 5 Subsampling of finite frames 6 L2 -Marcinkiewicz-Zygmund (MZ) inequalities 7 Least squares in the worst-case setting 8 Least squares in statistical learning 9 Cross-validation 10 Outlook

No description available.

Subject of study: Cilia and flagella are slender appendages of eukaryotic cells. They are actively bending structures and display regular bending waves. These active flagellar bending waves drive fluid flows on cell surfaces like in the case of the ciliated trachea or propels single cell micro-swimmers like sperm or alga. Objective: The axoneme is the evolutionarily conserved mechanical apparatus within cilia and flagella. It is comprised of a cylindrical arrangement of microtubule doublets, which are the elastic elements and dyneins, which are the force generating elements in the axonemal structure. Dyneins collectively bend the axoneme and must be specifically regulated to generate symmetric and highly asymmetric waveforms. In this thesis, I address the question of the molecular origin of the asymmetric waveform and test different theoretical descriptions for motor regulation. Approach: I introduce the isolated and reactivated Chlamydomonas axoneme as an experimental model for the symmetric and asymmetric flagellar beat. This system allows to study the beat in a controlled and cell free environment. I use high-speed microscopy to record shapes with high spatial and temporal resolution. Through image analysis and shape parameterization I extract a minimal set of parameters that describe the flagellar waveform. Using Chlamydomonas, I make use of different structural and motor mutants to study their effect on the shape in different reactivation conditions. Although the isolated axoneme system has many advantages compared to the cell-bound flagellum, to my knowledge, it has not been characterized yet. Results: I present a shape parameterization of the asymmetric beat using Fourier decomposition methods and find, that the asymmetric waveform can be understood as a sinusoidal beat around a circular arc. This reveals the similarities of the two different beat types: the symmetric and the asymmetric beat. I investigate the origin of the beat-asymmetry and find evidence for a specific dynein motor to be responsible for the asymmetry. I furthermore find experimental evidence for a strong sliding restriction at the basal end of the axoneme, which is important to establish a static bend. In collaboration with P. Sartori and F. Jülicher, I compare theoretical descriptions of different motor control mechanisms and find that a curvature controlled motor-regulation mechanism describes the experimental data best. We furthermore find, that in the dynamic case an additional sliding restriction at the base is unnecessary. By comparing the waveforms of intact cells and isolated reactivated axonemes, I reveal the effect of hydrodynamic loading, and the influence of boundary conditions on the shape of the beating flagella.

In den letzten Jahren hat das Teilgebiet des Maschinellen Lernens, das sich mit Graphdaten beschäftigt, durch die Entwicklung von spezialisierten Graph-Neuronalen Netzen (GNNs) mit mathematischer Begründung in der spektralen Graphtheorie große Sprünge nach vorn gemacht. Zusätzlich zu natürlichen Graphdaten können diese Methoden auch auf Datensätze ohne Graphen angewendet werden, indem man einen Graphen künstlich mithilfe eines definierten Adjazenzbegriffs zwischen den Samplen konstruiert. Nach dem neueste Stand der Technik wird jedes Sample mit einer geringen Anzahl an Nachbarn verknüpft, um gleichzeitig das dünnbesetzte Verhalten natürlicher Graphen nachzuahmen, die Stärken bestehender GNN-Methoden auszunutzen und quadratische Abhängigkeit von der Knotenanzahl zu verhinden, welche diesen Ansatz für große Datensätze unbrauchbar machen würde. Die vorliegende Arbeit beleuchtet die alternative Konstruktion von vollbesetzten Graphen basierend auf Kernel-Funktionen. Dabei quantifizieren die Verknüpfungen eines jeden Samples explizit die Ähnlichkeit zu allen anderen Samplen. Deshalb enthält der Graph eine quadratische Anzahl an Kanten, die die lokalen und nicht-lokalen Nachbarschaftsinformationen beschreiben. Obwohl dieser Ansatz in anderen Kontexten wie der Lösung partieller Differentialgleichungen ausgiebig untersucht wurde, wird er im Maschinellen Lernen heutzutage meist wegen der dichtbesetzten Adjazenzmatrizen als unbrauchbar empfunden. Aus diesem Grund behandelt ein großer Teil dieser Arbeit numerische Techniken für schnelle Auswertungen, insbesondere Eigenwertberechnungen, in wichtigen Spezialfällen, bei denen die Samples durch niedrigdimensionale Vektoren (wie z.B. in dreidimensionalen Punktwolken) oder durch kategoriale Attribute beschrieben werden. Weiterhin wird untersucht, wie diese dichtbesetzten Adjazenzinformationen in Lernsituationen auf Graphen benutzt werden können. Es wird eine eigene transduktive Lernmethode vorgeschlagen und präsentiert, eine Version eines Graph Convolutional Networks (GCN), das auf die spektralen und räumlichen Eigenschaften von dichtbesetzten Graphen abgestimmt ist. Schließlich wird die Anwendung von Kernel-basierten Adjazenzmatrizen in der Beschleunigung der erfolgreichen Architektur “PointNet++” umrissen. Im Verlauf der Arbeit werden die Methoden in ausführlichen numerischen Experimenten evaluiert. Zusätzlich zu der empirischen Genauigkeit der Neuronalen Netze liegt der Fokus auf wettbewerbsfähigen Laufzeiten, um die Berechnungs- und Energiekosten der Methoden zu reduzieren. / Over the past few years, graph learning - the subdomain of machine learning on graph data - has taken big leaps forward through the development of specialized Graph Neural Networks (GNNs) that have mathematical foundations in spectral graph theory. In addition to natural graph data, these methods can be applied to non-graph data sets by constructing a graph artificially using a predefined notion of adjacency between samples. The state of the art is to only connect each sample to a low number of neighbors in order to simultaneously mimic the sparse behavior of natural graphs, play into the strengths of existing GNN methods, and avoid quadratic scaling in the number of nodes that would make the approach infeasible for large problem sizes. In this thesis, we shine light on the alternative construction of kernel-based fully-connected graphs. Here the connections of each sample explicitly quantify the similarities to all other samples. Hence the graph contains a quadratic number of edges which encode local and non-local neighborhood information. Though this approach is well studied in other settings including the solution of partial differential equations, it is typically dismissed in machine learning nowadays because of its dense adjacency matrices. We thus dedicate a large portion of this work to showcasing numerical techniques for fast evaluations, especially eigenvalue computations, in important special cases where samples are described by low-dimensional feature vectors (e.g., three-dimensional point clouds) or by a small set of categorial attributes. We then continue to investigate how this dense adjacency information can be utilized in graph learning settings. In particular, we present our own proposed transductive learning method, a version of a Graph Convolutional Network (GCN) designed towards the spectral and spatial properties of dense graphs. We furthermore outline the application of kernel-based adjacency matrices in the speedup of the successful PointNet++ architecture. Throughout this work, we evaluate our methods in extensive numerical experiments. In addition to the empirical accuracy of our neural network tasks, we focus on competitive runtimes in order to decrease the computational and energy cost of our methods.

Subject of study: Cilia and flagella are slender appendages of eukaryotic cells. They are actively bending structures and display regular bending waves. These active flagellar bending waves drive fluid flows on cell surfaces like in the case of the ciliated trachea or propels single cell micro-swimmers like sperm or alga. Objective: The axoneme is the evolutionarily conserved mechanical apparatus within cilia and flagella. It is comprised of a cylindrical arrangement of microtubule doublets, which are the elastic elements and dyneins, which are the force generating elements in the axonemal structure. Dyneins collectively bend the axoneme and must be specifically regulated to generate symmetric and highly asymmetric waveforms. In this thesis, I address the question of the molecular origin of the asymmetric waveform and test different theoretical descriptions for motor regulation. Approach: I introduce the isolated and reactivated Chlamydomonas axoneme as an experimental model for the symmetric and asymmetric flagellar beat. This system allows to study the beat in a controlled and cell free environment. I use high-speed microscopy to record shapes with high spatial and temporal resolution. Through image analysis and shape parameterization I extract a minimal set of parameters that describe the flagellar waveform. Using Chlamydomonas, I make use of different structural and motor mutants to study their effect on the shape in different reactivation conditions. Although the isolated axoneme system has many advantages compared to the cell-bound flagellum, to my knowledge, it has not been characterized yet. Results: I present a shape parameterization of the asymmetric beat using Fourier decomposition methods and find, that the asymmetric waveform can be understood as a sinusoidal beat around a circular arc. This reveals the similarities of the two different beat types: the symmetric and the asymmetric beat. I investigate the origin of the beat-asymmetry and find evidence for a specific dynein motor to be responsible for the asymmetry. I furthermore find experimental evidence for a strong sliding restriction at the basal end of the axoneme, which is important to establish a static bend. In collaboration with P. Sartori and F. Jülicher, I compare theoretical descriptions of different motor control mechanisms and find that a curvature controlled motor-regulation mechanism describes the experimental data best. We furthermore find, that in the dynamic case an additional sliding restriction at the base is unnecessary. By comparing the waveforms of intact cells and isolated reactivated axonemes, I reveal the effect of hydrodynamic loading, and the influence of boundary conditions on the shape of the beating flagella.:Contents 1 Introduction. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Biology of Cilia and Flagella . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 The dimensions of flagellated micro-swimmers . . . . . . . . . . . . . . . . . 4 1.1.2 The symmetric and the asymmetric beat . . . . . . . . .. . . . . . . . . . . . 5 1.1.3 Chlamydomonas reinhardtii as a flagella model . . . . . . . . . . 5 1.2 The axoneme is the internal structure in eukaryotic cilia and flagella . . 6 1.3 Structure and function of microtubules and dyneins . . . . . . . . . . . 9 1.3.1 Microtubules: The structural elements in the axoneme . . . . . . 9 1.3.2 Dyneins: The force generators that drive the axonemal beat . . . 10 1.3.3 The asymmetries in the axoneme and consequences for the beat 17 1.4 Axonemal waveform models and mechanisms: from sliding to bending to beating . . . . . . . . . . . . . . 20 1.5 Geometrical representation and parameterization of the axonemal beat . . . . . . . . . . . . . . . 23 2 Questions addressed in this thesis . . . . . . . . . . . . . . 27 3 Material and Methods . . . . . . . . . . . . . . 29 3.1 Chlamydomonas cells: Axoneme preparation and motility assays . . . . 29 3.1.1 Culturing of Chlamydomonas reinhardtii cells . . . . . . . . . . . 29 3.1.2 Isolation, demembranation and storage of axonemes . . . . . . . 33 3.1.3 Reactivation of axonemes in controlled conditions . . . . . . . . . 35 3.1.4 Axoneme gliding assay using kinesin 1 . . . . . . . . . . . . . . . 36 3.2 Imaging and image processing . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 High-speed imaging of the flagella and axonemes . . . . . . . . . 38 3.2.2 Precise tracking of isolated axonemes and the flagella of cells . . 42 3.2.3 High throughput frequency evaluation of isolated axonemes . . . 47 3.2.4 Beat frequency characterization of the reactivated WT axoneme . . . . . . . . . . . . . . 49 4 Results and Discussion . . . . . . . . . . . . . . 53 4.1 The beat of the axoneme propagates from base to tip . . . . . . . . . . . 53 4.1.1 TEM study reveals no sliding at the base of a bend axoneme . . 53 4.1.2 The direction of wave propagation is directly determined from the reactivation of polarity marked axonemes . . . . . . . . . . 57 4.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2 The asymmetric beat is the superposition of a static semi-circular arc and a sinusoidal beat . . . . . . .. . . . . . . . . . . . . . . . . 61 4.2.1 The waveform is parameterized by Fourier decomposition in time . . . . . . . . . . . . . . 61 4.2.2 The 0th and 1st Fourier modes describe the axonemal waveform . . . . . . . . . . . . . . 65 4.2.3 General dependence of shape parameters on axoneme length and beat frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.4 The isolated axoneme is a good model for the intact flagellum . .. . . . . . . . . . . . . . 71 4.2.5 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 The circular motion is a consequence of the axonemal waveform . . . . . . . . . . . . . . . . . . . 79 4.3.1 Hydrodynamic relations for small amplitude waves explain the relation between swimming and shape of axonemes . . . . 79 4.3.2 The swimming path can be reconstructed using shape information and a hydrodynamic model . . . . . . . . . . . . . . . . 83 4.3.3 Motor mutations alter the direction of rotation of reactivated axonemes. . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.4 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 The molecular origin of the circular mean shape. . . . . . . . . . . . . . 89 4.4.1 Motor Mutations do not abolish the mean shape, a structural mutation does . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.2 The axoneme is straight in absence of ATP but bend at low ATP concentrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4.3 Viscous load decreases the mean curvature . . . . . . . . . . . . 99 4.4.4 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.5 Curvature-dependent dynein activation accounts for the shape of the beat of the isolated axoneme . . . . . . . . . . . . . . . . 103 5 Conclusions and Outlook . . . . . . . . . . . . . . . . 109 5.1 Summary of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Abbreviations . . . . . . . . . . . . . . . . 111 List of figures . . . . . . . . . . . . . . . . 116 List of tables . . . . . . . . . . . . . . . . 118 Bibliography

The spectral analysis of heart rate variability is a tool that gained more and more clinical importance in the latest years. It can be used in order to access autonomic function on the cardiovascular system through the evaluation of the different frequency bands of the HRV. So far different mathematical approaches have been used towards this aim, often with contradictory results. Therefore, the need for standardization of the methods seems more and more important. In this thesis 2 non-parametric, Fourier-based methods and two parametric based on autoregressive modeling were used in order to extract the power spectral density of patients with epilepsy. Their results were statistically compared to age matched controls. The analysis have shown that when a parametric method is used, a careful model order selection method must be used, and when this is accomplished, the power spectrum could more efficient highlight differences between controls and patients. The results between non-parametric and parametric methods were different, therefore these methods cannot be considered interchangeable. The analysis methodolgy established in this first part of the study has been used to analyse HRV signals from patients before and after deep brain stimulation. / Η φασματική ανάλυση της Μεταβλητότητας της Καρδιακής Συχνότητας (ΜΚΣ) χρησιμοποείται όλο και περισσότερο σε κλινικές μελέτες τα τελευταία χρόνια. Και αυτό γιατί μπορεί να δώσει πληροφορίες σχετικά με την λειτουργία του αυτόνομου νευρικού συστήματος πάνω στην καρδιά αναλύοντας το συχνοτικό περιεχόμενο των ΜΚΣ σημάτων σε διακριτές ζώνες συχνοτήτων. Μέχρι τώρα διαφορετικές μαθηματικές μέθοδοι έδωσαν διαφορετικά, συχνα αντικρουόμενα αποτελέσματα. Έτσι η ανάγκη λεπτομερής περιγραφής των μεθόδων φαίνεται όλο και περισσοτερο επιτακτική. Σε αυτή τη διπλωματική εργασία, δυο μη παραμετρικές μέθοδοι και δύο παραμετρικές βασισμένες σε μοντέλα αυτοπαλινδρόμησης (autoregressive modeling) εφαρμόστηκαν προκειμένου να υπολογιστεί το φάσμα ασθενών με χρόνια επιληψία. Τα αποτελέσματα συγκρίθηκαν με υγιείς εθελοντές ίδιου ηλικιακού προφίλ. Η ανάλυση έδειξε ότι όταν χρησιμοποιουνται παραμετρικές μέθοδοι, η επιλογή της τάξης του μοντέλου πρέπει να γίνεται με προσοχή και όταν αυτό γίνει, το φάσμα μπορεί να αναδείξει πιο αποτελεσματικά διαφορές μεταξύ ασθενών και υγειών εθελοντών. Τα αποτελέσματα μεταξύ παραμετρικών και μη παραμετρικών μεθόδων αποδείχθηκαν διαφορετικα, και κατά συνέπεια οι δύο αυτές κατηγορίες ανάλυσης δεν μπορούν να θεωρηθούν ίδιες. Η μεθοδολογία που αναπτύχθηκε στο πρώτο αυτό μέρος της εργασίας χρησιμοποιήθηκε για να αναλύσει σήματα ΜΚΣ από ασθενείς με Πάρκινσον πριν και μετά εν τω βάθει ερεθισμό (Deep brain simulation).

En synthèse d’images, reproduire les effets complexes de la lumière sur des matériaux transluminescents, tels que la cire, le marbre ou la peau, contribue grandement au réalisme d’une image. Malheureusement, ce réalisme supplémentaire est couteux en temps de calcul. Les modèles basés sur la théorie de la diffusion visent à réduire ce coût en simulant le comportement physique du transport de la lumière sous surfacique tout en imposant des contraintes de variation sur la lumière incidente et sortante. Une composante importante de ces modèles est leur application à évaluer hiérarchiquement l’intégrale numérique de l’illumination sur la surface d’un objet. Cette thèse révise en premier lieu la littérature actuelle sur la simulation réaliste de la transluminescence, avant d’investiguer plus en profondeur leur application et les extensions des modèles de diffusion en synthèse d’images. Ainsi, nous proposons et évaluons une nouvelle technique d’intégration numérique hiérarchique utilisant une nouvelle analyse fréquentielle de la lumière sortante et incidente pour adapter efficacement le taux d’échantillonnage pendant l’intégration. Nous appliquons cette théorie à plusieurs modèles qui correspondent à l’état de l’art en diffusion, octroyant une amélioration possible à leur efficacité et précision. / In image synthesis, reproducing the complex appearance of objects with subsurface light scattering, such as wax, marble and skin, greatly contributes to the realism of an image. Unfortunately, this added realism comes at a high computational cost. Models based on diffusion theory aim to reduce this computational cost by simulating the physical behaviour of subsurface light scattering while imposing smoothness constraints on the incident and outgoing light fields. An important component of these models is how they are employed to hierarchically evaluate the numerical integral of lighting over the surface of an object. This thesis will first review the existing literature on realistic subsurface lighting simulation, before investigating in more depth the application and extension of modern diffusion models in image synthesis. In doing so, we propose and evaluate a new hierarchical numerical integration technique that uses a novel frequency analysis of the incident and outgoing light fields to reliably adapt the sampling rate during integration. We realize our resulting theory in the context of several state-of-the-art diffusion models, providing a marked improvement in their efficiency and accuracy.