Frequency domain models for power electronic circuits are either based on iterative techniques such as Newton's method or linearised around an operating point. Iterative frequency domain models provide great accuracy as they are capable of calculating the exact switching instants of the device. On the other hand, the accuracy of a linearised frequency domain model relies on the magnitude of input waveform to be small so that the circuit's operating point does not vary or varies very little. However, an important advantage of a linearised model is its ability to provide insight into waveform distortion interaction, more specifically, the frequency cross-coupling around a power electronic circuit. In general, a linearised model for harmonic analysis would not normally include the description of feedback control. Likewise a linearised model for control analysis would usually disregard frequency interactions above the fundamental (or the most significant component); that is assuming the cross-coupling between harmonic frequencies does not affect the dynamics of control. However, this thesis proposes that a linearised model for control analysis shall also include the complete description of frequency cross-coupling between harmonics to produce the correct dynamic response. This thesis presents a harmonic state-space (HSS) model of an HVdc converter that incorporates the full effect of varying switching instants, both through control and commutation period dynamics, while remaining within the constraints of a linear time-invariant (LTI) system. An example is given using the HSS model to explain how a close to fifth harmonic resonance contributes to the dominant system response through the frequency cross-coupling of the converter and the controller feedback loop. The response of the system is validated against a time domain model built in PSCAD/EMTDC, and more importantly, the correct response cannot be produced without including the harmonic interactions beyond the fundamental frequency component.

The dynamical underpinnings of complex computation and information transmission within the brain, while of great interest to the neuroscience community at large, remain poorly understood. One of the striking manifestations of neuronal population activity is that of rhythmic oscillations in the local field potential. It is thought that distinct patterns of these oscillations such as cross-frequency coupling within a given spatial location and coherence between disparate brain regions may represent neuronal computation and communication, respectively. Here we show such dynamics within a human temporal neocortical in vitro model. In specific, we show theta-gamma cross frequency coupling in deep and superficial layers, phase coherence between layers at theta frequencies, and a measure of communication (phase dependent power correlations) between layers at theta frequency. Additionally, we show a novel correlation between communication across layers and cross frequency coupling within layers, demonstrating a dynamic link between local computation and intralaminar communication.

The dynamical underpinnings of complex computation and information transmission within the brain, while of great interest to the neuroscience community at large, remain poorly understood. One of the striking manifestations of neuronal population activity is that of rhythmic oscillations in the local field potential. It is thought that distinct patterns of these oscillations such as cross-frequency coupling within a given spatial location and coherence between disparate brain regions may represent neuronal computation and communication, respectively. Here we show such dynamics within a human temporal neocortical in vitro model. In specific, we show theta-gamma cross frequency coupling in deep and superficial layers, phase coherence between layers at theta frequencies, and a measure of communication (phase dependent power correlations) between layers at theta frequency. Additionally, we show a novel correlation between communication across layers and cross frequency coupling within layers, demonstrating a dynamic link between local computation and intralaminar communication.

This Master’s thesis deals with investigation of high-frequency oscillations in intracranial electroencephalography in patients with pharmacoresistant epilepsy. It describes individual types of oscillations with respect to their frequency definition, examines their physiological differences and occurrence. In addition to conventional high-frequency oscillations (up to about 600 Hz), it also focuses on oscillations with a frequency component above 1kHz. According to recent studies, these oscillations could have higherspecificity for the determination of pathological tissue in the epileptic brain. The data for this work was obtained by manual labeling and categorization of approximately 1500 sections of the stereoencephalographic record signals of patients undergoing surgical removal of the epileptic foci and subsequently monitored for success in the operation. Differences between individual groups of oscillations and resected or unresected tissues are investigated in this work by methods using calculations of entropy signals or cross frequency coupling. The most significant results were achieved for the classification group (FR + vFR) vs. uFR, methods frequency-amplitude coupling and sample entropy 1. When categorizing according to information about channel resection, the Shannon entropy is the most successful classification parameter.

A suite of signal processing algorithms designed for extracting information from brain electrophysiology and movement signals, along with new insights gained by applying these tools to understanding parkinsonism, were presented in this dissertation. The approach taken does not assume any particular stimulus, underlying activity, or synchronizing event, nor does it assume any particular encoding scheme. Instead, novel signal processing applications of complex continuous wavelet transforms, cross-frequency-coupling, feature selection, and canonical correlation were developed to discover the most significant electrophysiologic changes in the basal ganglia and cortex of parkinsonian rhesus monkeys and how these changes are related to the motor signs of parkinsonism. The resulting algorithms effectively characterize the severity of parkinsonism and, when combined with motor signal decoding algorithms, allow technology-assisted multi-modal grading of the primary pathological signs. Based on these results, parallel data collection algorithms were implemented in real-time embedded software and off-the-shelf hardware to develop a new system to facilitate monitoring of the severity of Parkinson's disease signs and symptoms in human patients. Off -line analysis of data collected with the system was subsequently shown to allow discrimination between normal and simulated parkinsonian conditions. The main contributions of the work were in three areas: 1) Evidence of the importance of optimally selecting multiple, non-redundant features for understanding neural information, 2) Discovery of signi ficant correlations between certain pathological motor signs and brain electrophysiology in different brain regions, and 3) Implementation and human subject testing of multi-modal monitoring technology.

Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-supervisée. / In neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations.

Cette dernière décennie a vu un certain nombre d'avancées significatives en mathématiques, en apprentissage computationnel et en traitement de signal, qui n'ont pas encore été pleinement exploitées en neurosciences. En particulier, l'évaluation de la connectivité dans les réseaux neuronaux peut grandement bénéficier de ces travaux. Nous proposons ici d'exploiter ces outils pour combler partiellement le fossé considérable qui existe encore entre la recherche connectomique à grande échelle (largement centrée sur des mesures indirectes de l'activité cérébrale comme l'Imagerie par résonance magnétique fonctionnelle (IRMf)) et les mesures physiologiques plus directes de l'activité cérébrale. Il est particulièrement important de combler ce fossé pour l'étude des propriétés physiologiques associées à divers états de conscience normaux et anormaux, notamment les troubles psychiatriques, le sommeil, l'anesthésie ou les états induits par les drogues. Les travaux récents sur l'induction d'états de conscience altérés par des agonistes non sélectifs de la sérotonine, tels que la psilocybine et le Diéthyllysergamide (LSD), en sont de bons exemples. Au cours des cinq dernières années, une résurgence rapide de la recherche sur la neurobiologie des tryptamines psychédéliques s'est produite, après une interruption d'un demi-siècle. Bien que ces substances présentent un grand potentiel pour éclairer des aspects jusqu'ici non interrogés du fonctionnement normal et anormal du cerveau, l'ampleur et le caractère inhabituel des changements qu'elles provoquent posent de sérieux défis aux chercheurs. La découverte de méthodes convaincantes et évolutives pour étudier ces données est d'une grande importance si nous voulons tirer parti de la fenêtre unique que ces substances atypiques offrent sur les aspects centraux de la conscience et des fonctions cérébrales anormales. Dans la présente thèse, nous résumons l'état actuel de la neuro-imagerie électrophysiologique en ce qui concerne l'étude des tryptamines psychédéliques, et nous démontrons un certain nombre de lacunes évidentes dans la recherche électrophysiologique actuelle sur les psychédéliques. Nous offrons également quelques modestes contributions méthodologiques au domaine. L'utilité de ces contributions est soutenue par quelques résultats empiriques intrigants, bien que préliminaires. Dans le premier chapitre, nous présentons l'histoire de la recherche neuroscientifique sur le LSD. Il a été rapporté que le LSD induit des déplacements de pics dans les spectres de puissance, en même temps que des diminutions de l'amplitude des pics. Le fait que ces effets soient liés entre eux et que la plupart des recherches menées jusqu'à présent n'aient pas cherché à les distinguer est uniformément négligé dans la littérature, ce qui, selon nous, peut conduire à de fausses interprétations. Le chapitre 2 examine certains des avantages plausibles ainsi que les obstacles sérieux à la recherche sur la connectivité du cerveau entier par magnétoencéphalographie (MEG), et propose plusieurs stratégies pour surmonter ces limites méthodologiques. Celles-ci comprennent des stratégies d'imagerie de source convaincantes, des développements nouveaux et récents dans la décomposition spectrale, des mesures de connectivité insensibles à la conduction volumique, et des implémentations évolutives de métriques de couplage interfréquence bien établies. Nous montrons que ces techniques peuvent être étendues à une grille corticale et sous-corticale de plus haute résolution que celle qui existe actuellement. Nous discutons également d'une mise en œuvre allégée de statistiques non paramétriques adaptées à ces données. Le troisième chapitre a pour but de démontrer l'efficacité de ces procédures, en montrant les résultats empiriques d'une étude de la connectivité du cerveau entier sous LSD par MEG. Le quatrième et dernier chapitre discute de ces résultats, ainsi que des précautions nécessaires et des orientations futures prometteuses pour ce type de recherche. Il propose des approches computationnelles supplémentaires qui pourraient étendre la portée de ces recherches et, plus généralement, de l'électrophysiologie du cerveau entier. Dans l'ensemble, le cadre méthodologique proposé dans ce travail surmonte les limitations endémiques précédentes, non seulement dans la recherche sur les psychédéliques, mais aussi dans la recherche électrophysiologique en général, et jette une lumière nouvelle sur sur les mécanismes centraux qui sous-tendent ces états de conscience anormaux, ainsi que sur les importantes précautions à prendre dans la recherche électrophysiologique. / The past decade has seen a number of significant advances in mathematics, computational learning, and signal processing, which have yet to be deployed in neuroscience. In particular the assessment of connectivity in neural networks has much to gain from this work. Here we propose these tools be leveraged to partially bridge the considerable gap that still exists between large-scale connectomics research (largely centered around indirect measures of brain activity such as fMRI), and more direct, physiological measures of brain activity. Bridging this gap is especially important to the study of physiological properties associated with various normal and abnormal states of consciousness including Psychiatric conditions, sleep, anaesthesia or drug-induced states. Exemplary of such research, is recent work surrounding the induction of altered states of consciousness by non-selective serotonin agonists such as Psilocybin and LSD. During the past five years, a rapid resurgence of research into the neurobiology of Psychedelic tryptamines has transpired, following a half-century hiatus. While these substances hold great potential to illuminate hitherto uninterrogated aspects of normal and abnormal brain function, the scope and unusual character of the changes they illicit pose serious challenges to researchers. Uncovering cogent and scalable methods for investigating such data is a matter of great importance if we are to leverage the unique window such atypical substances provide into central aspects of consciousness and abnormal brain function. In the present thesis, we summarize the current state of electrophysiological neuroimaging as it pertains to the study of Psychedelic tryptamines, and demonstrate a number of clear shortcomings in current electrophysiological research on Psychedelics. We also offer some modest methodological contributions to the field. The utility of these contributions is supported by some intriguing, albeit preliminary, empirical findings. In the first chapter, we present the history of neuroscientific research on LSD. LSD has been reported to induce peak shifts in power spectra, alongside decreases in peak amplitude. The fact that these effects are inter-related and most research so far has not sought to disambiguate them is uniformly overlooked in the literature, which we believe may lead to false interpretations. Chapter Two discusses some of the plausible advantages as well as serious barriers to whole-brain connectivity research in MEG, proposing several strategies to overcome these methodological limitations. These include cogent source imaging strategies, novel and recent developments in spectral decomposition, connectivity measures insensitive to volume conduction, and scalable implementations of well-established cross-frequency coupling metrics. We show that these techniques can be extended to a higher resolution cortical and subcortical grid than previously shown. We also discuss a lightweight implementation of non-parametric statistics suitable to such data. Chapter Three serves to demonstrate the efficacy of these procedures, showing empirical results from a whole-brain study of connectivity under LSD in MEG. The fourth and final chapter discusses these results, as well as necessary precautions and promising future directions for this kind of research. It proposes additional computational approaches that might extend the scope of such research and whole-brain electrophysiology more generally. Taken together, the methodological framework proposed in this work overcomes previous limitations endemic not only in Psychedelics research, but electrophysiological research broadly, and sheds new light on central mechanisms underlying these abnormal states of consciousness, as well as important precautions in electrophysiological research.

Made available in DSpace on 2014-12-17T15:28:49Z (GMT). No. of bitstreams: 1 RobsonST_DISSERT.pdf: 350196 bytes, checksum: eaf6055553dc1f6cec39e0f754c20635 (MD5) Previous issue date: 2011-12-02 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Brain oscillation are not completely independent, but able to interact with each other through cross-frequency coupling (CFC) in at least four different ways: power-to-power, phase-to-phase, phase-to-frequency and phase-to-power. Recent evidence suggests that not only the rhythms per se, but also their interactions are involved in the execution of cognitive tasks, mainly those requiring selective attention, information flow and memory consolidation. It was recently proposed that fast gamma oscillations (60 150 Hz) convey spatial information from the medial entorhinal cortex to the CA1 region of the hippocampus by means of theta (4-12 Hz) phase coupling. Despite these findings, however, little is known about general characteristics of CFCs in several brain regions. In this work we recorded local field potentials using multielectrode arrays aimed at the CA1 region of the dorsal hippocampus for chronic recording. Cross-frequency coupling was evaluated by using comodulogram analysis, a CFC tool recently developted (Tort et al. 2008, Tort et al. 2010). All data analyses were performed using MATLAB (MathWorks Inc). Here we describe two functionally distinct oscillations within the fast gamma frequency range, both coupled to the theta rhythm during active exploration and REM sleep: an oscillation with peak activity at ~80 Hz, and a faster oscillation centered at ~140 Hz. The two oscillations are differentially modulated by the phase of theta depending on the CA1 layer; theta-80 Hz coupling is strongest at stratum lacunosum-moleculare, while theta-140 Hz coupling is strongest at stratum oriens-alveus. This laminar profile suggests that the ~80 Hz oscillation originates from entorhinal cortex inputs to deeper CA1 layers, while the ~140 Hz oscillation reflects CA1 activity in superficial layers. We further show that the ~140 Hz oscillation differs from sharp-wave associated ripple oscillations in several key characteristics. Our results demonstrate the existence of novel theta-associated high-frequency oscillations, and suggest a redefinition of fast gamma oscillations / As oscila??es cerebrais n?o s?o completamente independentes, mas capazes de interagir umas com as outras atrav?s de acoplamentos entre frequ?ncias (cross-frequency coupling, doravante CFC) em pelo menos quatro diferentes modalidades: amplitudeamplitude, fase-fase (coer?ncia), fase-frequ?ncia e fase-amplitude. Evid?ncias recentes sugerem que n?o somente os ritmos per se, mas tamb?m as intera??es entre eles est?o envolvidas na execu??o de tarefas cognitivas, principalmente aquelas que requerem aten??o seletiva, transmiss?o de informa??es e consolida??o de mem?rias. Estudos recentes prop?em que oscila??es gama alto (60 150 Hz) transferem informa??es espaciais do c?rtex entorrinal medial para a regi?o CA1 do hipocampo atrav?s do acoplamento com a fase de teta (4 12 Hz). Apesar destas descobertas, entretanto, pouco se sabe sobre as caracter?sticas gerais dos CFCs em diversas regi?es cerebrais. Neste trabalho, registramos potenciais de campo local usando matrizes de multieletrodos implantadas no hipocampo dorsal para registro neural cr?nico. O acoplamento fase-amplitude foi avaliado por meio da an?lise de comodulogramas, uma ferramenta de CFC desenvolvida recentemente (Tort et al. 2008, Tort et al. 2010). Todas as an?lises de dados foram realizadas em MATLAB (MathWorks Inc). Descrevemos duas oscila??es funcionalmente distintas dentro da faixa de frequ?ncia de gama, ambas acopladas ao ritmo teta durante explora??o ativa e sono REM: uma oscila??o com um pico de atividade em ~80 Hz e uma mais r?pida centrada em ~140 Hz. As duas oscila??es s?o diferencialmente moduladas pela fase de teta conforme a camada de CA1; o acoplamento teta-80 Hz ? mais forte no stratum lacunosum-moleculare, enquanto que o acoplamento teta-140 Hz ? mais forte no stratum oriens-alveus. Este perfil laminar sugere que a oscila??o de 80 Hz origina-se das entradas do c?rtex entorrinal para as camadas profundas de CA1, e que a oscila??o de 140 Hz reflete a atividade de CA1 em camadas superficiais. Ademais, n?s mostramos que a oscila??o de 140 Hz difere-se das oscila??es ripples associadas com sharp-waves em diversos aspectos chave. Nossos resultados demonstram a exist?ncia de novas oscila??es de alta frequ?ncia associadas ? teta e sugerem uma redefini??o das oscila??es gama alto