<p>A brain-computer interface, BCI, is a technical system that allows a person to control the external world without relying on muscle activity. This thesis presents an EEG based BCI designed for automatic classification of two dimensional hand movements. The long-term goal of the project is to build an intuitive communication system for operation by people with severe motor impairments. If successful, such system could for example be used by a paralyzed patient to control a word processor or a wheelchair.</p><p>The developed BCI was tested in an offine pilot study. In response to an external cue, a test subject moved a joystick in one of four directions. During the movement, EEG was recorded from seven electrodes mounted on the subject's scalp. An autoregressive model was fitted to the data, and the extracted coefficients were used as input features to a neural network based classifier. The classifier was trained to recognize the direction of the movements. During the first half of the experiment, real physical movements were performed. In the second half, subjects were instructed just to imagine the hand moving the joystick, but to avoid any muscle activity.</p><p>The results of the experiment indicate that the EEG signals do in fact contain extractable and classifiable information about the performed movements, during both physical and imagined movements.</p>

A brain-computer interface, BCI, is a technical system that allows a person to control the external world without relying on muscle activity. This thesis presents an EEG based BCI designed for automatic classification of two dimensional hand movements. The long-term goal of the project is to build an intuitive communication system for operation by people with severe motor impairments. If successful, such system could for example be used by a paralyzed patient to control a word processor or a wheelchair. The developed BCI was tested in an offine pilot study. In response to an external cue, a test subject moved a joystick in one of four directions. During the movement, EEG was recorded from seven electrodes mounted on the subject's scalp. An autoregressive model was fitted to the data, and the extracted coefficients were used as input features to a neural network based classifier. The classifier was trained to recognize the direction of the movements. During the first half of the experiment, real physical movements were performed. In the second half, subjects were instructed just to imagine the hand moving the joystick, but to avoid any muscle activity. The results of the experiment indicate that the EEG signals do in fact contain extractable and classifiable information about the performed movements, during both physical and imagined movements.

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Instantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order. We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix. Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs. / Master of Science

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).

Le premier chapitre examine les caractéristiques statistiques à long terme des rendements financiers en France et aux USA. Les propriétés des différents actifs font apparaître qu’à long terme les actions procurent un risque sensiblement moins élevé. En outre, les propriétés de retour à la moyenne des actions justifient qu’elles soient utilisées dans une stratégie de cycle de vie comme « option par défaut » de plans d’épargne retraite. Le chapitre deux fournit une explication au débat sur l'hypothèse d’efficience des marchés. La cause du débat est souvent attribuée à la petite taille des échantillons et à la faible puissance des tests statistiques dédiés. Afin de contourner ce problème, nous utilisons l'approche développée par Campbell et Viceira (2005) qui utilisent une méthode VAR pour mettre en évidence l’existence de retour vers la moyenne dans le cours des actifs risqués.Le troisième chapitre évalue la vitesse de convergence des cours des actions. Un moyen classique pour caractériser la vitesse de retour vers la moyenne est la « demi-vie ». En comparant les indices boursiers de quatre pays développés (États-Unis, Royaume-Uni, France et Japon) sur la période 1950-2014, nous établissons une vitesse de convergence significative, avec une demi-vie entre 4,0 et 5,8 ans.Le dernier chapitre présente les résultats d'un modèle conçu pour étudier les interactions entre la démographie et les régimes de retraite. Afin d’étudier les risques inhérents à l’utilisation des revenus du capital pour financer les retraites, nous utilisons un « Trending OU process » au lieu d’un MBG classique pour modéliser les rendements. Pour un épargnant averse au risque le marché pourrait concurrencer les régimes par répartition. / Chapter one examines the long run statistical characteristics of financial returns in France and the USA for selected assets. This study clearly shows that the returns’ distributions diverge from the Gaussian strategy as regards longholding periods. Thereafter we analyze the consequences of the non-Gaussian nature of stock returns on default-option retirement plans.Chapter two provides a reasonable explanation to the strong debate on the Efficient Market Hypothesis. The cause of the debate is often attributed to small sample sizes in combination with statistical tests for mean reversion that lackpower. In order to bypass this problem, we use the approach developed by Campbell and Viceira (2005) who have settled a vectorial autoregressive methodology (VAR) to measure the mean reversion of asset returns.The third chapter evaluates the speed of convergence of stock prices. A convenient way to characterize the speed of mean reversion is the half-life. Comparing the stock indexes of four developed countries (US, UK, France and Japan) during the period 1950-2014, we establish significant mean reversion, with a half-life lying between 4,0 and 5,8 years.The final chapter provides some results from a model built in order to study the linked impacts of demography and economy on the French pension scheme. In order to reveal the risks that are contained in pension fund investment, we use a Trending Ornstein-Uhlenbeck process instead of the typical GBM for modeling stock returns. We find that funded scheme returns, net of management fees, are slightly lower thanthe PAYG internal rate of return.