In performing manual tasks, muscles are voluntarily contracted in order to produce force and orient the limb in the desired direction. Many occupational tasks are associated with frequent musculoskeletal disorders. In tasks involving skilful manipulation, very frequently the forces are focused on the upper limb and neck. Upper extremity cumulative trauma disorders are among the more common worker related injuries. These muscle disorders may be related to repetitive exertions, excessive muscle loads and extreme postures. One of the major challenges is to quantify the muscle load and researchers have tried various measures to quantify muscle load. Joint mechanical impedance can be a robust method to quantify muscle load. Joint mechanical impedance characterizes the dynamic torque-angle relationship of the joint. Joint impedance has been measured by earlier researchers, for limited tasks, by imparting force (or angle) perturbations on the joint and relating resultant angular (or force) changes. The joint impedance gives a quantitative measure related to muscle co-contraction level. Measurement of the mechanical impedance at the workplace may provide useful information relevant to the understanding of upper limb disorders. Electromyogram (EMG) is the electrical activity of the muscle. Usually, an estimate of the EMG amplitude is obtained from the raw waveform recorded from the surface of the skin. EMG amplitude estimates can be used to non-invasively estimate torque about joints. Presently, there exists no means by which mechanical impedance can be estimated non-invasively (i.e., without external perturbations). Therefore, we proposed the use of EMG to noninvasively estimate the joint mechanical impedance. Our objective in this project was to determine the extent to which surface EMG can be used to estimate mechanical impedance. Simulation studies were first performed to understand the extent to which this tool could be useful and to determine methods to be used for the experiment. The simulations were followed by evaluating and estimating mechanical impedance using data collected from one experimental subject. Simulations helped to devise processing techniques for the measured signals and also to determine the length of data to be collected. Low pass filters for derivatives (used in the development of impedance estimates) were designed. Subtracting out a polynomial was the best approach to attenuate a low frequency drift (artifact) that occurs in torque measurements. Thirty seconds of data provided impedance estimates with a relative error of 5% when EMG amplitude estimates with SNR of 15 were used. Experimental data from constant-posture, slowly force-varying background torque level showed that the elbow joint system behaved like a second order linear system between 2 Hz and 10 Hz. Co-contraction by subjects during experiments caused impedance estimates to be unexpectedly high even at low background torque. Further experiments would need to be conducted with the subjects being instructed to avoid co-contraction.

Cette thèse explore théoriquement et empiriquement certains aspects de la formation et de l’évolution des prix des actifs financiers observés en haute fréquence. Nous commençons par l’étude de la dynamique jointe de l’option et de son sous-jacent. Les données haute fréquence rendant observable le processus de volatilité réalisée du sous-jacent, nous cherchons à savoir si cette information est utilisée pour fixer les prix des options. Nous trouvons que le marché ne l’exploite pas. Les modèles de volatilité stochastique sont donc à considérer comme des modèles à forme réduite. Cette étude permet néanmoins de tester la pertinence d’une mesure de couverture empirique que nous appelons delta effectif. C’est la pente de la régression des rendements des prix de l’option sur ceux du sous-jacent. Elle fournit un indicateur de couverture assez satisfaisant et indépendant de toute modélisation. Pour la dynamique des prix, nous nous tournons dans les chapitres suivants vers des modèles plus explicites de la microstructure du marché. L’une des caractéristiques de l’activité de marché est son regroupement, ou clustering. Les processus de Hawkes, processus ponctuels présentant cette caractéristique, fournissent donc un cadre mathématique adéquat pour l’étude de cette activité. La représentation Markovienne de ces processus, ainsi que leur caractère affine quand le noyau est exponentiel, permettent de recourir aux puissants outils analytiques que sont le générateur infinitésimal et la formule de Dynkin pour calculer différentes quantités qui leur sont reliées, telles que les moments ou autocovariances du nombre d’évènements sur un intervalle donné. Nous commençons par un cadre monodimensionnel, assez simple pour éclairer la démarche, mais suffisamment riche pour permettre des applications telles que le groupement des instants d’arrivée d’ordres de marché, la prévision de l’activité de marché à venir sachant l’activité passée, ou la caractérisation de formes inhabituelles, mais néanmoins observées, de signature plot où la volatilité mesurée décroît quand la fréquence d’échantillonnage augmente. Nos calculs nous permettent aussi de rendre la calibration des processus de Hawkes instantanée en recourant à la méthode des moments. La généralisation au cas multidimensionnel nous permet ensuite de capturer, avec le clustering, le phénomène de retour à la moyenne qui caractérise aussi l’activité de marché observée en haute fréquence. Des formules générales pour le signature plot sont alors obtenues et permettent de relier la forme de celui-ci à l’importance relative du clustering ou du retour à la moyenne. Nos calculs permettent aussi d’obtenir la forme explicite de la volatilité associée à la limite diffusive, connectant la dynamique de niveau microscopique à la volatilité observée macroscopiquement, par exemple à l’échelle journalière. En outre, la modélisation des activités d’achat et de vente par des processus de Hawkes permet de calculer l’impact d’un méta ordre sur le prix de l’actif. On retrouve et on explique alors la forme concave de cet impact ainsi que sa relaxation temporelle. Les résultats analytiques obtenus dans le cas multidimensionnel fournissent ensuite le cadre adéquat à l’étude de la corrélation. On présente alors des résultats généraux sur l’effet Epps, ainsi que sur la formation de la corrélation et du lead lag. / This thesis explores theoretical and empirical aspects of price formation and evolution at high frequency. We begin with the study of the joint dynamics of an option and its underlying. The high frequency data making observable the realized volatility process of the underlying, we want to know if this information is used to price options. We find that the market does not process this information to fix option prices. The stochastic volatility models are then to be considered as reduced form models. Nevertheless, this study tests the relevance of an empirical hedging parameter that we call effective delta. This is the slope of the regression of option price increments on those of the underlying. It proves to be a satisfactory model-independent hedging parameter. For the price dynamics, we turn our attention in the following chapters to more explicit models of market microstructure. One of the characteristics of the market activity is its clustering. Hawkes processes are point processes with this characteristic, therefore providing an adequate mathematical framework for the study of this activity. Moreover, the Markov property associated to these processes when the kernel is exponential allows to use powerful analytical tools such as the infinitesimal generator and the Dynkin formula to calculate various quantities related to them, such as moments or autocovariances of the number of events on a given interval. We begin with a monovariate framework, simple enough to illustrate the method, but rich enough to enable applications such as the clustering of arrival times of market orders, prediction of future market activity knowing past activity, or characterization of unusual shapes, but nevertheless observed, of signature plot, where the measured volatility decreases when the sampling frequency increases. Our calculations also allow us to make instantaneous calibration of the process by relying on the method of moments. The generalization to the multidimensional case then allow us to capture, besides the clustering, the phenomenon of mean reversion, which also characterizes the market activity observed in high frequency. General formulas for the signature plot are then obtained and used to connect its shape to the relative importance of clustering or mean reversion. Our calculations also allow to obtain the explicit form of the volatility associated with the diffusive limit, therefore connecting the dynamics at microscopic level to the macroscopic volatility, for example on a daily scale. Additionally, modelling buy and sell activity by Hawkes processes allows to calculate the market impact of a meta order on the asset price. We retrieve and explain the usual concave form of this impact as well as its relaxation with time. The analytical results obtained in the multivariate case provide the adequate framework for the study of the correlation. We then present generic results on the Epps effect as well as on the formation of the correlation and the lead lag.

Obesity is a highly cited risk factor for knee osteoarthritis (OA) associated with increased risk of development of OA and accelerated disease progression. Rates of obesity are increasing internationally, and while obesity is well established as a risk factor, the precise role of obesity in knee OA pathogenesis and progression is not as clearly understood. Mechanical loading has been implicated as an important factor in knee OA initiation and progression. The purpose of this thesis was to further examine the roles of moderate knee OA disease presence and obesity on knee joint mechanics during gait, and to characterize their mechanical interaction. Two methods have been applied. First, principal component analysis has been applied to resultant waveforms from gait analysis and second, a sagittal plane joint contact force model has been applied. Using both methods, statistical differences in biomechanical loading has been associated with obesity, moderate knee OA, and their interaction.