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Over the years analysts have used the EM algorithm to obtain maximum likelihood estimates from incomplete data for various models. The general algorithm admits several appealing properties such as strong global convergence; however, the rate of convergence is linear which in some cases may be unacceptably slow. This work is primarily concerned with applying Anderson acceleration to the EM algorithm for Gaussian mixture models (GMM) in hopes of alleviating slow convergence. As preamble we provide a review of maximum likelihood estimation and derive the EM algorithm in detail. The iterates that correspond to the GMM are then formulated and examples are provided. These examples show how faster convergence is experienced when the data are well separated, whereas much slower convergence is seen whenever the sample is poorly separated. The Anderson acceleration method is then presented, and its connection to the EM algorithm is discussed. The work is then concluded by applying Anderson acceleration to the EM algorithm which results in reducing the number of iterations required to obtain convergence.

"In electronic structure computations, it is necessary to set up and solve a certain nonlinear eigenvalue problem to identify materials. In this dissertation, we first introduce the nonlinear eigenvalue problem and the currently prevailing Self-Consistent Field (SCF) method accelerated by the Anderson acceleration method. We then compare the Anderson acceleration method with the well-known Generalized Minimal Residual (GMRES) method and show that they are essentially equivalent when applied to linear systems. After that, we study a linearly constrained least-squares problem embedded in the Anderson procedure. We use numerical experiments to illustrate the convergence properties. Finally, we give a summary of our work and an outline of future research."

The sternocleidomastoid (SCM) and upper trapezius (UT) muscles are the primary dynamic stabilizers of the head and neck and likely attenuate head acceleration with direct and indirect impacts. Increasing the strength of the SCM and UT through cervical resistance training has been recommended to prevent concussions in football players. The purpose of this study was to examine the effects of an eight-week isoinertial cervical resistance training program on SCM and UT muscle activity (EMG) and kinematic responses of the head and neck during a standard football tackle in college-aged males. Sixteen college-aged males (21.6 ± 2.8 y, 94.6 ± 13.3 kg) with previous high school football or rugby playing experience completed an eight-week isoinertial cervical resistance training program consisting of three sets of 10 repetitions of neck extension, flexion, right and left lateral flexion at 60-80% of 10 repetition maximum two to three times a week. Isometric cervical strength, neck girth, EMG, and kinematic responses of the head and neck during a standard football tackle were measured before and after training. All kinematic data were gathered using a three-dimensional motion capturing system. Training resulted in 7 and 10% increases in isometric cervical extension and left lateral flexion strength, respectively, but no changes were seen in isometric flexion or right lateral flexion strength or neck girth. Additionally, training had no influence on the EMG responses of the SCM or UT, peak linear (7.23 vs. 7.59 g, p = 0.115; pre- vs. post-training) or angular (431.96 vs. 452.37 rad/s2, p = 0.864) head accelerations during the standard football tackle. The UT demonstrated approximately 40% higher absolute EMG activity than the SCM during tackling both before and after training. Under the current experimental conditions, despite modest increases in isometric cervical extension and left lateral flexion strength, the eight-week isoinertial cervical resistance training program failed to augment dynamic stabilization of the head and neck during a standard football tackle in college-aged males. Future research should examine the effects of both slow speed load-intensive and high speed low-to-moderate load intensity isoinertial training as well as plyometric training in decreasing head acceleration during football tackling for injury prevention purposes.

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This thesis addresses a central topic in auroral physics, namely particle accelerationproducing intense aurora as well as energetic plasma outflow. Cluster satellitemeasurements of electric and magnetic fields, electrons and ions, collected across auroralfield lines, are used to study various aspects of the quasi-static auroral accelerationregion (AAR), its relation to the auroral density cavity, and the relative role of quasistaticand Alfvénic acceleration for producing aurora.The acceleration potential structures and electro-dynamical features of a large-scaleauroral surge is studied based on data from the Cluster satellites, crossing differentmagnetic local time (MLT) sectors of a surge-horn system. This allows snapshots of theacceleration potential structure and of the current systems to be provided, including thefield-aligned current closure for the different segments of the surge-horn aurora.The relative role of quasi-static and Alfvénic acceleration for producing auroral arcs isaddressed for the case of a large-scale substorm surge, crossed by the Cluster C2 satellite. Thetwo contributions to the downward electron energy flux is estimated for each of the smallerscalearc structures crossed by C2 within and adjacent to the large-scale surge. For these, thequasi-static acceleration typically dominates, except for the polar cap boundary arc, and in thesurge head, where the Alfvénic contribution is significant.The occurrence of intense electric fields and associated plasma densities versus altitude andMLT is the subject of a statistical study based on 9.5 years of Cluster data, collected ataltitudes between 2 and 4 RE. Intense arc-associated electric fields occur in two altituderegions, separated by a gap around 2.8 RE. The low-altitude fields are interpreted as mainlyquasi-static and the high-altitude fields as mainly Alfvénic. The results which are supportedby estimates of the (ΔE/ΔB)/VA ratio, indicate that, on the average, the quasi-static fieldsextend up to 2.6 RE, above which a transition to Alfvénic fields occur.The auroral density cavity, intimately associated with the auroral acceleration process, wasthe subject of a statistical study based on Cluster data, collected between 2002 and 2007, ataltitudes between 2.0 RE and 5.5 RE. Decreasing electron densities are observed between 2 and 3.3 RE, and between 4.6 and 5.5 RE, corresponding to climbing the parallel potential hillof the AAR. Furthermore, the density is found to decrease while ascending above the AAR,indicating that the cavities are not necessarily confined by it. / <p>QC 20141110</p>

The primary objective of this study was to determine the acceleration characteristics of spinal manipulative therapy (SMT) and whether patient anthropometric parameters correlated with the SMT kinematic parameters. For this, a wireless tri-axial accelerometer was taped to the dorsum of a clinician’s hand to record the accelerations generated during clinical treatment of 95 symptomatic patients. Peak acceleration magnitudes differed significantly between spinal levels (p<0.0001; lumbar > cervical > thoracic = sacroiliac). The latencies of these peaks were also significantly different (p<0.0001; lumbar < cervical = thoracic < sacroiliac). Within a given spinal level, acceleration amplitudes varied over a wide range with temporal parameters remaining relatively constant. Overall, anthropometric parameters were poorly correlated with SMT parameters. In summary, distinct acceleration amplitudes were observed across spinal levels with relatively constant temporal factors. Thus, clinicians appear to vary the magnitude rather than the duration of the SMT thrust.

The primary objective of this study was to determine the acceleration characteristics of spinal manipulative therapy (SMT) and whether patient anthropometric parameters correlated with the SMT kinematic parameters. For this, a wireless tri-axial accelerometer was taped to the dorsum of a clinician’s hand to record the accelerations generated during clinical treatment of 95 symptomatic patients. Peak acceleration magnitudes differed significantly between spinal levels (p<0.0001; lumbar > cervical > thoracic = sacroiliac). The latencies of these peaks were also significantly different (p<0.0001; lumbar < cervical = thoracic < sacroiliac). Within a given spinal level, acceleration amplitudes varied over a wide range with temporal parameters remaining relatively constant. Overall, anthropometric parameters were poorly correlated with SMT parameters. In summary, distinct acceleration amplitudes were observed across spinal levels with relatively constant temporal factors. Thus, clinicians appear to vary the magnitude rather than the duration of the SMT thrust.

Thesis (Ph.D.)--Tufts University, 2001. / Adviser: Alexander Vilenkin. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 108-114). Access restricted to members of the Tufts University community. Also available via the World Wide Web;