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Human postural control is a complex process, but that is critical to understand in order to reduce the prevalence of occupational falls. Localized muscle fatigue (LMF), altered sensory input, and inter-individual differences (e.g. age and gender) have been shown to influence postural control, and numerous methods have been developed in order to quantify such effects. Recently, methods based on statistical mechanics have become popular, and when applied to center of pressure (COP) data, appear to provide new information regarding the postural control system. This study addresses in particular the stabilogram diffusion and Hurst exponent methods. An existing dataset was employed, in which sway during quiet stance was measured under different visual and surface compliance conditions, among both genders and different age groups, as well as before and after induction of localized muscle fatigue at the ankle, knee, torso, and shoulder. The stabilogram diffusion method determines both short-term and long-term diffusion coefficients, which correspond to open- and closed-loop control of posture, respectively. To do so, a "critical point" (or critical time interval) needs to be determined to distinguish between the two diffusion regions. Several limitations are inherent in existing methods to determine this critical point. To address this, a new algorithm was developed, based on a wavelet transform of COP data. The new algorithm is able to detect local maxima over specified frequency bands within COP data; therefore it can identify postural control mechanisms correspondent to those frequency bands. Results showed that older adults had smaller critical time intervals, and indicating that sway control of older adults was essentially different from young adults. Diffusion coefficients show that among young adults, torso LMF significantly compromised sway stability. In contrast, older adults appeared more resistance to LMF. Similar to earlier work, vision was found to play a crucial role in maintaining sway stability, and that stability was worse under eyes-closed (EC) than eyes-opened (EO) conditions. It was also found that the short-term Hurst exponent was not successful at detecting the effects of LMF on sway stability, likely because of a small sample size. The new critical point identification algorithm was verified to have better sensitivity and reliability than the traditional approach. The new algorithm can be used in future work to aid in the assessment of postural control and the mechanisms underlying this control. / Master of Science

Die Charakterisierung hochdimensionaler Systeme mit Lyapunov-Instabilität wird durch das Lyapunov-Spektrum und die zugehörigen Lyapunov-Vektoren ermöglicht. Für eine Vielzahl von derartigen Systemen (Coupled-Map-Lattices, Hartkugel-Systeme, Systeme mit ausgedehnten Potentialen ...) konnte durch die Untersuchung der Lyapunov-Vektoren die Existenz von hydrodynamischen Lyapunov-Moden nachgewiesen werden. Diese kollektiven Anregungen zeigen sich in Lyapunov-Vektoren, deren Lyapunov-Exponenten dem Betrage nach am kleinsten sind. Da Lyapunov-Exponenten charakteristische Zeitskalen innerhalb der Systeme repräsentieren, ist durch die Lyapunov-Moden eine Untersuchung des Langzeitverhaltens möglich. In dieser Arbeit werden die hydrodynamischen Lyapunov-Moden durch Molekulardynamiksimulationen von mehrkomponentigen Lennard-Jones-Flüssigkeiten untersucht. Die Charakterisierung der Lyapunov-Moden zeigt im weiteren eine Ähnlichkeit zu Dispersionsrelationen von Phononen.

This thesis focuses on possibility of chaotic (specially economic) time-series prediction. Chaotic time-series are unpredictable in long-term due to their high sensitivity on initial conditions. Nevertheless, their behavior should be more or less predictable in short-term. Goal of this thesis is to show, how much and if any prediction, is possible by non-linear prediction method, and try to reveal or to reject presence of chaotic behavior in them. Work is split into three chapters. Chapter One briefly introduces chosen important concepts and methods from this area. In addition, to describe some prediction methods, there are outlined which indicators and methods are possible to use in order to find possibilities and boundaries of this prediction. Chapter Two is focused on modifications of FracLab software, which is used for create this prediction. Last chapter is experimental. Besides the description of examined time-series and methods, it includes discussion of results.

The presented diploma thesis deals with the problem of determining the stress singularity exponent of the V-notch. This task can be divided into two parts. The first deals with the theoretical background, that means the basic relations of mechanics and the basic concepts of fracture mechanics. The second part deals with the elaboration of the Williams method and the creation of a program for calculating the stress singularity exponent.

The thesis deals with the design and optimization of artificial neural networks (specifically nonlinear autoregressive networks) and their subsequent usage in predictive application of stock market time series.

The objective of this diploma thesis is the stress-strain analysis of the crack terminating at the orthotropic bi-material interface suggested as the plane problem of the linear fracture mechanics. The first part is engaged in basic relations of the linear fracture mechanics. The second part is focused on the singularity exponent evaluation for the crack impinging and generally inclined with respect to the bi-material interface. It follows the determination of the generalized stress intensity factors applying the analytical-numerical approach represented by the finite element analysis. The last part of this work is focused on the testing of algorithms applied to the specific crack and bi-material interface configurations. A conclusion discusses the influence of the bi-material mechanical properties and the angel of the crack inclination to the obtained numerical results.