Continuous and discrete properties of stochastic processes

This thesis considers the interplay between the continuous and discrete properties of random stochastic processes. It is shown that the special cases of the one-sided Lévy-stable distributions can be connected to the class of discrete-stable distributions through a doubly-stochastic Poisson transform. This facilitates the creation of a one-sided stable process for which the N-fold statistics can be factorised explicitly. The evolution of the probability density functions is found through a Fokker-Planck style equation which is of the integro-differential type and contains non-local effects which are different for those postulated for a symmetric-stable process, or indeed the Gaussian process. Using the same Poisson transform interrelationship, an exact method for generating discrete-stable variates is found. It has already been shown that discrete-stable distributions occur in the crossing statistics of continuous processes whose autocorrelation exhibits fractal properties. The statistical properties of a nonlinear filter analogue of a phase-screen model are calculated, and the level crossings of the intensity analysed. It is found that rather than being Poisson, the distribution of the number of crossings over a long integration time is either binomial or negative binomial, depending solely on the Fano factor. The asymptotic properties of the inter-event density of the process are found to be accurately approximated by a function of the Fano factor and the mean of the crossings alone

Continuous and discrete properties of stochastic processes

This thesis considers the interplay between the continuous and discrete properties of random stochastic processes. It is shown that the special cases of the one-sided Lévy-stable distributions can be connected to the class of discrete-stable distributions through a doubly-stochastic Poisson transform. This facilitates the creation of a one-sided stable process for which the N-fold statistics can be factorised explicitly. The evolution of the probability density functions is found through a Fokker-Planck style equation which is of the integro-differential type and contains non-local effects which are different for those postulated for a symmetric-stable process, or indeed the Gaussian process. Using the same Poisson transform interrelationship, an exact method for generating discrete-stable variates is found. It has already been shown that discrete-stable distributions occur in the crossing statistics of continuous processes whose autocorrelation exhibits fractal properties. The statistical properties of a nonlinear filter analogue of a phase-screen model are calculated, and the level crossings of the intensity analysed. It is found that rather than being Poisson, the distribution of the number of crossings over a long integration time is either binomial or negative binomial, depending solely on the Fano factor. The asymptotic properties of the inter-event density of the process are found to be accurately approximated by a function of the Fano factor and the mean of the crossings alone

A COMPUTATIONAL BIOMECHANICS STUDY TO INVESTIGATE THE EFFECT OF MYOELECTRIC STIMULATION ON PERONEAL MUSCLES IN PREVENTING INVERSION-TYPE ANKLE LIGAMENTOUS SPRAIN INJURY

A three-dimensional multi-body lower limb model with 16 bones and 22 ligaments was developed to study ankle ligamentous inversion sprain. A male athlete who was diagnosed with a grade I anterior talofibular ligament (ATaFL) sprain during an accidental injury in laboratory in a published report. His ankle kinematics injury data profile was computed. The effect of delivering myoelectric stimulation on peroneal muscles was simulated as torques during ankle inversion. Largest strain in the ATaFL was 8.3%, 9.0% and 11.4%, respectively, at different inversion velocity thresholds of 300 deg/s, 400 deg/s and 500 deg/s. A ligament strain/sprain more than 10-15% would lead to a ligament tear suggesting that applied muscle moments could successfully prevent ankle inversion sprain when an injury identification threshold does not reach 400 deg/s

A COMPUTATIONAL BIOMECHANICS STUDY TO INVESTIGATE THE EFFECT OF MYOELECTRIC STIMULATION ON PERONEAL MUSCLES IN PREVENTING INVERSION-TYPE ANKLE LIGAMENTOUS SPRAIN INJURY

A three-dimensional multi-body lower limb model with 16 bones and 22 ligaments was developed to study ankle ligamentous inversion sprain. A male athlete who was diagnosed with a grade I anterior talofibular ligament (ATaFL) sprain during an accidental injury in laboratory in a published report. His ankle kinematics injury data profile was computed. The effect of delivering myoelectric stimulation on peroneal muscles was simulated as torques during ankle inversion. Largest strain in the ATaFL was 8.3%, 9.0% and 11.4%, respectively, at different inversion velocity thresholds of 300 deg/s, 400 deg/s and 500 deg/s. A ligament strain/sprain more than 10-15% would lead to a ligament tear suggesting that applied muscle moments could successfully prevent ankle inversion sprain when an injury identification threshold does not reach 400 deg/s

The Practices of Green Supply Chain Management towards Corporate Performances in Construction Industry

Green Supply Chain Management (GSCM) practices has different impact on the corporate performances while practitioners are not willing to implement practices that is irrelevant to their organization. Hence, to ensure the most appropriate investment on GSCM is implemented, this study is conducted to identify the relationship between GSCM practices and corporate performances in Malaysia construction industry. To conduct a literature review to figure the relationship between GSCM practices and corporate performances. Systematic literature review method is adopted in data collection stage. The findings of the study show that the green practices are correlated to the corporate performances and a comprehensive conceptual framework is formed from this study to describe the relationships between GSCM practices and corporate performances in Malaysia construction industry. Research on GSCM in Malaysia is still less in construction industry. However, the findings provide crucial insights for potential practitioners due to it consistency with prior studies which are related to GSCM in other industries and countries. Implementation of GSCM improves corporate performances in various dimensions. The construction industry should understand the functions and relationship of each element in GSCM to achieve best performance outcome in the form they desired. A comprehensive conceptual framework which shows the relationships of GSCM and its impact construction industry which allow the potential practitioners to understand the potential improvement in corporate performances is constructed through the systematic literature review