The method based on two-dimensional stochastic process was used to examine the short-term postural sway under eyes-open and eyes-closed conditions. Obtained parameters, i.e., matrix of the fluctuation strength and friction coefficient, describe the stochastic activity of the muscles of the lower limbs as well as mechanisms compensating that activity. The standard force platform was used to measure the center of pressure displacements. In this investigation 17 control subjects and 22 morbid obese subjects were included. It is shown that the method is useful in the study of the postural control system of morbid obese subjects. The muscles responsible for postural control in these subjects have exhibited larger stochastic activity, than these muscles in non-obese subjects. However morbid obese as well as non-obese subjects compensate additionally enlarged level of muscles activity after closure of their eyes. The morbid obesity causes an increase of the muscles' force but does not cause the impairment of the postural control system.
After summaries on Rayleigh's distribution and Wigner's surmise, the time evolution of Rayleigh-Wigner's statistics is studied and a suitable diffusion type equation is proposed. Also the variance and kurtosis of time evolution of Rayleigh's distribution are calculated. Obtained results may be useful in description of physical, social and biological processes.
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