We propose a novel class of mixed fluctuations with different orientations and fractal scaling features as a model for anisotropic two-dimensional (2D) trajectories hypothesized to appear in complex systems. Furthermore, we develop the oriented fractal scaling component analysis (OFSCA) to decompose such mixed fluctuations into the original orientation components. In the OFSCA, the original orientations are detected based on the principle that the original angles are orthogonal to the angles with the minimum and maximum scaling exponents of the mixed fluctuations. In our approach, the angle-dependent scaling properties are estimated using the Savitzky–Golay-filter-based detrended moving-average analysis (DMA), which has a higher detrending order than the conventional moving-average-filter-based DMA. To illustrate the OFSCA, we demonstrate that the numerically generated time-series of mixed fractional Gaussian noise (fGn) processes with non-orthogonal orientations and different scaling exponents is successfully decomposed into the original fGn components. We demonstrate the existence of oriented components in the 2D trajectories by applying OFSCA to real-world time-series, such as human postural fluctuations during standing and seismic ground acceleration during the great 2011 Tohoku-oki earthquake.
Introduction. In modern sports, a high level of physical performance of the athlete is due to the functional properties and condition of all body systems. Of particular importance is the assessment of the functional state of the central nervous system. At the same time, the potential risk of injuries increases with each passing year, so one of the main tasks of sports physicians, psychologists, physiologists, especially in high-achievement sports, is to reduce injuries in sports.
The aim of the study was to compare the state of psychophysiological functions of highly qualified athletes who specialize in sports with varying degrees of extremeness (snowboarding, downhill skiing, cross-country skiing).
Material and methods. To determine the state of psychophysiological functions of athletes used diagnostic complex "Diagnostics-1" (MV Makarenko, VS Lyzogub). The group of respondents included qualified athletes engaged in skiing, characterized by the predominance of dynamic speed and a high probability of injury. These sports make special demands primarily on the central nervous system of athletes. In accordance with the purpose of the work, we studied the latent periods of simple visual-motor reaction, simple and complex reaction of choice, the efficiency of sensorimotor activity and the dynamics of nervous processes in the feedback mode, the accuracy of the reaction to a moving object and the ratio of reactions of advance and delay, dynamic muscular endurance of the right and left hands (according to the tapping test), as well as the basic properties of the nervous system namely the functional mobility of nervous processes and the strength of nervous processes.
Results. Athletes with a higher degree of extreme sports and risk of injury (snowboarders and skiers) showed a higher psychophysiological status in terms of strength of nervous processes and indicators of reaction to a moving object, a higher level of dynamic muscular endurance in terms of tapping test.
Conclusions. The identified differences in the state of psychophysiological functions in athletes with varying degrees of extreme sports activities and the level of risk of injury can have prognostic value and be used to optimize sports improvement in these sports.
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