Super Attractor: Methods for Manifesting a Life beyond Your Wildest Dreams

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Buchthal F, Schmalbruch H. Contraction Times and Fibre Types in Intact Human Muscle. 1970;79(4):435–52. Bipedal gait, especially walking, has been the most decisive development of homo sapiens to surpass their ancestors and relatives [ 1]. In the past centuries further cyclic motions like swimming, cycling, rowing or skiing came along, to overcome natural obstacles, to facilitate traveling and then as leisure activities. Recently, cyclic motion descriptions have served as biological templates for developments in robotics together with developments in artificial intelligence [ 2]. Although cyclic movements are performed a thousand-fold each day in everyday life, their underlying composition and structure is not fully understood. Hurmuzlu Y, Basdogan C. On the measurement of dynamic stability of human locomotion. J Biomech Eng. 1994;116(1):30–6. pmid:8189711 To exclude the influence of the morphing as much as possible, we calculated a super attractor from 5 independent 1-hour-runs of each individual taken about 5 months before the actual measurements for running. For biking, as we did not have the data from months before,a super attractor was created out of four datasets to compare with the fifth one. Since our hypothesis was that an attractor is stable only within a given interval, the super attractor represents just one possible attractor configuration. It is important to note that these super attractors are independent of the 60 minutes data sets to be examined. Therefore, with the exception of the first minutes being influenced by the transient effect, the comparison should display results not varying much. And finally, the δM can be approximated by

Strogatz SH. Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry, and engineering. Reading, Mass.: Addison-Wesley Pub.; 1994. xi, 498 p. p. When simulating the kinematics and comparing it with real life data, we need to include the measurement error–noise —caused by the sensor characteristics. It can be obtained directly from measuring the output signals of the sensors at rest. The signal of an accelerometer is, subtracting the values caused by the earth’s gravitational field, modeled as white noise. (13) For this reason, we propose a mathematical model of the kinematic of the human cyclic motion based on acceleration data. It allows simulation of cyclic movement and comparison with measured data. We illustrate this model as a superposition of six mathematical terms covering the motion as a (1) limit-cycle attractor, (2) individual attractor morphing, (3) short time random fluctuation in form of “random walk”, (4) the transient effect describing initial oscillations around the attractor at the onset of the activity subsiding with increasing time, (5) a control process being activated when stride variations tend to exceed the morphed attractors’ boundaries, and (6) the influence of noise generated by the measurement device—accelerometers. Thus, this model allows extension of earlier findings specifically about the variability of subjects’ cyclic movement with its fixed and random components. Janssen D, Schöllhorn WI, Lubienetzki J, Fölling K, Kokenge H, Davids K. Recognition of Emotions in Gait Patterns by Means of Artificial Neural Nets. J Nonverbal Behav. 2008;32:79–92.

Discussion

Fig 7. All 5 runs of all 5 subjects compared to their personal, but independent super attractor for minutes 11 to 60. Hurmuzlu Y. Dynamics of bipedal gait: Part II—Stability analysis of a planar five-link biped. Journal of Applied Mechanics. 1993;60(2):337–43. Fluctuation in the form of a “random walk”. These are changes around a morphed attractor described with the iteration

Vieten MM, editor Triple F (F3) Filtering of Kinemaitc Data. ISBS 2004; 2004; Ottawa, Canada: Faculty of Health Science University of Ottawa.Sehle A, Vieten M, Mundermann A, Dettmers C. Difference in Motor Fatigue between Patients with Stroke and Patients with Multiple Sclerosis: A Pilot Study. Front Neurol. 2014;5:279. pmid:25566183 Dynamical systems in the physical world tend to arise from dissipative systems: if it were not for some driving force, the motion would cease. (Dissipation may come from internal friction, thermodynamic losses, or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee. Sehle A, Vieten M, Sailer S, Mundermann A, Dettmers C. Objective assessment of motor fatigue in multiple sclerosis: the Fatigue index Kliniken Schmieder (FKS). J Neurol. 2014;261(9):1752–62. pmid:24952620 Data Availability: All data files are available from zenodo.org under the direct link http://doi.org/10.5281/zenodo.3518415.