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

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Fig 1. Schematic two-dimensional depiction of the three-dimensional recognition horizon (red) and compared attractor (blue).

RU[ α, β] represents random generation with a uniform characteristic within the interval [ α, β]. With this definition the standard deviation of the random walk depends on the sampling frequency f S. Since the random walk must not be dependent on the specifics of a measurement–the sampling frequency f S -, we introduce a parameter ϕ (random walk’s strength), which does not change with the sampling frequency. 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 byHere, l is the data number. An aberration from the attractor can happen in any direction. We describe this using the angles ϑ and φ. Their actual values are random having a uniform distribution on the sphere with the polar and azimuthal angles: Data Availability: All data files are available from zenodo.org under the direct link http://doi.org/10.5281/zenodo.3518415.

Discover a faster, simpler path to publishing in a high-quality journal. PLOS ONE promises fair, rigorous peer review, Similarity rate of biking measurements (triangle pointing right) and simulations (triangle pointing left).

Conclusion

Barnes KR, Kilding AE. Strategies to improve running economy. Sports Medicine. 2015(45(1)):37–56. pmid:25164465 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.