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

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Bramble DM, Lieberman DE. Endurance running and the evolution of Homo. Nature. 2004;432(7015):345–52. pmid:15549097

With sign(…)being the signum and Θ(…)the step function. We set the maximal acceleration change to τ = 80 ms analogous to the style of a muscle’s timely response [ 24] with acceleration effectively lasting t M = 4⋅ τ = 320 ms, to obtain at attractor point j. Here b is the controlling constant and σ k( j) the attractor’s standard deviation, which is divided by the average of the attractor’s deviation 〈 σ k〉. This takes care of the changing width of the acceleration bundle. The correction term, being activated at time t b, is modeled asAs known from previous studies [ 21, 22] the influence of morphing and transient effect is small compared with the differences between individuals. While morphing is present in all trials, the transient effect is not observable in all cases (20 of 25 cases for running, 8 of 25 cases for biking). For biking, the transient effect is less prominent compared to running. We suspect the fixation of the legs with the foot connected to the pedal and the hip very much fixed onto the saddle, there is limited freedom in movement variation. The tibia position and its associated acceleration is often settled onto the attractor from the start onwards. A different situation is seen in running, where the kinematic chain is unfixed near the location of the accelerometer at the distal end of the tibia. Here the probability to start a movement close to the subject’s attractor, resulting in no visible transient effect, is small. Interestingly, the most experienced runners show the least transient effect. Fig 1. Schematic two-dimensional depiction of the three-dimensional recognition horizon (red) and compared attractor (blue). 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

Dingwell JB, Kang HG. Differences between local and orbital dynamic stability during human walking. J Biomech Eng. 2007;129(4):586–93. pmid:17655480 Data Availability: All data files are available from zenodo.org under the direct link http://doi.org/10.5281/zenodo.3518415. Limit-Cycle-Attractor can be regarded as the average of all cycles. This however, is an idealized definition, which cannot fully be met, since this would call for averaging of an infinite number of cycles. Instead, we approximate the attractor by a finite number of cycles, which for later examples we chose the number of complete cycles within a specified minute of the data collection. Clermont CA, Benson LC, Osis ST, Kobsar D, Ferber R. Running patterns for male and female competitive and recreational runners based on accelerometer data. Journal of sports sciences. 2019;37(2):204–11. pmid:29920155 Still the question remains, how to rate the attractors’ differences, when attractor approximations are calculated by averaging the cycles of different time intervals. Does it simply mean that when doing the averaging over longer time periods these differences will almost completely vanish? Or, does it mean that attractors are changing with time, even if these changes are small? So far, we do not have enough data to answer this question with certainty. However, from the results above we suggest that the second statement is more likely. There is a theoretical argument for this statement as well. While developing the mathematical description of cyclic motion, our first approach was without morphing. The idea was to have an attractor not dependent on time and the fluctuation based on a “random walk” characteristic only. This construct, however, did not allow describe the full data variability.Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos. 2000;10(4):848–63. pmid:12779434 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.