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

Product Information

Similarity rate of biking measurements (triangle pointing right) and simulations (triangle pointing left). 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 as 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 Enders H, Von Tscharner V, Nigg BM. Neuromuscular Strategies during Cycling at Different Muscular Demands. Medicine and science in sports and exercise. 2015;47(7):1450–9. pmid:25380476 Al-Zahrani KS, Bakheit MO. A historical review of gait analysis Reply from the Author. Neurosciences. 2008;13(4):460-. pmid:21063384

Fluctuation in the form of a “random walk”. These are changes around a morphed attractor described with the iteration

The factor 10 6 was introduced for convenience. For simulating the movement ϕ together with (see below) must be chosen to reproduce the statistical spread of the data around the attractor. Loske S, Nuesch C, Byrnes KS, Fiebig O, Scharen S, Mundermann A, et al. Decompression surgery improves gait quality in patients with symptomatic lumbar spinal stenosis. Spine J. 2018.

A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor). RN[1, σ M]( t) represents a normally distributed random element introducing some deviation from a perfect working controlling mechanism. 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 Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos. 2000;10(4):848–63. pmid:12779434Funding: AFF-grand "cyclic human motion - 2019" of the University of Konstanz. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The purpose of this paper was to find a quantitative description of cyclic motion with the capacity to simulate individuals’ characteristic movement. A model was proposed consisting of six contributing parts. Individual attractor, morphing, short time fluctuation, transient effect, control mechanism and sensor noise. Simulations based on this model showed the same distinctive variations as the measured data. In all cases the similarity analysis of same subjects produced higher results— and —compared with different subject combinations— and . Measurements of the respective simulations are clearly identifiable, confirming the model’s suitability for describing cyclic motion. The nine constants together with the subject’s attractor approximations are characteristic for a person’s movement and the influence of the recording sensors. All input, measured data, and simulation results, had a sampling frequency of 500 Hz. Further procedures, including generating graphs, were done after filtering with a ‘triple F low pass filter’ [ 27] with a cutoff frequency of 10 Hz. 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 Broscheid KC, Dettmers C, Vieten M. Is the Limit-Cycle-Attractor an (almost) invariable characteristic in human walking? Gait Posture. 2018;63:242–7. pmid:29778064