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

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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. Hurmuzlu Y, Basdogan C. On the measurement of dynamic stability of human locomotion. J Biomech Eng. 1994;116(1):30–6. pmid:8189711 Buchthal F, Schmalbruch H. Contraction Times and Fibre Types in Intact Human Muscle. 1970;79(4):435–52. 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 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.

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. 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 Hausdorff JM, Zemany L, Peng C, Goldberger AL. Maturation of gait dynamics: stride-to-stride variability and its temporal organization in children. J Appl Physiol (1985). 1999;86(3):1040–7. Vieten MM, editor Triple F (F3) Filtering of Kinemaitc Data. ISBS 2004; 2004; Ottawa, Canada: Faculty of Health Science University of Ottawa. 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.There exist two types of models describing human cyclic motion—theory driven and data driven [ 18]–both with its own strong and weak aspects. For example, a theory driven model as described by Gerritsen et al. [ 19] gives insight into the working of seven muscle groups within the lower extremities. The necessity of keeping the model manageable, in the mentioned paper by using a 2-dimensional rigid body model, leads to deviations from the actual movement. On the other hand the data driven model of Janssen et al. [ 18] was able to detect the influence of emotions onto the movement pattern. They applied deep machine learning by using artificial neural nets, allowing identification of subtle effects. While here the detection movement characteristics caused by emotions is nicely achieved, the specifics of the gait changes remained undetected. With the present paper we attempt a compromise, by not having to rely on anatomy and muscle function, but still trying to understand kinematic processes and the movement pattern quantitatively. A study on cycling at two different power outputs (150 W and 300 W) at a cadence of 90 rpm [ 20] found differences in the muscle activities detected via EMG, while kinematic data stayed almost unchanged. This result together with the stability of the individual’s attractor over time and after rehabilitation [ 21, 22] is motivation to examine the possibility to quantitatively describe movement without the knowledge of muscle activity. Discover a faster, simpler path to publishing in a high-quality journal. PLOS ONE promises fair, rigorous peer review, 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. The transient effect is a temporary oscillation around the attractor at the beginning of a cyclic movement. The starting value of the oscillation might be very individual, specific to the subject, and having a part of the starting value occurring by sheer chance. We model the deviation as the solution of a damped harmonic oscillator, where the transient term can be viewed as the departure from the morphed attractor 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

Alligood KT, Sauer T, Yorke JA. Chaos: an introduction to dynamical systems. New York: Springer; 1997. xvii, 603 p. p. Nashner LM. Balance adjustments of humans perturbed while walking. J Neurophysiol. 1980;44(4):650–64. pmid:7431045Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos. 2000;10(4):848–63. pmid:12779434

Funding: 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. Wilson RC, Jones PW. A comparison of the visual analogue scale and modified Borg scale for the measurement of dyspnoea during exercise. Clinical Science. 1989;76(3):277–82. pmid:2924519 Weich C, Jensen RL, Vieten M. Triathlon transition study: quantifying differences in running movement pattern and precision after bike-run transition. Sports Biomech. 2019;18(2):215–28. pmid:29141506 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) 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.

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. In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, [2] for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. Fluctuation in the form of a “random walk”. These are changes around a morphed attractor described with the iteration

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 obtainSehle 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 The kinematics of human cyclic motion seems rather simple at first glance. Detailed observations display a repeating structure and some fluctuation producing similar but not identical repetitive cycles of movements [ 3, 4]. These changes often describe a transient effect at the start of the movement [ 4– 6], as generally observed in dynamical systems [ 7, 8]. Moreover, various perturbations alter the regularity of the ongoing movement and stride time dynamics [ 9– 12]. Dingwell and Kang [ 13] describe these findings as ′inherent biological noise′, being local instabilities [ 14] during movements like walking, without causing falls or stumbles, meaning that the subjects move ′orbitally stable′. Nashner [ 15] pointed out, that the described continuity after perturbations is retained by adjusting parameters of the present walking motion rather than recruiting a new motor pattern (p. 650). 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.