A team approach to undergraduate research in biomathematics: Balance control

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 6, 2011, Pages 260-277

  Milton, J ^a   Radunskaya, A ^b   Ou, W ^c   Ohira, T ^a  

^a Joint Science Department of Claremont McKenna   (United States)

^b KECK GRADUATE INSTITUTE   (United States)

^c POMONA COLLEGE   (United States)

Author keywords

Dimension reduction; Education; Inverted pendulum; Noise; Pursuit; Time delay; Undergraduate

Indexed keywords

DIMENSION REDUCTION; INVERTED PENDULUM; NOISE; PURSUIT; UNDERGRADUATE;

EDUCATION COMPUTING; MATHEMATICAL MODELS; PROJECT MANAGEMENT; RESEARCH;

STUDENTS;

EID: 80053946378     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116614     Document Type: Article

References (64)

1. D. Acheson. From Calculus to Chaos: An introduction to dynamics. Oxford University Press, New York (1998).
2. A. Armenti, Jr., editor. The Physics of Sports. American Institute of Physics, New York (1992).
3. Y. Asai, Y. Tasaka, K. Nomura, T. Nomura, M. Casidio, P. Morasso A model of postural control in quiet standing: Robust compensation of delay-induced instability using intermittent activation of feedback control. PLoS ONE 4 (2009), e6169.
4. G. L. Baker, J. A. Blackburn. The pendulum: a case study in physics. Oxford University Press, New York, 2005.
5. H. C. Berg. Random walks in biology. Princeton University Press, New Jersey (1993).
6. A. Bottaro, Y. Yasutake, T. Nomura, M. Casidio, P. Morasso. Bounded stability of the quite standing position: An intermittent control model. Human Movement Science 27 (2008), 473-495.
7. R. Bormann, J. L. Cabrera, J. G. Milton, C. W. Eurich. Visuomotor tracking on a computer screen: An experimental paradigm to study dynamics of motor control. Neurocomputing 58-60 (2004), 517-523.
8. J. Boulet, R. Balasubramiam, A. Daffertshofer, A. Longtin. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics. Phil. Trans. Roy. Soc. A 368 (2010): 423-438.
9. J. L. Cabrera, J. G. Milton. On-off intermittency in a human balancing task. Phys. Rev. Lett. 89 (2002), 158702.
10. J. L. Cabrera, J. G. Milton. Human stick balancing: Tuning Lévy flights to improve balance control. CHAOS 14 (2004): 691.
11. J. L. Cabrera, R. Bormann, C. Eurich, T. Ohira, J. Milton. State-dependent noise and human balance control. Fluct. Noise Lett. 4 (2004), L107-L118.
12. S. A. Campbell, S. Crawford, K. Morris. Friction and the inverted stabilization problem. J. Dyn. Syst. Meas. Control. 130 (2008), 054502.
13. J. J. Chiel, R. D. Beer. The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. TINS 20 (1997), 553-557.
14. T. Cluff, R. Balasubramania R.. Motor learning characterized by changing Lévy distributions. PLoS One 4 (2009): e5998.
15. V. de Silva, J. B. Tenenbaum, J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000), 2319-2323.
16. T. M. H. Dijkstra, H. Katsumata, D. Sternad. The dialogue between data and model: passive stability and relaxation behavior in a ball bouncing task. Nonlinear Studies 11 (2004), 319-344.
17. B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems. SIAM, Philadelphia (2002).
18. C. W. Eurich, J. G. Milton JG. Noise-induced transitions in human postural sway. Phys. Rev. E 54 (1996): 6681-6684.
19. C. W. Eurich, K. Pawelzik. Optimal control yields power laws. In Artificial Neural Networks: Formal Models and Their Applications, Springer Lecture Notes in Computer Science Vol. 3697, edited by W. Duch, J. Kacprzyk, E. Oja and S. Zadronzny (Springer-Verlag, Berlin, 2005), pp. 365-370.
20. P. Foo, J. A. S. Kelso, G. D. de Guzman. Functional stabilization of fixed points: Human pole balancing using time to balance information. J. Exp. Psychol. Hum. Percept. Perform. 26 (2000), 1281-1297.
21. J. Guckenheimer. A robust hybrid stabilization strategy for equilibria. IEEE Trans. Automatic Control 40 (1995), 321-326.
22. T. Insperger. Stick balancing with reflex delay in case of parametric forcing. Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 2160-2168.
23. A. Kamimura, T. Ohira. Group chase and escape. New J. Physics 12 (2010), 053013.
24. T. A. Kuiken, L. A. Miller, R. D. Lipschutz, B. A. Lock, K. Stubblefield, P. D. Marasso, P. Zhou, G. A. Dumanian. Targeted reinnervation for enhanced prosthetic arm function in a woman with a proximal amputation: a case study. Lancet 369 (2007), 371-380.
25. A. D. Kuo. The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum. Mov. Sci. 26 (2007), 617-656.
26. S. S. Lafon. Diffusion Maps and Geometric Harmonics. PhD thesis, Yale University, 2004.
27. M. Landry, S. A. Campbell, K. Morris, C. O. Aguilar. Dynamics of an inverted pendulum with delayed feedback control. SIAM J. Appl. Dyn. Sys. 4 (2005), 333-351.
28. D. B. Lockhart, L. H. Ting. Optimal sensorimotor transformations for balance. Nat. Neurosci. 10 (2007), 1329-1336.
29. I. D. Loram, M. Lackie. Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. J. Physiol. (London) 540 (2002), 1111-1124.
30. I. D. Loram, C. N. Maganaris, M. Lakie. Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J. Physiol. (London) 564 (2005), 295-311.
31. J. Maynard Smith. Mathematical Ideas in Biology. Cambridge University Press, New York (1968).
32. T. A. McMahon. Muscles, Reflexes and Locomotion. Princeton University Press, New Jersey (1984).
33. B. Mehta, S. Schaal. Forwards models in visuomotor control. J. Neurophysiol. 88 (2002), 942-953.
34. J. G. Milton, S. S. Small, A. Solodkin. On the road to automatic: Dynamic aspects in the development of expertise. J. Clin. Neurophysiol. 21 (2004), 134-143.
35. J. G. Milton, J. L. Cabrera, T. Ohira. Unstable dynamical systems: Delays, noise and control. Europhys. Lett. 83 (2008), 48001.
36. J. G. Milton, T. Ohira, J. L. Cabrera, R. M. Fraiser, J. B. Gyorffy, F. K. Ruiz, M. A. Strauss, E. C. Balch, P. J. Marin, J. L. Alexander. Balancing with vibration: A prelude for "drift and act" balance control. PLOS One 4 (2009), e7427.
37. J. Milton, J. L. Cabrera, T. Ohira, S. Tajima, Y. Tonosaki, C. W. Eurich, S. A. Campbell. The time-delayed inverted pendulum: Implications for human balance control. Chaos 19 (2009), 026110.
38. J. Milton, J. L. Townsend, M. A. King, T. Ohira. Balancing with positive feedback: the case for discontinuous control. Phil. Trans. Roy. Soc. A 367 (2009), 1181-1193.
39. J. Milton, J. Gyorffy, J. L. Cabrera, T. Ohira. Amplitude control of human postural sway using Achilles tendon vibration. 16th US National Congress of Theoretical and Applied Mechanics (2010). State College, PA (USNCTAM2010-791).
40. J. G. Milton, A. E. Radunskaya, A. H. Lee, L. G. de Pillis, D. F. Bartlett. Team research at the biology-mathematics interface: Project management perspectives. CBE-Life Sciences Education 9 (2010), 316-322.
41. J. Milton, P. Naik, C. Chan, S. A. Campbell. Indecision is neural decision making models. Math. Model. Nat. Phenom. 5 (2010), 125-145.
42. J. Milton, J. Lippai, R. Bellows, A. Blomberg, A. Kamimura, T. Ohira. Visuomotor tracking tasks with delayed pursuit and escape. 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control (2011). Washington, D. C. (DETC2011-47312).
43. P. J. Nahin Chases and escapes: The mathematics of pursuit and evasion. Princeton University Press, Princeton, New Jersey (2007).
44. http://www.gnu.org/software/octave/
45. T. Ohira, J. Milton. Delayed random walks: Investigating the interplay between noise and delays. In: Delay Differential Equations: Recent Advances and New Directions, edited by B. Balachandran, T. Kalmár-Nagy and D. E. Gilman, Springer-Verlag, New York, pp. 305-335 (2009).
46. F. Patzelt, M. Riegel, U. Ernst, K. Pawelzik. Self-organized critical noise amplification in human closed loop control. Front. Comp. Neurosci. 1 (2007), Article 4, 1-9.
47. I. J. Pinter, R. von Swigchem, A. J. Knoek van Soet, L. A. Rozendaal. The dynamics of postural sway cannot be captured using a one-segment inverted pendulum model: A PCA on segment rotations during unperturbed stance. J. Neurophysiol. 100 (2008), 3197-3208.
48. A. B. Pippard. The inverted pendulum. Eur. J. Physics 8 (1987), 203-206.
49. http://pydelay.sourceforge.net/
50. https://code.astraw.com/projects/PyUniversalLibrary/
51. http://www.sagemath.org/
52. http://www.scipy.org/
53. S. H. Scott. Optimal feedback control and the neural basis of volitional motor control. Nature Rev, Neurosci. 5 (2004), 534-546.
54. J. R. Stirling, M. S. Zakynthinaki. Stability and the maintenance of balance following a perturbation from quiet stance. Chaos 14 (2004), 96-105.
55. G. Stepan. Delay effects in the human sensory system during balancing. Phil. Trans. Roy. Soc. A 367 (2009), 1195-1212.
56. N. Stepp. Anticipation in feedback-delayed manual tracking tracking of a chaotic oscillator. Exp. Brain Res. 198 (2009), 521-525.
57. A. Straw. An open-source library for realtime visual stimulus generation. Frontiers Neuroinformatics 11 (2008): doi: 10.3389.neuro.11.004:2008.
58. A. D. Straw, M. H. Dickinson. Motmot, an open-source toolkit for realtime video acquisition and analysis. Source Code for Biology and Medicine (2010). doi: 10.1186/1751-0473-4-5.
59. T. Vicsek. Closing in on evaders. Nature 466 (2010), 43-44.
60. S. Vogel. Comparative Biomechanics: Life's physical world. Princeton University Press, New Jersey (2003).
61. H. U. Voss. Anticipating chaotic synchronization. Phys. Rev. E 61 (2000), 5115-5119.
62. D. A. Winter, A. e. Patla, F. Prince, M. Ishac, K. Gielo-Perczak. Stiffness control in quiet standing. J. Neurophysiol. 80 (1998), 1211-1221.
63. M. S. Zakynthinaki, J. M. Madera Milla, A. López de Durana, C. A. Cordent Martinez, G. Rodriguez Romo, M. Stillero Quintana, J. Samperd Molinuevo. Rotated balance in humans due to repetitive rotational movement. Chaos 20 (2010), 013118.
64. V. Zatsiorsky. Biomechanics in Sports: Performance enhancement and injury prevention. Blackwell Science, Malden, MA (2000).