Impacts of statistical feedback on the flexibility-accuracy trade-offin biological systems (original) (raw)

References

1. Beek, P.J., Peper, C.E. and Stegeman, D.F.: Dynamical Models of Movement Coordination, Hum. Movement Sci. 14 (1995), 573–608.
   Google Scholar
2. Beek, P.J., Peper, C.E. and van Wieringen, P.C.W.: Frequency Locking, Frequency Modulation, and Bifurcations in Dynamic Movement Systems, In: Stelmach, G.E. and Requin, J. (eds.): Tutorials in Motor Behavior II, Amsterdam, 1992, pp. 599–622.
3. Borland,_L.: Microscopic Dynamics of the Nonlinear Fokker-Planck Equation, Phys. Rev. E 57 (1998), 6634–6642.
   Google Scholar
4. Borland, L., Pennini, F., Plastino, A.R. and Plastino, A.: The Nonlinear Fokker-Planck Equation with State-Dependent Diffusion - A Nonextensive Maximum Entropy Approach, Eur. Phys. J. B 12 (1998), 285–297.
   Google Scholar
5. Compte, A. and Jou, D.: Non-Equilibrium Thermodynamics and Anomalous Diffusion, J. Phys. A: Math. Gen. 29 (1996), 4321–4329.
   Google Scholar
6. Compte, A., Jou, D. and Katayama, Y.: Anomalous Diffusion in Linear Shear Flows, J. Phys. A: Math. Gen. 30 (1997), 1023–1030.
   Google Scholar
7. Cornell, E.A. and Wieman, C.E.: The Bose-Einstein Condensate, Sci. American 278(3) (1998), 26–31.
   Google Scholar
8. Daffertshofer, A., Peper, C.E. and Beek, P.J.: Spectral Analyses of Event-Related Encephalographic Signals, Phys. Lett. A 266 (2000), 290–302.
   Google Scholar
9. Daffertshofer, A., Peper, C.E., Frank, T.D. and Beek, P.J.: Spatio-Temporal Patterns of Encephalographic Signals During Polyrhythmic Ttapping, Hum. Movement Sci. 19 (2000), 475–498.
   Google Scholar
10. Dawson, D.A.: Critical Dynamics and Fluctuations for a Mean-Field Model of Cooperative Behavior, J. Stat. Phys. 31 (1983), 29–85.
    Google Scholar
11. DeGuzman, G.C. and Kelso, J.A.S.: Multifrequency Behavioral Patterns and the Phase Attractive Circle Map, Biol. Cybern. 64 (1991), 485–495.
    Google Scholar
12. Desai, R.C. and Zwanzig, R.: Statistical Mechanics of a Nonlinear Stochastic Model, J. Stat. Phys. 19 (1978), 1–24.
    Google Scholar
13. Dwight, H.: Tables of Integrals and Other Mathematical Data, MacMillan, New York, 1957.
    Google Scholar
14. Eu, B.C.: Kinetic Theory and Irreversible Thermodynamics, John Wiley and Sons, New York, 1992.
    Google Scholar
15. Fitts, P.M.: The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement, J. Exp. Psychol. 47 (1954), 381–391.
    Google Scholar
16. Frank, T.D.: On Nonlinear and Nonextensive Diffusion and the Second Law of Thermodynamics, Phys. Lett. A 267 (2000), 298–304.
    Google Scholar
17. Frank, T.D.: H-Theorem for Fokker-Planck Equations with Drifts Depending on Process Mean Values, Phys. Lett. A 280 (2001), 91–96.
    Google Scholar
18. Frank, T.D.: A Langevin Approach for the Microscopic Dynamics of Nonlinear Fokker-Planck Equations, Physica A 301 (2001), 52–62.
    Google Scholar
19. Frank, T.D.: Lyapunov and Free Energy Functionals of Generalized Fokker-Planck Equations, Phys. Lett. A 290 (2001), 93–100.
    Google Scholar
20. Frank, T.D. and Daffertshofer, A.: Nonlinear Fokker-Planck Equations whose Stationary Solutions Make Entropy-Like Functionals Stationary, Physica A 272 (1999), 497–508. IMPACTS OF STATISTICAL FEEDBACK 53
    Google Scholar
21. Frank, T.D. and Daffertshofer, A.: Exact Time-Dependent Solutions of the Renyi Fokker-Planck Equation and the Fokker-Planck Equations Related to the Entropies Proposed by Sharma and Mittal, Physica A 285 (2000), 351–366.
    Google Scholar
22. Frank, T.D. and Daffertshofer, A.: H-Theorem for Nonlinear Fokker-Planck Equations Related to Generalized Thermostatistics, Physica A 295 (2001), 455–474.
    Google Scholar
23. Frank, T.D. and Daffertshofer, A.: Multivariate Nonlinear Fokker-Planck Equations and Generalized Thermostatistics, Physica A 292 (2001), 392–410.
    Google Scholar
24. Frank, T.D., Daffertshofer, A. and Beek, P.J.: Stochastic Processes with Statistical Feedback, Unpublished manuscript (1998).
25. Frank, T.D., Daffertshofer, A. and Beek, P.J.: Multivariate Ornstein-Uhlenbeck Processes with Mean Field Dependent Coefficients - Application to postural sway, Phys. Rev. E 63 (2001), 011905.
    Google Scholar
26. Frank, T.D., Daffertshofer, A. and Beek, P.J.: On an Interpretation of Apparent Motion as a Self-Organizing Process, Behav. Brain Sci. (2001), in press.
27. Frank, T.D., Daffertshofer, A., Beek, P.J. and Haken, H.: Impacts of Noise on a Field Theoretical Model of the Human Brain, Physica D 127 (1999), 233–249.
    Google Scholar
28. Frank, T.D., Daffertshofer, A., Peper, C.E., Beek, P.J. and Haken, H.: Towards a Comprehensive Theory of Brain Activity: Coupled Oscillator Systems under External Forces, Physica D 144 (2000), 62–86.
    Google Scholar
29. Fuchs, A., Kelso, J.A.S. and Haken, H.: Phase Transitions in the Human Brain: Spatial Mode Dynamics, Int. J. Bif. and Chaos 2 (1992), 917–939.
    Google Scholar
30. Haken, H.: Synergetics, An introduction, Springer, Berlin, 1997.
    Google Scholar
31. Haken, H.: Advanced Synergetics, Springer, Berlin, 1983.
    Google Scholar
32. Haken, H.: Synergetic Computers and Cognition, Springer, Berlin, 1991.
    Google Scholar
33. Haken, H.: Principles of Brain Functioning, Springer, Berlin, 1996.
    Google Scholar
34. Haken, H. and Stadler, M.: Synergetics of Cognition, Springer, Berlin, 1990.
    Google Scholar
35. Hesse, C.H.: Stochastic Dynamics for Non-Linear Differential Equations of High Order, Internal report - SFB 404, University Stuttgart, Stuttgart, 1997.
    Google Scholar
36. Hesse, C.H. and Ramos, E.: Dynamic Simulation of a Stochastic Model for Particle Sedimentation in Fluids, Appl. Math. Modelling 18 (1994), 437–445.
    Google Scholar
37. Hoyt, D.F. and Taylor, C.R.: Gait and Energetics of Locomotion in Horses, Nature 292 (1981), 239–240.
    Google Scholar
38. Ito, K.: Stochastic Integral, Proc. Imperial Acad. Tokyo 20 (1944), 519–524.
    Google Scholar
39. Kaniadakis, G.: Nonlinear Kinetics Underlying Generalized Statistics, Physica A 296 (2001), 405–425.
    Google Scholar
40. Kelso, J.A.S.: Dynamic Patterns - The Self-Organization of Brain and Behavior, MIT Press, Cambridge, 1995.
    Google Scholar
41. Kelso, J.A.S., Bressler, S.L., Buchannan, S., DeGuzman, G.C., Ding, M., Fuchs, A. and Holroyd, T.: A Phase Transition in Human Brain and Behavior, Phys. Lett. A 169 (1992), 134–144.
    Google Scholar
42. Kelso, J.A.S., Scholz, J.P. and Schöner, G.: Non-Equilibrium Phase Transitions in Coordinated Biological Motion: Critical Fluctuations, Phys. Lett. A 118 (1986), 279–284.
    Google Scholar
43. Ketterle, W.: Experimental Studies of Bose-Einstein Condensation, Phys. Today 52(12) (1999), 30–35.
    Google Scholar
44. Kruse, P., Carmesin, H., Pahlke, L., Strüber, D. and Stadler, M.: Continuous Phase Transitions in the Perceptation of Multistabile Visual Patterns, Biol. Cybern. 40 (1996), 23–42.
    Google Scholar
45. Küchler, U. and Platen, E.: Strong Discrete Time Approximation of Stochastic Differential Equations with Time Delay, Math. Comput. Simulat. 54 (2000), 189–205.
    Google Scholar
46. Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence, Springer, Berlin, 1984.
    Google Scholar
47. Lenzi, E.K., Anteneodo, C. and Borland, L.: Escape Time in Anomalous DiffusiveMedia, Phys. Rev. E 63 (2001), 051109. 54 T.D. FRANK
    Google Scholar
48. Malacarne, L.C., Mendes, R.S., Pedron, I.T. and Lenzi, E.K.: Nonlinear Equation for Anomalous Diffusion: Unified Power-Law and Stretched Exponential Exact Solution, Phys. Rev. E 63 (2001), 030101.
    Google Scholar
49. Martinez, S., Plastino, A.R. and Plastino, A.: Nonlinear Fokker-Planck Equations and Generalized Entropies, Physica A 259 (1998), 183–192.
    Google Scholar
50. Minetti, A.E. and Alexander, R.M.: A Theory of Metabolic Costs for Bipedal Gaits, J. Theo. Biol. 29 (1997), 195–198.
    Google Scholar
51. Mottet, D. and Bootsma, R.J.: The Dynamics of Goal-Directed Rhythmic Aiming, Biol. Cybern. 80 (1999), 235–245.
    Google Scholar
52. Newell, K.M. and Corcos, D.M.: Variability and Motor Control, Human Kinetics Publishers, Champaign, 1993.
    Google Scholar
53. Park, H., Collins, D.R. and Turvey, M.T.: Dissociation of Muscular and Spatial Constraints on Patterns of Interlimb Coordination, J. Exp. Psychol. - Hum. Percept. Perform. 27 (2001), 32–47.
    Google Scholar
54. Peper, C.E. and Beek, P.J.: Are Frequency-Induced Transitions in Rhythmic Coordination Mediated by a Drop in Amplitude?, Biol. Cybern. 79 (1998), 291–300.
    Google Scholar
55. Peper, C.E., Beek, P.J. and van Wieringen, P.C.W.: Multifrequency Coordination in Bimanual Tapping: Asymmetrical Coupling and Signs of Supercriticality, J. Exp. Psychol. - Hum. Percept. Perform. 21 (1995), 1117–1138.
    Google Scholar
56. Reimann, P., Schmid, G.J. and Hänggi, P.: Universal Equivalence of Mean First-Passage Time and Kramers Rate, Phys. Rev. E 60 (1999), R1–R4.
    Google Scholar
57. Risken, H.: The Fokker-Planck Equation - Methods of Solution and Applications, Springer, Berlin, 1989.
    Google Scholar
58. Rosenbaum, D.A.: Human Motor Control, Academic Press, New York, 1991.
    Google Scholar
59. Shepard, R.N.: Perceptual-Cognitive Universals as Reflections of the World, Psychonomic Bulletin & Review 1 (1994), 2–28.
    Google Scholar
60. Shiino, M.: Dynamical Behavior of Stochastic Systems of Infinitely Many Coupled Nonlinear Oscillators Exhibiting Phase Transitions of Mean-Field Type: H-Theorem on Asymptotic Approach to Equilibrium and Critical Slowing Down of Order-Parameter Fluctuations, Phys. Rev. A 36 (1987), 2393–2412.
    Google Scholar
61. Stratonovich, R.L.: A New Representation for Stochastic Integrals and Equations, J. SIAM Control 4 (1966), 362–371.
    Google Scholar
62. Tass, P.A.: Phase Resetting inMedicine and Biology - Stochastic Modelling and Data Analysis, Springer, Berlin, 1999.
    Google Scholar
63. Tsallis, C.: Nonextensive Statistics: Theoretical, Experimental and Computational Evidences and Connectsions, Braz. J. Phys. 29 (1999), 1–35.
    Google Scholar
64. Tsallis, C. and Bukman, D.J.: Anomalous Diffusion in the Presence of External Forces: Exact Time-Dependent Solutions and Their Thermostatistical Basis, Phys. Rev. E 54 (1996), R2197–R2200.
    Google Scholar
65. Uhling, E.A. and Uhlenbeck, G.E.: Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases, Phys. Rev. 43 (1933), 552–561.
    Google Scholar
66. van den Broeck, C., Parrondo, J.M.R., Armero, J. and Hernandez-Machado, A.: Mean Field Model for Spatially Extended Systems in the Presence of Multiplicative Noise, Phys. Rev. E 49 (1994), 2639–2643.
    Google Scholar
67. van den Broeck, C., Parrondo, J.M.R. and Toral, R.: Noise-Induced Nonequilibrium Phase Transition, Phys. Rev. Lett. 73 (1994), 3395–3398.
    Google Scholar
68. van den Broeck, C., Parrondo, J.M.R., Toral, R. and Kawai, R.: Nonequilibrium Phase Transitions Induced by Multiplicative Noise, Phys. Rev. E 55 (1997), 4084–4094.
    Google Scholar
69. Wannier, G.H.: Statistical Physics, Dover Publications, New York, 1966.
    Google Scholar

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