1. The Presence of 1/f Scaling Reveals Coordination in Self- Organized Systems EWOMS Lisbon, June 4th-6th 2009 Maarten Wijnants 1 Ralf Cox 1 Fred Hasselman 1 Anna Bosman 1 & Guy Van Orden 2 1 Behavioral Science Institute, Radboud University, Nijmegen, the Netherlands 2 University of Cincinnati, OH M.Wijnants@pwo.ru.nl

2. Overview Introduction to Topics of Complexity Precision Aiming: –Non-Dominant Hand Practice –Kinematics –Speed-Accuracy Trade-Off Consequences for Theory and Modelling

3. 1/f in complex systems Long-Range Dependence: –Every Data Points Exerts an Influence of Some Magnitude on Every Other Data Point Variation Increases Rather than Stabilizes with Larger Sample Sizes Runs Against Standard Statistical Intuitions –Data = Signal + Noise –Central Limit Theorem  Presence and Relative Change of 1/f scaling is Telling of System Dynamics

4. How structured is it?

5. 1/f scaling and cognition: Two approaches Component-dominant dynamics –Traditional (information processing) approach in cognitive psychology –Independent components work at characteristic time scales –Summed effects of multiple time scale random processes can naturally yield 1/f spectra –E.g. Additive Factors (Sternberg) Word-naming: –Perception –Word recognition –Response selection –Action ADDITIVE + + e.g. Wagenmakers, Farell, & Ratcliff, 2004

6. 1/f scaling and cognition: Two approaches Interaction-dominant dynamics –1/f emerges through coordinated interactions between components –Components at different scales change each others dynamics –No statistically independent components: A single process extends across all time scales of variation INTERACTIVE e.g. Holden, Van Orden & Turvey, 2008

7. Participant power spectrum plus 20 % noiseParticipant power spectrum plus 30 % noise How does it change, what does it mean? Participant power spectrumParticipant power spectrum plus 10 % noise

8. Hypothesis 1/f scaling reveals the intrinsic dynamics of coordinated self-organized systems 1/f Scaling Changes as a Function of Mechanical, Anatomical, Physiological, Neural, Environmental, and/or Task-Related Constraints Degree of Skill and Perturbation of Task Performance Task performances cannot be fully understood or described in terms of mean behavior, hence at single levels of analysis i.e. Average movement duration or accuracy

9. Motor Coordination: Key Ingredients Degrees-of-freedom problem: –“the problem of how to compress the movement system’s state space of very many dimensions into a control space of very few dimensions” (Turvey, 1990, p. 939) A Synergy is a (meta) stable organization whose components are always ready to participate in other stable organizations Complex systems minimize their entropy production and energy dissipation as they self-organize  1/f scaling, phase-space dynamics and entropy measures provide a sensitive metric for such cooperative interactions

10. Precision aiming Average Movement Time Function of target size and distance between targets MT = a + b (ID) ID = log2 (2D / W) What about fluctuations over time?

11. Purposely difficult (ID = 6.9) F(4, 56) = 4.65, p <.01 F(4,56) = 3.62, p <.02 F(4,56) < 1 D = 24 cm W = 0.8 cm 5 blocks x 1100 trials Non-dominant hand F(4,56) = 3.87, p <.05

12. RQA in Motor Learning Recurring sequences of data points Recurring data points Complexity of deterministic structureAttractor strength ~ Lyapunov exp Nonlinear technique Transform original series into its embedding matrix (EM) based on delays higher dimensional recurrences captured by single variables By creating “time”/”space” delayed versions of the signal Setting a radius

13. Purposely easy (ID = 3) D = 8 cm W = 2 cm 5 blocks x 1100 trials Non-dominant hand No change in 1/f scaling No change in RQA measures All F (4,56)’s < 1

14. All F (4,56)’s < 1 RQA Dynamics

15. Conclusion High-ID condition: motor learning –More 1/f scaling with practice –More confined, less random, and stronger underlying attractor –Less random, more patterned –  compression of degrees-of-freedom Low-ID condition: overlearning –No change in 1/f –No change in reconstructed phase space –  No further compression of degrees-of-freedom

16. Kinematics and long-range correlations Higher-Order MT Dynamics Relate to Movement Duration and Accuracy –Differently in two radically different ID conditions Another Level of Analysis: Individual Oscillatory Movements –Kinematic Patterns: Velocity Profile, Acceleration Profile, Hooke’s Plot

17. Harmonicity Simple Harmonic Oscillation vs. Damped Oscillation Self-Sustained Oscillation (Kugler & Turvey, 1987) Energy Dissipation Index of Harmonicity (Guiard, 1993; 1997) Between conditions: Index-of-Difficulty (Mottet & Bootsma, 1999) Between participants: Speed-Accuracy Trade-Off

18. MT SL Higher-order dynamics Constraints: ID = 6.9 Energy minimization Emergent coordination Speed Accuracy H : -.60 -0.75 W D H :.60.50 H :.87 -.85 -.40.35.62 -.25 1/f noiseSampEn Kinematics -.60 1/f noiseSampEn 1/f noise SampEn -.45

19. MT SL Constraints: ID = 6.9 Energy minimization Emergent coordination Kinematics -.60 1/f noise Higher-order dynamics Fast Not accurate

20. MT SL Constraints: ID = 6.9 Energy minimization Emergent coordination Kinematics -.60 1/f noise Higher-order dynamics Slow Accurate

21. MT SL H : CEILING W D Kinematics.56 1/f noise Higher-order dynamics Constraints: ID = 3 Energy minimization Emergent coordination Accuracy : CEILING Speed: CEILING

22. Speed-accuracy trade-off and highly related levels of analysis High-ID condition: –More harmonious movements: faster and less accurate more 1/f in MT series, less 1/f in succesive line lengths More 1/f, lower dimensional attractor –speed-accuracy trade-off at three levels of analysis: Higher-order dynamics (fractal correlations, entropy) Movement time and terminal accuracy Kinematic patterns Low-ID condition –Kinematics show ceiling effect –Movement time and accuracy show ceiling effects –Fractal dynamics: win-win instead of trade-off Task constraints: –Win-win or trade-off

23. Comparing conditions ID = 6.9ID = 3 MT SL

24. Across-task differences Simple RT, Precision aiming: –Each trial is identical: same SIGNAL to respond and same RESPONSE –EXTERNAL sources of variation in Response Time are minimized  Variation must largely reflect INTERNAL sources Choice RT, Word-naming –Experimental trials differ: A different SIGNAL to respond and a different RESPONSE –EXTERNAL sources of variation in Response Time are introduced to the measured values  Variation must reflect INTERNAL sources to a lesser extent |  Discrete  |  Cyclic  | N responses 1 response 4 responses Data from: Van Orden, Holden, & Turvey, 2003; Kello, Beltz, Van Orden, & Turvey, 2007; Wijnants et al., 2009

25. Human Gait Old adults Parkinson disease (1) vs. Old adults (2) vs. Young adults (3) Repetition effects reduce RT and SD Facilitate WN performance Three blocks of 1100 same word stimuli Word-Naming

26. How does 1/f scaling change? Component-dominant dynamics –  The presence of specific processes affects the presence of 1/f scaling (AC or UC) –  Changing strategies Interaction-dominant dynamics –Adaptive basis of coordinated behavior –Scaling relations track the efficiency of the coordination of perception and action  Perturbations reduce the presence of 1/f scaling  Unsystematic variation, e.g. less coordinated behavior, whitens the data signal  More coordinated behaviors reveal more 1/f ADDITIVE INTERACTIVE

27. Variation increases with sample size –Longer data series pick up more 1/f scaling ( Van Orden, Holden, & Turvey, 2005) 1024 2048 8192

28. Cue Predictability in CRT (Kello, Beltz, Van Orden, & Turvey, 2007)

29. These results follow naturally from predictions of an interaction-dominant approach Component-dominant approaches should post- hoc explain: –New components for longer data series –New components for every independent stream of 1/f –Consistent changes in 1/f scaling with changes in task performance (at multiple levels of analysis) Modular or interactive dynamics?

30. Sum up Long-range dependence can be manipulated in predictable ways –Practice or more stable and coordinated behaviors shows more 1/f scaling –Stronger task constraints (external variation) perturb performances, fewer 1/f –More 1/f scaling goes with less random and stronger underlying attractors –1/f scaling is to some extent present in any repeated behaviors

31. Any Questions?... M.Wijnants@pwo.ru.nl