The Presence of 1f Scaling Reveals Coordination in

The Presence of 1/f Scaling Reveals Coordination in Self. Organized Systems EWOMS Lisbon, June 4 th-6 th 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. [email protected] ru. nl

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

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

How structured is it?

1/f scaling and cognition: Two approaches ADDITIVE • 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 e. g. Wagenmakers, Farell, & Ratcliff, 2004 + +

1/f scaling and cognition: Two approaches INTERACTIVE • 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 e. g. Holden, Van Orden & Turvey, 2008

How does it change, what does it mean? • Participant power spectrum plus 10 20 % noise 30

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

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

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

Purposely difficult (ID = 6. 9) F(4, 56) = 3. 62, p <. 02 • 5 blocks x 1100 trials • Non-dominant hand F(4, 56) = 4. 65, p <. 01 F(4, 56) = 3. 87, p <. 05 F(4, 56) < 1 W = 0. 8 cm D = 24 cm

RQA in Motor Learning Recurring sequences of data points Complexity of deterministic structure Recurring data points Attractor 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

Purposely easy (ID = 3) • • 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 W = 2 cm D = 8 cm

RQA Dynamics All F (4, 56)’s < 1

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

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

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

MT 1/f noise -. 60 Samp. En -. 45 SL Higher-order dynamics . 35 d ee 1/f noise cy ra cu Sp -. 40 Samp. En H : -. 60 -0. 75 -. 25 Ac cu Sp racy ee d Ac . 62 Constraints: ID = 6. 9 Energy minimization Emergent coordination 1/f noise D W Samp. En H : . 60. 50 Accuracy Speed H : . 87 -. 85 Kinematics

MT 1/f noise -. 60 Higher-order dynamics Constraints: ID = 6. 9 Energy minimization Emergent coordination • Fast • Not accurate Kinematics SL

MT 1/f noise -. 60 Higher-order dynamics Constraints: ID = 6. 9 Energy minimization Emergent coordination • Slow • Accurate Kinematics SL

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

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

Comparing conditions MT ID = 6. 9 SL MT SL ID = 3

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 | Discrete | Cyclic | • Choice RT, Word-naming – Experimental trials differ: A different SIGNAL to respond 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 N responses 1 response 4 responses Data from: Van Orden, Holden, & Turvey, 2003; Kello, Beltz, Van Orden, & Turvey, 2007; Wijnants et al. , 2009

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

How does 1/f scaling change? ADDITIVE • Component-dominant dynamics – The presence of specific processes affects the presence of 1/f scaling (AC or UC) – Changing strategies INTERACTIVE • 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

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

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

Modular or interactive dynamics? • These results follow naturally from predictions of an interaction-dominant approach • Component-dominant approaches should posthoc 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)

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

Any Questions? • . . . • M. [email protected] ru. nl