The Presence of 1f Scaling Reveals Coordination in

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The Presence of 1/f Scaling Reveals Coordination in Self. Organized Systems EWOMS Lisbon, June

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

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

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?

How structured is it?

1/f scaling and cognition: Two approaches ADDITIVE • Component-dominant dynamics – Traditional (information processing)

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

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

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

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

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

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

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

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

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

RQA Dynamics All F (4, 56)’s < 1

Conclusion • High-ID condition: motor learning – More 1/f scaling with practice – More

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

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 &

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

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

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

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

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

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

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

Across-task differences • Simple RT, Precision aiming: • – Each trial is identical: same

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

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

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

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)

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

Modular or interactive dynamics? • These results follow naturally from predictions of an interaction-dominant

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

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. Wijnants@pwo. ru. nl

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