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

transcript

The Presence of 1/f Scaling Reveals Coordination in Self-

Organized Systems

EWOMSLisbon, June 4th-6th 2009

Maarten Wijnants1 Ralf Cox1 Fred Hasselman1

Anna Bosman1 & Guy Van Orden2

1 Behavioral Science Institute, Radboud University, Nijmegen, the Netherlands2University of Cincinnati, OH

M.Wijnants@pwo.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

• 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

• 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

• Participant power spectrum plus 20 % noise• Participant power spectrum plus 30 % noise

How does it change, what does it mean?

• Participant power spectrum• Participant power spectrum plus 10 % noise

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 = log2 (2D / W)

• What about fluctuations over time?

Purposely difficult (ID = 6.9)

ND1 ND2 ND3 ND4 ND5

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

1 2 3 4 5

F(4,56) = 3.87, p < .05

RQA in Motor Learning

Recurring sequences of data points Recurring data points

Complexity of deterministic structure 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)

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

1.00 2.00 3.00 4.00 5.00

Session

All F (4,56)’s < 1

RQA Dynamics

1.00 2.00 3.00 4.00 5.00

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

Higher-order dynamics

Constraints:ID = 6.9

Energy minimizationEmergent coordinationSpeed

dAccuracy

Accuracy

H : -.60 -0.75 WD

H : .60 .50

H : .87 -.85

-.40 .35

.62 -.25

1/f noise SampEn

Kinematics

1/f noise SampEn

1/f noise

SampEn -.45

Energy minimizationEmergent coordination

Kinematics

-.601/f noise

• Fast • Not accurate

Kinematics

-.601/f noise

• Slow• Accurate

H : CEILING

Kinematics

.561/f noise

Constraints:ID = 3

Accuracy : CEILINGSpeed: CEILING

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

1 2 3 4

ID = 6.9 ID = 3

MTMT SL SL

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

Precisio

| 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

Human Gait

• Old adults Parkinson disease (1)

• vs. Old adults (2)

• vs. Young adults (3)

1.00 2.00 3.00

• Repetition effects reduce RT and SD

• Facilitate WN performance• Three blocks of 1100 same

word stimuli

Word-Naming

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

Variation increases with sample size

– Longer data series pick up more 1/f scaling (Van Orden, Holden, & Turvey, 2005)

Cue Predictability in CRT

(Kello, Beltz, Van Orden, & Turvey, 2007)

• 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?

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

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

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