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
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
AD
DIT
IVE
+
+
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
INT
ER
AC
TIV
E
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
block
-1.50
-1.00
-0.50
slo
pe
MT
ND1 ND2 ND3 ND4 ND5
block
0.50
0.60
0.70
0.80
mea
nm
t_c
ND1 ND2 ND3 ND4 ND5
block
0.00
20.00
40.00
60.00
accu
racy
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
block
0.00
0.25
0.50
0.75
1.00
sam
pen
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
-1.50
-1.00
-0.50
Sp
ectr
al s
lop
e M
T
All F (4,56)’s < 1
RQA Dynamics
1.00 2.00 3.00 4.00 5.00
block
20.00
30.00
40.00
50.00
rad
ius
1.00 2.00 3.00 4.00 5.00
block
10.00
20.00
30.00
40.00
50.00
60.00
det
1.00 2.00 3.00 4.00 5.00
block
0.50
1.00
1.50
ent
1.00 2.00 3.00 4.00 5.00
block
10.00
20.00
30.00
40.00
50.00
60.00
max
line
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 SL
Higher-order dynamics
Constraints:ID = 6.9
Energy minimizationEmergent coordinationSpeed
Speed
Spee
dAccuracy
Accuracy
Accur
acy
H : -.60 -0.75 WD
H : .60 .50
H : .87 -.85
-.40 .35
.62 -.25
1/f noise SampEn
Kinematics
-.60
1/f noise SampEn
1/f noise
SampEn -.45
MT SL
Constraints:ID = 6.9
Energy minimizationEmergent coordination
Kinematics
-.601/f noise
Higher-order dynamics
• Fast • Not accurate
MT SL
Constraints:ID = 6.9
Energy minimizationEmergent coordination
Kinematics
-.601/f noise
Higher-order dynamics
• Slow• Accurate
MT SL
H : CEILING
W
D
Kinematics
.561/f noise
Higher-order dynamics
Constraints:ID = 3
Energy minimizationEmergent coordination
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
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
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
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
Wo
rdN
amin
g
Ch
oice
RT
Sim
ple
RT
Precisio
naim
ing
| 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
1 2 3
GROUP
-1.00
-0.50
0.00
Sp
ectr
al S
lop
e
Human Gait
• Old adults Parkinson disease (1)
• vs. Old adults (2)
• vs. Young adults (3)
1.00 2.00 3.00
block
-0.60
-0.40
-0.20
0.00
slo
pe
• 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
AD
DIT
IVE
INT
ER
AC
TIV
E
Variation increases with sample size
– Longer data series pick up more 1/f scaling (Van Orden, Holden, & Turvey, 2005)
1024
2048
8192
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
