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Complexity in the Brain: Emergent behavior from complex interactions within and between neurons
Stan Gielen
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Content of presentation
• What is complex, intelligent behaviour ?– http://www.livesteaua.com/tags/robocup-videos/– http://www.robocup.nl/achievements.html
• The neural code: – Neuronal dynamics– Emergent behaviour of nonlinear interactions:
multi-stability and hysteresis• Distributed parallel processing
– The network connectivity is flexible by• Neuronal oscillations• Frequency modulation• Flexible task-dependent organisation
– What are the implicatons for control ?
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Once upon a time in 1997 ….
IBM Deep Blue
Gary Kasparov
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What is simple and what is difficult ?
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Is chess more complex than playing soccer ?
http://www.livesteaua.com/tags/robocup-videos/http://www.robocup.nl/achievements.html
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BrainComputing capacity : 10 petaflop
Storage capacity ~ 103 terabytes
Energy consumption ~ 30 Watt
1011 neurons
Time constant ~ 1 ms
Fujitsu K-Computer (nov 2011)Computing capacity : 10.5 petaflop*
Storage capacity ~ 10.5 terabyte
Energy consumption ~ 9.9 MW
88128 CPU-processors
Time constant ~1 ns
1 peta flop = 10^15 Floating Point Operations
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The neural code
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Currentcausing a magnetic field
Dipole,causing an electric field
EEG
MEG
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Donders Centre for Cognitive Neuroimaging
~ 100.000 times weaker than earth magnetic field
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You can get much further with a kind word and a gun, than with a kind word alone(Al Capone)
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You can get much further with a kind word and a gun, than with a kind word alone(Al Capone)
You can get much further with experiment and theory, than with experiment alone(Computational NeuroScience group, Nijmegen)
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Hodgkin-Huxley model
Fast variables• membrane potential V• activation rate for Na+ m
Slow variables• activation rate for K+ n• inactivation rate for Na+ h
-C dV/dt = gNam3h(V-Ena)+gKn4(V-EK)+gL(V-EL) + I
dm/dt = αm(1-m)-βmm
dh/dt = αh(1-h)-βhh
dn/dt = αn(1-n)-βnnddt
ddt
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Neuron at rest
-70 mV
IVVW 3
3
)(1 aVb
W
W
V
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-70 mV
IVVW 3
3
)(1 aVb
W
W
V
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-70 mV +40 mV
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Neurons are nonlinear oscillators
Fast variables• membrane potential V• activation rate for Na+ m
Slow variables• activation rate for K+ n• inactivation rate for Na+ h
-C dV/dt = gNam3h(V-Ena)+gKn4(V-EK)+gL(V-EL) + I
dm/dt = αm(1-m)-βmm
dh/dt = αh(1-h)-βhh
dn/dt = αn(1-n)-βnn
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Multi-stability and parallel processing
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Intra-cellular signaling
External input from other cells
nucleus
Ca2+
Calcium store
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Cells reveal non-linear behavior
• Cell mitosis• Gene-expression and protein synthesis (e.g. pancreas) • Folding/unfolding of proteins (hormone secretion)
Discrete statesOnce started: complete it
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Various stages of growth
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Various stable states of cells
Membrane potentialCalcium oscillations
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Caex
GCaLClex
GCl(Ca) ATPPMCA pump
Caer
ATP
SERCA pump
IP3R
Coupling : excitable membrane and intracellular calcium oscillations
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Stability analysis
)( )( SocCaClCaleakKm
m IIIIIdTdVC
mmdtdm
mm )1()55( mVVhmGI CaCa
mmdtdh
hh )1(
dtBCadIIIJII
dtdCa
SERCACalk
CaERIPPMCA
Calk
Cahm
cyt ][)(3,
2
SERCACalk
CaERIP
ER IIIdt
dCa
)(3
2
wwdtdw
ww )1(
BCakCaBCaTkdtBCad
offcytBon 2][][))(( txf
dtxd
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Poincaré map
)(~ tx
)()(~)( tytxtx
)( 1tx
)( 1 Ttx
)(~ tx
The map M : CnCn with
can be written in diagonal form with eigenvalues or Floquet multipliers with
Stability requires
)())(( TtxtxM
ses 2
s
0)( s1|| s
0))(~( txfdtxd
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Multi-stability and hysteresis
Gielen et al., Phys Rev Lett 2009
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Multi-stability and hysteresis
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Conclusion
• In a network of cells with the same conditions everywhere, (clusters of) cells can be in different states (multi-stability) depending on the past (hysteresis).
• Multi-stability allows that subsets of neurons in a network can be in different states (parallel processing !)
• Hysteresis ensures that, once a process is started, it is completed, even if external input changes.
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Liley model
1
)1(1)(
)()()(~
)(~
~,~
,)()(
)()()(
ˆ)(2
maxabs
max
,
l
ll
lklk
lk
th
llll
lklklllklklk
lklklk
lk
lklklk
lk
lkrk
eqlk
keqlk
klk
lkiel
klkkrk
kk
eSrSthS
tptthSNe
tIdtd
dtd
ehh
thhth
tIththhdtdh
Liley et al., Phys Rev E 2007
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P4P3O2O1FzCzPz
1 s70 V
Brain rhythmsEyes closed
Alpha-rhythm (about 10 Hz)
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Oscillatory activity in the brain at 40 – 80 Hz
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Hardware of the brain and functional connectivity
How is the connectivity modulated to tune the brain for each particular task ?
• dynamic interactions
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Canolty et al. Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies, PNAS 2010
Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies
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Dynamic interactions between neurons
1. Plasticity by learning• time scale seconds, hours, days, ….
2. Spike timing dependent plasticity• Time scale milliseconds to second• bottom-up process
3. Modulation of excitability by other neurons• Time scale tenth of millisecond• Top-down process• Responsible for rhythmic oscillations
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Human Brain Mapping 30:1791-1800 (2009)
Role of alpha-activity
Hypothesis : information is gated by inhibiting task-irrelevant regions.
Functional inhibition is reflected in oscillatory activity in the alpha band (8–13 Hz).
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Human Brain Mapping 30:1791-1800 (2009)
Larger alpha-activity: more false alarms !
Alpha activity reflects a state of reduced perception
We can predict false alarms !
Hypothesis : information is gated by inhibiting task-irrelevant regions. Thefunctional inhibition is reflected in oscillatory activity in the alpha band (8–13 Hz).
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Alpha-activity after rehearsal compared to that in “forgotten” condition
Inhibition is important in a word rehearsal taskHuygensgebouw
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Alpha-activity after rehearsal compared to that in “forgotten” condition
Inhibition is important in a word rehearsal task
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Alpha-activity after rehearsal compared to that in “forgotten” condition
Inhibition is important in a word rehearsal taskHuygensgebouw
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Dorsal = “WHERE”
Ventral = “WHAT
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Activity in posterior cortical areas (dorsal stream)
Identification Orientation
Selective inhibition of dorsal pathway for tasks requiring ventral stream
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Alpha activity is a mechanism to inhibit particular brain areas
What modulates the alpha activity ?
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Increase of Theta before a good response
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OOHPS !
Theta activity from frontal cortex is anti-correlated with alpha posterior
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alpha (10 Hz)
Theta (4-6 Hz)
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Summary: where are we ?1. Nonlinear system theory is the key to understanding complex
intelligent behaviour.• Neurons and neuronal interactions are nonlinear systems with
complex and highly interesting emergent properties:More is different !
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Summary: where are we ?1. Nonlinear system theory is the key to understanding complex
intelligent behaviour.• Neurons and neuronal interactions are nonlinear systems with
complex and highly interesting emergent properties:More is different !
2. We understand the basic principles of• neuronal dynamics• dynamics of neuronal interactions• simple emergent properties
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Summary: where are we ?1. Nonlinear system theory is the key to understanding complex
intelligent behaviour.• Neurons and neuronal interactions are nonlinear systems with
complex and highly interesting emergent properties:More is different !
2. We understand the basic principles of• neuronal dynamics• dynamics of neuronal interactions• simple emergent properties
3. We see a glimpse of• the basic principles of the neuronal code (neuronal firing, neuronal
oscillations, neuronal ensembles, flexible distributed parallel processing)
• how intelligent behaviour is represented in the brain4. We have no clue as to how the network is modified for the job and how the
connections between neuronal regions are modulated to optimize the network architecture.
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Challenges:
1.Understanding self-organization and changes in network architecture at various hierarchical levels by bottom-up and top-down processes2.Understanding the opportunities and limitations of the neural wetware (e.g. memory, decision making)
(see paper by Barabási)
What is required is a multi-disciplinary team of research groups to address complexity
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Thank you for your attention !
Special thanks to my collaborators
Magteld Zeitler Martin Krupa Ingo Bojak
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Functional Disconnection of Frontal Cortex and Visual Cortex in ADHD
index
middle
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Communication by coherence (CTC) hypothesis
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Synchronization of neuronal activity provides a label for cell assemblies
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Canolty et al. Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies, PNAS 2010
Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies
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Modulation of Gamma by Theta Rhythm
Short reaction time
Long reaction time