encoding of spatiotemporal patterns in sparse networks
DESCRIPTION
Encoding of spatiotemporal patterns in SPARSE networks. Antonio de Candia*, Silvia Scarpetta** *Department of Physics,University of Napoli, Italy **Department of Physics “E.R.Caianiello” University of Salerno, Italy. - PowerPoint PPT PresentationTRANSCRIPT
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Encoding of spatiotemporal patternsin SPARSE networks
Antonio de Candia*, Silvia Scarpetta**
*Department of Physics,University of Napoli, Italy
**Department of Physics “E.R.Caianiello” University of Salerno, Italy
Iniziativa specifica TO61-INFN: Biological applications of theoretical physics methods
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Oscillations of neural assembliesIn-vitro MEA recording In-vivo MEA recording
In cortex, phase locked oscillations of neural assemblies are used for a wide variety of tasks, including coding of information and
memory consolidation.(review: Neural oscillations in cortex:Buzsaki et al, Science 2004 -Network Oscillations T. Sejnowski Jour.Neurosc. 2006)
Phase relationship is relevantTime compressed Replay of sequences has been observed
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D.R. Euston, M. Tatsuno, Bruce L. McNaughton Science 2007
Fast-Forward Playback of Recent Memory Sequences in prefrontal
Cortex During Sleep.
Time compressed REPLAY of sequences
•Reverse replay has also been observed: Reverse replay of
behavioural sequences in hippocampal place
cell s during the awake state D.Foster & M. Wilson Nature 2006
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Models of single neuron• Multi-compartments models
• Hodgkin-Huxley type models
• Spike Response Models
• Integrate&Firing models (IF)
• Membrane Potential and Rate models
• Spin Models
jjiji
iiii
SJh
hSSSW )tanh(12
1)(
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Spike Timing Dependent Plasticity
From Bi and Poo J.Neurosci.1998STDP in cultures of dissociated rat hippocampal neurons
Learning is driven by crosscorrelations on timescale of learning kernel A(t)
Experiments:Markram et al. Science1997 (slices somatosensory cortex)Bi and Poo 1998 (cultures of dissociated rat hippocampal neurons)
f
f.
)( fi
fj ttA
fi
fj tt
LTP
LTD
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Setting Jij with STDP
)()()( ''' tttAtdtdtJ jiij )(A
)0(~
2)(~
Re AAJ jiij ji
j e
)cos(1
)(~
Re1
1jiji
P
ijij NA
NJJ
)cos(12
1)( ii tt Imprinting oscillatory
patterns
ieAA )(~
and 0)0(~
if
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The network
With STDP plasticity
jjiji
iiii
SJh
hSSSW )tanh(12
1)(
)cos(1
1ji
P
ijij NJJ
Spin model
Sparse connectivity
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Network topology• 3D lattice
• Sparse network, with z<<N connections per neuron
• z long range , and (1-z short range
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Definition of Order Parameters
j
jjN tStm )()( 1
If pattern 1 is replayed then 0||,0|| ,0|| 321 mmm
complex quantities
m
Re(m)Im(m)|m|
Units’ activity vs time
Order parameter vs time
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Capacity vs. Topology
N=13824
=1=0.3=0.1=0
Capacity P versus number z of connections per node, for different percent of long range connections
30% long range alwready gives very good performance
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Capacity vs Topology• Capacity P versus percent of long range
N= 13824Z=178
1.0
P= max number of retrievable patterns(Pattern is retrieved if order parameter |m| >0.45)
Clustering coefficient vs C=C-Crand
Experimental measures in C.elegans give C =0.23
Achacoso&Yamamoto Neuroanatomy ofC-elegans for computation (CRC-Press 1992)
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Experimental measures in C.elegans give C =0.23Achacoso&Yamamoto Neuroanatomy ofC-elegans for computation (CRC-Press 1992)
Clustering coefficient vs C=C-Crand
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Assuming 1 long range connection cost as 3 short range connectionsCapacity P is show at constant cost, as a function of C
Optimum capacity
3NL + NS = 170
N = 13824
C = C - Crand