Encoding of spatiotemporal patterns in SPARSE networks
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Transcript of Encoding of spatiotemporal patterns in SPARSE networks
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
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
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
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)(
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
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
The network
With STDP plasticity
jjiji
iiii
SJh
hSSSW )tanh(12
1)(
)cos(1
1ji
P
ijij NJJ
Spin model
Sparse connectivity
Network topology• 3D lattice
• Sparse network, with z<<N connections per neuron
• z long range , and (1-z short range
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
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
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)
Experimental measures in C.elegans give C =0.23Achacoso&Yamamoto Neuroanatomy ofC-elegans for computation (CRC-Press 1992)
Clustering coefficient vs C=C-Crand
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