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