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 Iniziativa specifica TO61-INFN: Biological applications of theoretical physics methods

Oscillations of neural assemblies In-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 Network Oscillations T. Sejnowski Jour.Neurosc. 2006) Phase relationship is relevant Time 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

Spike Timing Dependent Plasticity  From Bi and Poo J.Neurosci.1998 STDP 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. LTP LTD

Setting J ij with STDP Imprinting oscillatory patterns

The network  With STDP plasticity  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 If pattern 1 is replayed then complex quantities 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= Z=178 P= max number of retrievable patterns (Pattern is retrieved if order parameter |m| >0.45) Clustering coefficient vs   C=C-C rand Experimental measures in C.elegans give  C =0.23 Achacoso&Yamamoto Neuroanatomy of C-elegans for computation (CRC-Press 1992)

Experimental measures in C.elegans give  C =0.23 Achacoso&Yamamoto Neuroanatomy of C-elegans for computation (CRC-Press 1992) Clustering coefficient vs   C=C-C rand

Assuming 1 long range connection cost as 3 short range connections Capacity P is show at constant cost, as a function of  C Optimum capacity 3N L + N S = 170 N =  C = C - C rand