1. 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

2. 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 2004 - Network Oscillations T. Sejnowski Jour.Neurosc. 2006) Phase relationship is relevant Time compressed Replay of sequences has been observed

3. 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

4. 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

5. 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

6. Setting J ij with STDP Imprinting oscillatory patterns

7. The network  With STDP plasticity  Spin model  Sparse connectivity

8. Network topology 3D lattice Sparse network, with z<<N connections per neuron  z long range, and (1-  z short range

9. 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

10. 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

11. Capacity vs Topology Capacity P versus percent of long range  N= 13824 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)

12. 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

13. 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 = 13824  C = C - C rand