Encoding of spatiotemporal patterns in SPARSE networks

1. 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

2. In-vitro MEA recording In-vivo MEA recording Oscillations of neural assemblies 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. Time compressed REPLAY of sequences D.R. Euston, M. Tatsuno, Bruce L. McNaughton Science 2007 Fast-Forward Playback of Recent Memory Sequences in prefrontal Cortex During Sleep. • Reverse replay has also been observed: Reverse replay of behavioural sequences in hippocampal place cell s during theawake stateD.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. f f. t t Spike Timing Dependent Plasticity Experiments: Markram et al.Science1997 (slices somatosensory cortex) Bi and Poo 1998 (cultures of dissociated rat hippocampal neurons) LTP LTD 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)

6. Setting Jij with STDP Imprinting oscillatory patterns

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

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

9. Re(m) Im(m) |m| If pattern 1 is replayed then Definition of Order Parameters complex quantities Order parameter vs time Units’ activity vs time

10. g=1 g=0.3 g=0.1 g=0 Capacity vs. Topology 30% long range alwready gives very good performance N=13824 Capacity P versus number z of connections per node, for different percent of long range connections g

11. Capacity vs Topology • Capacity P versus percent of long range g N= 13824 Z=178 Clustering coefficient vs g DC=C-Crand Experimental measures in C.elegans give DC =0.23 Achacoso&Yamamoto Neuroanatomy of C-elegans for computation (CRC-Press 1992) P= max number of retrievable patterns (Pattern is retrieved if order parameter |m| >0.45)

12. Clustering coefficient vs g DC=C-Crand Experimental measures in C.elegans give DC =0.23 Achacoso&Yamamoto Neuroanatomy of C-elegans for computation (CRC-Press 1992)

13. Optimum capacity Assuming 1 long range connection cost as 3 short range connections Capacity P is show at constant cost, as a function of DC 3NL + NS = 170 N = 13824 DC = C - Crand