1. Burst Synchronization transition in neuronal network of networks Sun Xiaojuan Tsinghua University ICCN2010, Suzhou 2010-10-16

2. OUTLINE Background Background - Importance of synchronization in neuronal systems - Network of network structures of neuronal systems - Motivation of this work - Motivation of this work Burst synchronization (BS) transition in a neuronal network of networks Burst synchronization (BS) transition in a neuronal network of networks - Mathematical Models - Observed BS transition Conclusions Conclusions

3. Background

4. Importance of synchronization in neuronal systems Relationship between synchronization and cognitive behavior  Attention modulates synchronized neuronal firing in primate somatosensory cortex (Ref: Nature, 2000, 404: 187-190)  Attention modulates the firing rates of neurons in many parts of the visual system (Ref: Annu. Rev.Neurosci., 2000, 23, 315- 341)  Expectation boosts synchrony in motor cortex: neurons in the primary motor cortex become transiently synchronized when a stimulus appears, or when it is expected to appear but it does not (Ref: Science, 1997, 278: 1950-1953)  Rivalry induces changes in synchrony in V1 (Ref: PNAS, 1997, 94: 12699-12704)

5. Importance of synchronization in neuronal systems Relationship between synchronization and brain disorders DisorderNeural synchronyCognitive dysfunctions EpilepsyIncrease in local synchrony; evidence for a reduction in long- range synchronization Perception, executive, processes, memory, attention, social cognitive Alzheimer’ s disease Reduced neural synchrony during resting state; evidence for reduced functional connectivity Working memory, perception, attention, executive process Parkinson’ s disease Increase in neural synchrony in the basal ganglia, but also between subcortical-cortical structures Especially motor functioning, but also perception, working memory,attention, executive process

6.  clustered structure (Ref. C.C. Hilgetag, Neuroinformatics, 2004, 2: 353-360) Network of network structures of neuronal system Bars indicate borders between nodes in separate clusters.

7.  Not only clustered but also hierarchy (Ref. C.S. Zhou, et al. New J. Physics, 2007, 9: 178.) Network of network structures of neuronal system Neuronal system is complex and composed by network of networks

8. Motivation Cited from Ref: Shen Yu et al., PRE, 2008, 77: 031920

9. BS transition in a neuronal network of networks

10. Mathematical Models Equations of the discussed neuronal network

11. Mathematical Models Neuronal Network structure:

12. BS transition in HR neuronal network Two cases:  M=2, consider the effects of inter- and intra- coupling strength, the random link probability on synchronization of the clustered neuronal network  M>2, except for the above mentioned three factors, we will further consider the effects of cluster numbers on synchronization.

13. BS transition in HR neuronal network M=2

14. BS transition in HR neuronal network

19. Cited from PRE_77_031920

20. BS transition in HR neuronal network We turn back to the first equation of Eq.(1) and rewrite it as

22. BS transition in HR neuronal network M>2

23. BS transition in HR neuronal network M>2

24. Conclusions

25.  Under some conditions, coupling strength inside or between subnetworks and the number of links can change the synchrony of a neuronal network, which has clustered structures.  The number of subnetworks inside a network also influence the synchrony.  Our results may give some implications for the importance of synaptic plasticity in neuronal systems.

26. Thanks for your attention! Thanks Prof. Qishao Lu and Prof. Guanrong Chen