1. Ch 9. Rhythms and Synchrony 9.7 Adaptive Cooperative Systems, Martin Beckerman, 1997. Summarized by M.-O. Heo Biointelligence Laboratory, Seoul National University http://bi.snu.ac.kr/

2. 2 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/ Contents 9.7 Oscillations and Synchrony in the Visual Cortex and Hippocampus  9.7.1 Mean-Field Model of Cortical Oscillations  9.7.2 Delay Connections and Nearest-Neighbor Interactions  9.7.3 Burst Synchronization  9.7.4 Rhythmic Population Oscillations in the Hippocampus  9.7.5 Feature Integration

3. Mean-Field Model of Cortical Oscillations How limit cycle oscillations may arise in a single cortical column in response to external stimuli? 3 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

4. Dynamic Equations for the cortical column activities 4 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ Mean firing rate of excitatory neurons Mean firing rate of inhibitory neurons # of Excitatory neurons # of Inhibitory neurons Sigmoidal response fct. External inputs to the excitatory cells (No input to the Inhibitory neurons) Taylor Expansion with τ=0, r=0 Sum over the index i

5.  A stable fixed point characterizes the system at low-stimulus intensities.  There is a transition to limit cycle activity once the stimulus intensity increases beyond a critical value. 5 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

6. By coupling together a number of excitatory-inhibitory clusters  Introducing the phase variable through the deviations of the activities from the unstable fixed points 6 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/ If η is weak… The couplings proportional to η Oscillator Freq.

7. Delay Connections and Nearest-Neighbor Interactions Delay connections in a simplified oscillator unit obeying the followings. Results  When the time delays are either too small or too large, a system of two coupled units will relax to a stable fixed point.  There is a broad range of delays in the vicinity of 4 to 5 ms for which the system will exhibit stable limit cycle behavior.  Desynchronization was promoted by adding a second set of delay connections operating between next nearest neighbors. 7 Delay Damping Constant Noise inputs

8. Burst Synchronization Bush & Douglas  A network composed of excitatory pyramidal and inhibitory basket (smooth) neurons.  Showing a rapid onset of synchronous bursting with randomly varying interburst intervals. Koch & Schuster  Simplified Bush & Douglas Model  One containing all-to-all excitatory binary (McCulloch-Pitts) neurons  A single global inhibitor.  Generating burst synchronization without frequency locking  The neural circuitry functions as a coincidence detector  Inhibition improves frequency locking and determines the frequency of the oscillatory firing pattern. 8 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

9. Rhythmic Population Oscillations in the Hippocampus Hippocampus exhibits several different types of rhythmicity and has a number of possibly redundant mechanisms for inducing collective responses.  Hippocampal cells extend out widely arborizing axon collaterals those provide the connectivity to generate recurrent excitation.  GABAergic interneurons are present.  Inhibitory postsynaptic potentials (IPSP) are consistent with the timing required for recurrent inhibition.  Cells are capable of repetitive bursting  The membrane potential of single pyramidal cells can oscillate in the 4~10 Hz range.  Oscillatory cells in the entorhinal cortex projecting to hippocampal neurons can also drive cells into 4~10 Hz oscillations.  The 40-Hz oscillations  are a collective behavior of the network of inhibitory interneurons in the hippocampus. Mutual inhibition plays a key role for this.  Are from the intrinsic 40-Hz oscillatory interneurons. 9 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

10. Computational studies for the characteristics of hippocampal rhythmicity.  Traub et al.  200 excitatory neurons in a two-dimensional array  10 inhibitory neurons uniformly distributed across the array. –Two types: fast inhibition, slow one  When fast inhibition is present the bursting neurons self-organize into clusters of synchronously firing cells.  When fast inhibition is blocked, most of the cells in the population burst coherently. 10 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

11. Constant speed traveling waves of activity  Observed in EEG recordings –9000 model excitatory cells, each contacted 22 neurons; 20 of these excitatory, 2 of these inhibitory –900 inhibitory ones, each communicated 220 neurons; 200 excitatory, 20 inhibitory –Typical cell received 20 excitatory inputs and 20 inhibitory inputs.  Connection probability –Decreased exponentially with distance at a rate determined by space constants for excitatory and inhibitory units. 11 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

12. Feature Integration Binding problem  How attributes are integrated to produce a segmentation of the scene into its component surfaces and a segregation of objects from their backgrounds.  Candidate mechanisms  Through a convergence of low-level inputs into a small number of higher-level neurons called grandfather or cardinal cells located in object-specific cortical areas.  Through assembly coding - through flexible associations of large numbers of simultaneously active neurons. –Bound together by their synchronous firing –Experimental evidence that clusters of synchronously discharging cells form within one or more columns and in different cortical regions and hemispheres. 12 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/

13. Assembly coding and MRF-based integration-by- labeling are self-organizing processes that reinforce and improve the integration of features from one iteration to the next and are robust against noise. Visual cortical areas were built from feature selective cells arranged topographically into cortical columns. Assembly coding has been identified with gamma-band rhythmicity. 13 (C) 2009, SNU Biointelligence Lab, http://bi.snu.ac.kr/http://bi.snu.ac.kr/