| layout | title | date | author | summary | references | weight | |||
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notes |
28. Oscillations in Reverberating Loops |
2017-02-17 |
OctoMiao |
Oscillations in reverberating loops can be simplified and researched. |
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28 |
- Biological neuron networks have reverberating loops; inferior olive (IO).
- Periodic large-amplitude oscillations can happen even with each individual neurons firing at a significantly smaller rate or of irregular spike trains. Nicely explained in Fig. 8.11
- Strong oscillations with irregular spike trains is related to short-term memory and timing tasks.
- Binary neurons: potential of the ith neuron at time
$t_{n+1}$ is determined by the states of other neurons at time$t_n$ $u_i(t_{n+1})=w_{ij}S_j(t_n)$ . The state of neuron$S_i(t_n)$ is determined by the potential at time$t_{n}$ ,$S_i(t_n)=\Theta(u_i(t_n)-\theta)$ , where$\theta$ is threshold. - Approximate SRM to McClulloch-Pitts neurons with "digitized" states.
- For sparsely connect we can approximate the time evolution using independent events and find the probability.
- Fig. 8.12; The interactions are shown on the top panels. We start from a value of
$a_n$ , the iteration gives us the result of$a_{n+1}$ . Then the next step depends on the value of$a_{n+1}$ so we project it onto the dashed line$a_{n}=a_{n+1}$ . Then we use the new$a_n$ value to find the new$a_{n+1}$ .
- Random network with balanced excitations and inhibitions can generate broad interval distributions.
- Reverberating projections usually have both excitation and inhibitions.
- McClulloch-Pitts model with both excitations and inhibitions.
- The simplified model (SRM->McClulloch-Pitts) doesn't catch all the features, with inhibitory neurons in presence. The limit circle can grow substantially larger as size of the network increases.
- Information will drain away with noise. Fig. 8.15