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======Questions from TK 2020-04-01====== | ======Questions from TK 2020-04-01====== | ||
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=====Question 1===== | =====Question 1===== | ||
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</ | </ | ||
=====Question 2===== | =====Question 2===== | ||
- | The pca in your fig. 1 for both cases, show a good conservation for different sizes, although the two cases have different slope. So can these two mice in different state? | + | The PCA in your fig. 1 for both cases, show a good conservation for different sizes, although the two cases have different slope. So can these two mice in different state? |
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+ | It seems the slopes for the scaling regimes of both cases are about $1/2$, which is also the value quoted in Bialek' | ||
+ | </ | ||
=====Question 3===== | =====Question 3===== | ||
> However, whether the distributions of $m_i$ and $C_{i,j}$ are enough or the network topology also plays an important role does still need to be checked. Shuffling or re-sampling $m_i$ and $C_{i,j}$ from the observed distributions is a way of checking this. However, they are tricky since the result may not be a valid combination that can be generated by a distribution of system configurations. This is mentioned in http:// | > However, whether the distributions of $m_i$ and $C_{i,j}$ are enough or the network topology also plays an important role does still need to be checked. Shuffling or re-sampling $m_i$ and $C_{i,j}$ from the observed distributions is a way of checking this. However, they are tricky since the result may not be a valid combination that can be generated by a distribution of system configurations. This is mentioned in http:// | ||
What do you mean by marginal distribution? | What do you mean by marginal distribution? | ||
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+ | Randomly selecting neurons and keeping their $m_i$ and $C_{i,j}$ is kind of coarse-graining the network but preserving its structure. For selected neurons $i$ and $j$, their $m_i$, $m_j$ and $C_{i,j}$ are all preserved. But, if we are generating new values from the distributions of $m$ and $C$ then the original network structure will be lost. | ||
+ | </ | ||
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+ | The " | ||
+ | \[ | ||
+ | P(\sigma_i, | ||
+ | \] | ||
+ | With the marginal distribution $P(\sigma_i, | ||
+ | </ | ||
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=====Question 4===== | =====Question 4===== | ||
In the paper you quoted, they enlarge the system to 120 neurons by a quote in page 10 | In the paper you quoted, they enlarge the system to 120 neurons by a quote in page 10 | ||
"We thus generated several synthetic networks of 120 neuons | "We thus generated several synthetic networks of 120 neuons | ||
- | of hi and Cij observed experimentally." | + | of $m_i$ and $C_{i, |
+ | |||
+ | <color darkgreen> | ||
+ | I have attempted this. However, after the drawing, the Boltzmann learning that is performed to obtain $h_i$ and $J_{i,j}$ does not converge as well as the original system so I am leaving them running on the cluster. I will check the results after I am back in my office next week. | ||
+ | </ | ||
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+ | However, the fact that they are not converging well may be an indication that the generated $m_i$ and $C_{i,j}$ may not be fully valid since we only ensure its validity with spin pairs and not with higher order of spin combinations. When the values $m_i$ and $C_{i,j}$ are not valid, no solution of $h_i$ and $J_{i,j}$ can exactly reproduce $m_i$ and $C_{i,j}$ and there will be a none-zero minimum for the error. | ||
+ | </ | ||
=====Question 5===== | =====Question 5===== | ||
- | We can still try to follow our previous method, keeping the rank and shuffle only C(ij) within a small interval, similarly for mi. | + | We can still try to follow our previous method, keeping the rank and shuffle only $C_{i, |
If we increase the size of the interval, then we will get to completely reshuffle. Then we can check how sensitive | If we increase the size of the interval, then we will get to completely reshuffle. Then we can check how sensitive | ||
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+ | This should be OK. But, as above, we need to check the validity of resulting combination of $m_i$ and $C_{i,j}$. | ||
+ | </ | ||
=====Question 6===== | =====Question 6===== | ||
In this Bialek' | In this Bialek' |