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p:questions1 [2020/04/01 17:12] – created cjj | p:questions1 [2020/04/04 06:07] (current) – [Question 6] cjj | ||
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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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> My current understanding is that the mean $m_i$ and correlation $C_{i,j}$ are more universal (over different samplings of the system) than the inferred $h_i$ and $J_{i,j}$ in determining the thermodynamic behavior of the system. | > My current understanding is that the mean $m_i$ and correlation $C_{i,j}$ are more universal (over different samplings of the system) than the inferred $h_i$ and $J_{i,j}$ in determining the thermodynamic behavior of the system. | ||
- | Show evidences | + | Show evidences and analysis to support your claim?? also average |
Do we see this effect in all the data set we got from them? Those data sets have different numbers of ROI. | Do we see this effect in all the data set we got from them? Those data sets have different numbers of ROI. | ||
An assumption proved? | An assumption proved? | ||
+ | |||
+ | <color darkgreen> | ||
+ | This comes from sub-sampling with different sizes. The $m_i$, $C_{i,j}$ distributions are close to the original while the $h_i$, $J_{i,j}$ distributions show more deviation. | ||
+ | </ | ||
+ | {{ : | ||
+ | <color darkgreen> | ||
+ | Also, compare with the case of shuffling $J_{i,j}$: | ||
+ | </ | ||
+ | {{ : | ||
+ | <color darkgreen> | ||
+ | We see identical distributions of $h_i$ and $J_{i,j}$ with significant different $m_i$ and $C_{i,j}$ distributions. | ||
+ | </ | ||
+ | {{ : | ||
+ | <color darkgreen> | ||
+ | At the same time, the specific heat curve also changes dramatically upon shuffling as shown to the right. | ||
+ | </ | ||
=====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? |
+ | |||
+ | <color darkgreen> | ||
+ | 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:// |
- | However, this does not guaranty triplets or higher marginal distributions are all valid and the shuffled $m_i$ and $C_{i,j}$ can still be un-physical. This makes me wonder if this is one of the reason why this paper was not published. And, we need to think of different ways of perturbing the system to find the minimal criteria of when the collective properties of the system are preserved. | + | |
What do you mean by marginal distribution? | What do you mean by marginal distribution? | ||
+ | |||
+ | <color darkgreen> | ||
+ | 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. | ||
+ | </ | ||
+ | |||
+ | <color darkgreen> | ||
+ | The " | ||
+ | \[ | ||
+ | P(\sigma_i, | ||
+ | \] | ||
+ | With the marginal distribution $P(\sigma_i, | ||
+ | </ | ||
+ | |||
=====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. | ||
+ | </ | ||
+ | |||
+ | <color darkgreen> | ||
+ | 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 | ||
+ | |||
+ | <color darkgreen> | ||
+ | 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' | ||
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TK | TK | ||
+ | <color darkgreen> | ||
+ | I couldn' | ||
+ | </ |