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I'm trying to abstract the mathematical part of the problem as much as possible before the details follow, There's this dynamic data set that's $O(2^{32})$, a recent result described it as a power-law distribution, as average is approaching $1-2$ with a peak at $100$ as said. I was just motivated by the fact that there is a subset known to have sometimes values of $O(10^5)$ inside, and the 1st lesson on Statistics is that average is not enough to represent the data in such cases. Then I found previous results describing the same dataset as:

  • "is impossible to be modeled mathematically, since it is purely chaotic" (Stanford report Dec2015)

  • "Nevertheless, in the above graph there’s a distinct linear formation within the phenomenal chaos" (2017).

I came to this group to ask the Scientific opinion of the most specialized, all the complete files r downloadable & available online.

References

The Stanford Report poster

The median results 2017, although I think it has 2 groups/clusters one with a linearly increasing median & one adjacent to the X-axis (the majority by the newer results)

a fig From "Implementing A Church–Turing Deutsch Principle Machine on a Blockchain", Konstantinos Sgantzos,Department of Computer Science and Biomedical Informatics , University of Thessaly, Lamia, Greece,17-07-2017

The Utreexo graph 2019, with green text & colored lines added by me

. Ps. I added Laplace Transformation as a keyword because it is stated in the full copy of the Stanford report that it was used in processing the data set:

Two methods of doing this are either (1) entirely empirically or (2) based on a fitted distribution. The former case is simply a matter of sorting the lifespan dataset and splitting it into ten equally sized groups. The latter requires more processing. Understanding that the data should show signs of a Laplace or exponential distribution based the standard application of those distributions, the first step was to cluster the lifespan set using k-median (`1 penalty function) clustering. From there, we fitted either a Normal, Laplace, or Exponential (whichever was most likely) distribution to each cluster using maximum likelihood estimation and then formed a global distribution as a weighted sum.

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