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I'm trying to craft an example going through the math equation in Section 4.1 . I'm trying to show my work. Can you tell me if I've got it right and if not, help correct me?

4.1 Equation
Hx – Cumulative weight at node x – Let’s say 65
Hy – Cumulative weight at node y – Let’s say 70
Hz – Cumulative weight at node z – Let’s say 75
α – Try with 1
Pxy = exp( -1( 65 – 70 ) * ((75+74+…65)^(-1(65 – 75)) )^-1
Pxy = exp( 5) * (770^10))^-1
Pxy = 1.365e-29^5
Pxy = 4.737e-145

Bill Bisco
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1 Answers1

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Unfortunately, this doesn't look correct. Regardless of the actual numbers, you are not treating the sum as a sum but rather as a single summand. On top of that, you seem to be missing the exp function in a few places during your P_xy calculation.

Below I am pasting a sample calculation for a transaction x that is referenced by three other transactions y_1,y_2,y_3. That is, y_i⇝x for i=1,2,3.

So for example, the transition probability of going from x to y_3 is ≈ 32%.

SampleCalc

Phil-ZXX
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  • Am I not iterating over y as well? To go from z to x I have to pass through y (75, 74, 73, 72, 72, 71, 70!!!,..) Are you saying this Sigma is not Sigma notation? http://home.windstream.net/okrebs/page136.html – Bill Bisco Jan 16 '18 at 14:30
  • Is the math supposed to be 75^( -1(65 - 75) + 74^(-1(65 - 75) .... ? – Bill Bisco Jan 16 '18 at 14:32
  • I mean, generally, there are several issues. For one, the cum weight of x should be larger than the one of y. Secondly, neither ((75+74+…65)^(-1(65 – 75)))^-1 nor 75^( -1(65 - 75) + 74^(-1(65 - 75) has the exp function in it, so I am really not sure what you are calculating. – Phil-ZXX Jan 16 '18 at 15:28
  • The whitepaper says put random particles on sites on the tangle and have them walk towards the target. The walkers are defined as y approves x so so site x is somewhere earlier in the tangle and site y is a tip at the end? The tip should have a larger weight than a previous transaction earlier no? x should smaller than y no? – Bill Bisco Jan 16 '18 at 16:31
  • 6exp( 3 ) is the same as 6^3 or 666 or 216 no? In my comment above I said z is 75 and I start the sigma with 75 that should be 75 ^ ( -1 ( 65 - 75) and then I add that to the next right 74 ^ (-1 (65 - 75) ? – Bill Bisco Jan 16 '18 at 16:34
  • Earlier transactions have a higher weight (older = higher cum weight). You may want to consider asking a new (specific) question about all this, as the comment section is running out of space. – Phil-ZXX Jan 16 '18 at 16:37
  • Thank you for your added math equations! I am trying to wrap my head around the details. In your example, you are saying that we choose x as our site within the tangle and randomly walk to the tips. In our case, there are 3 tips with the weights you specified. But, aren't the tips supposed to have a weight of 1? I don't understand the example now. The whitepaper says nothing about sites traversing towards sites only towards the tips. – Bill Bisco Jan 17 '18 at 19:19
  • You start at transaction x and then randomly walk towards tips (via other transactions), you don't just jump to the tips. The 3 transactions i listed are not tips, they are historic transactions referencing x. Here we model only one step of the entire walk. The weights I listed are cumulative weight, and not individual weights. Hence they are larger than 1. – Phil-ZXX Jan 17 '18 at 19:23
  • So, basically the idea (which is not covered directly) is to choose how far in the past to select the main site and randomly walk towards sites (with a weight), a higher alpha means that we randomly walk towards higher weighted sites first. We can compare the probabilities of a site going through other transactions (your y1,y2, y3) to verify effect of the alpha. The disadvantage of a high alpha is that we will always be selecting the highest weight branch and there may be other legitimate branches which need verification too? – Bill Bisco Jan 17 '18 at 19:37
  • That is correct. – Phil-ZXX Jan 17 '18 at 19:50