Topic: NXT :: descendant of Bitcoin - Updated Information - page 612. (Read 2761629 times)

Just an update on my recent calculations.

I'm assuming that the algorithm currently used may be roughly approximated by the following model. Let g_i be the balance of ith account expressed in billions of NXT (so the sum of all balances equals 1). To decide who will generate the next block, take i.i.d. Uniform[0,1] random variables U₁,...,U_n (n is the total number of accounts; I'm assuming also that they are all forging), and calculate W_i=g_i/U_i. The account for which W_. is maximized, will forge, and the corresponding weight is called the weight of the block.

As noted before, this approach slightly favors bigger accounts; in order to make the forging power exactly (up to computational errors) proportional to the balance, one must use W_i=g_i/|ln U_i| instead. CfB told me that BCNext preferred not to use logs in order to discourage splitting of big accounts (what for - anybody knows?). Anyhow, if all g_i s are small (compared to total amount), then the two approaches are almost indistinguishable, and it's easy to justify it mathematically (will do it in the paper).
In the case of concurrent blockchains, wins the one for which the sum of inverse weights is minimal. (Currently wins the longest one, but these two approaches are, in fact, equivalent.)

Now, we consider the following situation: one big bad guy has b billions-of-NXT, and the others are poor, honest, and many. The bad guy (with his minions) "accidentally" disconnects from the network, and secretly forges a branch of length m. Let us consider the (future) situation with one-block-per-minute, and estimate the probability that this "bad" branch wins over the "good" one.

In the "ideal" situation (when the forging power is exactly proportional to the balance, the above approach with logarithms), the probability of this event will be of order
(4b(1-b))^m   for b<0.5.
Observe that 4b(1-b)<1 for b<0.5, so the probability decreases rather fast.

On the other hand, with the current setup (when one divides by uniform r.v. instead of dividing by log of it), this probability only tends to 0 for b<1/3 (I'll write the formula in the paper, since it's much more complicated). The reason for this is easy to explain: the inverse weight produced by good guys has Exponential(1-b) distribution, and so its expectation is 1/(1-b). Now, the inverse weight produced by the bad guy has Uniform[0,1/b] distribution, with expectation 1/(2b). Solving 1/(1-b)<1/(2b), we arrive to b<1/3.

Now, I'm not sure if there is a mathematical solution about how to fence off an attack of someone with b>1/3 (or b>0.5 in the other setting)...

In the next couple of weeks I'll go to a conference in Ulm and then receive an important visitor, so, most probably, I won't be able to read this thread in full (though, of course, I'll check PMs and read Damelon's summaries). Sure, I promise to type all these calculations in an organized way (style of modern math paper; will try to speed it up). Please, discuss it at https://forums.nxtcrypto.org/, this topic: https://forums.nxtcrypto.org/viewtopic.php?f=17&t=836

I am pleased to provide additional information regarding NMAC IPO share placement.  At this moment only 80 million shares are left for sale, 20 million have already been sold.

Due to strong demand we have developed the below allocation formula to be fair to those who expressed strong interest from early January.  As well as to distribute the shares to more investors.


1st Tier: 30 million shares (30%)

Maximum that can be purchased: 5,000,000 shares


2nd Tier: 25 million shares (25%)

Maximum that can be purchased: 2,500,000 shares


3rd Tier: 25 million shares (25%)

This allocation will be totally sold on the Nxt Asset Exchange.  The shares will be sold on AE launch day.


The below list are those investors who showed interest in financing NMAC from the beginning of early January.  Those at the top of the list will have first right to purchase shares over those lower on the list.


Pandaisftw - Jan 8
Danniego - Jan 8
Kbk00 - Jan 8
Abctc - Jan 9
Cromaclear - Jan 9
Neer.g - Jan 9
UtopianFuture - Jan 9
Benowl - Jan 9
Hash - Jan 14
Butterclown -  Jan 18
EXtatiC - Jan 21
Shin - Jan 21
Swartzfeger - Jan 22
Ezravdb - Jan 23
Okaynow - Jan 29
LemonAndFries - Feb 8

After business plan published:

Kodtycoon - Feb 25
Smaragda - Feb 25
eB101 - Feb 25
Damelon - Feb 25
KyLins - Feb 25
Rushi - Feb 25
Shenjie - Feb 25
Voldemort628 - Feb 26
Redsn0w - Feb 26
Pt2002 - Feb 27
Stoneone - Feb 27
Bezbezbez - Feb 27
Xcn - Feb 27
Sashsh - Feb 27

This process will run until March 9th, 11:59 PM GMT.  

After this time no one will have precedent over others wanting to buy shares from the 1st or 2nd tier.

PLEASE SEND ME A PM WITH THE AMOUNT OF SHARES  YOU WISH TO PURCHASE.  REQUESTS SHOULD BE WITHIN THE MAXIMUM ALLOWED AS MENTIONED ABOVE.




Re-polished Prospectus/Business Plan  
https://mega.co.nz/#!fEAUlaqD!7_wUKeM6gdtHZdTUrbRRpgg1MS8z_xi38k8IBb5_sJs


Best regards,
Landomata
Secretary
Nxt Mobile Applications Company

Pouncer & Anon check ur skype please!

awesome ppl, may I have a link to latest source code?

nxt serious coin wish to succeed

Where can I find more technical details about the AC? Is anyone actively working on it?

Interesting.

I don't really understand Java too well, but from taking a peek at the code it seems "account" is a hashmap and the number of accounts is the number of key-value mappings.

You've made me curious as to what the difference between yours and NRS may be.

Edit: actually, that was true in the old code.  I haven't even looked at the 0.8.x code base which may or may not do things differently now that it has an actual database.  Will have to look at that later.

I was in a fork

Great, please PM James, now we need some Doge volunteers to test DAC.

It is a good idea but how?

I am not a programmer but I have superior training in engineering. I'm trying to
follow you but sometimes I find it difficult.

we could act on several lines of work

a document where you could see each of the characteristics of nxt and practical example in real life of this feature.

Form working groups for projects to use nxt in any real-life activity in order to demonstrate its advantages.

Each project would be formed  minimum by a developer, a marketing especialist and a specialist in real activity and to later in fairs and events demonstrate the advantages of nxt ecosystem.

The mynxt.info one is done summing up all the unique accounts involved in any transaction since block 0.

One based on account balance of 1 or greater, the other based on existing public key?

Hmm?

Good point

I wonder where the difference is... probably different way of counting accounts.

ON BEHALF OF CIYAM (China firewall-censorship issues):

a) using a good password create a SHA256 of it
b) publish a hash that is the hash from a hashed “x” times
c) lock your account then after that is confirmed send a tx from your account to another (won’t be able to actually transfer any funds even after confirmed)
d) send a tx that provides the “x-1” hash (i.e. if you hash that you get the hash that was sent in b)
result is that tx from c can now *occur* and also the locking hash has now been changed

{"lastBlock":"11991592437029432970",
"numberOfAliases":63045,
"numberOfBlocks":77224,
"numberOfTransactions":135421,
"version":"0.8.3",
"totalEffectiveBalance":99465935000,
"cumulativeDifficulty":"2406269794605079",
"numberOfAccounts":25420}

Looks like we will cross 25k NXT accounts today: http://www.mynxt.info/charts/number_of_accounts.php

      
      77216      15985892217534139770   
      
      77215      2382970272294477859      
      
      77214      15401440438959943842
      
      77213      15663686671422955221   

77214      15401440438959943842

hello,you can come in to Chinese Nxt QQ community, QQ GROUP:347593833