Proof-of-Stake is going to be popular distributed consensus algorithm these days. Some properties of the algorithm are very promising, but there are some concerns about it around also.
In the first place, let me introduce myself. I'm Nxt core developer for last few months. To better understand Nxt forging algo I started to model it with Haskell(which is awesome for modelling purposes). Based on the model, two articles were published in my blog:
[li]Inside Proof-of-Stake CryptoCurrency pt. 1 - Basic Structures [url]http://chepurnoy.org/blog/2014/10/inside-a-proof-of-stake-cryptocurrency-part-1/[/url][/li]
[li]Inside Proof-of-Stake CryptoCurrency pt. 2 - Forging Algorithm [url]http://chepurnoy.org/blog/2014/10/inside-a-proof-of-stake-cryptocurrency-part-1/[/url][/li]
Using this model a friend of mine , andruiman (writing math phd now) made academic-like paper about statistical properties of Nxt forging algo: [url]https://www.scribd.com/doc/243341106/nxtforging-1[/url] (scroll down to view online, to download PDF without FB login use Mega hosting https://mega.co.nz/#!MJoRnByZ!9i6cZ89SvgtafIAVdlyuJEyqmNAPnvysxF6BCIKjePA ).
We plan to go further, and not around Nxt only. The next step is to make executable open-source simulation of forging process, then expand model. In the first place, we think to model blocktree storage for a forger with contributing to all possible chains of a tree (it's claimed to be a way to produce "nothing-at-stake" issue). We're also going to model some properties of proof-of-stake in more formal way with Coq theorem prover.
From this moment, we're going to call ourselves "Proof-of-Stake Research Group". Both of us are writing phds now(Computer Science / Math). In future we can expand number of participants for sure, but there's no need in that for now.
We're open to communicate with researchers / developers interesting in the topic.