: Nebulas Rank Nebulas 2018 6 v1.0.1
1... 1 2... 3 2.1... 3 2.2... 4 2.3 ( )... 4 3... 6 3.1... 6 3.2... 7 4 Nebulas Rank... 10 4.1... 10 4.2 (In-and-Out Degree)... 12 4.3 Wilbur... 14 5 Core Nebulas Rank ( )... 17 5.1... 17 5.2 ( )... 18 5.3... 18 6 Core Nebulas Rank... 18 6.1?... 18 6.2 Core Nebulas Rank... 19 7 Extended Nebulas Rank... 20 7.1 Extended Nebulas Rank... 20 7.2 Extended Nebulas Rank... 20 8... 21... 22 A.... 24 B.... 27
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2.. 2.1 2008 10 Satoshi Nakamoto,.., 3.,., (Namecoin)[5] (DNS), Open Assets (Colored coins),. (Turing-Complete),.. (Ethereum) [7]. (Smart Contracts),.. (Ethereum Virtual Machine, EVM) EVM., (DApp). DApp,,,., (Killer Dapps)., (Externally owned account, EOA).,... 2015 Chris Skinner (Value Web), (Value Ecosystem) (Value Exchanges) (Value Stores) 3
(Value Management Systems),. Chris. 2.2,.,.,,. PageRank [9]. Google PageRank., PageRank,, PageRank. PageRank Fleder, Kester, Pilai [10], PageRank. PageRank PageRank. Web 2.0 PageRank., PageRank, PageRank LeaderRank. PageRank, LeaderRank. LeaderRank ( ). PageRank (Sybil Attack). LeaderRank (, ),,.,. Nebulas Rank NEM, [17] (Proof of Work) (Proof of Stake) NEM (Proof of Importance), NCDawareRank[14]. NCDawareRank ( ) SCAN[15] [16] [17].,. 2.3 ( ) Nebulas Rank,. Hopcroft [18], PageRank 4
. Zhang, ( ) [19]. PageRank (Symmetric Network) [20][12]. : 1... 2. (out-degree),. 3.,. 4.,. Nebulas Core Nebulas Rank,. 5
3. Core Nebulas Rank. ( ) Core Nebulas Rank. 3.1..!. L U (L, U)!!. : L = (A, D, T)! (1) A D T!,!,! ( ). (tetrad) : D = {a d, a A, d R*}! (2) T = {(s, t, w, τ)}! (3) a! d a d d s, t, w τ! (!., 0 )!.!!,,. : u dom a. u U, a A! (4) 6
: A(u ) = { a A : u dom a}! (5) :! (6)...... 3.2,. [21],. u 1, u 2 U : A(u 1 ) A(u 2 ) = ϕ Nebulas Rank.,. (Velocity Factor)... : Nebulas ( )[3].., :. R.S Kroszner 6 2,795, [22].,. [23], V!. : M V = P Y! (7) 7
! M V P,!,!!,, (,!.) (GDP). (7). M Y 1 p! Nebulas (Nebulas NAS 4 % ), 2100.!., (7) : V (M + Δm) (s,t,w,τ) T w! (8) M = P Y Δm!.!, (New Keynesian Models)..,.. (, ),!!.. Y!, GDP,.,.,. (8)!. Y! : P Y P Y Y = C(a)! (9) a A C(a) a!!, Core Nebulas Rank. Nebulas.,. ( : Nebulas Proof of Devotion ) 8
( ).. 9
4 Nebulas Rank Core Nebulas Rank... : Core Nebulas Rank. [t 0 T, t 0 ]! : Θ(t 0 ) = {(s, t, w, τ) t 0 T τ t 0 w > 0 s t}! (10) Θ(t o ) d c τ!,,!!,!,!. a A C(a) Θ(t o )!!! Core Nebulas Rank : C(a) = Ω(β(a)) Ψ(γ(a)) β(a) a γ(a)! (11)!!!.. s : Nebulas ( )[3] Core Nebulas Rank : 1.!. 2. LeaderRank.,.., PageRank ( : LeaderRank) [20].. 4.3 21. K 4.1 β(a) [t 0 T, t o ] n, : B i B i+ 1 a A B o, B 1,, B n. : 10
d a o, d a 1,, d a n : d a (0), d a (1),, d a (n) d(i) a < d (i+ a 1),0 i n 1 β(a)!,! : (a) = ( d a (k) for n =2 k, k =1, 2, 3,... (d a (k) + da (k+1))/2 for n =2 k +1,k =1, 2, 3,... (12).,. w = 10, =2 v 1 v 2 w = 100, =1 w = 100, =5 w = 10, =3 H(v) ={(v, v1, 100, 1), (v1, v2, 10, 2), (v2, v3, 10, 3), (v3,v,10, 4)} v v 3 w = 10, =4.1: v 1 v 2 w = 100, =5 w = 90, =1 11 v v 3
!!! 4.2 (In-and-Out Degree).2:.1. (in-and-out)... : v H(v) H(v) {(v, v 1, w 1, τ 1 ), (v 1, v 2, w 2, τ 2 ),, (v i, v i+ 1, w i, τ i ),, (v n, v, w n+ 1, τ n+ 1 )},!! 1 i n: τ 1 τ i+ 1 (v 1, v 2, 100, 5) n.1,,..! : H 1 (v 1 ), H 2 (v 2 ),, H n (v n ) H i (v i ) (s i m, t i m, w i m, τ i m)!!, H i (v i ) w i m H i (v i )!!,! 0 : (s i, t i, w i, τ i ) T : w i w i m E((s, t, w, ),w m )= (s, t, w wm, ) if w 6= w m if w = w m Θ (t 0 ) = Θ(t 0 ) H i (v) {E(t), t H i (v i )} i = 1,2,, n! (13).2.1 ( ). 12
v!! p(v) :! p(v) = w (14) i (s i,v,w i,τ i ) Θ (t 0 ) v! : v,!! γ(v)! q(v) = w (15) i (v,t i,w i,τ i ) Θ (t 0 ) : q(v) arctan! p(v) ) (16) G(v) = (p(v) + q(v)) e 2 sin2 ( π 4.3 14. G(v) =(p(v)+q(v)) e 2sin2 ( 4 arctan q(v) p(v) ) 10 5 0 4 q(v) 2 0 0 2 p(v) 4.3: 13
γ(v) = ( θ G(v) G(v) + μ )λ! (17)! θ, μ, λ 4.3 Wilbur. Core Nebulas Rank. Nebulas Rank. Core Nebulas Rank f (x), Wilbur 1. Core Nebulas Rank,,. x 1 x 2 f (x) : 1. 0. x f (x 1 + x 2 ) > f (x 1 ) + f (x 2 ) x 1 > 0,x 2 > 0 (18) f(x) =x f(x) =x/(1 + e a+b x ) Nebulas Rank Nebulas Rank Factor.4: Nebulas x 1 x 2 2.. lim f (x 1 + x 2 ) = f (x 1 ) + f (x 2 ) x 1 > 0,x 2 > 0 x 1,x 2 (19) 1 (Sybil Attack) 1970 TV (Sybi)l. Dr. Cornelia Wilbur. Wilbur. 14
.,...4. f (x) = x /(1 + e a+ b x ) a > 1,b < 0 (20) A., (11) : C(v) = β(v) 1 + e γ(v) a+ b β(v) 1 + e c+ d γ(v) (21).5: Nebulas Rank Market Capitalization of Ethereum (USD) 2 1.5 10 9 Nebulas Rank ETH Market Cap. 0 10 20 30 40 50 60 Time (day) Core a, b, c, d. Core Nebulas Rank. Nebulas 2017 5 1 2017 6 30 ( : 3629091 3955158 ) ETH ( ) [24]..5 ETH Core Nebulas Rank ETH ( ) (21) Core Nebulas Rank. 15
Core Nebulas Rank. p 4.48 10 17 < 0.001 0.84427, (p ). (11) Core Nebulas Rank. 16
5 Core Nebulas Rank ( ) Core Nebulas Rank Nebulas Rank..........,,. 5.1 (21).., 0 β o. γ.,. β,.,,.,, 5.3...... 4.3 (21)..,. (Cycle-removal Algorithm). γ = 2β o C =.. (1 + e a+ b β 0)(1 + e c+ 2d β 0).. 2β 2 0. C = γ 2T β o T 2T β0 2. (1 + e a+ b β o)(1 + e ec + c c d β o ), 17
5.2 ( ) Sybil Attack P2P [25]. P2P. P2P. ID., ID. P2P (Redundancy),, ID. P2P ID ID ID. ID. ID. P2P. [26].... Core Nebulas Rank.. β o,. N N β = N γ K β K = 2 N 5.1,,. : C = N K β2 0 N (1 + e a+ b β 0 N )(1 + e c+ K d β 0) = Kβ 2 0 (1 + e a+ b β 0 N )(1 + e c+ K d β 0) (22) 5.3.. 6 Core Nebulas Rank Core Nebulas Rank Core Nebulas Rank. 6.1? Core Nebulas Rank.. Nebulas Rank. 18
Nebulas Rank :, IPFS, Genaro[27][28], Core Nebulas Rank. Core Nebulas Rank, Core Nebulas Rank., TPS. Core Nebulas Rank. Core Nebulas Rank Core Nebulas Rank., Core Nebulas Rank Core Nebulas Rank., Core Nebulas Rank.,, Core Nebulas Rank, Core Nebulas Rank. Core Nebulas Rank, Core Nebulas Rank. Core Nebulas Rank... 6.2 Core Nebulas Rank Core Nebulas Rank, Core Nebulas Rank,. Core Nebulas Rank., Nebulas Force Core Nebulas Rank., Core Nebulas Rank (LLVM IR ). Nebulas (NVM), Core Nebulas Rank Core Nebulas Rank.,. 19
7 Extended Nebulas Rank Core Nebulas Rank. Core Nebulas PoD( ) DIP( ), Core Nebulas Rank.,, Extended Nebulas Rank. Extended Nebulas Rank Core Nebulas Rank Nebulas. 7.1 Extended Nebulas Rank Nebulas. DApp. DApp... (Acyclic Graph), Page Rank Nebulas Rank. 7.2 Extended Nebulas Rank.,. Extendede Nebulas Rank,, Core Nebulas Rank. Extended Nebulas Rank, Core Nebulas Rank.., Extented Nebulas Rank Core Nebulas Rank. Extended Nebulas Rank Extended Nebulas Rank,. Extended Nebulas Rank. 20
8 Nebulas Rank.. Nebulas : Nebulas Rank..,., DApp. Dapps.. Nebulas... Nebulas. 21
[1] S. Meiklejohn, M. Pomarole, G. Jordan, K. Levchenko, D. McCoy, G. M. Voelker, and S. Savage, A fistful of bitcoins: characterizing payments among men with no names, in Proceedings of the 2013 conference on Internet measurement con- ference, pp. 127 140, ACM, 2013. [2] Http cookie. https://en.wikipedia.org/wiki/http_cookie. [3] Nabulas Technical White Paper. https://nebulas.io/docs/ NebulasTechnicalWhitepaper.pdf. Accessed: 2018-04-01. [4] S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, 2008. [5] Namecoin. https://namecoin.org. [6] Openassets protocol. http://github.com/openassets/ open-assets-protocol. [7] V. Buterin et al., Ethereum white paper, 2013. [8] Forget fintech welcome to the valueweb. http://thefinanser.com/2015/ 02/forget-fintech-welcome-to-the-valueweb.html/. [9] L. Page, S. Brin, R. Motwani, and T. Winograd, The pagerank citation ranking: Bringing order to the web., tech. rep., Stanford InfoLab, 1999. [10] M. Fleder, M. S. Kester, and S. Pillai, Bitcoin transaction graph analysis, arxiv preprint arxiv:1502.01657, 2015. [11] Q. Li, T. Zhou, L. Lu, and D. Chen, Identifying influential spreaders by weighted LeaderRank, Physica A: Statistical Mechanics and its Applications, vol. 404, pp. 47 55, 2014. [12] A. Cheng and E. Friedman, Manipulability of pagerank under sybil strategies, 2006. [13] NEM Technical Reference. http://nem.io/nem_techref.pdf. Accessed: 2017-08-01. [14] A. N. Nikolakopoulos and J. D. Garofalakis, NCDawareRank, Proceedings of the sixth ACM international conference on Web search and data mining - WSDM 13, no. February 2013, p. 143, 2013. [15] X. Xu, N. Yuruk, Z. Feng, and T. A. Schweiger, Scan: a structural clustering algorithm for networks, in Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 824 833, ACM, 2007. [16] H. Shiokawa, Y. Fujiwara, and M. Onizuka, Scan++: efficient algorithm for finding clusters, hubs and outliers on large-scale graphs, Proceedings of the VLDB Endowment, 22
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!!!! A. A.1 Proof of Property 1 proof x 1 > 0,x 2 > 0!. For any!, we have f (x 1 + x 2 ) = = = x 1 + x 2 1 + e a+ b (x 1+ x 2 ) x 1 1 + e + x 2 a+ b (x 1+ x 2 ) 1 + e a+ b (x 1+ x 2 ) x 1 1 + e b x 2 e a+ b x 1 + x 2 1 + e b x 1 e a+ b x 2 b < 0 0 < e (a+ b) x 1 < 1,0 < e b x 2< 1, In formula 21, we have!, so! moreover, x 1 1 + e b x 2 e a+ b x 1 > x 1 1 + e a+ b x 1 = f (x 1 ) x 2 1 + e b x 1 e a+ b x 2 > x 2 1 + e a+ b x 2 = f (x 2 ) is actually: f (x 1 + x 2 ) > f (x 1 ) + f (x 2 ) A.2 Proof of Property 2 proof x 1 > 0,x 2 > 0!. For any!, we have f (x 1 + x 2 ) f (x 1 ) f (x 2 ) = x 1 + x 2 1 + e x 1 x 2 a+ b (x 1+ x 2 ) 1 + e a+ b x 1 1 + e a+ b x 2 x 1 x 1! (23) = ( ) 1 + e b x 2 e a+ b x 1 1 + e a+ b x 1 x 2 x 2 + ( ) 1 + e b x 1 e a+ b x 2 1 + e a+ b x 2 g (x 1, x 2 ) h (x 1, x 2 ) Here we use function! represents the left part,! represents the right part: x 1 x 1! (24) g (x 1, x 2 ) = 1 + e b x 2 e a+ b x 1 24 1 + e a+ b x 1
!!!! x 2 x 2! (25) h (x 1, x 2 ) = 1 + e b x 1 e a+ b x 2 1 + e a+ b x 2 x 1 x 2 So (23) for! and!, their limits can be represented as: lim x 1,x 2 we have [ f (x 1 + x 2 ) f (x 1 ) f (x 2 )] = lim g (x 1, x 2 ) + x 1,x 2 lim h (x 1, x 2 ) x 1,x 2 g (x 1, x 2 ) = = < < x 1 x 1 1 + e b x 2 e a+ b x 1 1 + e a+ b x 1 x 1 e a+ b x 1 (1 e b x 2) (1 + e b x 2 e a+ b x 1) (1 + e a+ b x 1) x 1 e a+ b x 1 (1 + e a+ b x 1) (1 + e b x 2 e a+ b x 1) (1 + e a+ b x 1) = x 1 e a+ b x1 1 + e b x 2 e a+ b x 1 x 1 e a+ b x 1 1 + e a+ b x 1 = 1 + x 1 1 e a+ b x 1 x Calculate limit for!, according to L Hospital s rule, 1 1 + ea+ b x lim x 1 + x 1 = lim 1 x (e a b x ) e a+ b x = lim x 1 b e a b x b < 0 lim b e a b x = In formula 21, we have!, so!, moreover, x lim x 1 + x = 0 1 e a+ b x g (x 1, x 2 ) > 0, According to A.1, we have! so according to sandwich theorem: 25
!!! lim x 1,x 2 g (x 1, x 2 ) = 0 Similarly, we can get: lim x 1,x 2 h (x 1, x 2 ) = 0 So, lim x 1,x 2 [ f (x 1 + x 2 ) f (x 1 ) f (x 2 )] = 0 26
B. v1.0 v1.0.1 4.3 1 2 v1.0.2 27