ネットワーク科学 小さな世界のモデル

network science2

Transcript

1. - - 2017 ( ) 1 / 20
2. 1. ( ) , , , , , ( ) , , . ⇒ , 1967 , 2 , 5-6 . , , , 2007 ( ) 2 / 20
3. ( ) 3 / 20
4. ( ) 4 / 20
5. 0 1 2 3 4 5 6 7 8 , 7. 9 · 10 11 12 13 14 ( ) 5 / 20
6. Media Report ( ) 6 / 20
7. 80 ( ) 0 (89) 1 (32) 2 (32) 3 (44) 4 (36) 5 (52) 6 (53) 7 (35) 8 (36) 9 (35) 1 10 (10) 11 (10) 12 (10) 13 (14) ( ) 7 / 20
8. It’s a Small World 6 , S.Milgram, Psychology Today 1, 1967. WWW 19 d = 0.35 + 2 log10 N, R.Albert et al., Nature 401, 1999. , , , ! : , , ( ) 8 / 20
9. 2. Small World Model D.J.Watts and S.H.Strogatz, Nature, 393, 1998 ( ) 9 / 20
10. L C D.J.Watts and S.H.Strogatz, Nature, 393, 1998 ( ) 10 / 20
11. i Ci Ci def = i ki (ki − 1)/2 . C C def = 1 N i Ci . L ( ) 11 / 20
12. p(k) , l ∼ O(log N) l ≈ log Nl k (knn − 2) log(knn − 1) , Nl l , knn def = k2 / k . , , , 2013 , pp.93-95. , , O(log N) . , √ N 2 √ N. ( ) 12 / 20
13. 3. Scale-Free In A.L.Barab´ asi, LINKED, Perseus Pub., 2002 ⇒ ( ) 13 / 20
14. SF → , , , , , AS , WWW, , , , , ( ) 14 / 20
15. SF , 2 , x P(x) = Cx−γ SF . [cm] [mm] , A x = Ay , P′(y) = C(Ay)−γ = C′y−γ, C′ = CA−γ, −γ . , . , x = x′ x′P(x′) , , ( ). ( ) 15 / 20
16. = Gutenberg-Richter Web , . , 7 , , 2007 ( ) 16 / 20
17. Randon drift . 1 N individuals t=0 t=2 t=1 : : : : : : 6 2 7 11 5 8 9 20 4 6 6 1 17 8 20 4 9 20 6 7 9 6 2 8 20 6 1 ( ) 17 / 20
18. http://marketingis.jp/archives/74 ( ) 18 / 20
19. 4. 1 √ 2πσx exp − (log x − µ)2 2σ2 ( , , ⇒ , ( ) 19 / 20
20. n Xn an Xn = anXn−1 = anan−1 . . . a1X0 = Πn i=1 ai X0, , log Xn = log an + log an−1 + . . . + log a0 + log X0, , ai log Xn , Xn . ( ( ) 20 / 20