7. Our research is
based on
this paper
Published 15 June
A.Ishii et al,
New Journal of Physics
14 (2012) 063018
New Journal of Physics
The open–access journal for physics
The ‘hit’ phenomenon: a mathematical model of
human dynamics interactions as a stochastic
process
イギリスとドイツの物理学会の
共同運営の物理学論文誌で
世界的に非常に評価が高い
Akira Ishii1,3 , Hisashi Arakaki1 , Naoya Matsuda1 ,
Sanae Umemura1 , Tamiko Urushidani1 , Naoya Yamagata1
and Narihiko Yoshida1,2
1
Department of Applied Mathematics and Physics, Tottori University, Koyama,
Tottori 680-8552, Japan
2
Digital Hollywood University, Tokyo, Japan
E-mail: ishii@damp.tottori-u.ac.jp
New Journal of Physics 14 (2012) 063018 (22pp)
Received 3 December 2011
Published 14 June 2012
Online at http://www.njp.org/
doi:10.1088/1367-2630/14/6/063018
Impact Factor 3.9
A mathematical model for the ‘hit’ phenomenon in entertainment
within a society is presented as a stochastic process of human dynamics
interactions. The model uses only the advertisement budget time distribution as
an input, and word-of-mouth (WOM), represented by posts on social network
systems, is used as data to make a comparison with the calculated results. The
unit of time is days. The WOM distribution in time is found to be very close to the
revenue distribution in time. Calculations for the Japanese motion picture market
based on the mathematical model agree well with the actual revenue distribution
in time.
Abstract.
8. 今年6月15日のAFP電をきっかけに
世界で200以上の報道機関で報道
Press Release from New Journal of Physics
Physicists predict success of movies at the box office
Science
Forget Movie Critics, Mindless Internet Chatter Predicts Blockbusters and Bombs
AFP
Japanese physicists crack box office code
CNN
Can an eqquation predict box office success?
More than 200 media report this paper.
12月17日、アスキーJPにインタビュー記事掲載
16. ヒット現象の数理モデル
宣伝・広告
dI i (t)
= −aI i (t) + A(t) +
dt
N
∑ D I (t) + ∑ ∑ P
ij j
j≠i
I (t)I k (t)
ijk j
j
k
直接的コミュニケーション
間接的コミュニケーション
16
17. 確率過程を用いた、ヒット現象の数理モデルの導出
個々の消費者の購入意欲について方程式をたてる
dI i ( t )
= −aI i ( t ) + ∑ dij I j ( t ) + ∑ ∑ hijk d jk I j ( t ) I k ( t ) + fi ( t )
dt
j
j
k
ここで,
fi(t)
は消費者 i.へのランダムな影響(実際は広告宣伝)
I (t ) =
1
∑ Ii (t )
N i
アンサンブル平均を取ると
dI i (t )
dI (t ) d ⎛ 1
⎞ d I
1
= ∑ i = ⎜ ∑ I i (t )⎟ =
⎠
dt
N i dt
dt ⎝ N i
dt
∑ dij I j (t ) =
j
∑ dI j (t ) =
j
∑ ∑ p I (t ) I (t )
ijk j
j
1
1
dI j (t ) = ∑ d ∑ I j (t ) = Nd I (t )
∑∑
N i j
N j
i
dt
k
= p∑ ∑ I j (t ) I k (t )
j
=
= −a I (t ) + D I (t ) + P I (t ) + f (t )
2
k
1
∑ p∑ ∑ I j (t ) I k (t )
N i
j
k
=∑p
i
従って
d I (t )
k
1
∑ ∑ I j (t ) I k (t )
N j k
= Np ∑
i
1
1
∑ I j (t ) N ∑ I k (t )
N j
k
= N 2 p I (t )
2
where
Nd = D
N2p = P
1
∑ Δfi (t ) = Δfi (t ) = 0
N i
fi (t ) = f (t ) + Δfi (t )
A.Ishii et. al.,
New Journal of Physics 14 (2012) 063018 (22pp)
"The 'hit' phenomenon: a mathematical model of
human dynamics interctions
as s stochastic process"
23. 2
R factor : 0.256
wants / entry : 0.0961
R factor : 0.020
wants / entry : 0.1103
Hisashi Arakaki 2012 Department of Applied Mathematics and Physics, Tottori University
7
Hisashi Arakaki 2012 Department of Applied Mathem
24. 3
4
R factor : 0.158
wants / entry : 0.0846
R factor : 0.051
wants / entry : 0.0973
Hisashi Arakaki 2012 Department of Applied Mathematics and Physics, Tottori University
9
Hisashi Arakaki 2012 Department of Applied Mathe
25. 5
6
R factor : 0.038
wants / entry : 0.1111
R factor : 0.019
wants / entry : 0.0741
Hisashi Arakaki 2012 Department of Applied Mathem
Hisashi Arakaki 2012 Department of Applied Mathematics and Physics, Tottori University
11
26. Hisashi Arakaki 2012 Department of Applied Mathematics and Physics, Tottori University
13
27. “Mathematical model for the hit phenomenon as a stochastic process of interactions of human dynamics”
Akira Ishii, Hisashi Arakaki, Naoya Matsuda, Sanae Umemura, Tamiko Urushidani, Naoya Yamagata,
and Narihiko Yoshida
New Journal of Physics, in press
-
-/
/
/
/
/ 20
/
/
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