担当区分：筆頭著者   出版者・発行元：American Physical Society (APS)  

Ultraslow diffusion (i.e. logarithmic diffusion) has been extensively studied
theoretically, but has hardly been observed empirically. In this paper,
firstly, we find the ultraslow-like diffusion of the time-series of word counts
of already popular words by analysing three different nationwide language
databases: (i) newspaper articles (Japanese), (ii) blog articles (Japanese),
and (iii) page views of Wikipedia (English, French, Chinese, and Japanese).
Secondly, we use theoretical analysis to show that this diffusion is basically
explained by the random walk model with the power-law forgetting with the
exponent $\beta \approx 0.5$, which is related to the fractional Langevin
equation. The exponent $\beta$ characterises the speed of forgetting and $\beta
\approx 0.5$ corresponds to (i) the border (or thresholds) between the
stationary and the nonstationary and (ii) the right-in-the-middle dynamics
between the IID noise for $\beta=1$ and the normal random walk for $\beta=0$.
Thirdly, the generative model of the time-series of word counts of already
popular words, which is a kind of Poisson process with the Poisson parameter
sampled by the above-mentioned random walk model, can almost reproduce not only
the empirical mean-squared displacement but also the power spectrum density and
the probability density function.

DOI： 10.1103/PhysRevE.98.012308

arXiv

その他リンク： http://arxiv.org/pdf/1801.07948v5

担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（研究会，シンポジウム資料等）  

担当区分：筆頭著者,　責任著者   出版者・発行元：American Physical Society (APS)  

To elucidate the non-trivial empirical statistical properties of fluctuations
of a typical non-steady time series representing the appearance of words in
blogs, we investigated approximately five billion Japanese blogs over a period
of six years and analyse some corresponding mathematical models. First, we
introduce a solvable non-steady extension of the random diffusion model, which
can be deduced by modelling the behaviour of heterogeneous random bloggers.
Next, we deduce theoretical expressions for both the temporal and ensemble
fluctuation scalings of this model, and demonstrate that these expressions can
reproduce all empirical scalings over eight orders of magnitude. Furthermore,
we show that the model can reproduce other statistical properties of time
series representing the appearance of words in blogs, such as functional forms
of the probability density and correlations in the total number of blogs. As an
application, we quantify the abnormality of special nationwide events by
measuring the fluctuation scalings of 1771 basic adjectives.

DOI： 10.1103/PhysRevE.94.052317

arXiv

その他リンク： http://arxiv.org/pdf/1604.00762v4

掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s10955-014-0956-4

その他リンク： http://link.springer.com/article/10.1007/s10955-014-0956-4/fulltext.html

担当区分：筆頭著者,　最終著者,　責任著者   出版者・発行元：Public Library of Science (PLoS)  

By analysing the financial data of firms across Japan, a nonlinear power law
with an exponent of 1.3 was observed between the number of business partners
(i.e. the degree of the inter-firm trading network) and sales. In a previous
study using numerical simulations, we found that this scaling can be explained
by both the money-transport model, where a firm (i.e. customer) distributes
money to its out-edges (suppliers) in proportion to the in-degree of
destinations, and by the correlations among the Japanese inter-firm trading
network. However, in this previous study, we could not specifically identify
what types of structure properties (or correlations) of the network determine
the 1.3 exponent. In the present study, we more clearly elucidate the
relationship between this nonlinear scaling and the network structure by
applying mean-field approximation of the diffusion in a complex network to this
money-transport model. Using theoretical analysis, we obtained the mean-field
solution of the model and found that, in the case of the Japanese firms, the
scaling exponent of 1.3 can be determined from the power law of the average
degree of the nearest neighbours of the network with an exponent of -0.7.

DOI： 10.1371/journal.pone.0091704

arXiv

その他リンク： http://arxiv.org/pdf/1401.0124v2