Updated on 2022/04/09


Faculty of Economics Department of Business Administration Associate Professor


  • 博士(理学) ( 2013.3   東京工業大学 )

Research Areas

  • Informatics / Statistical science  / 大規模社会データ解析、数理・統計モデリング

  • Natural Science / Mathematical physics and fundamental theory of condensed matter physics  / 複雑システム科学、統計物理

  • Humanities & Social Sciences / Library and information science, humanistic and social informatics  / 近現在の新聞データ

  • Humanities & Social Sciences / Commerce  / マーケティング・ソーシャルリスニング

  • Informatics / Web informatics and service informatics  / ソーシャルメディア解析、計算社会科学、時間付きテキストデータ

Educational Background

  • Tokyo Institute of Technology   総合理工学研究科  

    - 2013.3

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    Country: Japan


Primary Subjects (Course) in charge

  • <学部>経営統計学Ⅰ、経営統計学Ⅱ、コンピュータ論Ⅰ、コンピュータ論Ⅱ



  • Empirical observations of ultraslow diffusion driven by the fractional dynamics in languages: Dynamical statistical properties of word counts of already popular words Reviewed

    Hayafumi Watanabe

    Physical Review E   98 ( 1 )   2018.1

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    Authorship:Lead author   Publisher: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


    Other Link: http://arxiv.org/pdf/1801.07948v5

  • 大規模ブログデータベースを用いた食の流行の現状把握システムの開発 Reviewed

    渡邊 隼史, 小森 あゆみ, 榊 剛史

    日本マーケティング学会 カンファレンス・プロシーディングス   5   162 - 174   2016.10

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    Authorship:Lead author, Corresponding author   Language:Japanese   Publishing type:Research paper (conference, symposium, etc.)  

  • Statistical properties of fluctuations of time series representing the appearance of words in nationwide blog data and their applications: An example of observations and the modelling of fluctuation scalings of nonstationary time series Reviewed

    Hayafumi Watanabe, Yukie Sano, Hideki Takayasu, Misako Takayasu

    Physical Review E   94 ( 5 )   2016.4

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    Authorship:Lead author, Corresponding author   Publisher: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


    Other Link: http://arxiv.org/pdf/1604.00762v4

  • Generalised Central Limit Theorems for Growth Rate Distribution of Complex Systems Reviewed

    Misako Takayasu, Hayafumi Watanabe, Hideki Takayasu

    Journal of Statistical Physics   155 ( 1 )   47 - 71   2014.4

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    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1007/s10955-014-0956-4

    Other Link: http://link.springer.com/article/10.1007/s10955-014-0956-4/fulltext.html

  • Mean field approximation for biased diffusion on Japanese inter-firm trading network Reviewed

    Hayafumi Watanabe

    PLoS ONE   9 ( 3 )   e91704 - e91704   2013.12

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    Authorship:Lead author, Last author, Corresponding author   Publisher: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


    Other Link: http://arxiv.org/pdf/1401.0124v2

  • Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms Reviewed

    Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu

    Physica A: Statistical Mechanics and its Applications   392 ( 4 )   741 - 756   2012.8

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    Authorship:Lead author, Corresponding author   Publisher:Elsevier BV  

    To elucidate allometric scaling in complex systems, we investigated the
    underlying scaling relationships between typical three-scale indicators for
    approximately 500,000 Japanese firms; namely, annual sales, number of
    employees, and number of business partners. First, new scaling relations
    including the distributions of fluctuations were discovered by systematically
    analyzing conditional statistics. Second, we introduced simple probabilistic
    models that reproduce all these scaling relations, and we derived relations
    between scaling exponents and the magnitude of fluctuations.

    DOI: 10.1016/j.physa.2012.10.020


    Other Link: http://arxiv.org/pdf/1208.1188v1

  • Biased diffusion on Japanese inter-firm trading network: Estimation of sales from network structure Reviewed

    Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu

    New Journal of Physics   14 ( 4 )   043034 - 043034   2011.11

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    Authorship:Lead author, Corresponding author   Publisher:IOP Publishing  

    To investigate the actual phenomena of transport on a complex network, we
    analysed empirical data for an inter-firm trading network, which consists of
    about one million Japanese firms and the sales of these firms (a sale
    corresponds to the total in-flow into a node). First, we analysed the
    relationships between sales and sales of nearest neighbourhoods from which we
    obtain a simple linear relationship between sales and the weighted sum of sales
    of nearest neighbourhoods (i.e., customers). In addition, we introduce a simple
    money transport model that is coherent with this empirical observation. In this
    model, a firm (i.e., customer) distributes money to its out-edges (suppliers)
    proportionally to the in-degree of destinations. From intensive numerical
    simulations, we find that the steady flows derived from these models can
    approximately reproduce the distribution of sales of actual firms. The sales of
    individual firms deduced from the money-transport model are shown to be
    proportional, on an average, to the real sales.

    DOI: 10.1088/1367-2630/14/4/043034


    Other Link: http://arxiv.org/pdf/1111.4852v1

  • Empirical analysis of collective human behavior for extraordinary events in blogosphere Reviewed

    Yukie Sano, Kenta Yamada, Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu

    Physical Review E   87 ( 1 )   2011.7

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    Publisher:American Physical Society (APS)  

    To uncover underlying mechanism of collective human dynamics, we survey more
    than 1.8 billion blog entries and observe the statistical properties of word
    appearances. We focus on words that show dynamic growth and decay with a
    tendency to diverge on a certain day. After careful pretreatment and fitting
    method, we found power laws generally approximate the functional forms of
    growth and decay with various exponents values between -0.1 and -2.5. We also
    observe news words whose frequency increase suddenly and decay following power
    laws. In order to explain these dynamics, we propose a simple model of posting
    blogs involving a keyword, and its validity is checked directly from the data.
    The model suggests that bloggers are not only responding to the latest number
    of blogs but also suffering deadline pressure from the divergence day. Our
    empirical results can be used for predicting the number of blogs in advance and
    for estimating the period to return to the normal fluctuation level.

    DOI: 10.1103/PhysRevE.87.012805


    Other Link: http://arxiv.org/pdf/1107.4730v4

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