Nation-wide economic activities are generally characterized by complex networks consisted of business firms, and such data for Japanese firms are provided for academic use by Teikoku Databank, which is the largest corporate credit research company in Japan. It is known that the transaction network has a scale-free structure [1] and non-trivial scaling rela-tions hold among firm sizes such as annual sales, number of employees and number of busi-ness partners [2]. Direct observation of preferential attachment is confirmed and a simple model of time evolution of network structure has been introduced [3]. As for money flow between interacting firms so-called the gravity law is known to hold [4], and a set of equations describing the whole monetary flow on the network has been introduced [5], and those results are already implemented in RESAS (Regional Economy Society Analyzing System) [6], which is a big-data analysis platform provided by the government of Japan. Percolation properties [7] and anatomical decomposition [8] are applied to quantitative description of network rigidity. From the viewpoint of data assimilation we are establishing methods to tune the frequency of 3-body motifs by generalizing the network construction model [9].

References
[1] Takaaki Ohnishi, Hideki Takayasu and Misako Takayasu
    Progress of Theoretical Physics Supplement No. 179 (2009) 157-166.
[2] Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu
   Physica A, 392, 741-756, 2013.
[3] Wataru Miura, Hideki Takayasu, and Misako Takayasu
   Phys. Rev. Lett. 108, 168701 (2012), 5 pages.  
[4] Koutarou Tamura, Wataru Miura, Misako Takayasu, Hideki Takayasu, Satoshi Kitajima,
   Hayato Goto
   International Journal of Modern Physics, 16, 93-104, 2012.
[5] Koutarou Tamura, Hideki Takayasu, Misako Takayasu,
   Phys. Rev. E91, 042815, 7 pages, 2015.
[6] https://resas.go.jp/#/13/13101
[7] Hirokazu Kawamoto, Hideki Takayasu, Henrik J Jensen, Misako Takayasu
   PLoSONE, 10(4): e0119979, 16 pages, 2015.
[8] Hirokazu Kawamoto, Hideki Takayasu, Misako Takayasu
   Scientific Reports, 7, 163, 8 pages (2017).  doi:10.1038/s41598-017-00242-4
[9] Jullian Maluck, Reik V.Donner, Hideki Takayasu, Misako Takayasu,
   JSTAT, to appear.

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1. Construction of  mathematical models of bankruptcy of firms from the big data
2. The probability distributions and the fluctuation scalings of the time series of key-word counts in nation-wide blog data.
3. Diffusion in Autoregressive Based Models for Financial Data
4. Causal Inference of Market Event Rates in Foreign Currency Market