Published Papers - Yamamoto Ken

Common lognormal behavior in legal systems

Ken Yamamoto

Journal of the Physical Society of Japan ( PHYSICAL SOC JAPAN )  86 ( 7 ) 073801   2017 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

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This study characterizes a statistical property of legal systems: the distribution of the number of articles in a law follows a lognormal distribution. This property is common to the Japanese, German, and Singaporean laws. To explain this lognormal behavior, tree structure of the law is analyzed. If the depth of a tree follows a normal distribution, the lognormal distribution of the number of articles can be theoretically derived. We analyze the structure of the Japanese laws using chapters, sections, and other levels of organization, and this analysis demonstrates that the proposed model is quantitatively reasonable.

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Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order

Ken Yamamoto

Journal of Applied Probability   54   1111 - 1124   2017 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

Analysis of a Stochastic Model for Bacterial Growth and the Lognormality of the Cell-Size Distribution

Ken Yamamoto, Jun-ichi Wakita

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN ( PHYSICAL SOC JAPAN )  85 ( 7 ) 074004   2016.07 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

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This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We find that the cell size is expressed as a sum of independent lognormal variables. We show numerically that the quality of the lognormal approximation greatly depends on the distributions of the growth rate and cell cycle. Furthermore, we show that actual parameters of the growth rate and cell cycle take values that give a good lognormal approximation; thus, the experimental cell-size distribution is in good agreement with a lognormal distribution.

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Phase Diagram of Collective Motion of Bacterial Cells in a Shallow Circular Pool

Jun-ichi Wakita, Shota Tsukamoto, Ken Yamamoto, Makoto Katori, Yasuyuki Yamada

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN ( PHYSICAL SOC JAPAN )  84 ( 12 ) 124001   2015.12 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

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The collective motion of bacterial cells in a shallow circular pool is systematically studied using the bacterial species Bacillus subtilis. The ratio of cell length to pool diameter (i.e., the reduced cell length) ranges from 0.06 to 0.43 in our experiments. Bacterial cells in a circular pool show various types of collective motion depending on the cell density in the pool and the reduced cell length. The motion is classified into six types, which we call random motion, turbulent motion, one-way rotational motion, two-way rotational motion, random oscillatory motion, and ordered oscillatory motion. Two critical values of reduced cell lengths are evaluated, at which drastic changes in collective motion are induced. A phase diagram is proposed in which the six phases are arranged.

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Topological Analysis of Rough Surfaces Using Persistent Homology

Ken Yamamoto

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN ( PHYSICAL SOC JAPAN )  84 ( 11 ) 113001   2015.11 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

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This letter investigates rough surfaces using a topological method. The horizontal cross section of a rough surface consists of "islands", and we focus on the topological changes in the island shapes (generation and annihilation of islands and lakes) with changes in elevation. We apply persistent homology to track these topological changes. We numerically confirm that the life spans of the islands and lakes follow power-law distributions, whose scaling exponents vary according to the roughness of the surface. We also provide a theoretical explanation for the relation between these scaling exponents and the roughness exponent with a simple scaling argument. The proposed method successfully connects a topological property with the roughness of a surface.

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Degree Distribution of Position-Dependent Ball-Passing Networks in Football Games

Takuma Narizuka, Ken Yamamoto, Yoshihiro Yamazaki

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN ( PHYSICAL SOC JAPAN )  84 ( 8 ) 084003   2015.08 [ Peer Review Accepted ]

Type of publication: Research paper (scientific journal)

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We propose a simple stochastic model describing the position-dependent ball-passing network in football (soccer) games. In this network, a player in a certain area in a divided field is a node, and a pass between two nodes corresponds to an edge. Our stochastic process model is characterized by the consecutive choice of a node depending on its intrinsic fitness. We derive an explicit expression for the degree distribution and find that the derived distribution reproduces that for actual data reasonably well.

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