藤原 義久

The correlation of firms' performance on a transaction network is studied by analyzing financial and transaction data. Statistically significant correlation coefficients are obtained as evidence for the firm interactions. The firm interactions are taken into account in the basic equation of firm activity. Forty percent of residuals are explained by considering the firm interactions. The overall structure of the transaction network, i.e., the connectivity of industry sectors, is analyzed. © 2008 Springer-Verlag.

A link in a supplier-customer network is usually a creditor-debtor relationship. If a firm goes into a state of financial insolvency or bankruptcy, then firms on its upstream are affected secondarily along the links. By using 10-year data from recent data on bankruptcy in Japan, we show that this "link effect" is by no means negligible in a nationwide economy. While the total debt of bankruptcy typically amounts to as much as a few percent of GDP in Japan, nearly 20% of all bankruptcies are due to the link effect. Interestingly, we find that such a link effect becomes comparable with other causes of bankruptcy, including poor performance in business (namely solo failure) with respect to the number of events, as the bankruptcy is larger. This means that the link effect grows for larger bankruptcies. Because the supplier-customer network has a heavy tail in its degree distribution, the ripple effect due to the bankruptcy chain is considerable. Since every firm is embedded in a giant network of production, this study would suggest the importance of understanding the heterogeneity in the large-scale network of suppliers and customers on a nationwide scale. © 2008 World Scientific Publishing Company.

We have conducted an agent-based simulation of chain bankruptcy. The propagation of credit risk on a network, i.e., chain bankruptcy, is the key to nderstanding largesized bankruptcies. In our model, decrease of revenue by the loss of accounts payable is modeled by an interaction term, and bankruptcy is defined as a capital deficit. Model parameters were estimated using financial data for 1,077 listed Japanese firms. Simulations of chain bankruptcy on the real transaction network consisting of those 1,077 firms were made with the estimated model parameters. Given an initial bankrupt firm, a list of chain bankrupt firms was obtained. This model can be used to detect high-risk links in a transaction network, for the management of chain bankruptcy.

Firm dynamics on a transaction network is considered from the standpoint of econophysics, agent-based simulations, and game theory. In this model, interacting firms rationally invest in a production facility to maximize net present value. We estimate parameters used in the model through empirical analysis of financial and transaction data. We propose two different methods (analytical method and regression method) to obtain an interaction matrix of firms. On a subset of a real transaction network, we simulate firm's revenue, cost, and fixed asset, which is the accumulated investment for the production facility. The simulation reproduces the quantitative behavior of past revenues and costs within a standard error when we use the interaction matrix estimated by the regression method, in which only transaction pairs are taken into account. Furthermore, the simulation qualitatively reproduces past data of fixed assets. © 2006 Elsevier B.V. All rights reserved.

Social networking sites (SNS) have recently used by millions of people all over the world. An SNS is a society on the Internet, where people communicate and foster friendship with each other. We examine a nation-wide SNS (more than six million users at present), mutually acknowledged friendship network with third million people and nearly two million links. By employing a community-extracting method developed by Newman and others, we found that there exists a range of community-sizes in which only few communities are detected. This novel feature cannot be explained by previous growth models of networks. We present a simple model with two processes of acquaintance, connecting nearest neighbors and random linkage. We show that the model can explain the gap in the community-size distribution as well as other statistical properties including long-tail degree distribution, high transitivity, its correlation with degree, and degree-degree correlation. The model can estimate how the two processes, which are ubiquitous in many social networks, are working with relative frequencies in the SNS as well as other societies.

This paper considers business networks. Through empirical study, we show that business networks display characteristics of small-world networks and scale-free networks. In this paper, we characterize firms as sales and bankruptcy probabilities. A correlation between sales and a correlation between bankruptcy probabilities in business networks are also considered. The results reveal that the correlation between sales depends strongly on the type of network, whereas the correlation between bankruptcy probabilities does so only weakly. © 2006 Elsevier B.V. All rights reserved.

ソーシャル・ネットワーキング・サービス（SNS: Social Networking Services）というWeb 上でのサービスが世界中で急激な拡大を続けている．SNS においては，先行研究では把握が困難な，相互認証された友人関係という人的ネットワークが大規模に顕在化している．本報告では，日本最大規模のSNS であるmixi（ミクシィ）の2005 年2 月15 日時点における36 万ノード・190 万リンクの人的ネットワークを分析した．基本的なネットワーク解析結果として，次数のゆるやかなスケールフリー性，高い凝集性が確認された．構造を視認するために粗視化を行った．近年開発された解析アルゴリズムを適用し部分的なつながり（link）が密になっている高密度集団（community）を抽出した．解析結果から独特な内部構造が視覚的に確認された．高密度集団は規模別に大中小の3 種類に大別された．詳細に高密度集団の人数のばらつきを調べると，集団の人数に全体のトレンドとしてZipf則が見いだされた．そして100 人から300 人ほどの高密度集団が分離されず，100 人以下から，300人以上の集団へとサイズがスキップするという現象を発見した．発見された内部構造は，既存のモデルでは説明できない独特のものであることを確認した．新しいコミュニケーション・インフラへの進化も期待できるSNS，その研究の端緒を報告する．Social Networking Services (SNS) have recently prevailed all over the World Wide Web. People grow up connections by making a tie to another who acknowledges as being a friend. Such a giant network of people, with each link being a mutually acknowledged friendship, has not ever been under previous investigation. This work analyzed the largest SNS in japan, called mixi, comprised of 360,000 nodes and 1.9million links as of February 15, 2005. Our analysis shows scale-free distribution of degree in its tail, and high cliquishness. To observe structure by coarse-graining, we employed a community (highly intra-connected group) extracting method developed by other researchers. As a result, we uncovered three classes of communities according to size. Overall rank-size plot shows Zipf's law for community-size distribution. Nevertheless, we found the existence of a skip in size, which implies absence of community between 100 and 300 in the number of people. This structure cannot be explained by models such as preferential attachment nor connecting nearest neighbor. We report some results of our analysis in anticipation to future advent and development of SNS as an innovative human communication infrastructure.

A workable microscopic model for firms' dynamics has been constructed. The model consists of firm agents and a bank agent dynamics of which are described by balance sheets. The size distribution of firms and the temporal evolution of the bank show critical dependence on whether or not firms use perfect information on their financial conditions to draw up next production plans. © 2005 American Institute of Physics.

The Japanese shareholding network existing at the end of March 2002 is studied empirically. The network is constructed from 2,303 listed companies and 53 non-listed financial institutions. We consider this network as a directed graph by drawing edges from shareholders to stock corporations. The lengths of the shareholder lists vary with the companies, and the most comprehensive lists contain the top 30 shareholders. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. The distribution of outgoing degrees is well explained by the power law function with an exponential tail. The exponent in the power law range is γ = 1.7. To understand these features from the viewpoint of a company's growth, we consider the correlations between the outgoing degree and the company's age, profit, and total assets. © 2005 American Institute of Physics.

As complex networks in economics, we consider Japanese shareholding networks as they existed in 1985, 1990, 1995, 2000, 2002, and 2003. In this study, we use as data lists of shareholders for companies listed on the stock market or on the over-the-counter market. The lengths of the shareholder lists vary with the companies, and we use lists for the top 20 shareholders. We represent these shareholding networks as a directed graph by drawing arrows from shareholders to stock corporations. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. This representation shows that for all years the distributions of outgoing degrees can be well explained by the power law function with an exponential tail. The exponent depends on the year and the country, while the power law shape is maintained universally. We show that the exponent strongly correlates with the long-term shareholding rate and the cross-shareholding rate.

The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks concerned with the automobile industry sector are discussed by using the visualized networks. The shareholding network is also considered as an undirected graph, because many quantities characterizing networks are defined for undirected cases. For this undirected shareholding network, we show that a degree distribution is well fitted by a power law function with an exponential tail. The exponent in the power law range is gamma=1.8. We also show that the spectrum of this network follows asymptotically the power law distribution with the exponent delta=2.6. By comparison with gamma and delta, we find a scaling relation delta=2gamma-1. The reason why this relation holds is attributed to the local tree-like structure of networks. To clarify this structure, the correlation between degrees and clustering coefficients is considered. We show that this correlation is negative and fitted by the power law function with the exponent alpha=1.1. This guarantees the local tree-like structure of the network and suggests the existence of a hierarchical structure. We also show that the degree correlation is negative and follows the power law function with the exponent nu=0.8. This indicates a degree-nonassortative network, in which hubs are not directly connected with each other. To understand these features of the network from the viewpoint of a company's growth, we consider the correlation between the degree and the company's total assets and age. It is clarified that the degree and the company's total assets correlate strongly, but the degree and the company's age have no correlation.

A shareholding network is represented by a symmetrical adjacency matrix. The random matrix theoretical approach to this matrix shows that the spectrum follows a power law distribution, ρ(λ) ∼ |λ| -δ, in the tail part. It is also shown that the degree distribution of this network follows a power law distribution, p(k) ∼ k -γ, in the large degree range. The scaling law δ= 2γ - 1 is found in this network. The reason why this relation holds is attributed to the local tree-like structure of the shareholding network. © 2004 Elsevier B.V. All rights reserved.

A firms growth and failure are the two sides of the same coin. This paper reports new phenomenological findings for firm size distribution and growth, and bankruptcy. This paper is based on [Y. Fujiwara et al., Physica A 335 (2004) 197] and on [Y. Fujiwara, Physica A 337 (2004) 219]. See also these proceedings for kinematical relationship between Pareto-Zipf and Gibrat's laws. © 2004 Elsevier B.V. All rights reserved.

We discuss Pareto-Zipf's law and Gibrat's law found in the high-end regions of personal income, company's income, and various measures of company size. The fact that these phenomenological laws coexist in wide range of data suggests some deep mathematical relations between them. In this paper we find just such relationships under the law of detailed-balance. This sets a basis for perturbative treatment of the economic change. © 2004 Elsevier B.V. All rights reserved.

We report several recent findings on income distribution. Using high-frequency data for personal income-tax in Japan, we have found that the probability distribution function of the growth-rate is independent from the income. We show that this Universality combined with the time-reversal invariance of the income distribution leads to the Pareto's law. We also find the same Universality holds for company's taxable income in Japan. © 2002 Elsevier Science B.V. All rights reserved.

As the first step toward a study of complex networks in economics, we consider business networks categorized into bipartite networks. Through empirical study we show the possibility that business networks will fall into the scale-free category. To have an idea about the clustering coefficient and the averaged path length for bipartite networks, we perform a one-mode reduction. We calculate the quantities for networks constructed by banks and companies before/after a merger among banks, and quantitatively show that the merger among banks increases the cliquishness of companies and decreases the typical separation between two companies. © 2002 Elsevier Science B.V. All rights reserved.

The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log-returns of stock prices to magnetization in the model and find that it is closely related to trading volume as observed in real markets. The cumulative distribution of log-returns exhibits scaling with exponents steeper than 2 and scaling is observed in the distribution of transition times between bull and bear markets. © 2002 Elsevier Science B.V. All rights reserved.

We propose a computational model which includes adaptive mutation and sexual selection, and investigate functional aspects of the model by examining self-adaptation processes of mutation under the sexual selection. In mating, each female observes males' traits in a phenotypic space, then chooses a male according to her own preference. Therefore, the selection pressure for males is different from that for females. This method was applied for the maximum search problem of a 2-dimensional complicated function. The simulation result showed that the proposed method can escape local optima by the runaway effect of males' traits and females' preferences, and this process leads the system to the intermittent evolution. In this phase, an asymmetrical mutation was driven, which provided the different roles of searching strategies depending on sex. The females were conservative with low mutation rates, while the males were innovative with higher mutation rates. As a result, the proposed method was able to search larger maxima than the conventional methods.

Recent advent of econophysics has been revealing interesting phenomenologies about speculative markets. Specifically, price fluctuations in such markets possess, while serially uncorrelated, long-memory in the magnitude or volatility, quite contrary to what is expected from efficient market hypothesis. The phenomenon is known as volatility clustering, and appears in the time-scales from minutes to months, or even a year. Additional property can be universally observed in the strongly correlated regime as relation between volatilities for different time-scales, or self-similarity. Though such properties have significant and practical implication in financial markets, little is known about the dynamical origin of them. We consider that these properties are manifestation of interdependent agents' aggregate dynamics involving a wide range of time-scales. By using a minimal but interesting model of interacting spins proposed by Bornholdt, we attempt to bridge between market model and phenomenologies concerning volatility by studying the statistical properties of simulation results. It is implied that long-memory and self-similarity are found but in a limited range of time-scales.

We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth distribution, while the rewiring of links in small-world networks encourages it. Inequal distributions obey log-normal distributions, which are produced by wealth clustering. The rewiring of links breaks the wealth clustering and makes wealth obey the mean field type (power law) distributions. A mechanism that explains the appearance of log-normal distributions with a power law tail is proposed.

顔表面の3次元画像を三角形メッシュにより近似する問題に進化的計算を用いる. 限られた数のノードを 元の曲面をできるだけ正確に近似し配置することが問題である. 1つの三角形分割内の各三角形の誤差に応じてそのノードを淘汰・増殖する方法と 複数の異なる三角形分割を集団と見なす遺伝的アルゴリズムの2つの進化的アルゴリズムを適用してそれらの比較検討を行う. さらに時間的に変化する顔の表面に適応的に再配置を行うことに前者の方法を適用する. この問題と同種の他分野の近似問題においても 本論文で提案する進化的アルゴリズムの有用性が期待される.We use evolutionary computation to approximate a human facial 3D image by a triangular mesh. The approximation problem is to locate a limited number of the node points in such a way that the mesh approximates the facial surface as well as possible. Two evolutionary algorithms are considered and compared. One algorithm selects and reproduces node points according to the approximation error of each triangle in a single triangulation. The other is genetic algorithm in which a set of different triangulations is regarded as a population. We also use the former algorithm to adapt the mesh to a changing facial expression. We expect that such evolutionary computation can be used in other engineering fields that share a similar approximation problem.

The thermodynamic second law in the evaporating black hole space-time is examined in the context of the two-dimensional dilaton black hole. The dynamical evolution of entropy is investigated by using the analytical perturbation method and the numerical method. It is shown that the thermodynamic second law holds in the vicinity of infalling shell and in the region far from the infalling shell in the case of the semi-classical CGHS model. The analysis of general models is also presented and its implication is discussed.

We study quasi-nonlinear evolution of the density perturbation in Newtonian gravity. Weak mode-mode coupling in a small range below the Jeans wavelength is considered. In order to extract nonlinear dynamics we utilize a reductive perturbation, which is well known in mechanics and hydrodynamics and improves a naive perturbation. We show that the basic equations for the acoustic wave reduce to a nonlinear Schrödinger equation. It describes a competition between dispersion originated from gravitational attraction and nonlinearity up to cubic order of the amplitude of the acoustic wave. In purely 1-dimensional motion, there exists localized structures as soliton solutions of two distinctive types depending on the wavelength. More interesting is an instability present in 3-dimensional motion. Namely, a progressive wave is unstable under a long-wave perturbation transverse to the direction of progression. It may imply a possible nonlinear growth of the density fluctuation below the Jeans scale.

The behavior of gravitational wave perturbations on a locally Minkowskian spacetime background containing a planar domain wall is investigated in the gauge-invariant general-relativistic framework. It is shown that for this particular background the domain wall does not emit gravitational waves spontaneously by its free oscillation in the first order, although it scatters incidental gravitational waves. This suggests that the amplitude of gravitational waves emitted from a domain wall is at least of second order in the oscillation amplitude of the domain wall. © 1994 The American Physical Society.

In (2+1)-dimensional gravity without matter, a spacetime is represented by a (pseudo-) Riemannian manifold of constant curvature. Though locally trivial, it can have a rich geometric structure, which is completely described by holonomy. The authors extracts an invariant of geometric structure out of holonomy. The author also shows an explicit construction of holonomy for hyperbolic manifolds which represent quantum nucleation of the universe in (2+1)-dimensional gravity.

The authors show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (i) no anisotropic expansion is allowed for Bianchi type V and VII (A not=0) and (ii) type IV and VI (A not=0,1) do not exist. In order to show them, they put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. They make clear the relation between the Bianchi-type symmetry of spacetime and spatial compactness, some parts of which seem to have gone unnoticed in the literature. Especially, it is shown under what conditions class-B Bianchi models do not possess compact spatial sections. Finally, they briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.

We investigate possibilities of topology change and nucleation of universes in the (2+1)-dimensional Einstein gravity model with negative cosmological constant. We demonstrate that topology change and nucleation phenomena can occur by quantum tunneling by explicitly constructing Euclidean signature hyperbolic 3-geometry. The amplitude is explicitly calculated in the WKB approximation. Point particles can be accommodated in this scheme as topological defects in space-time. They are pair created and annihilated when the universe changes its topology.

The authors have shown explicit examples of topology change of the universe by quantum tunnelling in the (2+1)-dimensional quantum gravity. They show that mass points can be created in pairs as spacetime defects in the course of the topology changing processes.

Dynamics of false-vacuum bubbles is analytically solved in (2+1)-dimensional space-time. The bubbles in our toy model are actually circular strings which separate the locally conical and the de Sitter spaces. Possible configuration and motion of bubbles are completely classified on the basis of the energy condition for the string sources.

We study the (2 + l)-dimensional classical gravity in the case of point sources of arbitrary motion using the maximal time slice and the conformal gauge for the spatial metric. The single moving particle case, in particular, exhibits a new feature distinct from the well-studied case.

We investigate the nucleation of a universe in a (2+1)-dimensional gravity model with a negative cosmological constant. There are a variety of universes born from nothing by quantum tunneling. Utilizing the powerful technique of hyperbolic geometry, we explicitly construct three-manifolds which describe the nucleation of a higher-genus universe. We calculate the wave function of the universe in the WKB approximation. © 1991 The American Physical Society.

We study topology-changing processes in (2+1)-dimensional quantum gravity with a negative cosmological constant. By playing the "gluing-many-polyhedra game" for hyperbolic geometry, we explicitly construct an infinite number of different instantonlike solutions. These solutions can be used to evaluate various topology-changing amplitudes in the WKB approximation. © 1991 The American Physical Society.

The (2+1)-dimensional Einstein gravity with a cosmological constant is studied in the ADM canonical formalism. Adopting York's time slice, we completely solve the initial-value problem and the time evolution equations with an initial spacelike 2-surface being a closed Riemann surface of genus zero and one. The result in a torus case is that the Teichmuller parameters for the torus follow a geodesic in the Teichmuller space but its motion asymptotically stops due to the presence of the cosmological constant.