arXiv subjects

Hideaki Aoyama

Publications and source records attributed to Hideaki Aoyama.

At least 37 records · Page 2Linked to original sources

arXiv2008

Labour Productivity Superstatistics

We discuss superstatistics theory of labour productivity. Productivity distribution across workers, firms and industrial sectors are studied empirically and found to obey power-distributions, in sharp contrast to the equilibrium theories of mainstream economics. The Pareto index is found to decrease with the level of aggregation, {\it i.e.}, from workers to firms and to industrial sectors. In order to explain these phenomenological laws, we propose a superstatistics framework, where the role of the fluctuating temperature is played by the fluctuating demand.

q-fin.GN↗

arXiv2008

Productivity Dispersion: Facts, Theory, and Implications

We study productivity dispersions across workers, firms and industrial sectors. Empirical study of the Japanese data shows that they all obey the Pareto law, and also that the Pareto index decreases with the level of aggregation. In order to explain these two stylized facts, we propose a theoretical framework built upon the basic principle of statistical physics. In this framework, we employ the concept of superstatistics which accommodates fluctuations of aggregate demand.

q-fin.GN↗

arXiv2007

Agent Simulation of Chain Bankruptcy

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.

q-fin.GN↗

arXiv2006

Response of Firm Agent Network to Exogenous Shock

This paper describes an agent-based model of interacting firms, in which interacting firm agents rationally invest capital and labor in order to maximize payoff. Both transactions and production are taken into account in this model. First, the performance of individual firms on a real transaction network was simulated. The simulation quantitatively reproduced the cumulative probability distribution of revenue, material cost, capital, and labor. Then, the response of the firms to a given exogenous shock, defined as a sudden change of gross domestic product, is discussed. The longer tail in cumulative probability and skewed distribution of growth rate are observed for a high growth scenario.

physics.soc-ph↗

arXiv2005

Change of ownership networks in Japan

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.

physics.soc-ph↗

arXiv2005

Shareholding Networks in Japan

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 gamma=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.

physics.soc-ph↗

arXiv2005

Heterogeneous Economic Networks

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.

physics.soc-ph↗

arXiv2003

Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto-Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically.

cond-mat.stat-mech↗

arXiv2002

Growth and Fluctuations of Personal Income

Pareto's law states that the distribution of personal income obeys a power-law in the high-income range, and has been supported by international observations. Researchers have proposed models over a century since its discovery. However, the dynamical nature of personal income has been little studied hitherto, mostly due to the lack of empirical work. Here we report the first such study, an examination of the fluctuations in personal income of about 80,000 high-income taxpayers in Japan for two consecutive years, 1997 and 1998, when the economy was relatively stable. We find that the distribution of the growth rate in one year is independent of income in the previous year. This fact, combined with an approximate time-reversal symmetry, leads to the Pareto law, thereby explaining it as a consequence of a stable economy. We also derive a scaling relation between positive and negative growth rates, and show good agreement with the data. These findings provide the direct observation of the dynamical process of personal income flow not yet studied as much as for companies.

cond-mat.dis-nn↗

arXiv2001

Classification of Type A N-fold supersymmetry

Type A N-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using sl(2) generators represented on a finite dimensional functional space. Using this sl(2) formalism we show a general method of constructing Type A N-fold supersymmetric models. We also present systematic generation of known models and several new models using this method.

hep-th↗

arXiv2001

N-fold Supersymmetry in Quantum Mechanics - General Formalism -

We report general properties of N-fold supersymmetry in one-dimensional quantum mechanics. N-fold supersymmetry is characterized by supercharges which are N-th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further investigation about a particular class of N-fold supersymmetric models which we dubbed type A. Algebraic equations which determine a part of spectra of type A models are presented, and the non-renormalization theorem are generalized. Finally, we present a possible generalization of N-fold supersymmetry in multi-dimensional quantum mechanics.

quant-ph↗

arXiv2001

Testing for Mathematical Lineation in Jim Crace's "Quarantine" and T. S. Eliot's "Four Quartets"

The mathematical distinction between prose and verse may be detected in writings that are not apparently lineated, for example in T. S. Eliot's "Burnt Norton", and Jim Crace's "Quarantine". In this paper we offer comments on appropriate statistical methods for such work, and also on the nature of formal innovation in these two texts. Additional remarks are made on the roots of lineation as a metrical form, and on the prose-verse continuum.

cs.CL↗

arXiv2001

sl(2) Construction of Type A N-fold supersymmetry

N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eigenvalues can be obtained for a portion of the spectra. We show that recently found Type A N-fold supersymmetry can be constructed by using sl(2) algebra, which provides a basis for the quasi-solvability. By this construction we find a condition for the Type A N-fold supersymmetry, which is less restrictive than the condition known previously. Several explicitly known models are also examined in the light of this construction.

hep-th↗

arXiv2001

Small-World Effects in Wealth Distribution

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.

cond-mat.stat-mech↗

arXiv2001

General Forms of a N-fold Supersymmetric Family

We report general forms of one family of the N-fold supersymmetry in one-dimensional quantum mechanics. The N-fold supersymmetry is characterized by the supercharges which are N-th order in differential operators. The family reported here is defined as a particular form of the supercharges and is referred to as ``type A''. We show that a quartic and a periodic potentials, which were previously found to be N-fold supersymmetric by the authors, are realized as special cases of this type A family.

quant-ph↗

arXiv2000

N-fold Supersymmetry for a Periodic Potential

We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the anticommutator of the supercharges is not the ordinary Hamiltonian, but is a polynomial of the Hamiltonian. (For this reason, the original Hamiltonian is referred to as the "Mother Hamiltonian".) This supersymmetry shares some features with the ordinary variety, the most notable of which is the non-renormalization theorem. An N-fold supersymmetry was earlier found for a quartic potential whose supersymmetry is spontaneously broken. Here we report that it also holds for a periodic potential, albeit with somewhat different supercharges, whose supersymmetry is not broken.

quant-ph↗

arXiv2000

Pareto's Law for Income of Individuals and Debt of Bankrupt Companies

We analyze the distribution of income and income tax of individuals in Japan for the fiscal year 1998. From the rank-size plots we find that the accumulated probability distribution of both data obey a power law with a Pareto exponent very close to -2. We also present an analysis of the distribution of the debts owed by bankrupt companies from 1997 to March, 2000, which is consistent with a power law behavior with a Pareto exponent equal to -1. This power law is the same as that of the income distribution of companies. Possible implications of these findings for model building are discussed.

cond-mat.stat-mech↗

arXiv1998

Isometric Lineation in English Texts: An Empirical and Mathematical Examination of its Character and Consequences

In this paper we build on earlier observations and theory regarding word length frequency and sequential distribution to develop a mathematical characterization of some of the language features distinguishing isometrically lineated text from unlineated text, in other words the features distinguishing isometrical verse from prose. It is shown that the frequency of syllables making complete words produces a flat distribution for prose, while that for verse exhibits peaks at the line length position and subsequent multiples of that position. Data from several verse authors is presented, including a detailed mathematical analysis of the dynamics underlying peak creation, and comments are offered on the processes by which authors construct lines. We note that the word-length sequence of prose is random, whereas lineation necessitates non-random word-length sequencing, and that this has the probable consequence of introducing a degree of randomness into the otherwise highly ordered grammatical sequence. In addition we observe that this effect can be ameliorated by a reduction in the mean word length of the text (confirming earlier observations that verse tends to use shorter words) and the use of lines varying from the core isometrical set. The frequency of variant lines is shown to be coincident with the frequency of polysyllables, suggesting that the use of variant lines is motivated by polysyllabic word placement. The restrictive effects of different line lengths, the relationship between metrical restriction and poetic effect, and the general character of metrical rules are also discussed.

cmp-lg↗