Shape of Growth Rate Distribution Determines the Type of Non-Gibrat's Property

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log-log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat's First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat's Second Property. Under detailed balance, Non-Gibrat's First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log-log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat's Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat's Properties in the mid-scale range.

Generating Individual Trajectories Using GPT-2 Trained from Scratch on Encoded Spatiotemporal Data

Following Mizuno, Fujimoto, and Ishikawa's research (Front. Phys. 2022), we transpose geographical coordinates expressed in latitude and longitude into distinctive location tokens that embody positions across varied spatial scales. We encapsulate an individual daily trajectory as a sequence of tokens by adding unique time interval tokens to the location tokens. Using the architecture of an autoregressive language model, GPT-2, this sequence of tokens is trained from scratch, allowing us to construct a deep learning model that sequentially generates an individual daily trajectory. Environmental factors such as meteorological conditions and individual attributes such as gender and age are symbolized by unique special tokens, and by training these tokens and trajectories on the GPT-2 architecture, we can generate trajectories that are influenced by both environmental factors and individual attributes

A Quantum Perfect Lattice Action for Monopoles and Strings

A quantum perfect lattice action in four dimensions can be derived analytically as a renormalized trajectory when we perform a block spin transformation of monopole currents in a simple but non-trivial case of quadratic monopole interactions. The spectrum of the lattice theory is identical to that of the continuum theory. The perfect monopole action is transformed exactly into a lattice action of a string model. A perfect operator evaluating a static potential between electric charges is also derived explicitly. If the monopole interactions are weak as in the case of infrared SU(2) QCD, the string interactions become strong. The static potential and the string tension is estimated analytically by the use of the strong coupling expansion and the continuum rotational invariance is restored completely.Comment: 16 pages, 1 figure; to be published in Phys. Lett.

Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain

We study 17 different statistical distributions for sizes obtained {}from the classical and recent literature to describe a relevant variable in the social sciences and Economics, namely the firms' sales distribution in six countries over an ample period. We find that the best results are obtained with mixtures of lognormal (LN), loglogistic (LL), and log Student's $t$ (LSt) distributions. The single lognormal, in turn, is strongly not selected. We then find that the whole firm size distribution is better described by a mixture, and there exist subgroups of firms. Depending on the method of measurement, the best fitting distribution cannot be defined by a single one, but as a mixture of at least three distributions or even four or five. We assess a full sample analysis, an in-sample and out-of-sample analysis, and a doubly truncated sample analysis. We also provide the formulation of the preferred models as solutions of the Fokker--Planck or forward Kolmogorov equation

余剰次元をコンパクト化したSU(2)格子ゲージ理論のスケーリングと有効次元

取得学位：博士(理学)，学位授与番号：博甲第519号，学位授与年月日：平成14年9月30日,学位授与年：200

A New Method for Measuring Tail Exponents of Firm Size Distributions

The authors propose a new method for estimating the power-law exponents of firm size variables. Their focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. On the one hand, as is well known a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effects. The authors modify the method proposed by Malevergne et al. (2011). In this way they can identify both the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. They apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries.This special issue follows the "First Unconventional Workshop on Quantitative Finance and Economics" held at the International Christian University in Tokyo the 21st–23th of February 2011, but is open also to contributions not presented in it

A perfect monopole action for SU(2) QCD

We found a quantum perfect lattice action in the 4-dimensional monopole current theory which is known as an effective theory in the infrared region of QCD. The perfect monopole action is transformed exactly into a lattice action of a string model. When the monopole interactions are weak as in the case of infrared SU(2) QCD, the string interactions are strong. The static potential and the string tension in this region can be estimated analytically by the use of the strong coupling expansion.Comment: Lattice99:Confinement sessio

Recent topics of infrared effective lattice QCD

Three topics concerning infrared effective lattice QCD are discussed. (1)Perfect lattice action of infrared SU(3) QCD and perfect operators for the static potential are analytically given when we assume two-point monopole interactions alone. The assumption seems to be justified from numerical analyses of pure SU(3) QCD in maximally abelian gauge. (2)Gauge invariance of monopole dominance can be proved theoretically if the gauge invariance of abelian dominance is proved. The gauge invariance of monopole condensation leads us to confinement of abelian neutral but color octet states after abelian projection. (3)A stochastic gauge fixing method is developed to study the gauge dependence of the Abelian projection, which interpolates between the maximally abelian (MA) gauge and no gauge fixing. Abelian dominance for the heavy quark potential holds even in the gauge which is far from Maximally Abelian one.Comment: LATTICE99(Poster),3 pages, LaTeX with 4 eps figure

Almost perfect quantum lattice action for low-energy SU(2) gluodynamics

金沢大学総合メディア基盤センター　We study various representations of infrared effective theory of SU(2) gluodynamics as a (quantum) perfect lattice action. In particular we derive a monopole action and a string model of hadrons from SU(2) gluodynamics. These are lattice actions which give almost cutoff independent physical quantities even on coarse lattices. The monopole action is determined by numerical simulations in the infrared region of SU(2) gluodynamics. The string model of hadrons is derived from the monopole action by using BKT transformation. We illustrate the method and evaluate physical quantities such as the string tension and the mass of the lowest state of the glueball analytically using the string model of hadrons. It turns out that the classical results in the string model are near to the one in quantum SU(2) gluodynamics. ©2000 The American Physical Society