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.

Emergence of power laws with different power-law exponents from reversal quasi-symmetry and Gibrat’s law

To explore the emergence of power laws in social and economic phenomena, the authors discuss the mechanism whereby reversal quasi-symmetry and Gibrat’s law lead to power laws with different powerlaw exponents. Reversal quasi-symmetry is invariance under the exchange of variables in the joint PDF (probability density function). Gibrat’s law means that the conditional PDF of the exchange rate of variables does not depend on the initial value. By employing empirical worldwide data for firm size, from categories such as plant assets K, the number of employees L, and sales Y in the same year, reversal quasi-symmetry, Gibrat’s laws, and power-law distributions were observed. We note that relations between power-law exponents and the parameter of reversal quasi-symmetry in the same year were first confirmed. Reversal quasi-symmetry not only of two variables but also of three variables was considered. The authors claim the following. There is a plane in 3-dimensional space (log K, log L, log Y ) with respect to which the joint PDF PJ (K,L, Y ) is invariant under the exchange of variables. The plane accurately fits empirical data (K,L, Y ) that follow power-law distributions. This plane is known as the Cobb-Douglas production function, Y = AKαLβ which is frequently hypothesized in economics.

Data Construction and Productivity Analysis on the Medical Device Manufacturing Industry in Japan

Medical devices play an essential role in healthcare. However, statistics on the Japanese medical device industry are insufficient. This study provides statistics for Japan’s medical device manufacturing industry from 1994 to 2016 using the Census of Manufacture (Ministry of Economy, Trade, and Industry). In addition, this study presents a fundamental analysis of industry, productivity analysis, and inter-industry comparison. As evaluated by labour productivity and total factor productivity, the medical device manufacturing industry (1) is research and development (R&D) intensive, (2) does not have sufficient investment in R&D, and (3) has low productivity. This study concludes that it is essential to improve the accuracy of data in the future and to publish data regularly

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.Comment: 22 pages, 17 figure

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

Intracellular energy depletion triggers programmed cell death during petal senescence in tulip

Programmed cell death (PCD) in petals provides a model system to study the molecular aspects of organ senescence. In this study, the very early triggering signal for PCD during the senescence process from young green buds to 14-d-old petals of Tulipa gesneriana was determined. The opening and closing movement of petals of intact plants increased for the first 3 d and then gradually decreased. DNA degradation and cytochrome c (Cyt c) release were clearly observed in 6-d-old flowers. Oxidative stress or ethylene production can be excluded as the early signal for petal PCD. In contrast, ATP was dramatically depleted after the first day of flower opening. Sucrose supplementation to cut flowers maintained their ATP levels and the movement ability for a longer time than in those kept in water. The onset of DNA degradation, Cyt c release, and petal senescence was also delayed by sucrose supplementation to cut flowers. These results suggest that intracellular energy depletion, rather than oxidative stress or ethylene production, may be the very early signal to trigger PCD in tulip petals

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

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

Altered Homeostasis of CD4+ Memory T Cells in Allogeneic Hematopoietic Stem Cell Transplant Recipients: Chronic Graft-versus-Host Disease Enhances T Cell Differentiation and Exhausts Central Memory T Cell Pool

AbstractAn increased risk of late infection is a serious complication after allogeneic hematopoietic stem cell transplantation (AHSCT), especially for recipients with defective CD4+ T cell recovery. Although chronic graft-versus-host disease (cGVHD) negatively influences CD4+ T cell reconstitution, the mechanisms leading to this defect are not well understood. We found that the proportion of CD27− CD4+ T cells was remarkably increased in ASHCT recipients with cGVHD or with repetitive infectious episodes. Isolated CD27− CD4+ T cells from ASHCT recipients had significantly shortened telomere length, displayed enhanced vulnerability to activation-induced cell death, and showed extremely reduced clonal diversity, when compared with CD27− CD4+ T cells from healthy donors. Also, CD27+ CD4+ T cells from AHSCT recipients easily lost their expression of CD27 in response to antigen stimulation regardless of cGVHD status. Taken together, these data indicate that homeostasis of memory CD4+ T cells from AHSCT recipients is altered, and that they easily transit into CD27− effector memory T cells. Increased in vivo T cell stimulation observed in recipients with cGVHD further promotes the transition to effector memory cells, a change that decreases the central memory CD4+ T cell pool and consequently weakens the recipient’s defense against persistently infecting pathogens