Universal fluctuations in growth dynamics of economic systems

The growth of business firms is an example of a system of complex interacting units that resembles complex interacting systems in nature such as earthquakes. Remarkably, work in econophysics has provided evidence that the statistical properties of the growth of business firms follow the same sorts of power laws that characterize physical systems near their critical points. Given how economies change over time, whether these statistical properties are persistent, robust, and universal like those of physical systems remains an open question. Here, we show that the scaling properties of firm growth previously demonstrated for publicly-traded U.S. manufacturing firms from 1974 to 1993 apply to the same sorts of firms from 1993 to 2015, to firms in other broad sectors (such as materials), and to firms in new sectors (such as Internet services). We measure virtually the same scaling exponent for manufacturing for the 1993 to 2015 period as for the 1974 to 1993 period and virtually the same scaling exponent for other sectors as for manufacturing. Furthermore, we show that fluctuations of the growth rate for new industries self-organize into a power law over relatively short time scales.Comment: 15 pages, 7 figure

Scaling behavior in economics: I. Empirical results for company growth

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the ``new'' companies in each year and find it to be well approximated by a log-normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of one year, and for companies with approximately the same size $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France (April 1997

Scaling behavior in economics: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France (April 1997

Population pharmacokinetics of cyclophosphamide and metabolites in children with neuroblastoma: a report from the children's oncology group.

Cyclophosphamide-based regimens are front-line treatment for numerous pediatric malignancies; however, current dosing methods result in considerable interpatient variability in tumor response and toxicity. In this pediatric population, the authors' objectives were (1) to quantify and explain the pharmacokinetic variability of cyclophosphamide and 2 of its metabolites, hydroxycyclophosphamide (HCY) and carboxyethylphosphoramide mustard (CEPM), and (2) to apply a population pharmacokinetic model to describe the disposition of cyclophosphamide and these metabolites. A total of 196 blood samples were obtained from 22 children with neuroblastoma receiving intravenous cyclophosphamide (400 mg/m2/d) and topotecan. Blood samples were quantitated for concentrations of cyclophosphamide, HCY, and CEPM using liquid chromatography-mass spectrometry and analyzed using nonlinear mixed-effects modeling with the NONMEM software system. After model building was complete, the area under the concentration-time curve (AUC) was computed using NONMEM. Cyclophosphamide elimination was described by noninducible and inducible routes, with the latter producing HCY. Glomerular filtration rate was a covariate for the fractional elimination of HCY and its conversion to CEPM. Considerable interpatient variability was observed in the AUC of cyclophosphamide, HCY, and CEPM. These results represent a critical first step in developing pharmacokinetic-linked pharmacodynamic studies in children receiving cyclophosphamide to determine the clinical relevance of the pharmacokinetic variability in cyclophosphamide and its metabolites

MPSalsa a finite element computer program for reacting flow problems. Part 2 - user`s guide

This manual describes the use of MPSalsa, an unstructured finite element (FE) code for solving chemically reacting flow problems on massively parallel computers. MPSalsa has been written to enable the rigorous modeling of the complex geometry and physics found in engineering systems that exhibit coupled fluid flow, heat transfer, mass transfer, and detailed reactions. In addition, considerable effort has been made to ensure that the code makes efficient use of the computational resources of massively parallel (MP), distributed memory architectures in a way that is nearly transparent to the user. The result is the ability to simultaneously model both three-dimensional geometries and flow as well as detailed reaction chemistry in a timely manner on MT computers, an ability we believe to be unique. MPSalsa has been designed to allow the experienced researcher considerable flexibility in modeling a system. Any combination of the momentum equations, energy balance, and an arbitrary number of species mass balances can be solved. The physical and transport properties can be specified as constants, as functions, or taken from the Chemkin library and associated database. Any of the standard set of boundary conditions and source terms can be adapted by writing user functions, for which templates and examples exist

MPSalsa a finite element computer program for reacting flow problems. Part 2 - user`s guide

This manual describes the use of MPSalsa, an unstructured finite element (FE) code for solving chemically reacting flow problems on massively parallel computers. MPSalsa has been written to enable the rigorous modeling of the complex geometry and physics found in engineering systems that exhibit coupled fluid flow, heat transfer, mass transfer, and detailed reactions. In addition, considerable effort has been made to ensure that the code makes efficient use of the computational resources of massively parallel (MP), distributed memory architectures in a way that is nearly transparent to the user. The result is the ability to simultaneously model both three-dimensional geometries and flow as well as detailed reaction chemistry in a timely manner on MT computers, an ability we believe to be unique. MPSalsa has been designed to allow the experienced researcher considerable flexibility in modeling a system. Any combination of the momentum equations, energy balance, and an arbitrary number of species mass balances can be solved. The physical and transport properties can be specified as constants, as functions, or taken from the Chemkin library and associated database. Any of the standard set of boundary conditions and source terms can be adapted by writing user functions, for which templates and examples exist

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.Comment: 4 pages with 4 postscript figures (uses Revtex 3.1, Latex2e, multicol.sty, epsf.sty and rotate.sty). Submitted to PR