Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirical test of the theory and its application, based on the empirical analysis of the dynamics of market shares in the product market. We estimate directly the average growth rate of market shares and its standard deviation, the birth rates and the "death" (hazard) rate of products. We find that temporal variations and product differences of the observed power-law exponents can be fully captured by the theory with no adjustable parameters. Our results can be generalized to many systems for which the statistical properties revealed by power law exponents are directly linked to the underlying generating mechanism

Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units

In-plane magnetic reorientation in coupled ferro- and antiferromagnetic thin films

By studying coupled ferro- (FM) and antiferromagnetic (AFM) thin film systems, we obtain an in-plane magnetic reorientation as a function of temperature and FM film thickness. The interlayer exchange coupling causes a uniaxial anisotropy, which may compete with the intrinsic anisotropy of the FM film. Depending on the latter the total in-plane anisotropy of the FM film is either enhanced or reduced. Eventually a change of sign occurs, resulting in an in-plane magnetic reorientation between a collinear and an orthogonal magnetic arrangement of the two subsystems. A canted magnetic arrangement may occur, mediating between these two extremes. By measuring the anisotropy below and above the N\'eel temperature the interlayer exchange coupling can be determined. The calculations have been performed with a Heisenberg-like Hamiltonian by application of a two-spin mean-field theory.Comment: 4 pages, 4 figure

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

Universal features in the growth dynamics of complex organizations

We analyze the fluctuations in the gross domestic product (GDP) of 152 countries for the period 1950--1992. We find that (i) the distribution of annual growth rates for countries of a given GDP decays with ``fatter'' tails than for a Gaussian, and (ii) the width of the distribution scales as a power law of GDP with a scaling exponent $\beta \approx 0.15$. Both findings are in surprising agreement with results on firm growth. These results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms.Comment: 4 pages, 7 ps figures, using Latex2e with epsf rotate and multicol style files. Submitted to PR

Business experience and start-up size: buying more lottery tickets next time around?

This paper explores the determinants of start-up size by focusing on a cohort of 6247 businesses that started trading in 2004, using a unique dataset on customer records at Barclays Bank. Quantile regressions show that prior business experience is significantly related with start-up size, as are a number of other variables such as age, education and bank account activity. Quantile treatment effects (QTE) estimates show similar results, with the effect of business experience on (log) start-up size being roughly constant across the quantiles. Prior personal business experience leads to an increase in expected start-up size of about 50%. Instrumental variable QTE estimates are even higher, although there are concerns about the validity of the instrument

A Kinematic Approach for Efficient and Robust Simulation of the Cardiac Beating Motion

Computer simulation techniques for cardiac beating motions potentially have many applications and a broad audience. However, most existing methods require enormous computational costs and often show unstable behavior for extreme parameter sets, which interrupts smooth simulation study and make it difficult to apply them to interactive applications. To address this issue, we present an efficient and robust framework for simulating the cardiac beating motion. The global cardiac motion is generated by the accumulation of local myocardial fiber contractions. We compute such local-to-global deformations using a kinematic approach; we divide a heart mesh model into overlapping local regions, contract them independently according to fiber orientation, and compute a global shape that satisfies contracted shapes of all local regions as much as possible. A comparison between our method and a physics-based method showed that our method can generate motion very close to that of a physics-based simulation. Our kinematic method has high controllability; the simulated ventricle-wall-contraction speed can be easily adjusted to that of a real heart by controlling local contraction timing. We demonstrate that our method achieves a highly realistic beating motion of a whole heart in real time on a consumer-level computer. Our method provides an important step to bridge a gap between cardiac simulations and interactive applications

Asymmetric magnetization reversal in exchange-biased hysteresis loops

This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.Polarized neutron reflectometry is used to probe the in-plane projection of the net-magnetization vector M of polycrystalline Fe films exchange coupled to twinned (110) MnF2 or FeF2 antiferromagnetic (AF) layers. The magnetization reversal mechanism depends upon the orientation of the cooling field with respect to the twinned microstructure of the AF, and whether the applied field is increased to (or decreased from) a positive saturating field; i.e., the magnetization reversal is asymmetric. The reversal of the sample magnetization from one saturated state to the other occurs via either domain wall motion or magnetization rotation on opposite sides of the same hysteresis loop

Disturbance of deep-sea environments induced by the M9.0 Tohoku Earthquake

The impacts of the M9.0 Tohoku Earthquake on deep-sea environment were investigated 36 and 98 days after the event. The light transmission anomaly in the deep-sea water after 36 days became atypically greater (∼35%) and more extensive (thickness ∼1500 m) near the trench axis owing to the turbulent diffusion of fresh seafloor sediment, coordinated with potential seafloor displacement. In addition to the chemical influx associated with sediment diffusion, an influx of 13C-enriched methane from the deep sub-seafloor reservoirs was estimated. This isotopically unusual methane influx was possibly triggered by the earthquake and its aftershocks that subsequently induced changes in the sub-seafloor hydrogeologic structures. The whole prokaryotic biomass and the development of specific phylotypes in the deep-sea microbial communities could rise and fall at 36 and 98 days, respectively, after the event. We may capture the snap shots of post-earthquake disturbance in deep-sea chemistry and microbial community responses