Superlinear Scaling for Innovation in Cities

Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.Comment: 5 pages, 5 figures, 1 table, submitted to Phys. Rev. E; references corrected; figures corrected, references and brief discussion adde

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

Diagnosing, modeling, and testing a multiplicative stochastic Gent-McWilliams parameterization

A depth-independent isotropic Gent-McWilliams (GM) transport parameter [kappa] is diagnosed from an idealized eddy-resolving primitive equation simulation. The optimal depth-independent isotropic GM parameterization is only able to model less than 50% of the diagnosed total tendency of temperature induced by unresolved mesoscale eddies. A spatio-temporal stochastic model of the GM parameter is developed based on the diagnosed values; the graphical lasso is used to estimate the spatial correlation structure. The stochastic model is used as a stochastic parameterization in low-resolution model simulations. The low-resolution stochastic simulation does a poor job of reproducing the temporal mean of large-scale temperature. Deterministic GM parameterizations and multiplicative stochastic GM parameterizations with unrealistic structure result in significantly more-accurate large-scale temperature in the low-resolution simulations. These results suggest that either the depth-independence or the isotropy of the GM parameterization are unrealistic as models of the eddy tracer transport, or that a stochastic GM parameterization should include an additive component.</p

Can greater muscularity in larger individuals resolve the 3/4 power-law controversy when modelling maximum oxygen uptake?

BACKGROUND: The power function relationship, MR = a.m(b), between metabolic rate (MR) and body mass m has been the source of much controversy amongst biologists for many years. Various studies have reported mass exponents (b) greater than the anticipated 'surface-area' exponent 0.67, often closer to 0.75 originally identified by Kleiber. AIM: The study aimed to provide a biological explanation for these 'inflated' exponents when modelling maximum oxygen uptake (max), based on the observations from this and previous studies that larger individuals develop disproportionately more muscle mass in the arms and legs. RESEARCH DESIGN AND SUBJECTS: A cross-sectional study of 119 professional soccer players from Croatia aged 18-34 was carried out. RESULTS: Here we confirm that the power function relationship between max and body mass of the professional soccer players results in an 'inflated' mass exponent of 0.75 (95% confidence interval from 0.56 to 0.93), but also the larger soccer players have disproportionately greater leg muscle girths. When the analysis was repeated incorporating the calf and thigh muscle girths rather than body mass as predictor variables, the analysis not only explained significantly more of the variance in max, but the sum of the exponents confirmed a surface-area law. CONCLUSIONS: These findings confirm the pitfalls of fitting body-mass power laws and suggest using muscle-girth methodology as a more appropriate way to scale or normalize metabolic variables such as max for individuals of different body sizes