The evolutionary origin of general statistics in a biochemical reaction network is studied here to explain the power-law distribution of reaction links and the power-law distribution of chemical abundance. Using cell models with catalytic reaction networks, we have confirmed that the power-law distribution for the abundance of chemicals emerges by the selection of cells with higher growth rates...

1 Synopsis Although the power law has been broadly accepted in measurement and air infiltration standards, and in many air infiltration calculation methods, the assumption that the power law is true over the range of pressures that a building envelope experiences has not been well documented. In this paper, we examine the validity of the power law through theoretical analysis, laboratory measur...

We propose new evolutionary stochastic models for the web graph and other massive networks, where edges are deleted over time and an edge is chosen to be deleted with probability inversely proportional to the in-degree of the destination. The degree distributions of graphs generated by our models follow a power law. A rigorous proof of power law degree distributions is given using martingales a...

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have conjectured that preferential connectivity and incremental growth are both required for the power law distribution. In this paper, we propose a different web graph...

“Our analysis finds Earth’s lakes are power-law distributed for lakes ≥ 8.5 km2 (Fig. 2). Lakes < 8.5 km2 deviate from the power-law distribution such that there are fewer of these small lakes than expected if small lakes conformed to the same power-law distribution as large lakes. Across the range of lake sizes conforming to a power-law distribution, the tail exponent is τ = 1.97 (+ /− 0.01), ...

Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and con...

The statistical dynamics of optical solitons, in a non-Kerr law media, is studied in this paper. The Langevin equations are derived and it is proved that the solitons travel through a fiber with a fixed mean velocity. The non-linearities that are considered here are the power law, parabolic law and the dual-power law types.

Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the...

We investigate whether articulatory movement trajectories follow the nonlinear invariant relationship between the tangential velocity and the curvature, i.e. the one-third power law. The power law holds for articulatory trajectories of phonetic rendering, although the exponent is in the range 0.35–0.42 when averaged across speakers and emotions but is relatively invariant under speaker/emotion ...

It is sometimes claimed that different types of size data in biology follow a power law. Here, a formal statistical test of the power law for discrete size data is described. The test is based on embedding the power law in the nonparametric family of distributions for which frequency is nonincreasing with size. A parametric bootstrap is used to assess significance. The test is applied to four d...