Many processes and models produce trees with depth scaling logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this motivation, we analyze numerically two branching models leading to non-logarithmic depth scaling. For the first one, Ford’s alphamode...

Allometry has been used to demonstrate a power-law scaling relationship in the brain of premature born infants. Forty-nine preterm infants underwent neonatal MRI scans and neurodevelopmental testing at age 2. Measures of cortical surface area and total cerebral volume demonstrated a power-law scaling relationship (α = 1.27). No associations were identified between these measures and investigate...

The expected number of new infections per day per infectious person during an epidemic has been found to exhibit power-law scaling with respect to the susceptible fraction of the population. This is in contrast to the linear scaling assumed in traditional epidemiologic modeling. Based on simulated epidemic dynamics in synthetic populations representing Los Angeles, Chicago, and Portland, we fin...

Abstract. Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and human in different situations are quite different. This paper proposes a universal optimization model, a random walker following scaling laws (whose traveling distances in each step follow a power law distribution with exponent α) tri...

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power l...

The universal scalability law (USL) is an analytic model used to quantify application scaling. It is universal because it subsumes Amdahl’s law and Gustafson linearized scaling as special cases. Using simulation, we show: (i) that the USL is equivalent to synchronous queueing in a load-dependent machine repairman model and (ii) how USL, Amdahl’s law and Gustafson scaling can be regarded as boun...

A power-law scaling relationship describes tsunami runup heights at ten locations in Japan. Knowledge of the scaling law for tsunamis can be the basis for probabilistic forecasting of the size and number of future events and for estimating probabilities of extremely large events. Using tsunami runup data archived by the U.S. National Geophysical Data Center, we study ten locations where the tsu...

We study the collective dynamics of oscillator-network systems in the presence of noise. By focusing on the time-averaged fluctuation of dynamical variable of interest about the mean field, we discover a scaling law relating the average fluctuation to the node degree. The scaling law is quite robust as it holds for a variety of network topologies and node dynamics. Analyses and numerical suppor...

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's...