* Corresponding author, funded by the Engineering and Physical Sciences Research Council (EPSRC), UK and British Telecommunications PLC Abstract: Recent developments in Internet mapping and metrification as well as research into scale-free networks has given us an insight into modelling inter-connected IP networks. A number of topology generators have emerged which attempt to generate topologie...

Population distribution analysis contains useful information regarding decision making of networks’ deployment. However, both the public and the private sector should decide the development of networks based on qualitative and quantitative criteria, such as the application of power laws. In this work, one of the most widely used power laws applied in demographics, the Zipf’s law, is tested over...

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows ho...

Recently, many research contributions focus on showing that specific real-life phenomena or measured quantities of our everyday life obey a power-law, a scale free distribution. Inspired by the numerous studies in power-laws, in this paper, we explore the existence of power-law relationships in musical data. We provide the context where such power-laws do exist, and we give experimental results...

Layered and nanotubular systems that are metallic or graphitic are known to exhibit unusual dispersive van der Waals (vdW) power laws under some circumstances. In this paper we investigate the vdW power laws of bulk and finite layered systems and their interactions with other layered systems and atoms in the electromagnetically non-retarded case. The investigation reveals substantial difference...

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon...

We introduce a mechanism for generating power law distributions, referred to as highly optimized tolerance (HOT), which is motivated by biological organisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. We suggest that power laws in these sy...

In the literature on scientific explanation, there is a classical distinction between explanations of particular facts and explanations of laws. This paper is about explanations of laws, more specifically about microexplanations of laws in physics. We investigate whether providing unificatory information has a surplus value in micro-explanations of physical laws. Unificatory information is info...

– We investigate the dynamics of a modified Burridge-Knopoff model by introducing a dissipative term to mimic the bursts of acoustic emission (AE) from rock samples. The model explains many features of the statistics of AE signals observed in experiments such as the crossover in the exponent value from relatively small amplitude AE signals to larger regime, and their dependence on the pulling s...

Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we analyze scaling relationships related to energy acquisition and transformation and power-laws related to fluctuations in numbers. Our aim is to show how individual level attributes can help to explain and predict patterns at the ...