We consider a cosmic ray spectrum that is a power law in momentum down to a cutoff and derive a lower cutoff corresponding to Ekin ∼ (30− 60) MeV from the observed ionization rates in nearby diffuse clouds. While the real spectra of cosmic rays may not be so simple, we argue that one expects a substantial change in the spectra at such energies and that, at first approximation, a power law spect...

We study the length distribution of a particular class of DNA sequences known as the 5' untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very cle...

The Internet topology at the Autonomous Systems level (AS graph) has a power– law degree distribution and a tier structure. In this paper, we introduce the Interactive Growth (IG) model based on the joint growth of new nodes and new links. This simple and dynamic model compares favorable with other Internet power–law topology generators because it not only closely resembles the degree distribut...

Tsonis and Tsonis [1] study rank-ordered distributions of the number of occurrences of protein domains in four different organisms, and they argue that the power-law decay, f ϰ 1/r, of the number f of occurrences of a protein domain with its rank r suggests the presence of linguistic features in eukaryotic genomes, and that this finding " may lead to important clues about the evolution of langu...

Recently, Fabrikant, Koutsoupias and Papadimitriou [7] introduced a natural and beautifully simple model of network growth involving a trade-off between geometric and network objectives, with relative strength characterized by a single parameter which scales as a power of the number of nodes. In addition to giving experimental results, they proved a power-law lower bound on part of the degree s...

Power laws arise through many natural processes. Zipf showed that the frequencies of words, as they appear in Shakespeare’s Hamlet, follow a power law distribution. Mandelbrot explained this effect as a result of an underlying information-theoretic optimization problem. Miller invoked doubt by showing that a very simple mechanism could also explain the presence of power laws: A monkey typing wo...

The scaling exponent of a 1/ f noise time series is commonly estimated from the power-law slope of its Fourier power spectrum. Here I show that because 1/ f noises typically have significant power above the Nyquist frequency, measurements of their power spectra will often be severely distorted by aliasing, not only near the Nyquist frequency, but also far below it. I show that spectral aliasing...

A new compact physics-based Alpha-Power Law MOSFET Model is introduced to enable projections of low power circuit performance for future generations of technology by linking the simple mathematical expressions of the original Alpha-Power Law Model with their physical origins. The new model, verified by HSPICE simulations and measured data, includes: 1) a subthreshold region of operation for eva...