A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions

In Phys. Rev. Letters (73:2), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical fit to Zipf"s "law" cannot be used as a criterion for similarity to natural languages. Although DNA is a presumably "organized system of signs" in Mandelbrot"s (1961) sense, and observation of statistical featurs of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's "gramar" and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an M-sided die or a finite-state branching process.

Optimal Approximations of the Frequency Moments

We give a one-pass, O~(m^{1-2/k})-space algorithm for estimating the k-th frequency moment of a data stream for any real k>2. Together with known lower bounds, this resolves the main problem left open by Alon, Matias, Szegedy, STOC'96. Our algorithm enables deletions as well as insertions of stream elements.