Recently, an enrichment of identical matching sequences has been found in many eukaryotic genomes. Their length distribution exhibits a power law tail raising the question of what evolutionary mechanism or functional constraints would be able to shape this distribution. Here we introduce a simple and evolutionarily neutral model, which involves only point mutations and segmental duplications, a...

simple grammar and the effects of individuals' popularity on the phylogeny of language are studied based on a multi-agent computational model. In this model, a bottom-up syntactic development is traced, in which the global syntax in sentences is gradually formed from local sequential information. Assuming that the popularity of individuals follows a power-law distribution, we demonstrate that a...

Motivated by the fact that many empirical time series--including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values--exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two pa...

We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative details of the dynamics. We focus attention on planar, non-axisymmetric power-law potentials, in particular the logarithmic potential. We confirm the presence...

We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain β functions for the decay rate and coupling at one loop. Assuming colored (power-law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially ...

In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical...

Non-relativistic potential models are considered of the pure power V (r) = sgn(q)r and logarithmic V (r) = ln(r) types. It is shown that, from the spectral viewpoint, these potentials are actually in a single family. The log spectra can be obtained from the power spectra by the limit q → 0 taken in a smooth representation Pnl(q) for the eigenvalues Enl(q). A simple approximation formula is deve...

We present detailed measurements of the temperature dependence of the Hall and longitudinal resistances on a quantum Hall device [(GaAs(7)] which has been used as a resistance standard at NIST. We find a simple power law relationship between the change in Hall resistance and the longitudinal resistance as the temperature is varied between 1.4 K and 36 K. This power law holds over seven orders o...

A generalization of the Prentice's law is presented in this paper. The idea consists of removing some (but not all) of the approximations that comprise the paraxial approach. In that way, we obtain a new formulation that permits us to compute the prismatic power of a lens made up of arbitrary refracting surfaces, and to improve the precision obtained by Prentice's law when applied to monofocal ...

We study several quintessence models which are singular at Q = 0, and use a simple initial constraint Qi ≥ Hinflation/2π to see when they enter tracking regime, disregarding the details of inflation. We find it can give strong constraints for the inverse power-law potential V = V0Q −α, which has to enter tracking regime for lnz ∼ 10. While for the supergravity model V = V0Q −αexp(kQ2/2), the co...