With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here I show that, for many high-level functional categories, the number of genes in the category scales as a power-law in the total number of genes in the genome...

A detailed investigation of the scaling properties of the fully finite O(n) systems, under periodic boundary conditions, with long-range interaction, decaying algebraically with the interparticle distance r like r(-d-sigma), below their upper critical dimension, is presented. The computation of the scaling functions is done to one loop order in the nonzero modes. The results are obtained in an ...

With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here I show that, for many high-level functional categories, the number of genes in the category scales as a power-law in the total number of genes in the genome...

The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanović and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy – Riemann equations, the scaling properties associated...

We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the ±1 Ising model with nearest neighbour and body diagonal interaction, the spin-1 model with states 0,±1, and ...

We present a spectral analysis of continuous scaling algorithm for matrix and operator scaling. The main result is that if the input or has gap, then natural gradient flow linear convergence. This implies simple descent also convergence under same assumption. gap condition closely related to notion quantum expander studied in information theory. provides bounds on some important quantities prob...

In this article, we analyse an integral equation of the second kind that represents solution N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify scaling stability constants- and thus approximation error- with respect to number involved spheres. We develop a new priori error demonstrates -independent continuous discrete formulation...

the acid-base equilibrium of lorazepam was studied by means of potentiometry andmultiwavelengths spectrophotometry. the stoichiometric equilibrium constants were determinedat 25 °c and constant ionic strength 0.1 mol l-1 (nacl). the acidity constants pk1=1.58±0.05and pk2=11.67±0.07 were found by potentiometry, and pk1=1.54±0.02 and pk2=11.61±0.03 bymulti-wavelengths spectrophotometry. potentiom...

We gain tight rigorous bounds on the renormalization fixed point for period doubling in families of unimodal maps with degree 4 critical point. use a contraction mapping argument to bound essential eigenfunctions and eigenvalues linearization operator controlling scaling added noise. Multi-precision arithmetic directed rounding is used operations space analytic functions yielding power series c...

The static magnetic field dependence of chemical exchange linebroadening in NMR spectroscopy is investigated theoretically and experimentally. Two-site exchange (A / B) is considered with site A more highly populated than site B (pa > pb), a shift difference between sites equal to ∆ω, and an exchange rate constant given by kex. The exchange contribution to the transverse relaxation rate constan...