A simple general approximation for the distribution of gapped local alignment scores is presented, suitable for assessing significance of comparisons between two protein sequences or a sequence and a profile. The approximation takes account of the scoring scheme (i.e. gap penalty and substitution matrix or profile), sequence composition and length. Use of this formula means it is unnecessary to...

I report on recent progress in our understanding of the structure of CDM halos, and in particular of the inner mass profile of galaxysized systems. Numerical simulations have consistently shown that the density profiles of CDM halos steepen monotonically from the center outwards, with slopes shallower than isothermal near the center and steeper than isothermal near the virial radius. Ongoing de...

In this note, we present the asymptotic expansions of the null distributions of some test statistics for k-sample profile analysis under general conditions. It extents Maruyama (2007, Asmptotic expansions of the null distributions of some test statistics for profile analysis in general conditions. J. Statist. Plann. Inference, 137, 506-526)’s result of two-sample case to k-sample (k ≥ 2) situat...

Varying coefficient model has been popular in the literature. In this paper, we propose a profile least squares estimation procedure to its regression coefficients when its random error is an auto-regressive (AR) process. We further study the asymptotic properties of the proposed procedure, and establish the asymptotic normality for the resulting estimate. We show that the resulting estimate fo...

By analytical methods we study the large time properties of the solution of a simple one-dimensional model of stochastic Stokes’ drift. Semi-explicit formulae allow us to characterize the behaviour of the solutions and compute global quantities such as the asymptotic speed of the center of mass or the effective diffusion coefficient. Using an equivalent tilted ratchet model, we observe that the...

The concept of pulled fronts with a cutoff epsilon has been introduced to model the effects of the discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (pulled fronts are the fronts that propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed v* of small linear perturbations around the unst...

We show that the solutions of nonlinear diffusion equations of the form ut = ∆Φ(u) appearing in filtration theory may present complicated asymptotics as t → ∞ whenever we alternate infinitely many times in a suitable manner the behavior of the nonlinearity Φ. Oscillatory behaviour is demonstrated for finite-mass solutions defined in the whole space when they are renormalized at each time t > 0 ...

We characterize the asymptotic behaviour of the compression associated to a uniform embedding into some Lp-space for a large class of groups including connected Lie groups with exponential growth and wordhyperbolic finitely generated groups. This also provides new and optimal estimates for the compression of a uniform embedding of the infinite 3regular tree into some Lp-space. The main part of ...

We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation as t approaches the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data.

We consider the motion of a compressible viscous fluid in the asymptotic regime of low Mach and high Reynolds numbers under strong stratification imposed by a conservative external force. Assuming a bi-dimensional character of the flow, we identify the limit system represented by the so-called lake equation the Euler system supplemented by an anelastic type constraint imposed by the limit densi...