542 research outputs found
Pointwise wave behavior of the Navier-Stokes equations in half space
In this paper, we investigate the pointwise behavior of the solution for the
compressible Navier-Stokes equations with mixed boundary condition in half
space. Our results show that the leading order of Green's function for the
linear system in half space are heat kernels propagating with sound speed in
two opposite directions and reflected heat kernel (due to the boundary effect)
propagating with positive sound speed. With the strong wave interactions, the
nonlinear analysis exhibits the rich wave structure: the diffusion waves
interact with each other and consequently, the solution decays with algebraic
rate.Comment: Comments and references are added and some typos are corrected.
Accepted by DCDS-
On a Markov chain related to the individual lengths in the recursive construction of Kingman's coalescent
Kingman's coalescent is a widely used process to model sample genealogies in
population genetics. Recently there have been studies on the inference of
quantities related to the genealogy of additional individuals given a known
sample. This paper explores the recursive (or sequential) construction which is
a natural way of enlarging the sample size by adding individuals one after
another to the sample genealogy via individual lineages to construct the
Kingman's coalescent. Although the process of successively added lineage
lengths is not Markovian, we show that it contains a Markov chain which records
the information of the successive largest lineage lengths and we prove a limit
theorem for this Markov chain.Comment: 13 pages, 2 figure
Pointwise wave behavior of the Navier-Stokes equations in half space
In this paper, we investigate the pointwise behavior of the solution for the
compressible Navier-Stokes equations with mixed boundary condition in half
space. Our results show that the leading order of Green's function for the
linear system in half space are heat kernels propagating with sound speed in
two opposite directions and reflected heat kernel (due to the boundary effect)
propagating with positive sound speed. With the strong wave interactions, the
nonlinear analysis exhibits the rich wave structure: the diffusion waves
interact with each other and consequently, the solution decays with algebraic
rate.Comment: Comments and references are added and some typos are corrected.
Accepted by DCDS-
Model-Robust Designs for Quantile Regression
We give methods for the construction of designs for linear models, when the
purpose of the investigation is the estimation of the conditional quantile
function and the estimation method is quantile regression. The designs are
robust against misspecified response functions, and against unanticipated
heteroscedasticity. The methods are illustrated by example, and in a case study
in which they are applied to growth charts
Kingman's model with random mutation probabilities: convergence and condensation II
A generalisation of Kingman’s model of selection and mutation has been made in a previous paper which assumes all mutation probabilities to be i.i.d.. The weak convergence of fitness distributions to a globally stable equilibrium was proved. The condensation occurs if almost surely a positive proportion of the population travels to and condensates on the largest fitness value due to the dominance of selection over mutation. A criterion of condensation was given which relies on the equilibrium whose explicit expression is however unknown. This paper tackles these problems based on the discovery of a matrix representation of the random model. An explicit expression of the equilibrium is obtained and the key quantity in the condensation criterion can be estimated. Moreover we examine how the design of randomness in Kingman’s model affects the fitness level of the equilibrium by comparisons between different models. The discovered facts are conjectured to hold in other more sophisticated models
Asympotic behavior of the total length of external branches for Beta-coalescents
We consider a -coalescent and we study the asymptotic behavior of
the total length of the external branches of the associated
-coalescent. For Kingman coalescent, i.e. , the result
is well known and is useful, together with the total length , for Fu
and Li's test of neutrality of mutations% under the infinite sites model
asumption . For a large family of measures , including
Beta with , M{\"o}hle has proved asymptotics
of . Here we consider the case when the measure is
Beta, with . We prove that
converges in to
. As a consequence, we get that
converges in probability to . To prove the
asymptotics of , we use a recursive construction of the
-coalescent by adding individuals one by one. Asymptotics of the
distribution of normalized external branch lengths and a related moment
result are also given
- …