417 research outputs found
Asymptotic behaviour of a semilinear elliptic system with a large exponent
Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad
v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad
\Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where
is a bounded convex domain in with smooth boundary
We study the asymptotic behaviour of the least energy
solutions of this system as We show that the solution remain
bounded for large and have one or two peaks away form the boundary. When
one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
Replacing linear diffusion by a degenerate diffusion of porous medium type is
known to regularize the classical two-dimensional parabolic-elliptic
Keller-Segel model. The implications of nonlinear diffusion are that solutions
exist globally and are uniformly bounded in time. We analyse the stationary
case showing the existence of a unique, up to translation, global minimizer of
the associated free energy. Furthermore, we prove that this global minimizer is
a radially decreasing compactly supported continuous density function which is
smooth inside its support, and it is characterized as the unique compactly
supported stationary state of the evolution model. This unique profile is the
clear candidate to describe the long time asymptotics of the diffusion
dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure
Detection of selection signatures for ear carriage in Maltese goat breed
Selection and breeding practices in goats have led to the fixation of several traits. This is probably due to the standardization of several peculiar morphological characteristics that have always been one of the major exclusion criteria of individuals from selection. Among these, ear carriage is one of the most ancient and considered a signature of domestication in several species, such as the dog, pig, sheep and goat (Boyko et al., 2010). The availability of improved genomic analyses tools for goats may provide useful information on genes involved in this trait. By studying, for example, the homozygosity decay of haplotypes (contiguous length of alleles) such information can be detected. In the current study, we focused on the Maltese goat, a breed showing floppy ears, in comparison with other Italian breeds using a goat medium density SNP chip (Nicoloso et al., 2015). A total 48,767 SNP markers for 369 animals belonging to 16 breeds or populations were analyzed. Genotypes were imputed within population excluding markers without known position on the current genome assembly (ARS1, Bickhart et al., 2017). Population analysis using MDS, ADMIXTURE and fastSTRUCTURE confirmed the good differentiation among the populations. Integrated Haplotype Score (iHS, Sabeti et al., 2007) was performed for each population, comparing the regions detected on the Maltese breed with the others considered to detect genes that may be involved into shaping ear morphology. These results may provide new insights into ear carriage phenotype by detecting genes that play a pivotal role in shaping the goat phenotypic diversity
A second eigenvalue bound for the Dirichlet Schroedinger operator
Let be the th eigenvalue of the Schr\"odinger
operator with Dirichlet boundary conditions on a bounded domain and with the positive potential . Following the spirit of the
Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the
spherically rearranged potential , we prove that . Here denotes the ball, centered at the
origin, that satisfies the condition .
Further we prove under the same convexity assumptions on a spherically
symmetric potential , that decreases
when the radius of the ball increases.
We conclude with several results about the first two eigenvalues of the
Laplace operator with respect to a measure of Gaussian or inverted Gaussian
density
A volumetric Penrose inequality for conformally flat manifolds
We consider asymptotically flat Riemannian manifolds with nonnegative scalar
curvature that are conformal to , and so that
their boundary is a minimal hypersurface. (Here, is open
bounded with smooth mean-convex boundary.) We prove that the ADM mass of any
such manifold is bounded below by , where is the
Euclidean volume of and is the volume of the Euclidean
unit -ball. This gives a partial proof to a conjecture of Bray and Iga
\cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.Comment: 7 page
Remarks on the extension of the Ricci flow
We present two new conditions to extend the Ricci flow on a compact manifold
over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi
Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds
We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold,
where the L^2 norm of all second derivatives of the function involving
horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian.
Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE
in non-divergence form with bounded measurable coefficients. The method of
proof is through a Bochner technique. The Heisenberg group is seen to be en
extremal manifold for our inequality in the class of manifolds whose Ricci
curvature is non-negative.Comment: 13 page
Prenatal Brain MR Imaging: Reference Linear Biometric Centiles between 20 and 24 Gestational Weeks
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The conservation of human functional variants and their effects across mammals
Despite the clear potential of livestock models of human functional variants to provide important insights into the biological mechanisms driving human diseases and traits, their use to date has been limited. Generating such models via genome editing is costly and time consuming, and it is unclear which variants will have conserved effects across species. In this study we address these issues by studying naturally occurring livestock models of human functional variants. We show that orthologues of over 1.6 million human variants are already segregating in domesticated mammalian species, including several hundred previously directly linked to human traits and diseases. Models of variants linked to particular phenotypes, including metabolomic disorders and height, are preferentially shared across species, meaning studying the genetic basis of these phenotypes is particularly tractable in livestock. Using machine learning we demonstrate it is possible to identify human variants that are more likely to have an existing livestock orthologue, and, importantly, we show that the effects of functional variants are often conserved in livestock, acting on orthologous genes with the same direction of effect. Consequently, this work demonstrates the substantial potential of naturally occurring livestock carriers of orthologues of human functional variants to disentangle their functional impacts
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