Search results for "ta111"

Paradigm of tunable clustering using Binarization of Consensus Partition Matrices (Bi-CoPaM) for gene discovery

2013

Copyright @ 2013 Abu-Jamous et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Clustering analysis has a growing role in the study of co-expressed genes for gene discovery. Conventional binary and fuzzy clustering do not embrace the biological reality that some genes may be irrelevant for a problem and not be assigned to a cluster, while other genes may participate in several biological functions and should simultaneously belong to multiple clusters. Also, these algorithms cannot generate tight cluster…

Localized forms of the LBB condition and a posteriori estimates for incompressible media problems

2018

Abstract The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompres…

Accessible parts of boundary for simply connected domains

2018

For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with a suitable John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obta…

Weak separation condition, Assouad dimension, and Furstenberg homogeneity

2015

We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.

Curve packing and modulus estimates

2018

A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c &gt; 0$. We strengthen Marstrand's result by showing that for $p &gt; 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} &gt; 0$.

Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations

2015

In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\\ u=0 & \text{on }\partial B, \end{cases} \] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.

Removable singularities for div v=f in weighted Lebesgue spaces

2018

International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.

Geometry and quasisymmetric parametrization of Semmes spaces

2014

We consider decomposition spaces R/G that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on R/G constructed via modular embeddings of R/G into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R/G×R by R for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, to the defining sequences for R/G. We give a necessary condition and a sufficient condition for the existence of parametrization. The necessary condition answers negatively a question of Heinonen and Semmes on quasisymmetric parametrizabi…

Integration by parts on generalized manifolds and applications on quasiregular maps

2016

Tensor tomography in periodic slabs

2018

Abstract The X-ray transform on the periodic slab [ 0 , 1 ] × T n , n ≥ 0 , has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless n = 0 . We characterize the kernel of the geodesic X-ray transform for L 2 -regular m -tensors for any m ≥ 0 . The characterization extends to more general manifolds, twisted slabs, including the Mobius strip as the simplest example.