We study an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and Gevrey spatial regularity of strong solutions to the IBVP in 2D (3D resp.). Asymptotically in time, we show that the solution converges to a con...

Texture analysis plays an important role in applications like automated pattern inspection, image and video compression, content-based image retrieval, remotesensing, medical imaging and document processing, to name a few. Texture Structure Analysis is the process of studying the structure present in the textures. This structure can be expressed in terms of perceived regularity. Our human visua...

Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. However, in contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents an estimate for piecewise polynomial subdivision surfaces by pointing out that curvature conti...

The paper is concerned with Lp error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron ...

On December 3, 2012, following the Third Abel conference, in honor of Endre Szemerédi, Terence Tao posted on his blog a proof of the spectral version of Szemerédi’s regularity lemma. This, in turn, proves the original version.

Abstract Random forest (RF) is one of the algorithms choice in many supervised learning applications, be it classification or regression. The appeal such tree-ensemble methods comes from a combination several characteristics: remarkable accuracy variety tasks, small number parameters to tune, robustness with respect features scaling, reasonable computational cost for training and prediction, th...