The β-skeleton {Gβ(V )} for a point set V is a family of geometric graphs, defined by the notion of neighborhoods parameterized by real number 0 < β < ∞. By using the distance-based version definition of β-skeletons we study those graphs for a set of points in R d space with l1 and l∞ metrics. We present algorithms for the entire spectrum of β values and we discuss properties of lens-based and ...

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the `1,2 and the `1,∞ version have been studied in detail and efficient algorithms exist, there are still open questions regarding other `1,p variants. We characterize conditions for solutions of the `1,p GroupLasso for all p-norms with 1 ≤ p ≤ ∞, and we present a unified active set algorithm. For a...

Numerical experiments in literature on compressed sensing have indicated that the reweighted l1 minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for sparse signal via weighted l1 minimization from the insight of the classical NSP (null space property) and RIC (restricted isometry constant) bound. We first int...

In this paper we present a robust method for simultaneous registration of multiple 3D scans. Rigid registration is an important task in many applications such as surface reconstruction, navigation and computer aided design. The goal of 3-D (rigid) registration is to align surfaces through a (rigid) transformation. A large number of existing registration algorithms are dependent on finding match...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as geometrical of Banach space ensures the have Mazur–Ulam property. We prove that X enjoys this if and only C(K, X) also show same result holds $$L_\infty (\mu ,X)$$ $$L_1(\mu .