We consider “one-at-a-time” coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the L1-penalized regression (lasso) in the lterature, but it seems to have been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with...

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(κ; ρ) is extended to the setting where the force points can be in the interior of the domain, radial SLE(κ) becomes chordal SLE(κ; ρ), with ρ = κ− 6, and vice versa. We also write down the martingales describing the Radon–Nykodim derivative of SLE(κ; ρ1, . . . , ρn) with...

The hardware and software designs need a clear, consistent and universally accepted definition of the coordinate system for the LAT. This note specifies the global LAT instrument coordinate system; the terminology, numbering, and orientation of detector planes in the TKR and CAL; and tower numbering, the local tower coordinate systems, and detector element numbering within a tower. The conventi...

A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based upon the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant coordinate system for the multivariate data. Consequently, we view this met...

Practical solid modeling systems are plagued by numerical problems that arise from using oating-point arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information might consist of explicit plane equations, with oating-point coeecients; the combinatorial information might consist of face, edge, and vertex ...

An algebra for geometric reasoning is developed that is amenable to software implementation. The features of the algebra are chosen to support geometric programming of the variety found in computer graphics and computer aided geometric design applications. The implementation of the algebra in C++ is described, and several examples illustrating the use of this software are given.

We describe an algorithm which allows a behavior-based robot to learn on the basis of positive and negative feedback when to activate its behaviors. In accordance with the philosophy of behavior-based robots, the algorithm is completely distributed: each of the behaviors independently tries to find out (i) whether it is relevant (ie. whether it is at all correlated to positive feedback) and (ii...

This paper introduces a new group of multi-dimensional coordinate spaces. The main objective is to visualize n-dimensions in the same graphical space and time. This paper is divided into three parts. The first part shows the literature review about dimension and coordinate systems (Cartesian plane and coordinate space). The second part will present how the multi-dimensional coordinate spaces wo...