Brittenden J, Cotton SC, Elders A, Ramsey CR, Norrie J, Burr J, Campbell B, Bachoo P, Chetter I, Gough M, Earnshaw J, Lees T, Scott J, Baker SA, Francis J, Tassle E, Scotland G, Wileman S, Campbell MK. (Division of Applied Medicine, The Health Services Research Unit, and the Health Economics Research Unit, University of Aberdeen; Department of Vascular Surgery, NHS Grampian, Aberdeen Royal Infi...

A space-efficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four space-efficient algorithms for computing the convex hull of a planar point set.

Abstract—We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ-capacity as a functio...

C 1-surface splines deene tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conce...

When using the convex hull approach in the boundary modeling process, ModelBased Calibration (MBC) software suites – such as Model-Based Calibration Toolbox from MathWorks – can be computationally intensive depending on the amount of data modeled. The reason for this is that the half-space representation of the convex hull is used. We discuss here another representation of the convex hull, the ...

We consider poset models of topological spaces and show that every T1-space has an bounded complete algebraic poset model, thus give a positive answer to a question asked in a recent paper by Waszkiewicz. It is also proved that every T1-space is homeomorphic to the maximal point space of a d-space. In the classic general topology, people are mainly interested in the spaces which satisfy at leas...

Color gamut characterization is an essential step in the ICC profile generation for imaging devices. It is also needed as part of evaluation and comparison of image quality achievable by different imaging systems. A novel technique is presented for characterizing the color gamut of an imaging device via ray tracing in the CIELAB color space. Initially, the convex hull of the set of measurement ...

This theorem is similar to the well known result that any point in the convex hull of a set E in an w-dimensional euclidean space lies in the convex hull of some subset of E containing at most n-\-l points [l, 2 ] . 1 In these theorems the set E is an arbitrary set in the space. The convex hull of E, denoted by H(E), is the set product of all convex sets in the space which contain E. A euclidea...

We have previously shown on a range of benchmarks [Langdon and Buxton, 2001b] genetic programming (GP) can automatically fuse given classifiers of diverse types to produce a combined classifier whose Receiver Operating Characteristics (ROC) are better than [Scott et al., 1998]’s “Maximum Realisable Receiver Operating Characteristics” (MRROC). I.e. better than their convex hull. Here our techniq...