Optimal Algorithms for Some Intersection Radius Problems

Abstract --Zusammenfassung Optimal Algorithms for Some Intersection Radius Problems. The intersection radius of a set of n geometrical objects in a d-dimensional Euclidean space, E d, is the radius of the smallest closed hypersphere that intersects all the objects of the set. In this paper, we describe optimal algorithms for some intersection radius problems. We first present a linear-time algorithm to determine the smallest closed hypcrsphere that intersects a set of hyperplanes in E ~, assuming d to be a fixed parameter. This is done by reducing the problem to a linear programming problem in a (d + 1)-dimensional space, involving 2n linear constraints. We also show how the prune-and-search technique, coupled with the strategy of replacing a ray by a point or a line can be used to solve, in linear time, the intersection radius problem for a set of n line segments in the plane. Currently, no algorithms are known that solve these intersection radius problems within the same time bounds. AM

The exchangeability of shape

<p>Abstract</p> <p>Background</p> <p>Landmark based geometric morphometrics (GM) allows the quantitative comparison of organismal shapes. When applied to systematics, it is able to score shape changes which often are undetectable by traditional morphological studies and even by classical morphometric approaches. It has thus become a fast and low cost candidate to identify cryptic species. Due to inherent mathematical properties, shape variables derived from one set of coordinates cannot be compared with shape variables derived from another set. Raw coordinates which produce these shape variables could be used for data exchange, however they contain measurement error. The latter may represent a significant obstacle when the objective is to distinguish very similar species.</p> <p>Results</p> <p>We show here that a single user derived dataset produces much less classification error than a multiple one. The question then becomes how to circumvent the lack of exchangeability of shape variables while preserving a single user dataset. A solution to this question could lead to the creation of a relatively fast and inexpensive systematic tool adapted for the recognition of cryptic species.</p> <p>Conclusions</p> <p>To preserve both exchangeability of shape and a single user derived dataset, our suggestion is to create a free access bank of reference images from which one can produce raw coordinates and use them for comparison with external specimens. Thus, we propose an alternative geometric descriptive system that separates 2-D data gathering and analyzes.</p

A study of genotypic differences in the malting quality of barley

207 leaves : ill., appendicesThesis (Ph.D.1973) from the Dept. of Agronomy, University of Adelaid

School of Computing Science,

We investigate the notion of relevance as it pertains to ‘commonsense’, subjunctive conditionals. Relevance is taken here as a relation between a property (such as having a broken wing) and a conditional (such as birds typically fly). Specifically, we explore a notion of ‘causative ’ relevance, distinct from ‘evidential ’ relevance found, for example, in probabilistic approaches. A series of postulates characterising a minimal, parsimonious concept of relevance is developed. Along the way we argue that no purely logical account of relevance (even at the metalevel) is possible. Finally, and with minimal restrictions, an explicit definition that agrees with the postulates is given.

Improving TCP Performance with Periodic Disconnections over Wireless Links

Since 1988, when the congestion control functions were first introduced, the performance of TCP has been greatly improved