We prove a general Borg-type result for reflectionless unitary CMV operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on the unit circle. This extends a recent result of Simon in connection with a periodic CMV operator with spectrum the whole unit circle. In the course of deriving the Borg-type result we also use exponential...

The range of an AUV is dictated by its finite energy source and minimising the energy consumption is required to maximise its endurance. One option to extend the endurance is by obtaining the optimum hydrodynamic hull shape with balancing the trade-off between computational cost and fluid dynamic fidelity. An AUV hull form has been optimised to obtain low resistance hull. Hydrodynamic optimisat...

A requirement common to most dynamic vision applications is the ability to track objects in a sequence of frames. This problem has been extensively studied in the past few years, leading to several techniques, such as Unscented Particle Filter based trackers, that exploit a combination of the (assumed) target dynamics, empirically learned noise distributions and past position observations. Whil...

Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract CaratheodoryTchakaloff (CATCH) submeshes for compressed Least Squares fitting. 2010 AMS subject classification: 41A10, 65D32.

Let G be a simple Lie group of real rank one, with Iwasawa decomposition KAN̄ and Bruhat big cell NMAN̄ . Then the space G/MAN̄ may be (almost) identified with N and with K/M , and these identifications induce the (generalised) Cayley transform C : N → K/M . We show that C is a conformal map of Carnot–Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplicat...

This paper introduces a generalized Schur algorithm in the Krein space with an indefinite inner product. Concepts such as Caratheodory classes and Schur classes used in the classical Schur algorithm cannot be applied in the Krein space since the positivedefiniteness corresponds merely to the nonsingularity in the Krein space. We note also that these problems appear when fast algorithms for subo...

A set K of vertices in a connected graph is M-convex if and only if for every pair of vertices in K, all vertices of all chordless paths joining them also lie in K. Carathtodory, Helly and Radon type theorems are proved for M-convex sets. The Caratheodory number is 1 for complete graphs and 2 for other graphs, The Helly number equals the size of a maximum clique. The Radon number is one more th...

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so...

The two independent domestication events in the genus Oryza that led to African and Asian rice offer an extremely useful system for studying the genetic basis of parallel evolution. This system is also characterized by parallel de-domestication events, with two genetically distinct weedy rice biotypes in the US derived from the Asian domesticate. One important trait that has been altered by ric...

Given a finite set of points P ⊆ R, we would like to find a small subset S ⊆ P such that the convex hull of S approximately contains P . More formally, every point in P is within distance from the convex hull of S. Such a subset S is called an -hull. Computing an -hull is an important problem in computational geometry, machine learning, and approximation algorithms. In many real world applicati...