We consider the problem minx(x−t)′A(x−t) subject to x′Bx+2b′x = k where A is positive definite or positive semidefinite. Commonly occurring statistical variants of this problem are discussed within the framework of a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) t takes special forms (especially t = 0 which, u...

This paper provides an overview of a number of techniques developed within our group to perform 3D reconstruction and image segmentation based of the application of energy minimisation concepts. We begin with classical snake techniques and show how similar energy minimisation concepts can be extended to derive globally optimal segmentation methods. Then we discuss more recent work based on geod...

It has been extensively observed that languages minimise the distance between two related words. Dependency length minimisation effects are explained as a means to reduce memory load and for effective communication. In this paper, we ask whether they hold in typically short spans, such as noun phrases, which could be thought of being less subject to efficiency pressure. We demonstrate that mini...

This paper describes a method for stereoscopic rectification with geometric distortion minimisation, to generate suitable image pairs for 3D viewing applications. The current state of the art technique is not optimal as it lacks appropriate mathematical constraints. We present a new approach that enforces the same distortion minimisation criterion with more computational efficiency whilst also ...

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a...

Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the state-space explosion problem. Among other abstraction techniques, bisimulation minimisation has proven to shorten computation times significantly, but, usually, the full state space needs to...

Summary This article analyses static buckling of the so-called Gao beam nonlinear model. It considers pure problems in which vertical loads are omitted. The analysis, using minimisation energy and concept a modified Rayleigh quotient, leads to new results regarding critical load necessary for buckling, existence number post-buckling solutions. Computational provided cases with fixed axial loadi...