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No description available.

This thesis presents a general framework and method for detection of an object in a video based on apparent motion. The object moves, at some unknown time, differently than the “background” motion, which can be induced from camera motion. The goal of proposed method is to detect and segment the object as soon it moves in an online manner. Since motion estimation can be unreliable between frames, more than two frames are needed to reliably detect the object. Observing more frames before declaring a detection may lead to a more accurate detection and segmentation, since more motion may be observed leading to a stronger motion cue. However, this leads to greater delay. The proposed method is designed to detect the object(s) with minimum delay, i.e., frames after the object moves, constraining the false alarms, defined as declarations of detection before the object moves or incorrect or inaccurate segmentation at the detection time. Experiments on a new extensive dataset for moving object detection show that our method achieves less delay for all false alarm constraints than existing state-of-the-art.

Pure mathematics is often classified as continuous or discrete, that is into topology and combinatorics. Classical topology is the study of spaces in the small, modern topology or homology theory is the study of their large scale structure. The latter and its applications to General Systems Theory and implications on computer programming are the subject of our investigations. A general homology theory includes boundary and adjoint operators defined over a graded category. Singular homology theory describes the structure of high dimensional Simplicial complexes, and is the basis of Kron's tearing of electrical networks. De ~ham Cohomology Theory describes the structure of exterior differential forms used to ~nalyse distributed fields in high dimensional spaces. Likewise optimal control ~roblems can be described by abstract homology theories. Ideas from tensor theory are ~sed to identify the homological structure of Leontief's economic model as a real ~xample of an optimal control system. The common property of each of the above ~ystems is that of optimisation or equivalently the mapping of an error to zero. The ~~iterion may be a metric in space, or energy in an electrical or mechanical network ~~ system, or an abstract cost function in state space or money in an economic system ~~d is always the product of a covariant and a contravariant variable. ~e axiomatic nature of General Homology Theory depends on the definition of an ~~missable category, be it group, ring or module structure. Similarly real systems ~~e analysed in terms of mutually recursive algebras, vector, matrix or polynomial. ~~rther the group morphisms or mode operators are defined recursively. An orthogonal ~~mputer language, Algo182, is proposed which is capable of manipulating the objects ~~scribed by homological systems theory, thus alleviating the tedium and insecurity t~curred in iDtplementing computer programs to analyse engineering systems.

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No description available.

The development of a vaccine against some strains of the human papillomavirus (HPV) has led to many interesting public health questions [1]. We address some of these questions in the following work. We develop a compartmental mathematical model and examine the effect of waning immunity, vaccinating individuals prior to their becoming sexually active and the current government policy of vaccinating only females [2]. We calculate parameters based on data. We consider both time-dependent and age dependent ODE models and an age- and time-dependent PDE model and compare the results. We find the “effective” R0 value, Re0, for the time-dependent models. We introduce optimal control to both the time-dependent and age-dependent ODE models to assess the most cost-effective method for introducing the vaccine into a population. We find that the duration of protection offered by the vaccine can influence whether it is possible to eradicate infection from the population. We find the critical proportion to vaccinate to eradicate the disease. We see that introducing male vaccination would lead to a greater proportion of individuals to be vaccinated if the disease is to be eradicated. The PDE model shows that the proportion of females vaccinated has a large impact on the proportion of females infected. We show that it is cost-effective to vaccinate males and females. Our results support current government policy for age of vaccination [2]. We conclude that potential waning immunity will impact the success of the vaccine. We broadly support government policy for vaccination but recommend including male vaccination to most cost-effectively eradicate the disease.

by Koon-Sun Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 40-41). / Chapter Chapter 1 --- Introduction and Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Preliminaries --- p.4 / Chapter 1.3 --- A brief review of A-optimal designs --- p.8 / Chapter Chapter 2 --- D-optimal Designs --- p.13 / Chapter 2.1 --- A D-optimal design problem --- p.13 / Chapter 2.2 --- A theorem for D-optimal designs --- p.14 / Chapter Chapter 3 --- E-optimal Designs --- p.18 / Chapter 3.1 --- An E-optimal design problem --- p.18 / Chapter 3.2 --- A theorem for E-optimal designs --- p.19 / Chapter Chapter 4 --- An alternative method for computing CL vectors --- p.31 / Chapter Chapter 5 --- Conclusions --- p.36 / References --- p.40

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We investigate algorithms for different steps in the decision making process, focusing on systems where we are uncertain about the outcomes but can quantify how probable they are using random variables. Any decision one makes in such a situation leads to a distribution of outcomes and requires a way to evaluate a decision. The standard approach is to marginalise the distribution of outcomes into a single number that tries in some way to summarise the value of each decision. After selecting a marginalisation approach, mathematicians and decision makers focus their analysis on the marginalised value but ignore the distribution. We argue that we should also be investigating the implications of the chosen mathematical approach for the whole distribution of outcomes. We illustrate the effect different mathematical formulations have on the distribution with one-stage and sequential decision problems. We show that different ways to marginalise the distributions can result in very similar decisions but each way has a different complexity and computational cost. It is often computationally intractable to approximate optimal decisions to high precision and much research goes into developing algorithms that are suboptimal in the marginalised sense, but work within the computational budget available. If the performance of these algorithms is evaluated they are mainly judged based on the marginalised values, however, comparing the performance using the full distribution provides interesting information: We provide numerical examples from dynamic pricing applications where the suboptimal algorithm results in higher profit than the optimal algorithm in more than half of the realisations, which is paid for with a more significant underperformance in the remaining realisations. All the problems discussed in this thesis lead to continuous optimisation problems. We develop a new algorithm that can be used on top of existing optimisation algorithms to reduce the cost of approximating solutions. The algorithm is tested on a range of optimisation problems and is shown to be competitive with existing methods.