No description available.

No description available.

No description available.

No description available.

Under the democratic systems of government instilled in many sovereign states, the party in government maintains a constitutional right to call an early election. While the constitution states that there is a maximum period between elections, early elections are frequently called. This right to call an early election gives the government a control to maximize its remaining life in power. The optimal control for the government is found by locating an exercise boundary that indicates whether or not a premature election should be called. This problem draws upon the body of literature on optimal stopping problems and stochastic control. Morgan Poll’s two-party-preferred data are used to model the behaviour of the poll process and a mean reverting Stochastic Differential Equation (SDE) is fitted to these data. Parameters of this SDE are estimated using the Maximum Likelihood Estimation (MLE) Method. Analytic analysis of the SDE for the poll process is given and it will be proven that there is a unique solution to the SDE subject to some conditions. In the first layer, a discrete time model is developed by considering a binary control for the government, viz. calling an early election or not. A comparison between a three-year and a four-year maximum term is also given. A condition when the early exercise option is removed, which leads to a fixed term government such as in the USA is also considered. In the next layer, the possibility for the government to use some control tools that are termed as ‘boosts’ to induce shocks to the opinion polls by making timely policy announcements or economic actions is also considered. These actions will improve the government’s popularity and will have some impacts upon the early-election exercise boundary. An extension is also given by allowing the government to choose the size of its ‘boosts’ to maximize its expected remaining life in power. In the next layer, a continuous time model for this election timing is developed by using a martingale approach and Ito’s Lemma which leads to a problem of solving a partial differential equation (PDE) along with some boundary conditions. Another condition considered is when the government can only call an election and the opposition can apply ‘boosts’ to raise its popularity or just to pull government’s popularity down. The ultimate case analysed is when both the government and the opposition can use ‘boosts’ and the government still has option to call an early election. In these two cases a game theory approach is employed and results are given in terms of the expected remaining life in power and the probability of calling and using ‘boosts’ at every time step and at certain level of popularity.

Under the democratic systems of government instilled in many sovereign states, the party in government maintains a constitutional right to call an early election. While the constitution states that there is a maximum period between elections, early elections are frequently called. This right to call an early election gives the government a control to maximize its remaining life in power. The optimal control for the government is found by locating an exercise boundary that indicates whether or not a premature election should be called. This problem draws upon the body of literature on optimal stopping problems and stochastic control. Morgan Poll’s two-party-preferred data are used to model the behaviour of the poll process and a mean reverting Stochastic Differential Equation (SDE) is fitted to these data. Parameters of this SDE are estimated using the Maximum Likelihood Estimation (MLE) Method. Analytic analysis of the SDE for the poll process is given and it will be proven that there is a unique solution to the SDE subject to some conditions. In the first layer, a discrete time model is developed by considering a binary control for the government, viz. calling an early election or not. A comparison between a three-year and a four-year maximum term is also given. A condition when the early exercise option is removed, which leads to a fixed term government such as in the USA is also considered. In the next layer, the possibility for the government to use some control tools that are termed as ‘boosts’ to induce shocks to the opinion polls by making timely policy announcements or economic actions is also considered. These actions will improve the government’s popularity and will have some impacts upon the early-election exercise boundary. An extension is also given by allowing the government to choose the size of its ‘boosts’ to maximize its expected remaining life in power. In the next layer, a continuous time model for this election timing is developed by using a martingale approach and Ito’s Lemma which leads to a problem of solving a partial differential equation (PDE) along with some boundary conditions. Another condition considered is when the government can only call an election and the opposition can apply ‘boosts’ to raise its popularity or just to pull government’s popularity down. The ultimate case analysed is when both the government and the opposition can use ‘boosts’ and the government still has option to call an early election. In these two cases a game theory approach is employed and results are given in terms of the expected remaining life in power and the probability of calling and using ‘boosts’ at every time step and at certain level of popularity.

A useful measure of quality of a global optimisation algorithm such as simulated annealing is the length of time it must be run to reach a global optimum within a certain accuracy. Such a performance measure assists in choosing and tuning algorithms. This thesis proposes an approach to obtaining such a measure through successive approximation of a generic stochastic global optimisation algorithm with a sequence of stochastic processes culminating in backtracking adaptive search. The overall approach is to approximate the progress of an optimisation algorithm with that of a model process, backtracking adaptive search. The known convergence rate of the model then provides an estimator of the unknown convergence rate of the original algorithm. Parameters specifying this model are chosen based on observation of the optimisation algorithm. The optimisation algorithm may first be approximated with a time-inhomogeneous Markovian process defined on the problem range. The distribution of the number of iterations to convergence for this averaged range process is shown to be identical with that of the original process. This process is itself approximated by a time-homogeneous Markov process in the range, the asymptotic averaged range process. This approximation is defined for all Markovian optimisation algorithms and a weak condition under which its convergence time closely matches that of the original algorithm is developed. The asymptotic averaged range process is of the same form as backtracking adaptive search, the final stage of approximation. Backtracking adaptive search is an optimisation algorithm which generalises pure adaptive search and hesitant adaptive search. In this thesis the distribution of the number of iterations for which the algorithm runs in order to reach a sufficiently extreme objective function level is derived. Several examples of backtracking adaptive search on finite problems are also presented, including special cases that have received attention in the literature. Computational results of the entire approximation framework are reported for several examples. The method can be applied to any optimisation algorithm to obtain an estimate of the time required to obtain solutions of a certain quality. Directions for further work in order to improve the accuracy of such estimates are also indicated.

Modelling of volcanic ashfall has been attempted by volcanologists but very little work has been done by mathematicians. In this thesis we show that mathematical models can accurately describe the distribution of particulate materials that fall to the ground following an eruption. We also report on the development and analysis of mathematical models to calculate the ash concentration in the atmosphere during ashfall after eruptions. Some of these models have analytical solutions. The mathematical models reported on in this thesis not only describe the distribution of ashfall on the ground but are also able to take into account the effect of variation of wind direction with elevation. In order to model the complexity of the atmospheric flow, the atmosphere is divided into horizontal layers. Each layer moves steadily and parallel to the ground: the wind velocity components, particle settling speed and dispersion coefficients are assumed constant within each layer but may differ from layer to layer. This allows for elevation-dependent wind and turbulence profiles, as well as changing particle settling speeds, the last allowing the effects of the agglomeration of particles to be taken into account.

Microplitis croceipes, one of the nectar feeding parasitoid wasps, has been found to associatively learn chemical cues through feeding. The experiments on M. croceipes are performed and recorded by a Sony camcorder in the USDA-ARS Biological Control Laboratory in Tifton, GA, USA. The experimental videos have shown that M. croceipes can respond to Coffee odour in this study. Their detection capabilities and the behaviour of M. croceipes with different levels of coffee odours were studied. First, the data that are related to trained M. croceipes behaviour was extracted from the experimental videos and stored in a Microsoft Excel database. The extracted data represent the behaviour of M. croceipes trained to 0.02g and then exposed to 0.001g, 0.005g, 0.01g, 0.02g and 0.04g of coffee. Secondly, indices were developed to uniquely characterise the behaviour of trained M. croceipes under different coffee concentrations. Thirdly, a preliminary model and its parameters were developed to classify the response of trained wasps when exposed to these five different coffee odours. In summary, the success of this thesis demonstrates the usefulness of data analysis for interpreting experimental data, developing indices, as well as understanding the design principles of a simple model based on trained wasps.

No description available.