The analysis of presence/absence data of plant species by regression analysis is the subject of this thesis. A nonparametric approach is emphasized, and methods which take into account correlations between species are also considered. In particular, generalized additive models (GAMs) are used, and these are applied to species’ responses to greenhouse scenarios and to examine multispecies interactions. Parametric models are used to estimate optimal conditions for the presence of species and to test several niche theory hypotheses. An extension of GAMs called vector GAMs is proposed, and they provide a means for proposing nonparametric versions of the following models: multivariate regression, the proportional and nonproportional odds model, the multiple logistic regression model, and bivariate binary regression models such as bivariate probit model and the bivariate logistic model. Some theoretical properties of vector GAMs are deduced from those pertaining to ordinary GAMs, and its relationship with the generalized estimating equations (GEE) approach elucidated. / Whole document restricted, but available by request, use the feedback form to request access.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

This thesis consists of two parts. The first part proposes a new model – the Markov-modulated Hawkes process with stepwise decay (MMHPSD) to investigate the seismicity rate. The MMHPSD is a self-exciting process which switches among different states, in each of which the process has distinguishable background seismicity and decay rates. Parameter estimation is developed via the expectation maximization algorithm. The model is applied to data from the Landers earthquake sequence, demonstrating that it is useful for modelling changes in the temporal patterns of seismicity. The states in the model can capture the behavior of main shocks, large aftershocks, secondary aftershocks and a period of quiescence with different background rates and decay rates. The state transitions can then explain the seismicity rate changes and help indicate if there is any seismicity shadow or relative quiescence. The second part of this thesis develops statistical methods to examine earthquake sequences possessing ancillary data, in this case groundwater level data or GPS measurements of deformation. For the former, signals from groundwater level data at Tangshan Well, China, are extracted for the period from 2002 to 2005 using a moving window method. A number of different statistical techniques are used to detect and quantify coseismic responses to P, S, Love and Rayleigh wave arrivals. The P phase arrivals appear to trigger identifiable oscillations in groundwater level, whereas the Rayleigh waves amplify the water level movement. Identifiable coseismic responses are found for approximately 40 percent of magnitude 6+ earthquakes worldwide. A threshold in the relationship between earthquake magnitude and well–epicenter distance is also found, satisfied by 97% of the identified coseismic responses, above which coseismic changes in groundwater level at Tangshan Well are most likely. A non-linear filter measuring short-term deformation rate changes is introduced to extract signals from GPS data. For two case studies of a) deep earthquakes in central North Island, New Zealand, and b) shallow earthquakes in Southern California, a hidden Markov model (HMM) is fitted to the output from the filter. Mutual information analysis indicates that the state having the largest variation of deformation rate contains precursory information that indicates an elevated probability for earthquake occurrence.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

Optical tweezers using highly focussed laser beams can be used to exert forces and torques and thus drive micromachines. This opens up a new field of microengineering, whose potential has yet to be fully realized. Until now, methods that have been used for modelling optical tweezers are limited to scatterers that are homogeneous or that have simple geometry. To aid in designing more general micromachines, I developed and implemented two main methods for modelling the micromachines that we use. These methods can be used for further proposed structures to be fabricated. The first is a FDFD/T-matrix hybrid method that incorporates the finite difference frequency domain (FDFD) method, which is used for inhomogeneous and anisotropic media, with vector spherical wave functions (VSWF) to formulate the T-matrix. The T-matrix is then used to calculate the torque of the trapped vaterite sphere, which is apparently composed of birefringent unit crystals but the bulk structure appears to be arranged in a sheaf-of-wheat fashion. The second method is formulating the T-matrix via discrete dipole approximation (DDA) of complex arbitrarily shaped mesoscale objects and implementing symmetry optimizations to allow calculations to be performed on high-end desktop PCs that are otherwise impractical due to memory requirements and calculation time. This method was applied to modelling microrotors. The T-matrix represents the scattering properties of an object for a given wavelength. Once it is calculated, subsequent calculations with different illumination conditions can be performed rapidly. This thesis also deals with studies of other light scattering phenomena including the modelling of scattered fields from protein molecules subsequently used to model FRET resonance, determining the limits of trappability, interferometric Brownian motion and the comparison between integral transforms by direct numerical integration and overdetermined point-matching.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

The New Zealand Ministry of Fisheries relies on fishery assessments to determine suitable catch quotas for exploited fisheries. Currently, 628 fish stocks are managed in New Zealand using the Quote Management System, which includes the 8 com- mercial flatfish species caught within the Exclusive Economic Zone. These eight species of flatfish, which includes four species of flounder, two species of sole, brill and turbot, are currently managed using a combined catch quota. Since these eight species are managed using a common catch quota, there is concern that some of the individual species may be under or over-fished. This thesis describes work involving the flatfish species caught in the FLA3 man- agement area, around the south island of New Zealand. The FLA3 management area contains three key species: New Zealand sole, lemon sole, and sand flounder. Due to the nature and limitations of the data available, simple biomass dynamic models were applied to these species. The maximum likelihood and Bayesian goodness of fit techniques were used to estimate the model parameters. Three models were used: the Fox model, the Schaefer model and the Pella-Tomlinson model with m = 3. As a mathematical/statistical exercise, these models were used to conduct a risk analysis to analyse the advantages and disadvantages of six management options for setting a TACC. However, because of issues over the way that the parameter K has been modelled (due to necessity caused by the lack of data), this should not be seen as an appropriate method for estimating the fish stock. Conclusions were drawn from the results regarding suitable future action for the assessment and management of flatfish stock in FLA3.

No description available.

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.

Researchers are frequently faced with the problem of analyzing incomplete and often unbalanced genotype-by-environment (GxE) matrices which arise as a trials programme progresses over seasons. The principal data for this investigation, arising from a ten year programme of onion trials, has less than 2,300 of the 49,200 combinations from the 400 genotypes and 123 environments. This 'sparsity' renders standard GxE methodology inapplicable. Analysis of this data to identify onion varieties that suit the shorter, hotter days of tropical and subtropical locations therefore presented a unique challenge. Removal of some data to form a complete GxE matrix wastes information and is consequently undesirable. An incomplete GxE matrix can be analyzed using the additive main effects and multiplicative interaction (AMMI) model in conjunction with the EM algorithm but proved unsatisfactory in this instance. Cluster analysis has been commonly used in GxE analyses, but current methods are inadequate when the data matrix is incomplete. If clustering is to be applied to incomplete data sets, one of two routes needs to be taken: either the clustering procedure must be modified to handle the missing data, or the missing entries must be imputed so that standard cluster analysis can be performed. A new clustering method capable of handling incomplete data has been developed. 'Two-stage clustering', as it has been named, relies on a partitioning of squared Euclidean distance into two independent components, the GxE interaction and the genotype main effect. These components are used in the first and second stages of clustering respectively. Two-stage clustering forms the basis for imputing missing values in a GxE matrix, so that a more complete data array is available for other GxE analyses. 'Two-stage imputation' estimates unobserved GxE yields using inter-genotype similarities to adjust observed yield data in the environment in which the yield is missing. This new imputation method is transferrable to any two-way data situation where all observations are measured on the same scale and the two factors are expected to have significant interaction. This simple, but effective, imputation method is shown to improve on an existing method that confounds the GxE interaction and the genotype main effect. Future development of two-stage imputation will use a parameterization of two-stage clustering in a multiple imputation process. Varieties recommended for use in a certain environment would normally be chosen using results from similar environments. Differing cluster analysis approaches were applied, but led to inconsistent environment clusterings. A graphical summary tool, created to ease the difficulty in identifying the differences between pairs of clusterings, proved especially useful when the number of clusters and clustered observations were high. 'Cluster influence diagrams' were also used to investigate the effects the new imputation method had on the qualitative structure of the data. A consequence of the principal data's sparsity was that imputed values were found to be dependent on the existence of observable inter-genotype relationships, rather than the strength of these observable relationships. As a result of this investigation, practical recommendations are provided for limiting the detrimental effects of sparsity. Applying these recommendations will enhance the future ability of two-stage imputation to identify those onion varieties that suit tropical and subtropical locations.