568 resultados para mathematical application


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A recent advance in biosecurity surveillance design aims to benefit island conservation through early and improved detection of incursions by non-indigenous species. The novel aspects of the design are that it achieves a specified power of detection in a cost-managed system, while acknowledging heterogeneity of risk in the study area and stratifying the area to target surveillance deployment. The design also utilises a variety of surveillance system components, such as formal scientific surveys, trapping methods, and incidental sightings by non-biologist observers. These advances in design were applied to black rats (Rattus rattus) representing the group of invasive rats including R. norvegicus, and R. exulans, which are potential threats to Barrow Island, Australia, a high value conservation nature reserve where a proposed liquefied natural gas development is a potential source of incursions. Rats are important to consider as they are prevalent invaders worldwide, difficult to detect early when present in low numbers, and able to spread and establish relatively quickly after arrival. The ‘exemplar’ design for the black rat is then applied in a manner that enables the detection of a range of non-indigenous species of rat that could potentially be introduced. Many of the design decisions were based on expert opinion as data gaps exist in empirical data. The surveillance system was able to take into account factors such as collateral effects on native species, the availability of limited resources on an offshore island, financial costs, demands on expertise and other logistical constraints. We demonstrate the flexibility and robustness of the surveillance system and discuss how it could be updated as empirical data are collected to supplement expert opinion and provide a basis for adaptive management. Overall, the surveillance system promotes an efficient use of resources while providing defined power to detect early rat incursions, translating to reduced environmental, resourcing and financial costs.

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A method of eliciting prior distributions for Bayesian models using expert knowledge is proposed. Elicitation is a widely studied problem, from a psychological perspective as well as from a statistical perspective. Here, we are interested in combining opinions from more than one expert using an explicitly model-based approach so that we may account for various sources of variation affecting elicited expert opinions. We use a hierarchical model to achieve this. We apply this approach to two problems. The first problem involves a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. The second concerns the time taken by PhD students to submit their thesis in a particular school.

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In the past two decades there has been increasing interest in branding tourism destinations in an effort to meaningfully differentiate against a myriad of competing places that offer similar attractions and facilities. The academic literature relating to destination branding commenced only as recently as 1998, and there remains a dearth of empirical data that tests the effectiveness of brand campaigns, particularly in terms of enhancing destination loyalty. This paper reports the results of an investigation into destination brand loyalty for Australia as a long haul destination in a South American market. In spite of the high level of academic interest in the measurement of perceptions of destinations since the 1970s, few previous studies have examined perceptions held by South American consumers. Drawing on a model of consumer-based brand equity (CBBE), antecedents of destination brand loyalty was tested with data from a large Chilean sample of travelers, comprising a mix of previous visitors and non-visitors to Australia. Findings suggest that destination brand awareness, brand image, and brand value are positively related to brand loyalty for a long-haul destination. However, destination brand quality was not significantly related. The results also indicate that Australia is a more compelling destination brand for previous visitors compared to non-visitors.

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Plant biosecurity requires statistical tools to interpret field surveillance data in order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveillance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion process that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling whitefly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hierarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an application to interpret surveillance data for exotic plant pests with uncertain spread rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly extent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that excessive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biosecurity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs.

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Reliable infrastructure assets impact significantly on quality of life and provide a stable foundation for economic growth and competitiveness. Decisions about the way assets are managed are of utmost importance in achieving this. Timely renewal of infrastructure assets supports reliability and maximum utilisation of infrastructure and enables business and community to grow and prosper. This research initially examined a framework for asset management decisions and then focused on asset renewal optimisation and renewal engineering optimisation in depth. This study had four primary objectives. The first was to develop a new Asset Management Decision Framework (AMDF) for identifying and classifying asset management decisions. The AMDF was developed by applying multi-criteria decision theory, classical management theory and life cycle management. The AMDF is an original and innovative contribution to asset management in that: · it is the first framework to provide guidance for developing asset management decision criteria based on fundamental business objectives; · it is the first framework to provide a decision context identification and analysis process for asset management decisions; and · it is the only comprehensive listing of asset management decision types developed from first principles. The second objective of this research was to develop a novel multi-attribute Asset Renewal Decision Model (ARDM) that takes account of financial, customer service, health and safety, environmental and socio-economic objectives. The unique feature of this ARDM is that it is the only model to optimise timing of asset renewal with respect to fundamental business objectives. The third objective of this research was to develop a novel Renewal Engineering Decision Model (REDM) that uses multiple criteria to determine the optimal timing for renewal engineering. The unique features of this model are that: · it is a novel extension to existing real options valuation models in that it uses overall utility rather than present value of cash flows to model engineering value; and · it is the only REDM that optimises timing of renewal engineering with respect to fundamental business objectives; The final objective was to develop and validate an Asset Renewal Engineering Philosophy (AREP) consisting of three principles of asset renewal engineering. The principles were validated using a novel application of real options theory. The AREP is the only renewal engineering philosophy in existence. The original contributions of this research are expected to enrich the body of knowledge in asset management through effectively addressing the need for an asset management decision framework, asset renewal and renewal engineering optimisation based on fundamental business objectives and a novel renewal engineering philosophy.

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Evaluation, selection and finally decision making are all among important issues, which engineers face in long run of projects. Engineers implement mathematical and nonmathematical methods to make accurate and correct decisions, whenever needed. As extensive as these methods are, effects of any selected method on outputs achieved and decisions made are still suspicious. This is more controversial and challengeable, where evaluation is made among non-quantitative alternatives. In civil engineering and construction management problems, criteria include both quantitative and qualitative ones, such as aesthetic, construction duration, building and operation costs, and environmental considerations. As the result, decision making frequently takes place among non-quantitative alternatives. It should be noted that traditional comparison methods, including clear-cut and inflexible mathematics, have always been criticized. This paper demonstrates a brief review of traditional methods of evaluating alternatives. It also offers a new decision making method using, fuzzy calculations. The main focus of this research is some engineering issues, which have flexible nature and vague borders. Suggested method provides analyzability of evaluation for decision makers. It is also capable to overcome multi criteria and multi-referees problems. In order to ease calculations, a program named DeMA is introduced.

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To obtain minimum time or minimum energy trajectories for robots it is necessary to employ planning methods which adequately consider the platform’s dynamic properties. A variety of sampling, graph-based or local receding-horizon optimisation methods have previously been proposed. These typically use simplified kino-dynamic models to avoid the significant computational burden of solving this problem in a high dimensional state-space. In this paper we investigate solutions from the class of pseudospectral optimisation methods which have grown in favour amongst the optimal control community in recent years. These methods have high computational efficiency and rapid convergence properties. We present a practical application of such an approach to the robot path planning problem to provide a trajectory considering the robot’s dynamic properties. We extend the existing literature by augmenting the path constraints with sensed obstacles rather than predefined analytical functions to enable real world application.

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This review collects and summarises the biological applications of the element cobalt. Small amounts of the ferromagnetic metal can be found in rock, soil, plants and animals, but is mainly obtained as a by-product of nickel and copper mining, and is separated from the ores (mainly cobaltite, erythrite, glaucodot and skutterudite) using a variety of methods. Compounds of cobalt include several oxides, including: green cobalt(II) (CoO), blue cobalt(II,III) (Co3O4), and black cobalt(III) (Co2O3); four halides including pink cobalt(II) fluoride (CoF2), blue cobalt(II) chloride (CoCl2), green cobalt(II) bromide (CoBr2), and blue-black cobalt(II) iodide (CoI2). The main application of cobalt is in its metal form in cobalt-based super alloys, though other uses include lithium cobalt oxide batteries, chemical reaction catalyst, pigments and colouring, and radioisotopes in medicine. It is known to mimic hypoxia on the cellular level by stabilizing the α subunit of hypoxia inducing factor (HIF), when chemically applied as cobalt chloride (CoCl2). This is seen in many biological research applications, where it has shown to promote angiogenesis, erythropoiesis and anaerobic metabolism through the transcriptional activation of genes such as vascular endothelial growth factor (VEGF) and erythropoietin (EPO), contributing significantly to the pathophysiology of major categories of disease, such as myocardial, renal and cerebral ischaemia, high altitude related maladies and bone defects. As a necessary constituent for the formation of vitamin B12, it is essential to all animals, including humans, however excessive exposure can lead to tissue and cellular toxicity. Cobalt has been shown to provide promising potential in clinical applications, however further studies are necessary to clarify its role in hypoxia-responsive genes and the applications of cobalt-chloride treated tissues.

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In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

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and non-union of bony fractures has been proposed since 1966, little has been known about the effect of HBOT on bone marrow stem cells (BMSC). The aim of this study is to investigate the effect of HBO treatment on osteogenetic differentiation of BMSC and potential application in bone tissue engineering. Adhesive stromal cells harvested from bone marrow were characterized by mesenchymal differentiation potential, cell surface markers and their proliferation capacity. Mesenchymal stem cells, which demonstrated osteogenic, chondrogenic and adipogenic differentiation potential and expressed positively for CD 29, CD 44, CD 73, CD 90, CD 105, CD 166 and negatively for CD34 and CD 45, were selected and treated in a laboratory-scale HBO chamber using different oxygen pressures and exposure times. No obvious effect of HBO treatment on BMSC proliferation was noticed. However, cytotoxic effects of HBO were considerably less pronounced when cells were cultured in medium supplemented with 10% FBS in comparison to medium supplemented with 2% FCS, as was evaluated by WST-1 assay. Under HBO treatment, bone nodules were formed in three days, which was clearly revealed by Von Kossa staining. In contrasts, without HBO treatment, bone nodules were not detected until 9-12 days using the same inducing culture media. Calcium deposition was also significantly increased after three days of HBO treatments compared to no HBO treatment. In addition it was also found that oxygen played a direct role in the enhancement of BMSC osteogenic differentiation, which was independent of the effect of air pressure.

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The use of appropriate features to represent an output class or object is critical for all classification problems. In this paper, we propose a biologically inspired object descriptor to represent the spectral-texture patterns of image-objects. The proposed feature descriptor is generated from the pulse spectral frequencies (PSF) of a pulse coupled neural network (PCNN), which is invariant to rotation, translation and small scale changes. The proposed method is first evaluated in a rotation and scale invariant texture classification using USC-SIPI texture database. It is further evaluated in an application of vegetation species classification in power line corridor monitoring using airborne multi-spectral aerial imagery. The results from the two experiments demonstrate that the PSF feature is effective to represent spectral-texture patterns of objects and it shows better results than classic color histogram and texture features.

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We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

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The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

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Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

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Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.