Dynamic breast MRI: Image registration and its impact on enhancement curve estimation

A novel algorithm for performing registration of dynamic contrast-enhanced (DCE) MRI data of the breast is presented. It is based on an algorithm known as iterated dynamic programming originally devised to solve the stereo matching problem. Using artificially distorted DCE-MRI breast images it is shown that the proposed algorithm is able to correct for movement and distortions over a larger range than is likely to occur during routine clinical examination. In addition, using a clinical DCE-MRI data set with an expertly labeled suspicious region, it is shown that the proposed algorithm significantly reduces the variability of the enhancement curves at the pixel level yielding more pronounced uptake and washout phases.

A two-factor model of the U.K. yield curve

I model the forward premium in the U.K. gilt-edged market over the period 1982–96 using a two-factor general equilibrium model of the term structure of interest rates. The model permits the decomposition of the forward premium into separate components representing interest rate expectations, the risk premia associated with each of the underlying factors, and terms capturing the direct impact of the variances of the factors on the shape of the forward curve.

Seasonal growth and growth rate-colony size relationships in six species of saxicolous lichens

The pattern of seasonal growth and the relation of growth rate to colony size were studied in four foliose and two crustose species of saxicolous lichens. A new method of measuring growth was used whereby the advance of a sample of lobes along millimetres marked on the substrate was measured under a magnification of x10. Three peaks of growth were found(in March, June and November) for the foliose species and a single peak (in May to August) for the crustose species. THe peaks of growth corresponded approximately to peaks of rainfall. Growth rate in relation to increasing colony size fell in a smooth exponential curve when expressed on a cm squared/ cm squared/ unit time basis. The result is consistent with a linear radial rate for most of the thallus sizes for the six species. There is also evidence for an exponential incresae in growth rate initially until about 1.5 cm thallus diameter in two of the sepcies when the linear radial rate is achieved.

Factors determining the growth curve of the foliose lichen Parmelia conspersa

Growth curves of the foliose lichen Parmelia conspersa (Ehrh. Ex Ach.)Ach. Were obtained by plotting radial growth (RGR, mm yr-1) of the fastest measured lobe, the slowest measured lobe, a randomly selected lobe, and by averaging a sample of lobes from each thallus against thallus diameter. Growth curves derived from the fastest-growing lobe and by averaging lobes were asymptotic and could be fitted by the growth model of Aplin and Hill. Mean lobe width increased with thallus size, reaching a maximum at approx. 4.5 cm thallus diameter. In four out of six thalli, radial growth of lobes over four months was positively correlated with initial lobe width or area. The RGR of isolated lobes was unaffected until the base of the lobe was removed to within 1-2 mm of the tip. The concentration (micrograms mg-1 biomass) of ribitol, arabitol and mannitol was greater in the marginal lobes of large than in small thalli. The results suggested that the growth curve of P. conspersa is determined by processes that occur within individual marginal lobes and can be explained by the Aplin and Hill model. Changes in lobe width and in the productive capacity of individual lobes with thallus size are likely to be more important factors than the degree of translocation within the lobe in determining the growth curve.

Growth curve of the lichen Rhizocarpon geographicum

Data on the growth curve of the lichen Rhizocarpon geographicum were obtained by measuring the radial growth rates (mm per 1.5 years) of 39 thalli from 2 to 65 mm in diameter growing in the same environment. An Aplin and Hill plot (r2 – r1 against ln r2 – ln r1) of the data and regression analyses suggested an initial phase of growth (up to a diameter of about 7 mm) in which the relative growth rate increased rapidly. This was followed by a phase in which the relative growth rate fell but the radial growth rate continued to rise (7 to 20 mm in diameter). Radial growth was then relatively constant until about 45 mm diameter and then declined. The Aplin and Hill model did not fit the data as a whole but may apply for a transient period in thalli between about 7 and 16 mm in diameter. The curve shows some similarities to that suggested by lichenometric studies but differs in showing a less steep decline in growth rate after the ‘great’ period.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

Modeling foreign exchange rate pass-through using the exponential GARCH

In this chapter, the authors use an EGARCH-ECM to estimate the pass-through effects of Foreign Exchange (FX) rate changes and changes in producers' prices for 20 U.K. export sectors. The long-run adjustments of export prices to FX rate changes and changes in producers' prices are within the range of -1.02% (for the Textiles sector) and -17.22% (for the Meat sector). The contemporaneous Pricing-To-Market (PTM) coefficients are within the range of -72.84% (for the Fuels sector) and -8.05% (for the Textiles sector). Short-run FX rate pass-through is not complete even after several months. Rolling EGARCH-ECMs show that the short and long-run effects of changes in FX rate and producers' prices vary substantially, as do asymmetry and volatility estimates before equilibrium is achieved.

Using min-sum loopy belief propagation for decentralised supply chain formation

Modern business trends such as agile manufacturing and virtual corporations require high levels of flexibility and responsiveness to consumer demand, and require the ability to quickly and efficiently select trading partners. Automated computational techniques for supply chain formation have the potential to provide significant advantages in terms of speed and efficiency over the traditional manual approach to partner selection. Automated supply chain formation is the process of determining the participants within a supply chain and the terms of the exchanges made between these participants. In this thesis we present an automated technique for supply chain formation based upon the min-sum loopy belief propagation algorithm (LBP). LBP is a decentralised and distributed message-passing algorithm which allows participants to share their beliefs about the optimal structure of the supply chain based upon their costs, capabilities and requirements. We propose a novel framework for the application of LBP to the existing state-of-the-art case of the decentralised supply chain formation problem, and extend this framework to allow for application to further novel and established problem cases. Specifically, the contributions made by this thesis are: • A novel framework to allow for the application of LBP to the decentralised supply chain formation scenario investigated using the current state-of-the-art approach. Our experimental analysis indicates that LBP is able to match or outperform this approach for the vast majority of problem instances tested. • A new solution goal for supply chain formation in which economically motivated producers aim to maximise their profits by intelligently altering their profit margins. We propose a rational pricing strategy that allows producers to earn significantly greater profits than a comparable LBP-based profitmaking approach. • An LBP-based framework which allows the algorithm to be used to solve supply chain formation problems in which goods are exchanged in multiple units, a first for a fully decentralised technique. As well as multiple-unit exchanges, we also model in this scenario realistic constraints such as factory capacities and input-to-output ratios. LBP continues to be able to match or outperform an extended version of the existing state-of-the-art approach in this scenario. • Introduction of a dynamic supply chain formation scenario in which participants are able to alter their properties or to enter or leave the process at any time. Our results suggest that LBP is able to deal easily with individual occurences of these alterations and that performance degrades gracefully when they occur in larger numbers.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.