bluuebunny/crossref_metadata_2025 huggingface dataset:
A Semi-staggered Residual Distribution Method for 2- and 3-D Steady Inviscid Compressible Flows
Authors: Catalano L A
Published: November 2023

In the last few years, a great effort has been devoted by CFD researchers to develop new and more sophisticated compressible flow solvers which aim at modelling the complex multidimensional wave propagation more correctly than the standard 1-D solvers. Among these, the author has contributed to the development of a genuinely multidimensional upwind method for the solution of the Euler equations based on simple-wave decomposition models [l]: assuming a piece-wise linear distribution of the parameter vector [ineq] on a cell-vertex triangular grid, a set of five-to-six simple wave contributions to the flux-balance over each cell are analytically computed and then split to the downwind nodes of the cell itself by means of the fluctuation splitting N-scheme of [2]. The resulting first-order-accurate algorithm, accelerated by a standard FAS multigrid strategy using an optimal Runge-Kutta scheme as smoother [3] and combined with an adaptive grid-refinement technique [4], has been proven very accurate and efficient for solving complex flow problems in all regimes [1, 4, 5]. However, as demonstrated in [6], a model employing a number of waves higher than the number of equations fails in satisfying the linearity preservation property introduced in [2], which guarantees that all properties (order of accuracy, monotonicity) of the scalar space discretization schemes are retained when solving the entire system. As a consequence, the accuracy of the six-wave fluctuation splitting method is limited to first order, and a significant amount of numerical entropy is generated at solid walls. For such a reason, the extension to the solution of viscous flow problems seems unfeasible and the simple wave methodology has been recently abandoned in favour of using a characteristic decomposition model, which satisfies the linearity preservation property cited above.
Conservative Interface Algorithm for Overlapped Structured/Structured, Structured/Unstructured Grids
Authors: Wang Z J
Published: November 2023

Multi-zonal overlapped grid approach (Chimera) provides a very powerful means of handling complex geometries in Computational Fluid Dynamics (CFD). With Chimera, different zones (or blocks) can intersect each other in an arbitrary manner. Independent/modular grid generation and parts library of frequently used component grids become possible, drastically reducing the degree of difficulty and user time associated with grid generation. With its first introduction into CFD about a decade ago by Steger et al [15], and Benek et al [1], [2], Chimera has been extended to solve both steady and unsteady Navier-Stokes equations for complex geometries ([8]—[9]). For example, transonic flow around the complete space shuttle vehicle with over 16 million grid points was simulated successfully in [11], and an unsteady flow around a tiltrotor helicopter under forward flight was solved with moving overlapped grids [9].
Multiresolution Analysis on Unstructured Meshes : Application to CFD
Authors: Abgrall R
Published: November 2023

The simulation of engineering problems require more and more sophisticated numerical models, and finer and finer meshes discretising complex geometries. Even with the most powerful computers, these tasks are very challenging ; cheaper computing techniques are needed.
An Adaptive Finite Element Method for Turbulent Flow Simulations
Authors: Arnoux-Guisse F , Bonnin O , Sousa L Léal De , Nicolas G
Published: November 2023

The main problems that the finite element code N3S deals with are thermo-hydraulic problems concerning flows with heat transfers in the various components of nuclear power plants such as head adapter, reactor vessel, steam generator pipes. N3S has also been applied to various studies in flow configurations where the fluid is either compressible or incompressible such as external aerodynamics (flow around vehicles or in the urban environment). Specific applications required complementary developments like turbomachinery, flow around cooling towers.
A Temporal Refinement Algorithm for Unstructured Mesh Methods
Authors: Batten P , Lambert C , Toro E F , Saunders R , Causon D M
Published: November 2023

In recent years a number of promising new adaptive spatial refinement techniques have been developed for the numerical solution of partial differential equations on both structured and unstructured meshes[2, 1, 6, 4]. The use of dynamic local mesh adaption within a Cartesian mesh framework has proved extremely powerful in simulating a number of unsteady flows involving moving shock waves[2, 5, 3]. Aside from the obvious benefit of providing greater resolution for a fixed computational cost, the success of these adaptive Cartesian mesh methods can be attributed to the use of matured, high resolution total variation diminishing type schemes and the application of temporal refinement, a technique which allows different regions of the physical domain to advance with different time steps. Whilst bounded higher order methods for unstructured elements are continuing to improve, temporal refinement appears to be continuing an exclusive deployment in adaptive Cartesian mesh methods.
An Adaptive CFD Solver for Time-Dependent Environmental Flow Problems
Authors: Berzins M , Gaskell P H , Sleigh A , Speares W , Tomlin A , Ware J M
Published: November 2023

This paper will describe the application of the SPRINT2D unstructured mesh finite volume code to time-dependent environmental problems and show that the combination of space and time adaptivity makes it possible to gain greater insight into CFD problems. The code has been written through a joint Shell Research Ltd (Thornton Research Centre) and Leeds University (School of Computer Studies) Research programme. The key feature of the software is that applications codes may be written which are based on a toolkit of robust numerical routines. The paper outlines some of these routines and shows how they have been applied to two example problems. Sections 2 and 3 describe the finite volume discretization scheme and the mesh generation and adaptivity routines for unstructured triangular meshes. Section 4 covers the method of lines time integration approach using a range of explicit and implicit time integration methods for both stiff and nonstiff o.d.e.s. A simple spatial error estimate is used to adapt the mesh, and controlled in conjunction with the time error to balance the two errors. Sections 5 and 6 describe the numerical examples while Section 7 contains a summary and outlines an extension of the approach to three dimensional problems.
An Efficient Relaxation Method for a Centred Navier-Stokes Solver
Authors: Corre B , Khalfallah K , Lerat A
Published: November 2023

An implicit unsteady scheme of Lax-Wendroff type was developed in ([5]-[10]) to solve the Euler and Navier-Stokes equations; its internal dissipation is very low but just sufficient to compute accurate solutions of steady aerodynamic problems without using any artificial viscosity or upwinding. Practical calculations yielded very satisfactory results in terms of accuracy (see [6),(10)). These results were obtained by using an approximate spatial factorization of the implicit stage. Recently, the efficiency of the 2D and 3D Euler solver was greatly improved by applying some line relaxation method ([2), (7)). The aim of this paper is to study a similar method for viscous problems. The structure of the original Navier-Stokes solver does not allow a direct extension of the relaxation method to the viscous case. Therefore a new hybrid scheme has been developed : it offers features well suited for an efficient relaxation - basically diagonal dominance - and meanwhile preserves the solution accuracy thanks to a low numerical dissipation in the viscous zone.
Interaction laws and domain decomposition
Authors: Boer B F A de , Veldman A E P
Published: November 2023

With the advent of parallel computers the concept of domain decomposition has become increasingly popular. In the aerodynamic community this concept has been used ever since the ‘discovery’ of the boundary layer by Prandtl in 1904. He divided the flow field in two regions: a thin viscous shear layer and an external region with inviscid flow. The communication between these regions takes place in terms of pressure distribution and displacement thickness. The pressure is closely related to the external streamwise velocity Ue, which in terms of a streamfunction ψ can be written as ue= ∂ ψ/ ∂n is normal to the shear layer). The displacement thickness is immediately related to the streamfunction ψ itself. Hence we recognize, what is nowadays called, a domain-decomposition method with Dirichlet-Neumann coupling.
A TVD Flow Algorithm for FAME
Authors: Onslow S H , Peshkin D A
Published: November 2023

The challenge of generating computational meshes for complex three-dimensional configurations has been the subject of many years work at DRA Farnborough. One approach pursued has been that of using composite, overlapping meshes. Following this approach, the configuration to be meshed is divided into a number of elementary geometric features and then each feature is given its own mesh. The method used is called Feature Associated Mesh Embedding (FAME), and has proved capable of providing high quality meshes for realistic aircraft configurations.
Discrete Mathematics and its Application to Ecology
Authors: Maini Philip
Published: November 2023

In this chapter we will illustrate how simple mathematical ideas can be used to understand how a population grows. We first consider the well-known problem which generates the Fibonacci sequence. Consider a population of rabbits. Suppose that every pair of rabbits can reproduce only twice, when they are one and two-months old, and that each time they produce exactly one new pair of rabbits. Assume that all newborn rabbits survive. The problem here is to see if we can predict how many newborn rabbits there will be in a certain generation given an initial newborn rabbit population.
Channels, Pipes and Rivers
Authors: Needham Dayid
Published: November 2023

The flow of water arises in many everyday situations. For example, on a large scale, in the oceans, in rivers and canals and in lakes, or, on a smaller scale, in heating or drainage pipes and channels. In this class we will develop a simple mathematical model to describe and characterize water flows which occur m closed and open channels.
Toward the twentieth century: from ancient optics to relativity theory
Authors: Pais Abraham
Published: November 2023

The year was 1903. The Wright brothers had launched the first successful manned airplane flight. Henry Ford had founded his motor company. The first Tour de France had been run and the first World Series in baseball had been played (Boston beat Pittsburgh). Paul Gauguin and Camille Pissarro had died, and Pablo Picasso was in his blue period. Copenhagen had its first Social Democratic mayor and its first motorized taxicab. Niels R yberg Finsen had become the first Dane to win a Nobel Prize, in medicine.
How Bohr secured his permanent base of operations
Authors: Pais Abraham
Published: November 2023

The contributions which mark out Planck, Einstein, and Bohr as the founders of the quantum theory are now in place. Planck’s on blackbody radiation (5g) and Einstein’s on the light-quantum and on heat capacities ((5h) and (Sc)) have been sketched only lightly; Bohr’s on atomic structure has been dealt with in much more detail, as befits this book.
Toward the edge of physics in the Bohr style, and a bit beyond
Authors: Pais Abraham
Published: November 2023

The first international physics conference after World War II was held from 22 to 27 July 1946 at the Cavendish Laboratory. Its themes were ‘Fundamental particles and low temperatures’. In the preface to the proceedings one reads: ‘The subject of Fundamental Particles is nowadays so wide that the arrangement of the programme was not easy.’ The opening address was given by Bohr. It is entitled ‘Problems of elementary particle physics’.
In which Bohr moves full steam into his later years
Authors: Pais Abraham
Published: November 2023

As the curtain rises for the final act, we see Bohr at age 60, still holding centre stage, still in full vigor, still running up steps two at a time.Bohr has now reached the zenith of his influence. He has become a public figure of the first rank, he and Margrethe often being called Denmark’s second royal family. High dignitaries visit his home. From Denmark, the king and queen, cabinet ministers, and ambassadors come for dinner.
Epilog
Authors: Pais Abraham
Published: November 2023

Physicists and other friends, young and old, sent expressions of sorrow and sympathy to Margrethe Bohr and her family.* So did dignitaries from various parts of the world.President Kennedy wrote to Mrs Bohr: ‘I am deeply saddened by Professor Bohr’s death. American scientists, indeed all American citizens who knew doctor Bohr’s name and his great contributions, have respected and venerated him for more than two generations ... We are forever indebted to him for the scientific inspiration he brought along on his many visits to the United States, and especially for his great contribution to the atomic center at Los Alamos.
Introduction
Authors: Barbour A D , Holst Lars , Janson Svante
Published: November 2023

One of the oldest limit theorems of probability is the Poisson ‘law of small numbers’. In its simplest form, it states that the binomial distribution Bi (n,p) converges to the Poisson distribution Po(λ) as n→; ∞, if p =λ/n for some λ> 0, as was proved by Poisson (1837), pp. 205–207. The first person to have appreciated its use in the statistical analysis of rare events seems to have been von Bortkewitsch (1898), who emphasized that statistical methods were not only applicable to data consisting of large numbers, even though normal approximation might no longer be appropriate. His analysis of the numbers of Prussian soldiers killed each year as a result of being kicked by horses has proved particularly memorable, although it was only one of several sets of data that he considered. What is more important is that he showed that the Poisson distribution fitted the data very closely, by tabulating the expected and observed frequencies and by comparing the sample variance with the sample mean.
Independent and dissociated terms
Authors: Barbour A D , Holst Lars , Janson Svante
Published: November 2023

When approximating the distribution of a sum W of independent indicator random variables (Iα, α ∈ Γ), there are many methods available. The simple formula for the characteristic function allows Fourier inversion and complex analytic techniques to be brought into play directly, or as applied by Kerstan (1964). Alternatively, the use of these techniques in an operator framework, as in Le Cam (1960) and Deheuvels and Pfeifer (1988), brings excellent results. That the Stein–Chen method also works well in this context is hardly surprising—independence is mathematically a very powerful tool—but, in view of the many competing possibilities, it is perhaps not to be expected that dramatically better results can be proved.
Measurement, Regression, and Calibration
Authors: Brown Philip J
Published: November 2023

The book starts with a range of examples and develops techniques progressively, starting with standard least squares prediction of a single variable from another and moving onto shrinkage techniques for multiple variables. Chapters 6 and 7 refer mostly to methods that have been specifically developed for spectroscopy. The other chapters are quite general in their applicability. Likelihood and Bayesian inference features strongly, the latter allowing flexible analysis of a wide range of multivariate regression problems. The last chapter presents some Bayesian approaches to pattern recognition. For teaching purposes instructors may find particular chapters sufficiently self contained to recommend in isolation as reference or reading material. For example chapter 4 gives an in depth development of a range of shrinkage techniques. including partial least squares regression, ridge regression and principal components regression; together with discussion of the recently proposed continuum regression. Chapter 8 on pattern recognition may also be of us by itself in courses on multivariate analysis and Bayesian Statistics.
Introduction
Authors: Brown Philip J
Published: November 2023

This book is concerned with relating sets of variables. It mostly concentrates on regression models relating two sets of variables. The variables are measurements, or transformations of measurements, taken on an experimental unit. It is desired to predict one set of variables from the other set. Multiple, multivariate, linear, and non-linear regression models are analysed from a perspective of prediction.
Simple linear regression
Authors: Brown Philip J
Published: November 2023

Suppose a single random variable Y is such that for a given value of another variable X = x, the conditional expectation is linear in x :

Here Y might be some measure of lung function and x the cumulative exposure to asbestos dust for a building worker. We may note that x may not be the originally measured variable, it may rather be some function of it; the same applies to Y. What is required is that linearity of conditional expectation holds for the calculated variables, and that in obtaining a measurement pair (xi,Yi) on each of n workers, uncorrelated errors Ei, with constant variance, add to eqn (2.1) to give the random observation Yi, so that
Regularized multiple regression
Authors: Brown Philip J
Published: November 2023

The Gauss-Markov theorem lends considerable weight to the use of least-squares as a method of fitting a linear parametric model. It provides ‘best’ estimators. It does, however, have a very restricted notion of what is best. Firstly it confines attention to estimators linear in the response Y. Secondly it looks only at unbiased estimators. Thirdly it minimizes mean-squared error, that is, it is concerned with expected squared error or quadratic loss: in the scalar case it uses is as an estimator of θ. Even retaining quadratic loss, there may be estimators which are either biased or non-linear in Y or both, which have an average performance far better than least-squares over much of the relevant parameter space. Such estimators may be introduced in a variety of ways. They are often thought to be particularly apt when the model matrix, X, becomes singular or rather near to singular. They are sometimes called regularized estimators and at other times shrinkage estimators, due to the reduced length of the estimated regression parameter vector compared to that of least-squares. The term regularized emanates from the method of regularization in approximation theory literature. Introducing a Lagrange multiplier, λ., this amounts to minimization of or its Hilbert space generalization. Their use as estimators or predictors comprises a large literature; a much smaller literature addresses wider inferential questions. In the model (3.7) assumed here, where columns of X have mean zero, generally, as in standard least-squares estimation.
Regression on curves
Authors: Brown Philip J
Published: November 2023

This chapter extends the discussion of regression modelling to the situation where the set of explanatory variables is indexed by a variate, frequency, or time, and when plotted as in Fig. 1.5 each set of explanatory variables forms a discretized curve. These variables essentially form some sub-sampled sequence of a continuous random process, so that there is an order to the variables and often the sub-sampling will be at equally spaced intervals of the underlying continuous variate (frequency or time). The number, q, typically here large, of explanatory random variables, will be denoted Y(q) = (Y1, Y2, ..., Yq,) and will be used to predict the response or interest variable, here univariate and denoted as X. Training data are available for which both the interest variable and the explanatory variables are observed on n specimens. In this chapter we assume that the data may be viewed as obtained at random so that we are in the random or natural calibration case as opposed to the more problematic controlled calibration where the interest variable has been strictly designed in the training data. In effect the calibration paradigm just reduces to standard regression prediction except that we have reversed the roles of X and Y. As in Chapter 4, the number q of explanatory variables may be very much larger than the number of observations, and there is a high degree of indeterminacy in fitting linear models. The detergent example described in Section 6.9 has n=l2 and q = 43 extracted frequencies, but had the full set of frequencies been used q would be 1168, leading to the full set of 12 Y(q) shown in Fig. 1.5. In this example component 2 of Table 1.4 serves as the twelve X-observations for calibration.
Non-linearity and selection
Authors: Brown Philip J
Published: November 2023

All the models so far considered have been linear in the unknown parameters. This allows the fitting of models non-linear in the measured variables, but at the expense of consequent non-linearity in prediction after controlled calibration. In this chapter we address these non-linear models, both from the viewpoint of exploring the extra complexities that arise and of reviewing methods for avoiding them. In particular variable selection techniques can be used to pick variables for which a linear model holds. This can be particularly advantageous in relating spectra to composition in that the spectral curve measured at a large number of wavelengths embodies a considerable degree of redundancy, and wavelengths may be selected at which the model relating absorbance to composition is quite linear. At other wavelengths which are avoided the relationship may be far from linear. We start in Section 7.2 by offering some diagnostics for detecting non-linearity and interaction and illustrate these on the sugars data described in Example 1.6. Then methods of variable selection are reviewed and illustrated on the same data as well as the detergent data of Example 1.5. Finally, properties of non-linear models relating to possible multimodality of inference are explored in Section 7.10. The earlier sections of the chapter focus on near-IR spectral data but the issues are quite general.
Pattern recognition
Authors: Brown Philip J
Published: November 2023

This chapter explores the use of Bayes theorem in simple applications of pattern recognition and identification. The main development that follows is of discrimination between p multivariate normal populations. This introductory section concludes with two examples on updating evidence in applications of medical screening and of forensic science. In the training data the p populations are identified by p dummy variables, 1 for the presence of that population, 0 for absence. For each observation in the training data these constitute the x-variables corresponding to q-variate Y. Once a linear relationship between x and Y is established, in future it is desired to predict the x (population of origin) from an observed q-vector Z (the future Y). This is classical discrimination, and directly parallels the calibration paradigm of the rest of this book. In particular, recall the direct link between the regression of Y on x and that of x on Y of Section 5.5. This algebraic link does not depend on whether x is a random variable. In particular there is the well-known two-population result that linear discrimination as developed by Fisher can be reproduced by regression of the dummy variable, which identifies the population of origin, on the q variates. However, there is one special feature here: the x-variables are identifiers of the population and not continuous variates. It is therefore desirable and possible to further give the probability that the future Z derives from each of the p populations.
Experimental strategies
Authors: Atkinson A C , Doney A N
Published: November 2023

We are mainly concerned with experiments where the purpose is to elucidate the behaviour of a system by fitting an approximating function or model. The distinction is with experiments where the prime interest is in estimating differences, or other contrasts, in yield between units receiving separate treatments. Often the approximating function will be a low-order polynomial. But, as in Chapter 18, the models may sometimes be non-linear functions representing knowledge of the mechanism of the system under study. There are several advantages to summarizing and interpreting the results of an experiment through a fitted model.
Models and least squares
Authors: Atkinson A C , Doney A N
Published: November 2023

The plots in Chapter 4 illustrate some of the forms of relationship between an m-dimensional factor x and the true response η (x), which will often be written as η (x, β), to stress dependence on a vector of p unknown parameters β. For a first-order model p = m +1. Measurements of η (x) are subject to error, giving observations y. Often the experimental error is additive and the model for the observations is
Mixture experiments
Authors: Atkinson A C , Doney A N
Published: November 2023

We shall chiefly consider the case when the remaining factors, if any, do not vary during the experiment. Then (12.1) defines the q components of a mixture. In mixture experiments the response will depend only on the proportions of the components in the mixture, for example an alloy, but not on the total amount. Experiments of this kind occur frequently in such areas as chemistry, medicine, and agriculture. An extensive survey of mixture experiments is given by Cornell (1990).
Experiments with both qualitative and quantitative factors
Authors: Atkinson A C , Doney A N
Published: November 2023

This chapter is concerned with the design of experiments when the response depends on both qualitative and quantitative factors. In the chemical industry the yield of a process might depend not only on the quantitative factors temperature and pressure, but also on such qualitative factors as the batch of raw material and the type of reactor. Likewise, an antibiotic might be given orally or by an injection, a qualitative factor with two levels. The composition and dosage of the antibiotic could be the quantitative factors.
Blocking response surface designs
Authors: Atkinson A C , Doney A N
Published: November 2023

This chapter, like Chapter 13, is concerned with the design of experiments when the response depends on both qualitative and quantitative factors. For the exact designs of Chapter 13 the number of trials at each level of the qualitative factor is determined by the search algorithm. However, if the qualitative factor corresponds to a blocking variable there may be a specified, and possibly non-constant, number of trials at each level of the qualitative factor. Examples include the number of plots in a field in an agricultural field trial and the number of runs on a chemical plant that can be obtained from a single batch of raw material.
Restricted design regions
Authors: Atkinson A C , Doney A N
Published: November 2023

A major advantage of a general theory such as that of optimum experimental design is the provision of methods for the solution of non-standard problems. In this chapter we illustrate this consequence of the theory through the construction of designs for non-standard design regions. For response surface models these are regions which are neither cubical nor spherical and so are not covered by the results of Chapter 11. For mixture designs, the non-standard regions depart from the simplex for which designs were derived in Chapter 12. A description of a variety of non-standard design problems is given by Snee (1985). His major theme is the usefulness of the computer in the design and conduct of a wide variety of experiments. One area of application is the construction of D-optimum designs for irregular experimental regions. He gives seven examples of such regions and discusses desirable properties of designs, but does not calculate the D-optimum designs. The examples giving rise to non-standard regions are listed briefly below before we consider four examples in more detail.
Clustering from the Perspective of Combinatorial Data Analysis
Authors: Arabie Phipps , Huber Lawrence J .
Published: November 2023

Perhaps the most well-developed and commonly used form of combinatorial data analysis is clustering, which we might characterize as those methods concerned in some way with the identification of homogeneous groups of objects, based on whatever data are available. The literature of cluster analysis is enormous and precludes our giving much space to applications; fortunately, the Classification Society of North America publishes an annual bibliography, Classification Literature Automated Search Service, based on citations to “classic” articles and books as compiled by the Institute for Scientific Information. The target articles being cited are drawn largely from the periodicals’ literature of clustering and multidimensional scaling; after considerable winnowing, 876 citations were given for 1992 (Volume 21; Day, 1992).
Uniform saddlepoint approximations
Authors: Jensen Jens Ledet
Published: November 2023

One of the main motivations for using saddlepoint approximations is that they work well in the tail of the distribution. In the preceding chapters we formulated this in such a way that the relative error is small in a large deviation region. In particular, the results of Section 2.2 hold uniformly for the saddlepoint θ in a compact set of the interior of the definition range of the Laplace transform. However, in an application of a saddlepoint approximation, one still needs to consider whether the particular value of the saddlepoint θ and the number of observations n give rise to a small error. It is therefore important to know that in a number of situations the error is actually uniformly small for θ over all of its definition range. Such uniformity results are also of interest in theoretical considerations, an example of which is discussed in Jensen and Johansson (1990). Uniformity does not hold generally, as has been demonstrated in Example 2.4.7. The situation given in Example 2.4.7 is that of a steep exponential family. However, it is also easy to construct a regular exponential family for which the approximation is not uniformly valid. If, for example, one considers the density x  −1 exp(−x), x > l, one finds that ζ3(θ) ∼ 2{- log(l - θ)}1/2 for θ  -+ l, and so the saddlepoint approximation will break down for θ  -+ l. In this section general results will be stated that specify conditions under which the saddlepoint approximation holds uniformly. In the following section the important class of almost log-concave densities is considered, and in Section 6.3 we turn to the situation where the density looks like either a gamma density or a beta density. Sections 6.1-6.3 deal with continuous variables and in Section 6.4 a parallel theory for lattice variables is given. Finally, in Section 6.5 the general formulation of Section 6.1 is used to discuss the case of independent but not identically distributed variables.
Markov chains
Authors: Jensen Jens Ledet
Published: November 2023

In all the preceding chapters the main emphasis has been on sums of independent terms. The Esscher tilting described in Section 1.4 then leads to the study of a new sum of independent terms, and traditional Edgeworth expansions can be used. In this chapter we will study sums defined on a Markov chain. As we will see below, the tilted measure is almost a Markov chain, the difference being that a term appears which depends on the intial and the final states of the Markov chain. To obtain Edgeworth expansions under this new measure requires special techniques that we describe in Section 9.2. The general results given in this chapter will only cover a subclass of Markov chains; intuitively we cover those chains having a compact state space. For example, in the general discussion we do not cover the standard AR(l) process Xn+1 = α:Xn + ∈n with { ∈n } being an i.i.d. sequence with a normal distribution. The AR(l) process is treated as a special example in Section 9.4.
Nonstandard situations
Authors: Jensen Jens Ledet
Published: November 2023

The saddlepoint approximations discussed in the preceding chapters of this book have been for the situation where the coordinates of the random vector of interest have been either lattice variables or continuous variables, the latter in the sense that they admit a density w.r.t. Lebesgue measure. For the applications, especially those of Chapter 5, this has been a natural restriction. However, there are situations of some practical importance outside this class. The most prominent ones are linear rank statistics in nonparametric statistics and resampling from an empirical distribution function. Some of these examples are discussed in this section, and we compare the use of the lattice version of the saddlepoint approximation with the use of the continuous version.
Bayesian decision-making
Authors: Lindsey J K
Published: November 2023

Observations of phenomena are always made in conditions where previous theoretical knowledge, or perhaps more informal ideas, about the data generating mechanism are available. As far as possible, these are embodied in the model for the data generating mechanism. The likelihood function contains all of the information in the (new) data for estimation of parameters in this model being entertained and, for this reason, is central to inference procedures. As we have seen in Sections 3.6.4 and 6.4.1, prior empirical information can be incorporated by combining likelihoods. Thus, where possible, any such prior knowledge and information should be used. In a scientific context, only models which are thought to be relevant will be considered, but always with an eye to detecting the unexpected. They are to be ranked by the empirical information from the data, previous and present. However, when decisions, implying actions, must be made, the situation changes and an additional new model, for human behaviour, is required. Prior knowledge relating the models for the data generating mechanism to the decisions, and subsequent actions, will generally be available. If this can be formalized in a precise mathematical way, then it can be combined with the information in the likelihood function to yield a description of the posterior knowledge about the data generating mechanism after obtaining the observations. This model for human behaviour, based on changes in human beliefs, is known as a Bayesian approach.
Levels of representation of goal-directed actions
Authors: Jeannerod Marc
Published: November 2023

This chapter deals with how an action can be neurally represented. The term ‘action’ includes a vast number of neural states, depending on whether the action is intended, planned, imagined, observed from another agent, or executed. Thus the definition of action that will be used here is broader than the behavioral motor aspect of the phenomenon that makes muscles contract and limbs move. Many of our actions remain unexecuted. It is essential to study the covert stages of action, the action representation, in order to understand the mechanisms that ultimately lead to overt behavior.
Morita Equivalence
Authors: Reiner I
Published: November 2023

We shall need to study the relationship between A-modules and M ^modules, where as usual Mn(^) is the ring of all n x n matrices over the ring Δ. The generalization of this relationship leads to the concept of Morita equivalence, and we sketch here some of the main results of this theory. As references, we cite Bass [I], P. M. Cohn[1], Faith [I]. While the general theory holds for abelian categories, we shall make the simplifying assumption that our categories are in fact categories of modules.
Intrinsic procedures
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

In a language that has a clear orientation towards scientific applications there is an obvious requirement for the most frequently required mathematical functions to be provided as part of the language itself, rather than expecting each user to code them afresh. When provided with the compiler, they are normally coded to be very efficient and will have been well tested over the complete range of values that they accept. It is difficult to compete with the high standard of code provided by the vendors.
Interoperability with C
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

Fortran 2003 provides a standardized mechanism for interoperating with C. Clearly, any entity involved must be such that equivalent declarations of it may be made in the two languages. This is enforced within the Fortran program by requiring all such entities to be interoperable. We will explain in turn what this requires for types, variables, and procedures. They are all requirements on the syntax so that the compiler knows at compile time whether an entity is interoperable. We continue with examining interoperability for global data and then discuss some examples. We conclude with a new syntax for defining sets of integer constants that is useful in this context.
Somnolence and its management
Authors: Hilton-Jones David , Damian, Maxwell , Meola Giovanni
Published: November 2023

Excessive daytime sleepiness (EDS) is an extremely common, but under­ recognized, feature of myotonic dystrophy (Hilton-Jones 1997). In addition to the obvious functional consequences for the patient, it may be distressing for relatives and carers. The wife of one patient described her upset when she would return from work and start to tell her husband about her day’s activities, only to find that he had already fallen asleep. This led to gradually reducing communication and a sense of increasing frustration for both parties. It may be an important factor in limiting employability. EDS is a contraindication to driving and in many countries there are specific legal restrictions. There is potential for confusing EDS with apathy, an often cited but still relatively poorly understood aspect of the condition. However, apathy and fatigue have been shown not to correlate with EDS, functional disability or depression (Rubinsztein et al. 1998; Van Der Werf et al. 2003).
Improving lender offers using consumer preferences
Authors: Keeney Ralph L , Oliver Robert M
Published: November 2023

Acquiring and managing financial loan portfolios are major components of the retail credit business in the United States. Such portfolios include household mortgages, automobile loans, equity lines of all types, and credit cards. The total amount loaned is estimated to be between 8 and 13 trillions of dollars in the United States alone (Federal Reserve 2002). It is obviously important to manage those portfolios in a way. that is. consistent with portfolio objectives.

Different lenders may naturally have different objectives that they hope to achieve in managing their portfolios. Many are means objectives, such as minimize required loan loss reserves. minimize the cost per new customer acquired. maximize the response rate on acquisitions mailings to acquire new customers. minimize time from billing to collection, and minimize the default rate on loans. Means objectives matter because they eventually have an impact on the economic performance of the portfolio. Two fundamental objectives for the economic performance of many loan portfolios are maximize profits and maximize market share.
The flat-maximum effect and generic linear scoring models: a test
Authors: Overstreet George A , Bradley Edwin L , Kemp Robert S
Published: November 2023

Predicting human behaviour patterns with linear correlation models has challenged researchers for the past five decades. Although most observers generally concede that humans are inferior to such models in combining information. linear scoring models are, unfortunately. plagued by the flat-maximum effect. or the ‘curse of insensitivity ‘.2 As Love and Love (1986) observe, ‘the predictive ability of linear models is insensitive to large variation in the size of regression weights and to the number of predictors ‘. Even more intriguingly. regression weights can be approximated by simpler systems. such as unit or equal weights, with minimal reduction in predictive accuracy. In essence. seemingly different linear scoring models tend to produce indistinguishable predictive outcomes.
Detecting credit card fraud using expert systems
Authors: Leonard Kevin J
Published: November 2023

The incidence of consumer credit card fraud has been on the increase worldwide over the past 2 years. In Canada alone. the cost of credit card fraud totaled (for Visa and Master card) more than 46 million Canadian dollars for 1991. This number compares to totals of about $29 million for 1990 and only $19 million for 1989 (Appleby 1992). The two predominant growth areas are that of counterfeit fraud (where an unauthorized duplicate of the card exists in circulation) and that of non-receipt fraud (where a re-issued card is intercepted by a third party). In both instances. the cardholder is unaware that a copy of his or her card is in the hands of criminals and hence. the fraud is not reported. Consequently, the amount of financial exposure for the financial institution is substantially higher than that for a lost or stolen card, for example, where the cardholder is aware almost immediately. The lost or stolen card is usually reported within the first day to the issuing company and a block is placed on that account. thereby limiting spending.

The objective of this chapter is to construct and implement a rule-based. expert system model to detect the fraudulent usage of credit before the fraud activity has been reported by the cardholder. If this can be accomplished, the credit granting institution will NOT have to rely on the cardholder to report the fraudulent activity. In the case of counterfeit fraud. for example. this can take a substantial number of days-on average, 8-10 days according to bank statistics. The methodology is as follows. Suspicious activity can be detected from deviations from ‘normal ‘ spending patterns through the use of expert systems. As a result. the customer can be contacted and the account blocked (if so warranted--all within the first few hours of the fraud
The Birth Of A Paradigm
Authors: Scott Alwyn
Published: November 2023

“If I have seen further than others,” said Isaac Newton, “it is because I have stood on the shoulders of giants.” As we would not seem to see further than others because we stand on the facesof giants, this book begins with a historical introduction, noting salient contributions to nonlinear science that have been made over the past century and a half. More broadly, the present chapter is a study of the ways—constructive and otherwise—that the scientific community has met with new ideas.
Linear Wave Theory
Authors: Scott Alwyn
Published: November 2023

In this book are presented a variety of methods for solving nonlinear partial differential equations (PDEs); thus it is appropriate to begin with a brief review of some techniques that can be used for solving linear PDEs. (One should learn to walk before trying to run.)The plan for this chapter is first to apply some basic analytical techniques to linear limits of the nonlinear PDEs displayed in Chapter 1, augmented with a selection of practice problems. This brief review is followed by introductions to linear stability theory and linear scattering theory.
The Classical Soliton Equations
Authors: Scott Alwyn
Published: November 2023

An exciting development in nonlinear science during the 1970s was the gradual realization that certain nonlinear partial differential equations display a variety of exact solutions. These include not only solitary waves-known since the nineteenth century studies of Russell, Bazin, and Boussinesq—but solutions involving an arbitrary number of solitary waves of varying speeds and amplitudes undergoing a collective collision. In such events, the solitary waves are now called “solitons,” emphasizing their particle-like character, because they leave the inter action region of space-time with exactly the same speeds and amplitudes that they had upon entry [61]. (As was noted in the introduction, Russell observed hydrodynamic solitary waves passing through each other without change, but he provided no analytic explanation for the phenomenon.)
Radiation Protection Issues In Brachytherapy
Authors: Bownes Peter
Published: November 2023

Everyone involved in work with radioactive substances should be trained in the principles of radiation safety. The three general principles of radiation protection that should be followed are: Protective measures should always be in place to keep the dose levels as low as reasonably practicable (ALARP). In summary, a fundamental requirement is that the use of ionizing radiation should be optimized so that the patient receiving the treatment, and the hospital staff and the general public are not irradiated unnecessarily. In this chapter, radiation protection issues will be discussed for sealed source brachytherapy only. It will address the regulations associated with brachytherapy and how they are implemented into safe practice in the clinical environment.
Endolumenal Brachytherapy: Bronchus And Oesophagus
Authors: Hoskin Peter
Published: November 2023

With the advent of high dose-rate (HDR) afterloading systems using fine catheters of 2 mm diameter, it is now possible to pass high dose-rate afterload ing sources readily into the bronchus or oesophagus. The techniques are well defined but their place in the management of these tumours where external beam has a well established role remains uncertain. As with all types of brachytherapy, HDR afterloading offers the opportunity to deliver a high localized dose of radiation to a defined area within the bronchus or oesophagus. Catheters can be placed intraluminally in the bronchus or oesophagus with relative ease requiring moderate sedation at bronchoscopy or the passage of a nasogastric tube. Most treatments are delivered as single doses and therefore a day case or one night stay in hospital is sufficient.
Breast Brachytherapy
Authors: Hoskin Peter
Published: November 2023

Breast irradiation forms a major part of the activity in any radiotherapy centre. The vast majority of patients receive external beam treatment and only a selected minority are considered for brachytherapy. This, in part, reflects the availability of expertise and resources to deliver brachytherapy and, in part, the efficiency and efficacy of breast boost treatments with electron beams. There are however specific indications where brachytherapy should be considered, in particular, where a high dose of radiation is required to an underlying breast tumour, which might exceed skin tolerance.
Management of familial adenomatous polyposis and other inherited polyposis syndromes
Authors: Sheridan E , Houlston R S
Published: November 2023

Colorectal polyps can be grouped according to their histology. The most important subgroups are adenomatous polyps and hamartomatous polyps. Adenomatous polyps account for around 30 to 50 per cent of all polyps and are premalignant lesions. They are detectable in around 15 to 20 per cent of the population by age 50, the risk increasing with age (Fig. 9.1). Autopsy series suggest that the incidence is even higher, with 60 per cent of men having a polyp by age 50 compared with only 40 per cent of women.
How to speak and read logic
Authors: Bornat Richard
Published: November 2023

Education is about ideas rather than facts. The ideas of logic, and especially the ideas of formal logic, will be new and strange to most of my readers. New ideas need new words, new technical language. Outsiders sometimes call technical language ‘jargon’ and imagine that experts are hiding something by not sticking to everyday English.
Connectives
Authors: Bornat Richard
Published: November 2023

For each connective in turn I describe what a formula using the connective means, and then present inference rules which make those meanings work in formal proofs. The descriptions of meaning are informal, and based on the definition of circumstances in which a fair-minded person would feel forced to accept the claim made by a formula. Part III makes these descriptions more mathematically precise.