bluuebunny/crossref_metadata_2025 huggingface dataset:
Discrete data
Authors: Krzanowski W J
Published: November 2023

Most of the problems that have been discussed thus far have assumed the data presented for analysis are quantitative. In many multivariate data sets, however, some or all of the measured variables may be qualitative. For such variables, an assumption of multivariate normality is manifestly inappropriate, and methods of analysis that are radically different from those considered earlier must therefore be sought. Discrete quantitative variables having only a few possible values also come under the same umbrella, and currently popular usage is to term the collection of all such variables as discrete multivariate data. We first consider the case where all variables in a data set are discrete, and later turn to the treatment of a mixture of discrete and continuous data.
Doing the sums
Authors: Budd C J , Sangwin C J
Published: November 2023

In Chapter 7 we looked at ways of writing whole numbers. The Hindu system of number bases, which we still use, turned out to be ideal and negative number bases are an interesting modem development. In this chapter we will introduce the logarithm. The discovery of the logarithm, by John Napier, was perhaps the most important advance in practical calculation methods after the introduction of the Hindu, decimal number system. The logarithm, like many things in mathematics, turns out to have a much deeper significance and greater use than simply helping us calculate. In the second half of this chapter we go on to describe a practical implementation of logarithms: the slide rule. The slide rule is also an example of what is known as an analogue computer. Most modem computers are digital and they store and manipulate information as strings of ones and zeros. We saw binary arithmetic in Chapter 7. Some computers, in particular early computers, were not digital and used other technologies, such as flowing liquids or mechanical links. The importance of these things are now becoming forgotten, particularly with the rise of the electronic calculator. We ask you to do as many of the exercises as you can with only paper and pencil. Of course, your calculator is useful to help you to check your answers.
Epidemiolog
Authors: Lindsey J K
Published: November 2023

As its name suggests, the field of epidemiology arose from the study of epidemics. However, this discipline now has a much wider coverage, looking at public health in all its aspects, not just those involving infectious diseases. It uses a number of special techniques and some rather specific terminology.

Epidemiological research aims to study phenomena related to health in natural populations. It attempts to detect nonstandard events and to determine the reasons, called risk factors, behind them.
The principles of the uptake and chemical speciation of the elements in biology
Authors: Fraústo da Silva J J R , Williams R J P
Published: November 2023

The essential features of the study of the chemistry of a compound or system containing any number of elements involve (1) isolation of the compound, (2) analysis of its composition, (3) description of its structure, and (4) examination of properties, including stability, spectral features, and kinetic activities.
Formation of the savannah
Authors: Ulfstrand Staffan
Published: November 2023

Africa has not always existed, at least not as a separate continent in the shape we recognize today. During the Mesozoic era the Earth’s land masses were joined in two enormous blocks: a northern landmass called Laurasia, and a southern land-mass called Gondwanaland which included Antarctica, Australia, Africa, the Indian subcontinent, and South America.
Lion prides—nursery schools and death patrols
Authors: Ulfstrand Staffan
Published: November 2023

It is early afternoon in the Masai Mara. The view is fantastic. Because of the severe drought on the short grass plains, a large portion of the Serengeti’s herbivore herds are gathered here. The grass is lush in the Masai Mara and rivers and waterholes provide abundant water. There are grazing herds of wildebeest in all directions and the zebra’s bark can be heard all around. As usual, the zebras look plump, healthy, spirited, and trim.
Bonobos: ‘make love, not war’
Authors: Ulfstrand Staffan
Published: November 2023

In the 1930s it was realized that Africa was home to two species of chimpanzee. Pan troglodytesis distributed from Guinea in the west to Uganda and Tanzania in the east and was discussed in Chapter 11. In a considerably more limited area south of the Congo River lives another species—the bonobo, Pan paniscus, previously called pygmy chimpanzee. Since this species is not much smaller than the ‘regular’ chimpanzee its name was changed to bonobo. Bonobos are more slender and have slightly longer arms than chimpanzees and, in addition, have distinctive cranial characteristics. Young chimpanzees have pink faces at birth whereas young bonobos have black faces. One clear feature that differentiates these two species is the pitch of their voices: bonobo calls are much higher in pitch, and sound ‘childish’ compared to chimpanzee voices. The most recent common ancestor of chimpanzees and bonobos lived 2–2.5 million years ago, which is half the time that the human lineage has been separated from the combined chimpanzee–bonobo lineage.
Small steps, long journey
Authors: Ulfstrand Staffan
Published: November 2023

Modern evolutionary biology has shown that humans are characterized by a history much older than our own species—the result of millions of years of accumulated adaptations to a precarious, savage, and dangerous world. Unlike the universe, we didn’t come into being via a dramatic Big Bang, but rather—to quote the British evolutionary anthropologist Robert Foley—via a long series of hiccups. Our physical and psychological qualities show repeated cycles of variation and rejection. The remarkable adaptations in all living creatures, including the human brain, have arisen and evolved through differences in individual reproductive success. Biology originated from the bowels of physics and chemistry via this simple mechanism. From each generation, some survive and go on to influence future generations, while most disappear without a trace. Each being alive today can proudly state: all my ancestral mothers and fathers lived long enough to pass on their genes to the next generation.
Compatibility of characters
Authors: Semple Charles , Steel Mike
Published: November 2023

In biology, ‘characters’ describe attributes of the species under consideration and are the data that biologists typically use to reconstruct phylogenetic trees. Mathematically, characters are functions. A natural biological constraint is that the reconstructed phylogenetic trees have the property that each of the characters could have ‘evolved’ without ‘reverse’ or ‘convergent transitions’. In this chapter, we formalize this notion and explore the underlying mathematical properties of characters that allow us to construct such phylogenetic trees.
Keeping in Time With Your Body Clock
Authors: Waterhouse J M , Minors D S , Waterhouse M E , Reilly T , Atkinson G
Published: November 2023

Why am I always tired? Why can't I sleep at night? Why do I suffer from jetlag? We all have a body clock, a biological structure that controls how we feel, our mental and physical performance, and whether we are active or asleep. This is nature's response to our rhythmic environment, dominated by day and night. Though the body clock normally adjusts us to daytime activity and night time sleep, it can go wrong or be tricked by lifestyle changes. This can result in jetlag, some forms of insomnia and even depression. Keeping in time with your body clock provides clear and accessible advice on how to live with, and not against, your body clock. In a clear and accessible style, it explains how the body clock works, how and why it can work against you, and the measures you can take to optimise your feeling of health and wellbeing. It also explains the role of the body clock in illness, and how an understanding of this can increase your feeling of health. An essential book for anyone who wants to better understand their body and optimise their feeling of health and wellbeing.
Operator Theory Basics
Authors: Evans David E , Kawahigashi Yasuyuki
Published: November 2023

This chapter introduces the most basic functional analysis of operators on Hilbert spaces. To avoid unnecessary complication, we try to minimize complexity in only proving what is absolutely essential to the general aims. Thus we restrict attention to separable Hilbert spaces and their operators—and not prove the more traditional aspects of an introductory functional analysis course such as a more general Banach space theory including the Hahn-Banach theorem, open mapping theorem, principle of uniform boundedness etc. In order to make much of the earlier chapters accessible to an undergraduate audience, we also avoid as much as possible measure theoretic considerations. Indeed the contents of the first three chapters are based on final year undergraduate courses.
Axiomatization of Paragroups
Authors: Evans David E , Kawahigashi Yasuyuki
Published: November 2023

In Section 10.2, we express the higher relative commutants of subfactors in terms of bimodules with the techniques of Chapter 9. Section 10.3 deals with the rather easy axiom of unitarity of connections. We will study the renormalization axiom in Section 10.4. This expresses a certain type of symmetry of the system, and will play an important role in the following chapters. Section 10.5 studies the flatness axiom. In actual computations and applications, this is the most important axiom. The abstract definition of a paragroup is completed in this section. The most fundamental examples of paragroups are presented in Section 10.6. These really are finite groups, and we will show how to regard them as paragroups.
String Algebras And Flat Connections
Authors: Evans David E , Kawahigashi Yasuyuki
Published: November 2023

We introduced a notion of commuting squares in Section 9.6, and will now characterize finite dimensional commuting squares in Section 11.2. In Section 11.3, we give a construction of subfactors from certain commuting squares. This is in the converse direction of the construction of a paragroup from a subfactor in Chapter 10, but the construction of a subfactor in this section starts with properties weaker than the full set of axioms of paragroups. (The paragroup of the subfactor may not then be the data that we started with.)
The science of musical sound
Authors: Taylor Charles
Published: November 2023

Sound of any kind involves changes of pressure in the air around us; for example, in ordinary speech the pressure just outside the mouth increases and decreases by not more than a few parts in a million. But to be detected by our ears and brains as sound, these changes have to be made fairly rapidly. This can be demonstrated easily by inflating a balloon and then gently squeezing it between thumb and finger. This creates quite large pressure changes without any attendant sound; but inserting a pin creates a change that can very readily be heard.
Faggot’s fretful fiasco
Authors: Stewart Ian
Published: November 2023

If you look at a guitar, mandolin, or lute—any stringed instrument with frets—you’ll see that the frets get closer and closer together as the note gets higher. This is a nuisance for the player, because there’s less room to fit the fingers in and because the distances you move your finger to get higher notes is not proportional to that for lower ones. But there’s a good reason why the frets have to be spaced the way they are: the notes won’t sound right otherwise. This is a consequence of the physics of vibrating strings.
Microtones and projective planes
Authors: Gamer Carlton , Wilson Robin
Published: November 2023

For hundreds of years mathematicians and musicians have been intrigued by the musical systems obtained when an octave is divided up, not into the usual twelve tones with which we are all familiar, but into a smaller or larger number of tones. Certain of these systems, such as the 19-tone, 31-tone and 53-tone equal-tempered systems, have been much investigated, since they give rise to tunings that more closely approximate particular intervals in the harmonic series (‘just’ tunings) than does the 12-tone equally tempered system; a table comparing these tunings is given below.
Law, lies, and videotape: malingering as a legal phenomenon
Authors: Jones Michael A
Published: November 2023

In the context of the civil law, although malingering may not be uncommon, it is rarely necessary for a court to reach a positive finding that an individual is malingering, given the manner in which the forensic process deals with the evidence when making findings of ‘fact’. A conclusion that a claimant is malingering effectively involves an allegation of fraud, which could have potentially serious consequences for the claimant beyond failing in the immediate claim. It is not simply a question of resolving a dispute between medical experts as to whether the claimant’s symptoms are genuine or feigned. In many instances, it may be almost impossible for a court or tribunal to conclude that the claimant is malingering without wholly convincing evidence, such as video observation of the claimant over a period of time.
Ethnicity, Health, and Primary Care
Authors: Kai Joe
Published: November 2023

There is increasing ethnic diversity in our society posing challenges for health professionals and health care. Existing texts on ethnicity and health are often esoteric and academic in focus, accessible to researchers and policy analysts rather than health practitioners. Other texts consider a single health topic or cultural group. Ethnicity, Health and Primary Care is a new book, intended as a broad but concise and practical introduction to ethnicity and health care for a wide range of health professionals – general practitioners, GP registrars, practice and community nurses, bilingual workers, medical students and other health practitioners in training. Although focusing on primary care, the book's general principles and its clinical coverage will be highly relevant to other health and social care practitioners, in addition to those developing and commissioning health services. Chapters have been written to enable busy practitioners and students to grasp the essentials quickly and easily. The book aims to stimulate readers to learn about and develop an effective approach to ethnic diversity in health care. Rather than be an encyclopaedia of different ethnic groups and cultural practices, this book emphasises the need for practitioners to respond to people as individuals within a broader understanding of the diverse needs of communities. It thus promotes generic principles for good practice wherever diversity has an impact. Having underlined these principles the book considers major clinical topics and groups arguably of particular concern for the health of diverse ethnic communities.
Transaction cost economics and principal–agent theory: insights into investigations of outbreaks of infectious diseases
Authors: Jamasji-Pavri Azarmeen
Published: November 2023

Outbreaks of infectious disease occur when the incidence rises above the normal endemic level (Barker and Rose 1990) or when there are two or more linked cases of the same disease. The purpose of investigating these outbreaks is to identify the cause of the outbreak so that control measures can be implemented. Systematic, routine procedures exist for the investigation process. The plethora of instructional literature regarding these procedures (Goodman et al. 1990; Palmer 1990; Palmer 1995; Mackenzie and Goodman 1996; Reingold 1998) indicates their acceptance by the public health community. Despite the existence of technical literature on the subject, the situation-specific nature of outbreaks makes it impossible for a ‘gold standard’ to exist.
The Heavens in Motion
Authors: Acheson David
Published: November 2023

The appearance of unfamiliar objects in the sky has caused excitement – not to say panic – since earliest times. Even in 1910, when Halley’s comet was due, some of the American newspaper coverage struck a distinctly.
A Brief History of л
Authors: Acheson David
Published: November 2023

When we first meet the number 1r = 3.14159 . . . it is all about circles. In particular, if we have a circle of radius r, then circumference = 2лr, and area = лr  2. The first of these formulae is more or less what we mean by the number 1r. For if we regard it as ‘obvious’ that the circumference of a circle is proportional to its diameter, then the ratio.
The Spirit of Copenhagen
Authors: Pais Abraham
Published: November 2023

In his letter with New Year’s wishes for 1926, Bohr wrote to Rutherford: ‘We have had a very busy time all the autumn with the enlargement of the institute, but now I hope that we shall have more quiet working conditions for some time.’ The renovation took longer than he had expected, however. In May he wrote: ‘The work on the reconstruction is now almost completed.’ That project may again have taxed his strength. In any event, during June and July Bohr was out with a serious influenza followed by some weeks of complete rest.
Some non-linear time series models
Authors: Tong Howell
Published: November 2023

In recent years, quite a few non-linear time series models have been proposed. We list some of these in this chapter and, whenever appropriate, include a brief description of the background. Detailed analyses of a selection of these models will be given in later chapters. In many cases, results are still incomplete and much research is going on at present. Possibly the single most important class of non-linear time series models which are directly motivated by dynamical systems is the class of non-linear autoregression.
Statistical aspects
Authors: Tong Howell
Published: November 2023

We have been looking at the ensemble properties, that is properties pertaining to the collection of all realizations/sample paths. Under ergodicity /stationarity, these properties will tell us about the long-run behaviour of each realization. Now, we are going to study the ‘inverse problem’ of inferring something about the ensemble properties from one, or more precisely part of one, single realization. This falls within the domain of statistical inference. Before performing any formal statistical procedure, it is always good practice to examine the data graphically. A number of graphical methods have been in routine use in time series modelling. For example, time series data plots, sample autocorrelation function plots, sample partial autocorrelation function plots, sample spectral density functions, histograms, plots of differenced data, plots of instantaneously transformed data, etc., have been used as standard practice.
Case studies
Authors: Tong Howell
Published: November 2023

Although systematic studies of non-linear time series modelling are fairly recent activities, non-linearity has been recognized for quite a considerable time. In the past, a popular approach was first to pass the data through a simple non-linear filter (e.g. a limiter; cf. the hard censoring device of §3.3.2) and then the filtered data could be modelled by a linear model. This is somewhat similar in spirit to the pre-whitening approach advocated by Tukey in the 1950s in spectral analysis (see e.g. Priestley 1981, p. 556). An early example of successful application of this prefiltering approach to non-linear time series modelling was in control engineering (see e.g. Otomo et al. 1972).
General commentary
Authors: Pearson E S , Plackett R L , Barnard G A
Published: November 2023

Gosset went to Dublin in the autumn of 1899 to take up the post of a Brewer with Arthur Guinness, Son & Co. Ltd. He was twenty-three years old, and his ability had been shown by the scholarships which took him to Winchester College and Oxford University, where he had been trained in mathematics and science. Guinness was a long-established and important business, the management of which had decided on the greater use of scientific methods in the brewing of stout. This policy was implemented by a series of appoint ments of men from Oxford or Cambridge with science degrees, so that Gosset joined a group of colleagues with the same social background, among whom he found those of a similar age who shared his interest in the outdoor activities offered by the Irish coast and countryside. Within a few years, he was married, and his home near Dublin soon became the centre of his family life and a widening circle of friends.

During his early years with Guinness, Gosset was presented with problems in the analysis of experimental data from brewery work. He had no knowledge of statistical methods, and turned for assistance to standard textbooks on the combination of observations.
Lower bounds
Authors: Barbour A D , Holst Lars , Janson Svante
Published: November 2023

We now tum to the problem of finding lower bounds for Poisson approximation. Although the Stein–Chen method is widely applicable, it would be much less interesting if it did not give accurate estimates, at least in the sense that the upper bounds it gave were of the right order of magnitude. Of course, bad choices of the couplings (Ui, Vi) can always lead to poor estimates, and it may not necessarily be obvious how to recognize the best possible choices, so that some sort of qualification is needed.
Spacings
Authors: Barbour A D , Holst Lars , Janson Svante
Published: November 2023

Different aspects of spacings have been considered previously; see Holst and Hiisler (1984) and the references therein. In Barbour and Holst (1989), Poisson approximation with a rate of convergence was obtained for the number of big spacings; some weaker bounds are given in Holst, Kennedy and Quine (1988). Below, we obtain such results for big and small m-spacings. First, suitable couplings are constructed in Section 7.1, and then the cases with m 1, that is ordinary spacings, and m > 1 are considered in Sections 7.2 and 7.3.
The analysis of experiments
Authors: Atkinson A C , Doney A N
Published: November 2023

This book is primarily concerned with the design of experiments rather than with their analysis. However, in this chapter we give analyses of three sets of data to illustrate some points in least squares and the related design criteria. The second example is an analysis of Derringer’s elastomer data from Chapter 1 (Example 1.2) in order to illustrate the importance of trans formations of the response in providing simple models. The third example is an analysis of a 25-1 experiment, a class of designs for which there is no obvious estimate of error. Half-normal plots of effects combined with the analysis of variance provide a parsimonious model, i.e. one with few parameters. But we begin with the analysis of a straightforward example with only one explanatory variable, the data on carbon monoxide production given in Table 1.1.
Analysis of covariance with random effects
Authors: Longford Nicholas T
Published: November 2023

This chapter deals with models which combine ordinary regression and within-cluster correlation. The development closely parallels the combination of linear regression and ANOVA into the analysis of covariance (ANCOVA). Our focus is on settings with large numbers of clusters, or clusters being a random sample from a population, and so parsimonious description of (adjusted) between-cluster differences is a relevant issue. The principal difference between ANCOVA and our approach is in the role of the levels of the factor (clusters). In ANCOVA the effects associated with each cluster are unknown constants (they are fixed), in the random-effects approach, which we refer to as random-effects analysis of covariance, they are random.
Random regression coefficients
Authors: Longford Nicholas T
Published: November 2023

In Chapter 2 we studied the analysis of covariance with random effects as a method for the description of between-cluster differences.
Transformation of the basic approximation
Authors: Jensen Jens Ledet
Published: November 2023

In this section we will use the tools given in Sections 3.1 and 3.2. We will consider the marginal density and distribution function of Z = g(Y1, ..., Yd) E Rd1 when the density of Y = (Y1, ..., Yd) has a particular form. The situation we have in mind is where Y is the sufficient statistic based on n observations with n tending to infinity.
Tests in exponential families
Authors: Jensen Jens Ledet
Published: November 2023

In the literature on asymptotic expansions for distribution functions there are two classical ways of presenting the results. Either one writes down the expansion for the statistic originally of interest directly, or one adjusts the statistic in such a way that the expansion for the adjusted statistic takes a particularly simple form.
Compound sums
Authors: Jensen Jens Ledet
Published: November 2023

Sums of the form ΣN  i=1  X  i , where N is a random variable independent of the X  is, appear in many contexts. The application that has motivated the results given in this chapter is the description of the total claim amount presented to an insurance company over a fixed time period. There, N is the number of claims and the X  is are the individual claims, which are assumed to be independent. Thus an alternative title for this chapter could be Applications of saddlepoint approximations in risk theory. Historically, this application actually seems to be the origin of saddlepoint approximations to distribution functions. For the case where N is Poisson distributed, Esscher (1932) used a tilting formula equivalent to (1.4.4) and wrote an approximation corresponding to (2.2.6), including the B  0 and B  3 functions. For an insurance company making economic plans it is important to know the probabilities of very large total claim amounts. Being especially interested in the tail of the distribution it is natural to look for approximations with a small relative error. In this section we start by establishing the basic inversion formulas and approximation formulas, and in the following section we derive results for the case where N is a Poisson variable.
Alternative approximations
Authors: Jensen Jens Ledet
Published: November 2023

The way the saddlepoint approximation was introduced in Chapter 2 was via the simple idea of replacing [ineq] in (1.4.6) and (1.4.3) by a normal density or by an Edgeworth expansion. This is quite a reasonable approach when thinking of the limit n ⟺ ∞. However, in applications we of course have a finite n and one can ask if there are better approximations than the normal approximation for [ineq]. For a one-dimensional variable the kinds of things one can look out for are the range of the variable and possible limiting forms of the density as θ -, T2, where T2 is the upper end point of the definition range of the Laplace transform. If the limiting form is a normal density, Proposition 6.1.8 indicates that the relative error of the saddlepoint approximation wiJI go to zero forθ -, T2, for a fixed n. On the other hand, Corollary 6.3.2 shows that for the gamma-like and beta-like densities the limiting form will be a centered gamma density. It therefore seems natural to try out a gamma approximation to the density [ineq] in these situations.
Structured transition matrices
Authors: Lindsey J k.
Published: November 2023

In the previous chapter, we encountered certain models of Markov chains which can be applied to mobility data. There, the models involved square tables, although usually in more than two dimensions. In this chapter, we shall study a number of special models applicable to square tables in particular, such as transition matrices, and we shall concentrate on certain patterns which may occur in such tables.
Maximal orders over discrete valuation rings
Authors: Reiner I
Published: November 2023

Throughout this chapter, R denotes a discrete valuation ring with quotient field K, maximal ideal P = πR≠0, and residue class field R = R/P. We have already seen in (10.5) that the study of maximal R-ordcrs in separable K-algcbras can be reduced to the case of central simple algebras. We shall investigate this case in detail here, by using the results from Chapter III on maximal orders in skewficlds, and then applying the Morita equivalence between skewfields and full matrix algebras over skcwficlds.
Maximal Orders over Dedekind Domains
Authors: Reiner I
Published: November 2023

In this second method, we give some straightforward generalizations of some of the familiar proofs in algebraic number theory. Indeed, this same dichotomy already occurs in algebraic number theory. One can develop the ideal theory of Dedekind domains either from the standpoint of valuation theory (first approach), or by manipulations with the ideals themselves (second approach). Just as in algebraic number theory, however, we cannot in the long run avoid the use of P-adic completions. Many of the deeper results depend on the interrelations between the global and local theories.
Whence Fortran?
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

This book is concerned with the Fortran 95 and Fortran 2003 programming languages, setting out a reasonably concise description of the whole of each. The form chosen for its presentation is that of a textbook intended for use in teaching or learning the language.
Program units and procedures
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

As we saw in the previous chapter, it is possible to write a complete Fortran program as a single unit, but it is preferable to break the program down into manageable units. Each such program unit corresponds to a program task that can be readily understood and, ideally, can be written, compiled, and tested in isolation. We will discuss the three kinds of program unit, the main program, external subprogram, and module.
Allocatable array extensions
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

The subject of this chapter is another standardized extension1 of Fortran 95. It involves the use of allocatable arrays as dummy arguments, function results, and components of structures. Pointer arrays may be used instead, but there are significant advantages for memory management and execution speed in using allocatable arrays when the added functionality of pointers is not needed. We describe the extensions to Fortran 95 that were detailed in the Technical Report and which are all now part of Fortran 2003. We also describe the few related Fortran 2003 features that were not in the Technical Report, with a clear indication of this in each case.
Type parameters and procedure pointers
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

This chapter combines the separate topics of type parameter extensions and procedure pointers. The type parameter extensions consist of the addition of deferred type parameters, type parameter enquiry, and the ability to parameterize derived types.
Object-oriented programming
Authors: Metcalf Michael , Reid John , Cohen Malcolm
Published: November 2023

The object-oriented approach to programming and design is characterized by its focus on the data structures of a program rather than the procedures. Often, invoking a procedure with a data object as its principal argument is thought of as ‘sending a message’ to the object. Typically, special language support is available for collecting these procedures (sometimes known as ‘methods’) together with the definition of the type of the object.
Credit scoring using neural and evolutionary techniques
Authors: Yobas Mumine B , Crook, Jonathan N , Ross Peter
Published: November 2023

The aim of this chapter is to compare the predictive ability of linear discriminant analysis (LDA), neural networks (NNs), genetic algorithms (GAs), and decision trees (DTs) in the classification of credit card applicants. All four techniques have been awlied to the same dataset and the results of the three evolutionary techniques are compared with the LDA results published in Crook et al. (1992).

Whilst many credit-scoring agencies have experimented with the latter three techniques, few offer products which use them (Desai et al. 1997) and the same applies to credit-granting organizations. Because of the commercial value of particular models there are very few publicly available comparisons between these techniques in the credit-scoring context. The published literature suggests mixed results: some find that traditional techniques correctly classify a greater proportion of applications than AI techniques, others the reverse
Segmentation in Markov chain consumer credit behavioural models
Authors: Ho Joseph , Thomas Lyn C , Pomroy, T A , Scherer William T
Published: November 2023

Financial institutions have for many years been interested in modeling the behavior of their customers. One approach has been to develop default based scoring systems (Thomas 2000) which seek to map the behavior of a customer in the near past to their default states in a year ‘s time. These are based on classification techniques like logistic regression, classification trees, or linear programming. The customers score is then used to make operational and credit decisions such as increasing the overdraft permitted. An alternative approach is to model the customers behavior in terms of the ‘state ‘ of their account using Markov chain models. The states usually describe the different stage of delinquency of the customers accounts, for example. 1 month overdue. Markov chain models have been used mainly in debt provisioning to forecast the expected losses through default in different time periods in the future. However. with the growing importance of customer relationship management (Schniede1.:jans and Loch 1994) and a move in the financial organizations objectives from minimizing defaults to maximizing profit there is increasing interest in these Markov chain models as a way of modeling the dynamical behavior of the consumer.
Reaction-Diffusion Systems
Authors: Scott Alwyn
Published: November 2023

At about the time that John Scott Russell was systematically studying hydrodynamic solitons on a Scottish canal, Michael Faraday, the self-taught English experimental physicist and physical chemist, began to present his annual “Christmas Lectures” on selected aspects of natural philosophy to young people at London’s Royal Institution. Among the most popular of these were a series of six talks entitled “The Chemical History of a Candle,” and beginning with a bold claim [20]:There is no better, there is no more open door by which you can enter into the study of natural philosophy than by considering the physical phenomena of a candle.
Inverse Scattering Methods
Authors: Scott Alwyn
Published: November 2023

In Chapter 3, we studied the soliton-that remarkable dynamic entity discovered experimentally by John Scott Russell in the nineteenth century and rediscovered in the course of numerical studies by Zabusky and Kruskal in the mid-1960s-and learned about Backlund transforms and N-soliton formulas, which will be used to expand the range of soliton perturbation theory in the next chapter. Throughout these discussions there floats an air of mystery. How is it that solutions of nonlinear partial differential equations are able to display such unexpected properties? An answer to this question is that each soliton equation is related to a linear scattering operator in the following manner.
Quantum Lattice Solitons
Authors: Scott Alwyn
Published: November 2023

In general, the soliton is a classical phenomenon. The calculation of quantum corrections to John Scott Russell’s “Wave of Translation” is unnecessary; and for a tsunami or Jupiter’s Great Red Spot, such an effort would be absurd. Yet there are solitons that emerge at the level of molecules and molecular crystals, and for these the constraints of quantum theory are important. The aim of this chapter is to introduce the theory of quantum lattice solitons in a manner that is helpful for understanding such experimental studies.
Proofs with quantifiers
Authors: Bornat Richard
Published: November 2023

A man is on trial for murder. He’s a minor gangster and between you, me and the judge, we think he did it. But English justice, like constructive logic, doesn’t search for truth. Court cases are decided by argument; the law is about proof and disproof. (An oversimplification: for the rest of this chapter let’s pretend).
Disproof in a mathematical model
Authors: Bornat Richard
Published: November 2023

Fig. 8.1 shows a Jape proof attempt which is in trouble. A raw novice, afraid to use a backwards step from line 4, has made an — elim.
A simple programming language
Authors: Bornat Richard
Published: November 2023

Real-world programming languages are complicated, partly because they are designed to support much more than the basic description of machine activity. Modern languages ease the task of maintaining programs, using libraries, explaining programs to managers, and lots more. They have features — variable typing, for example — which are designed to help you avoid simple programming mistakes.
Arrays
Authors: Bornat Richard
Published: November 2023

The proof of the primacy checker in Chapter 14 is fun in a daft sort of way, but it’s a bit too much about arithmetic. The arithmetic algorithms are more fun and even a bit useful, but they are completely about arithmetic.
Background
Authors: Kaye Richard
Published: November 2023

Although the reader is not expected to know anything about nonstandard models of arithmetic, we will assume a little knowledge of model theory and arithmetic ( or rather, recursion theory.) The purpose of this chapter is to review this background material. But first, a few general remarks. In the text, ‘s. t.’ is an abbreviation for ‘such that’, ‘iff’ is an abbreviation for ‘if and only if’, and □ denotes the end (or absence) of a proof. The exercises are part of the text, so should be read, and preferably attempted! An * against an exercise indicates that the result will be used later in the text, a + indicates that the exercise is slightly harder than usual.
The axioms of Peano Arithmetic
Authors: Kaye Richard
Published: November 2023

The quotations at the head of this chapter is how Peano stated his famous five axioms of arithmetic. (His notation looks surprisingly modern. In particular his use of ⊃) for implication and set-inclusion has become the modern-day ⊃i and ⊃, , although the ‘subset’ relation symbol ⊃) is now written the other way round, as ⊆ !) Essentially, Peano’s axioms are those of PA− together with the second-order induction axiom where X ranges over all subsets of the domain of the stucture under consideration, and x, y range over elements of this domain.
Models of PA
Authors: Kaye Richard
Published: November 2023

Although it is very instructive (and useful!) to see how number theory can be formalized within PA, the study of PA starts to become interesting when we consider the formal system from without. In this chapter we take our first look at nonstandard models of PA, and our investigation is focused on the order-type of these models, and in particular their initial segments. Our first observation is that proper initial segments always exist.
Satisfaction
Authors: Kaye Richard
Published: November 2023

This is the chapter that no one wanted to have to write: the material here is technical and difficult to describe clearly, yet it is very necessary for later work. I have put it off as long as possible, but cannot do so any longer.
The calculus of variations
Authors: Pinch Enid R
Published: November 2023

As we saw in Chapter 1, the calculus of variations is concerned with the optimization of functional. There we used (x, y) for the coordinates of a point in the plane and y = y(x) to represent the equation of a plane curve. In order to set up a uniform notation for the remainder of the book we shall re-name our variables, letting t be the independent variable and x the dependent; so (t, x) represents a general point and x = x(t) the equation of a curve. The simplest problem that we can pose is that of finding, out of all the curves that join two fixed points, the equation of the curve that minimizes a given functional.
Optimal control I: Theory
Authors: Pinch Enid R
Published: November 2023

We are now familiar with the ideas and methods of the calculus of variations. In particular we have studied the minimization of integrals in the presence of constraints (isoperimetric problems) and we are well aware of how crucial the choice of the class of admissible functions is to the development of the theory. In this chapter and those that follow we will examine the theory of optimal control and our experience in the calculus of variations will be invaluable. As we shall see, modern optimal control can be looked at as a development of the classical theory of Euler and Lagrange development in which we are forced to deal with admissible functions that are less well-behaved than those we have met so far. The problem remains one of minimizing an integral subject to constraints (although the constraints are now differential) and the fundamental theorem is a generalization of the Euler-Lagrange equation. The fundamental theorem that we will meet later in this chapter is technically a more difficult result to prove than that of Euler and Lagrange. The proof, although rather lengthy, does not involve any results other than those covered in undergraduate courses in analysis. An outline of the proof is given in this chapter and the full proof in Chapter 6. There are a number of theorems that underpin the proof and these are stated and proved in Chapter 6.
Proof of the maximum principle of Pontryagin
Authors: Pinch Enid R
Published: November 2023

We now turn to the proof of Theorem 4.1, the Pontryagin maximum principle. The reader may find it helpful to read the outline proof in Chapter 4 before starting this chapter.
Complex and almost-complex manifolds
Authors: Willmore T J
Published: November 2023

A complex structure on a real vector space V is a linear endomorphism J of V such that J2 = - 1, where I stands for the identity transformation of V. A real vector space with a complex structure can be given the structure of a complex vector space.
Special Riemannian Manifolds
Authors: Willmore T J
Published: November 2023

The subject of special Riemannian manifolds is so rich that it is impossible to include many interesting and important examples in this chapter. For example, we have the book by Wolf (1967) of 408 pages devoted to manifolds of constant curvature. We have the book by Besse (1987) of 510 pages devoted to the study of Einstein spaces. Another book by Besse (1978) of 262 pages is devoted to the special topic of manifolds with closed geodesics.
Stochastic shortest-path problems
Authors: Shier Douglas R
Published: November 2023

The final section of Chapter 8 introduced multistate systems: those in which the components assume a finite number of distinct modes. One particular instance of this type of system frequently arises in the modelling of various transportation, communication, and project planning networks. For example, it may be required to transport material from a warehouse to a distribution centre. If the travel times along the associated highway network are known, then it would be desirable to ship the material along a timewise shortest path between the warehouse and the distribution centre. In reality, the travel times will be subject to uncertainty, depending, for instance, on the volume of traffic, the timing of traffic lights, and construction delays. Consequently, each road segment in the highway network can be viewed as having a range of travel times, specified by a probability distribution. Another example concerns the scheduling of complex projects, which can be modelled using a network of tasks (corresponding to edges) and their precedences (Elmaghraby 1977). If the duration of each task is known exactly, then the completion time in such a project planning network corresponds to a longest (or ‘critical’) path from the project start node to the project completion node. Most realistically, however, the actual duration of each task is subject to uncertainty and so it is best represented by a probability distribution.
Aspects Of Parallel Computing
Authors: Burrage Kevin
Published: November 2023

The main thrust of this monograph is to produce an up-to-date exposition of the current state of the art of numerical methods for solving IVPs in a parallel environment. As will be seen, any algorithmic implementation is architecture dependent and so before any attempts can be made in the development of such methods, the nature of the underlying computing environment should be considered. There is (at the time of writing in August 1994) an enormous variety of parallel computing architectures with completely different programming paradigms, and so the aim of this chapter is to acquaint the reader with the types of parallel machines that are now available and to present a general discussion on various aspects of parallel computing. Although two companies (Thinking Machines and Kendall Square) have only recently (late 1994) stopped trading, their products will still be discussed as their machines represent a significant step in the evolution of supercomputing.
Diverse Approaches To Parallelism
Authors: Burrage Kevin
Published: November 2023

In this chapter a number of different approaches to developing parallel algorithms for differential systems will be discussed. Some of these approaches will offer a modest performance while some offer the possibility of massive parallelism. In the case of linear systems of either initial value or boundary value type there is a possibility of massive parallelism by exploiting the structure of the ensuing linear systems through such techniques as cyclic reduction and block linear algebra and various approaches are discussed in sections 6.1, 6.2 and 6.3. A second approach to parallelism involves exploiting parallelism to improve the robustness and efficiency of existing algorithms and this approach is described in sections 6.4 and 6.5, with particular reference to extrapolation and deferred correction techniques. Finally the concept of parallelism across the steps will be introduced and a number of different approaches will be analysed from parallel shooting to predictor-corrector techniques.
Introduction
Authors: Chapman Jonathan , Rowbottom Frederick
Published: November 2023

The logical approach to topos theory, working with a language for a topos, has been hampered by difficulties in tackling proofs involving a geometric morphism (the most important notion of morphism between topoi). This is unfortunate, since a topos gives a radical notion of ‘set’ (or at least, of higher-order logic) and this approach deals with it as such.
The relative Giraud theorem
Authors: Chapman Jonathan , Rowbottom Frederick
Published: November 2023

Giraud first proved the theorem, relative to Set (Grothendieck and Verdier (1972, IV.1.2)). See also Makkai and Reyes (1977, 1.4), Johnstone (1977, 0.45), Barr (1985, 6.8). Mitchell found an elementary description of the existence of a set of generators (cf. Fourman (1977), Fourman and Scott (1979)). Then Diaconescu gave a categorical proof of the Giraud theorem relative to an arbitrary base topos (cf. Diaconescu (1975) or Johnstone (1977, 4.46)). Our proof internalizes the one given in Chapman (1982, Chapter 3) (the general form of which is similar to Johnstone (1977, 0.45)). It is not necessary for the reader to have seen any of the above proofs, in order to follow ours.
Diophantine equations
Authors: Ellis Graham
Published: November 2023

A basic property of integers is that they can be expressed uniquely as a product of prime numbers. In this chapter we investigate other rings having a similar type of unique factorization property. As a means of motivating our investigation, let us begin by considering two number theoretic puzzles involving so-called Diophantine equations.