bluuebunny/crossref_metadata_2025_split huggingface dataset:
Case studies
Authors: Tong Howell 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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 &gt; 1 are considered in Sections 7.2 and 7.3.
The analysis of experiments
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
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

Abstract
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.
Transformation of the basic approximation
Authors: Jensen Jens Ledet 
Published: November 2023

Abstract
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.
Compound sums
Authors: Jensen Jens Ledet 
Published: November 2023

Abstract
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

Abstract
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.
Maximal orders over discrete valuation rings
Authors: Reiner I 
Published: November 2023

Abstract
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

Abstract
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.
Program units and procedures
Authors: Metcalf Michael , Reid John , Cohen Malcolm 
Published: November 2023

Abstract
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

Abstract
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.
Object-oriented programming
Authors: Metcalf Michael , Reid John , Cohen Malcolm 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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).
Background
Authors: Kaye Richard 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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.
The calculus of variations
Authors: Pinch Enid R 
Published: November 2023

Abstract
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

Abstract
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.
Special Riemannian Manifolds
Authors: Willmore T J 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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.