bluuebunny/crossref_metadata_2025 huggingface dataset:
The elements of musical expression
Authors: Pratt George
Published: November 2023

The aim in this chapter is to break down the total experience of listening to music into separate elements. You will find the division rather artificial, of course: how can anyone listen to the melodic intervals at the beginning of Beethoven’s Fifth Symphony without being conscious of the vigorous rhythmic patterns too? But it is helpful to divide this total experience of listening into its constituent parts, first, to focus attention on them, and second to break down the whole process of analysing music by ear into manageable proportions.
Playing by ear
Authors: Pratt George
Published: November 2023

Chapter 9, ‘Imaging’, was concerned with internal processes, with generating an impression of sound in the mind. In this chapter the aim is to add to that internal process a further stage, of externalizing sound accurately through instruments. Externalizing is something we constantly do with the voice. Children learn nursery rhymes by first listening, and then singing what they have heard. To some extent we do the same when learning to play an instrument. Most teachers demonstrate what is required, both physically and musically, in any particular musical situation; conductors verbalize articulation and sing phrasings in order to communicate their intentions.
G-spaces
Authors: Félix Yves , Oprea John , Tanré Daniel
Published: November 2023

The history of group actions is intimately tied up with the development of both algebraic topology and Lie group theory. In this chapter, we show how minimal models can be used to study compact Lie group actions on manifolds. We focus on certain aspects of group actions that are especially amenable to model techniques. Throughout the chapter, G will generally denote a Lie group acting on a compact manifold M . Certain properties of M will be apparent. For instance, when the action is free (i.e. no point in M is left fixed by any g G ), we have a principal G -bundle M M/G with the particular consequence that χ (M) 0.
Publications Of Gene H. Golub
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Books

[B1] Recent Advances In Numerical Analysis, edited by Carl de Boor and Gene

H. Golub, Academic Press (1978).

[B2] Proceedings of Symposia In Applied Mathematics, Volume XXII, Numerical Analysis, edited by Gene H. Golub and Joseph Oliger, American Mathematical Society (1978).
Chebyshev Semi-Iterative Methods, Successive Over-Relaxation Iterative Methods, And Second-Order Richardson Iterative Methods, Parts I And Ii (With R. S. Varga)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

I was invited, in 1960 I believe, by Abe Taub at the University of Illinois, to a colloquium lecture there, and before the lecture, I was asked by Professor Taub what my current research was. I mentioned two areas, one being the use of Chebyshev polynomials in the theory of iterative methods in linear algebra. Taub mentioned then that he had a student (who turned out to be Gene Golub) working on similar ideas. What I learned later was that Taub told Gene that “if Varga publishes first, you will have to write a new thesis”. During that visit, I later met Gene, who was visibly shaken about all of this, and I suggested that we discuss this further over coffee. There was indeed overlap in our results, but Gene did things that I hadn’t done, and conversely. We then agreed to write a paper, in two parts, which appeared in Numerical Mathematics in 1961. This paper was surely better than either of us could have done alone, and it was quite a successful research paper, which was highly referenced. Adding to all of this is that Gene has often said that “Varga saved my life,” meaning that he didn’t have to write a second thesis! I have often been asked why Gene and I didn’t write more papers together. Sincerely, it would have been nice, but I wandered, as time went by, more into approximation theory and complex function theory, where my PhD thesis arose, and Gene had chosen other interesting areas in which to work. He had been a stellar figure in the area of numerical analysis, and this field owes him much for his deep and useful research results.
A Generalized Conjugate Gradient Method For Non-Symmetric Systems Of Linear Equations (With Paul Concus)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Second International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 15–19 1975; Lecture Notes in Economics and Mathematical Systems, vol. 134, R. Glowinski and R. L. Lions, eds. Springer-Verlag, 56–65 (1976). Gene Golub and I prepared this paper immediately after completion of the paper “A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations” with Dianne O’Leary (1976). Please see my background comments for that paper, which follows as Chapter 8.
A Generalized Conjugate Gradient Method For The Numerical Solution Of Elliptic Partial Differential Equations (With Paul Concus And Dianne P. O’leary)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Although Gene Golub and I first met in 1960, when he came to California, and have been friends since, it was only in the early 1970s that we discovered that our scientific interests had overlapped. The catalyst was the appearance of fast Poisson solvers. I was interested in using them (or related fast Helmholtz solvers) to develop efficient methods for obtaining numerical solutions of certain nonseparable elliptic partial differential equations, and Gene Golub, from a numerical linear algebra point of view, was interested in iterative methods that might exploit such solvers. Shortly after our first joint results, which utilized Chebyshev acceleration, the conjugate gradient method was beginning to receive fresh interest as an iterative method. Our attention turned toward using that method as the convergence accelerator. Such a use was much in the air then and was being looked at by others for particular underlying iteration splittings. At about the same time Dianne O’Leary appeared at Stanford as a graduate student, and she was becoming interested in these subjects also. The following paper ensued. We were very enthusiastic over the results, but as sometimes happens when naming offspring, we called the method by a name that didn’t stick. What is labeled here as the generalized conjugate gradient method is designated more popularly, and more descriptively, as the preconditioned conjugate gradient method.
Singular Value Decomposition And Least Squares Solutions (With C. Reinsch)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

method, then state of the art. We see that the singular values are the square roots of the eigenvalues of the positive (semi)definite matrices AHA or A AH. This means numerical difficulties with the accurate computation of the smaller singular values, which usually are the more interesting ones and should be computed as precisely as possible. An equally severe problem is the correct association of the eigenvectors of AHA (columns of V ) with the eigenvectors of A AH (columns of U ) which are not unique in the event of multiple eigenvalues.
The Differentiation Of Pseudo-Inverses And Non-Linear Least Squares Problems Whose Variables Separate (With V. Pereyra)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

The work on this paper originated during a 1972 visit to the Northern Patagonia city of Bariloche, Argentina, by invitation of Hugo Scolnik. Although a skiing resort, Bariloche was best visited at the time during the summer due to its lack of roads, rather than the winter, when we spent three weeks there. The work continued by snail mail (I was in Caracas, Venezuela at the time) and during my periodical visits to Serra House at Stanford.
Generalized Cross-Validation As A Method For Choosing A Good Ridge Parameter (With M. Heath And G. Wahba)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

The paper I co-authored with Gene and Grace Wahba was written while I was a graduate student at Stanford. The division of labor was roughly that Grace came up with the background theory and motivating applications, Gene suggested the algorithmic approach, and I did the implementation. Among the graduate students at Stanford at the time, I suppose I was a natural choice for this project because I had previously worked on ill-posed problems at Oak Ridge National Laboratory, so I already knew about regularization, etc. I thought we made a very complementary team. Grace was very much at home with reproducing kernel Hilbert spaces, which provided the theoretical framework for this research, whereas my knowledge of them is still rather fuzzy to this day. But Grace wouldn’t have been able to push her ideas through to concrete fruition and prove their merit without the computational know-how that Gene and I brought to the project.
On Direct Methods For Solving Poisson’s Equation (With B. L. Buzbee And C. W. Nielson)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Deciphering, Analyzing and Extending Buneman’s Stabilization of Cyclic Odd-Even Reductions – An Exercise in Good Fortune, Even Serendipity! Clair Nielson was a scientist in the fusion energy division at Los Alamos. About 1968 or 1969, Clair acquired a software subroutine that involved a very fast, direct technique for solving Poisson’s equation on a rectangle. The routine had been written by Oscar Buneman at the Stanford Linear Accelerator and Buneman didn’t document the mathematical details in it.
Matrices, Moments, And Quadrature (With GeRard Meurant)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P
Published: November 2023

Gene has been interested for a long time in moments, quadrature and their relations to orthogonal polynomials, and as the French quote above says, he pursued his goal for many years always improving his results. He realized in the 1970s that bounds can be obtained for matrix moments using quadrature formulas. is paper with Welsch, Gene has shown how to compute the nodes and weights of such a quadrature rule by using the eigenvalues and eigenvectors of the tridiagonal matrix given by the three-term recurrence of the orthogonal polynomials corresponding to the measure of the Riemann–Stieltjes integral.
Least Accessible But Not Inaccessible: Lobbying The Council And The European Council
Authors: Hayes-Renshaw Fiona
Published: November 2023

The Council and the European Council are important (some would argue the most important) and powerful actors in the European Union (EU) today. Although the similarity in their names frequently gives rise to confusion, they are separate (if interlinked) bodies with distinct decision-making roles. The Council (increasingly together with the European Parliament) is the EU’s chief decision-making body on day-to-day issues, while the European Council takes the strategic decisions that shape the future of Europe. Given their respective pivotal roles, it seems only logical to assume that these two bodies and their members are the object of intense lobbying activity on the part of those whose aim it is to attempt to influence the outcome of European-level deliberations.
Stability
Authors: Jordan D W , Smith P
Published: November 2023

The word ‘stability ‘ has been used freely as a descriptive term in earlier chapters. In Chapter 2, equilibrium points are classified as stable or unstable according to their appearance in the phase diagram. Roughly speaking, if every initial state close enough to equilibrium leads to states which continue permanently to be close, then the equilibrium is stable. Some equilibrium states may be thought of as being more stable than others; for example, all initial states near a stable node lead ultimately into the node, but in the case of a centre there always remains a residual oscillation after disturbance of the equilibrium. Limit cycles are classified as stable or unstable according to whether or not nearby paths spiral into the limit cycle.
Stability By Solution Perturbation: Mathieu ‘s Equation
Authors: Jordan D W , Smith P
Published: November 2023

Stability or instability of nonlinear systems can often be tested by an approximate procedure which leads to a linear equation describing the growth of the difference between the test solution and its neighbours. By Theorem 8.9 the stability or instability of the original system resolves itself into the question of the boundedness or otherwise of the solutions of the linear equation. This ‘variational equation ‘ often turns out to have a periodic coefficient (Mathieu ‘s equation) and the properties of such equations are derived in this chapter. The fact that the solutions to be tested are themselves usually known only approximately can also be assimilated into this theory.
Bifurcations And Manifolds
Authors: Jordan D W , Smith P
Published: November 2023

A characteristic of nonlinear oscillating systems which has become a subject of considerable recent interest is the great variety of types of response of which they are capable as initial conditions or parameter values change. The passage from one set of responses to another often occurs very suddenly, or ‘catastrophically ‘: instances of this were shown in Section 1.7 in connection with a parameter-dependent conservative system, and in Section 7.3 on the jump phenomenon of Duffing ‘s equation. Further examples of such changes are given in the present chapter, the linking concept being the idea of bifurcation, where the sudden change in behaviour occurs as a parameter passes through a critical value, called a bifurcation point.
Introduction
Authors: Galton Francis
Published: November 2023

Lee is a successful, smart, business executive, rising 35 and rising through the ranks at the same time. He is considered effective and dynamic at work. In fact, it’s more than that. He does not suffer fools gladly, and if he thinks colleagues or suppliers are trying to pull one over on him, he is quick to speak his mind. He can be very cutting, and fly into a deep rage, during which he will tell people what he thinks of them and their behaviour without sparing their blushes. As a result, though he is good at what he does, he builds up enemies.
Character Matters
Authors: Allport Gordon
Published: November 2023

t might be conventional to begin with Hippocrates, and his ideas about the four humours, or with some other ancient conception of personality types. I prefer, however, to begin our story with an article published by Sir Francis Galton in The Fortnightly Review for 1884 entitled ‘The Measurement of Character’. Galton is an apt place to begin for a number of reasons. As Charles Darwin’s first cousin, Galton was an early champion of evolution and of the view that evolution is relevant to humans. The way he could think of applying it was filtered through his Victorian preconceptions about society and societies, and so does not seem appropriate to us today. However, his basic intuition that the theory of natural
Singing with Your Own Voice
Authors: Nettle Daniel
Published: November 2023

The evidence I have presented in this book points to some very clear conclusions. There are (at least) five broad personality dimensions along which we all differ, and which cause us to behave in certain ways rather than other ways. A great deal of what happens in our interests, careers, relationships, romantic lives, and health follows from where we fall along these continua. The determinant of where we fall is how our brains are wired up, and the determinants of how the relevant parts of our brains get wired up are firstly genetics, and secondly, various early life influences over which we have no control and which seem essentially irreversible.
Stability by solutionperturbation: Mathieu’s equation
Authors: Jordan D W , Smith P
Published: November 2023

where m is any positive integer. A well-known result in matrix algebra states that if E has eigenvalues μi , then Em has eigenvalues μm i . The system will only have a solution of period T if there exists a unit eigenvalue. It will have a solution of period mT if μm = 1, which means that μ must be an mth root of unity. The stability regions can be seen by consulting Figure 9.3 (in NODE, showing the stability diagram for Mathieu’s equation). We must assume that α = L+a –l > 0, since otherwise the string would become slack. A pendulum with a light, rigid suspension is placed upside-down on end, and the point of suspension is caused to oscillate vertically with displacement y upwards given by y = ε cos ωt, ε 1. Show that the equation of motion is where a is the length of the pendulum, g is gravitational acceleration and θ the inclination to the vertical. Linearize the equation for small amplitudes and show that the vertical positionis stable (i.e. the motion of the pendulum restricts itself to the neighbourhood of the vertical: it does not topple over) provided ε2 2/(2ag) > 1. For further discussion of the inverted pendulum and its stability see Acheson (1997).
Euler–Poincaré reduction: Rigid body and heavy top
Authors: Holm Darryl D , Schmah Tanya , Stoica Cristina , Ellis David C P
Published: November 2023

The Lie group SO(3) plays a double role in the mechanics of the rigid body: it is the configuration space, and it is also the symmetry group of the Lagrangian. This allows us to introduce a specific procedure for obtaining the reduced dynamics on the quotient space TSO(3)/SO(3). This procedure, called Euler–Poincaré reduction, applies to arbitrary Lie groups, which makes it powerful in a variety of applications. For instance, we will apply it in later chapters in the study of pseudo-rigid bodies and fluids.
Momentum maps
Authors: Holm Darryl D , Schmah Tanya , Stoica Cristina , Ellis David C P
Published: November 2023

Lie group symmetries of the Hamiltonian are associated with conserved quantities. For example, the fallow of any SO(3)-invariant Hamiltonian vector field on T ∗R conserves angular momentum, q p. More generally, given a Hamiltonian H on a phase space P that is invariant under a canonical action of a Lie group G, there often exists a momentum map J : P g* that is conserved by the fallow of the Hamiltonian vector field.
Integrability of EPDiff in 1D
Authors: Holm Darryl D , Schmah Tanya , Stoica Cristina , Ellis David C P
Published: November 2023

This partial differential equation (PDE) describes shallow-water dynamics at quadratic order in the asymptotic expansion for unidirectional shallow-water waves on a free surface under gravity. The previous chapter discussed its elastic particle-collision solution properties in the dispersionless case for which the linear terms on the right side of eqn (13.1) are absent.
Continuum equations with advection
Authors: Holm Darryl D , Schmah Tanya , Stoica Cristina , Ellis David C P
Published: November 2023

A fluid flow possesses circulation, if the integral of the tangential component of its velocity u is non-zero around any smooth closed loop Ct moving with the fluid. A geometrical object such as a closed circulation loop embedded in the fluid flow is an example of a Lagrangian quantity. Such quantities are said to be frozen into the fluid flow. A theorem of vector calculus due to Kelvin and Stokes links the fluid’s circulation with its vorticity – defined as the curl of its velocity.
Populations, Samples and Data Summary
Authors: Krzanowski Wojtek J
Published: November 2023

We live in an age when data gathering is commonplace. Most readers will at one time or another have been asked to fill in a questionnaire, or to assist in an investigation, or to take part in a survey, or to collect data on some topic of interest. Recent examples to have come the author’s way have included a questionnaire from the local theatre to elicit information on frequency of attendance, preferences in programming and attitude towards ticket prices; a doorstep survey on awareness of various commercial products included in advertising campaigns; some research into the relative popularity of different degree programmes involving mathematics at UK universities; and an unexpected invitation by the local supermarket to participate in a tasting session designed to evaluate customers’ preferences in soft drinks.
Linear Models and Least Squares
Authors: Krzanowski Wojtek J
Published: November 2023

The previous chapters have been mainly concerned with statistical principles, the focus being essentially on explaining the underlying logic of statistical reasoning while keeping mention of specific statistical techniques as some what incidental to this focus. For the second half of the book we turn more directly to statistical techniques, but the emphasis will still be on rationale and objectives rather than on technical details. There are now very many statistical tools available to the investigator, so that the inexperienced researcher may feel overwhelmed when trying to select an appropriate method for analysing his or her data.
Generalising the Linear Model
Authors: Krzanowski Wojtek J
Published: November 2023

We start by reviewing the most general form of the linear model, namely the multiple regression model, but stating it in a slightly more formal way than we did in Chapter 6. This model is the simplest one for studying the dependence of a response variable y on a set of explanatory variables x  1, x  2, . . . , xk.
Special Topics
Authors: Krzanowski Wojtek J
Published: November 2023

This book has not been primarily concerned with the details of statistical techniques, but rather with the underlying philosophy behind them and with the inferential processes that make it possible for us to draw conclusions from their results. We have tried to use as broad a brush as possible, and to cover most of the general situations in which this statistical reasoning is applicable. However, there is one very fundamental assumption that must be satisfied in any given situation if this reasoning is to lead to valid conclusions, and this is that any measurements made on different individuals/units must be independent of each other.
The internationalization of mathematics in a world of nations, 1800–1960
Authors: Parshall Karen Hunger
Published: November 2023

Mathematics has a history with elements of both the contingent and the transcendent. Over the course of the nineteenth century, as the emergence of nation states increasingly defined a new geopolitical reality in Europe, competition among states manifested itself in the self-conscious adoption of the contingent, cultural standards of those states viewed as the ‘strongest’. In the case of mathematics, these self-consciously shared cultural standards centred on educational ideals, the desire to build viable and productive professional communities with effective means of communication, and the growing conviction that personal and national reputation was best established on an international stage (Parshall 1995).
Tracing mathematical networks in seventeenth-century England
Authors: Stedall Jacqueline
Published: November 2023

In 2000, Cambridge University Library purchased a unique and important collection of mathematical papers from the library of the Earls of Macclesfield at Shirburn Castle in Oxfordshire. The Macclesfield Collection, previously inaccessible to scholars since the early nineteenth century, consists of items once owned by William Jones, tutor to a son of the family in the early eighteenth century. It includes not only a number of Newton manuscripts (see Mandelbrote 2002), but also letters and papers that Jones inherited from John Collins, who in the later seventeenth century had himself been an assiduous collector of mathematical writings.
Engineering the Neapolitan state
Authors: Mazzotti Massimo
Published: November 2023

In 1808 a corps of civil engineers was constituted in the southern Italian Kingdom of Naples to provide it with new infrastructures and to implement a plan of economic and technological renewal. The activity of the corps led to controversy, however. In part the debate concerned their mathematical and scientific knowledge: was it sound? And could it legitimate their reshaping of the Neapolitan landscape? Around this debate, two opposite views of mathematics and of its relationship to engineering practices took shape: that of the engineers and that of their critics.
John Aubrey and the ‘Lives of our English mathematical writers’
Authors: Bennett Kate
Published: November 2023

One Sunday evening in February 1680, John Aubrey smoked a pipe of tobacco and dreamed up a new literary project. Stimulated by his collaborative work on a Life of Thomas Hobbes, he resolved to write ‘my honoured friend Sir William Petty’s life, which will be a fine thing, and which he shall peruse himselfe, and then it shall be left for Posterity herafter, to read (published)’. He started immediately ‘to scribble a sheet of paper close’ with notes which he intended soon to ‘enlarge’ into three Lives ‘of the worthy and ingeniose Knight Sir William Petty from his cradle; Sir Christopher Wren the like.
Learning arithmetic: textbooks and their users in England 1500–1900
Authors: Denniss John
Published: November 2023

Numbering’, ‘reckoning’, ‘cyphering’, and even ‘arithmetic’ itself are words that now have an archaic ring to them, but for centuries there have been textbooks entirely devoted to these subjects. As the Hindu-Arabic numerals began to pass westwards from Baghdad in the ninth century they were accompanied by treatises that explained how to write and use them. In the Latin West such treatises became known as ‘Algorisms’ (after al-Khwārizmī, the author of the best known of them), and their contents became the essential core of all later textbooks on arithmetic for many centuries.
People and numbers in early imperial China
Authors: Cullen Christopher
Published: November 2023

For a historian of Chinese mathematics, it is a challenging, and indeed slightly depressing experience to read the first Chapter of Thomas Heath’s History of Greek mathematics (1921, 10–25). For there we find as a natural preliminary to the main topic of the book a careful dissection of the stages of evolution of the reference and content of the various Greek terms that Heath decided to translate as ‘mathematics’, ‘mathematician’, and so on.
Bayesian Nonparametric Modelling for Spatial Data Using Dirichlet Processes
Authors: Gelfand Alan E , Guindani Michele , Petrone Sonia
Published: November 2023

Modelling for spatially referenced data is receiving increased attention in the statistics and the more general scientific literature with applications in, e.g., environmental, ecological and health sciences. Bayesian nonparametric modelling for unknown population distributions, i.e., placing distributions on a space of distributions is also enjoying a resurgence of interest thanks to their amenability to MCMC model fitting. Indeed, both areas benefit from the wide availability of high speed computation. Until very recently, there was no literature attempting to merge them. The contribution of this paper is to provide an overview of this recent effort including some new advances. The nonparametric specifications that underlie this work are generalizations of Dirichlet process mixture models. We attempt to interrelate these various choices either as generalizations or suitable limits. We also offer data analytic comparison among these specifications as well as with customary Gaussian process alternatives.
Bayesian Relaxation: Boosting, The Lasso, and Other LαNorms
Authors: Holmes Chris C , Pintore Alexandre
Published: November 2023

Modern genomics has reinforced the need for statistical methods which can explore low-dimensional structure in very high dimensional data. Classical Relaxation methods, including Boosting and Lα Regularisation, have proved remarkably successful in addressing such problems and have arguably had an important influence on the field of modern regression analysis. Relaxation methods are best described as iterative model fitting procedures which start from a simple null model and then walk along a path of increasing model complexity by incrementing parameter values at each stage. Such methods are ideally suited to the analysis of genomics data because they usually provide ‘automatic’ selection and shrinkage of predictors. In this paper, we consider relaxation methods from a fully probabilistic standpoint, accommodating model uncertainty through prior distributions on the set of relaxation paths. We suggest to make inference by Importance Sampling over paths which retains the principle characteristics of Relaxation. This new probabilistic relaxation methods are built upon a connection between Regularisation and Generalised Ridge Regression. Results seem to suggest that these algorithms are of practical importance as alternatives to standard Bayesian methods and add weight to our belief that modelling the variance components of Bayesian GLMs provides a powerful and attractive approach to model determination in modern data analysis.
Deriving Bayesian and Frequentist Estimators from Time-Invariance Estimating Equations: A Unifying Approach
Authors: Mira Antonietta , Baddeley Adrian
Published: November 2023

Time-invariance estimating equations (Baddeley, 2000) are a recipe for constructing estimators of the parameter of any stochastic model, using properties of auxiliary Markov chains associated with the model. In this paper we extend the time-invariance framework to a Bayesian context. We recover some well known Bayesian estimators and construct new ones. We find some interesting relationships between Bayesian and frequentist estimators and set up a unifying approach.
Dynamic Matrix-Variate Graphical Models*
Authors: Carvalho Carlos M , West Mike
Published: November 2023

This paper introduces a novel class of Bayesian models for multivariate time series analysis based on a synthesis of dynamic linear models and graphical models. The models are then applied in the context of financial time series for predictive portfolio analysis providing a significant improvement in performance of optimal investment decisions.
Partial Convexification of Random Probability Measures*
Authors: Kokolakis George , Kouvaras George
Published: November 2023

The construction of an absolutely continuous random probability measure is examined here. To achieve this we propose a ‘partial convexification’ procedure of a random process, such as the Dirichlet, resulting in a multimodal distribution function.
The Marginalization Paradox and Probability Limits*
Authors: Wallstrom Timothy C
Published: November 2023

Dawid, Stone, and Zidek have shown that when improper priors are used in a particular type of problem, it is often impossible to obtain a marginal posterior from an associated likelihood through formal application of Bayes’ law. This is the marginalization paradox (MP). Sudderth has shown that the MP can be resolved in the setting of finitely-additive probability. In this paper, I show that it can also be resolved in the usual countably-additive setting.
Itoô;’s Formula
Authors: Medvegyev Péter
Published: November 2023

Itô’s formula is the most important relation of stochastic analysis. The formula is a stochastic generalization of the Fundamental Theorem of Calculus. Recall that for an arbitrary process X, for an arbitrary differentiable function f and for an arbitrary partition (t(n) of an interval [0, t]
Kähler Manifolds
Authors: Joyce Dominic D
Published: November 2023

In this chapter we shall introduce the very rich geometry of complex and Kähler manifolds. Complex manifolds are manifolds with a geometric structure called a complex structure, which gives every tangent space the structure of a complex vector space. They are defined in 5.1, together with complex submanifolds and holomorphic maps. Section 5.2 discusses tensors on complex manifolds, and their decomposition into components using the complex structure, and 5.3 defines holomorphic vector bundles over a complex manifold.
Organization of the Process and Beginning of the Negotiations
Authors: Christoffersen Poul Skytte
Published: November 2023

Before describing the how of the Commission’s involvement in the enlargement process, a brief reference to the why is in place, not least because the Commission’s role is not self-evident.
International legal instruments and frameworks for invasive species
Authors: Poorter Maj De
Published: November 2023

The natural biogeographical barriers of oceans, mountains, rivers, and deserts provided the isolation in which species and ecosystems evolved. Increasingly, these barriers have lost their effectiveness as economic globalization has resulted in an exponential increase in the movement of organisms from one part of the world to another (Carlton 1999; McNeely et al. 2001). Increasing volumes of trade, travel, and tourism have led to more species than ever before being moved around the world, on land, in the air and sea.
Management of invasive fish
Authors: Ling Nicholas
Published: November 2023

Current understanding of the biology of fish invasions and the development of statistical tools for their prevention lags well behind comparable knowledge for other taxonomic groups such as birds and plants (Veltman et al. 1996; Goodwin et al. 1999). A recent analysis of fish introductions in Europe (Garcia-Berthou et al. 2005) warns that the probability of introduced fish becoming established far exceeds that proposed for other taxonomic groups, such as the ‘tens’ rule of Williamson and Fitter (1996b).
Mirrors in the Brain—How Our Minds Share Actions and Emotions
Authors: Rizzolatti Giacomo , Sinigaglia Corrado , Anderson Frances
Published: November 2023

Emotions and actions are powerfully contagious; when we see someone laugh, cry, show disgust, or experience pain, in some sense, we share that emotion. When we see someone in distress, we share that distress. When we see a great actor, musician or sportsperson perform at the peak of their abilities, it can feel like we are experiencing just something of what they are experiencing. Yet only recently, with the discover of mirror neurons, has it become clear just how this powerful sharing of experience is realised within the human brain. This book provides, for the first time, a systematic overview of mirror neurons, written by the man who first discovered them. In the early 1990’s Giacomo Rizzolatti and his co-workers at the University of Parma discovered that some neurons had a surprising property. They responded not only when a subject performed a given action, but also when the subject oberved someone else performing that same action. These results had a deep impact on cognitive neuroscience, leading the neuroscientist VS Ramachandran to predict that ‘mirror neurons would do for psychology what DNA did for biology’. The unexpected properties of these neurons have not only attracted the attention of neuroscientists. Many sociologists, anthropologists, and even artists have been fascinated by mirror neurons. The director and playwright Peter Brook stated that mirror neurons throw new light on the mysterious link that is created each time actors take the stage and face their audience - the sight of a great actor performing activates in the brain of the observer the very same areas that are active in the performer - including both their actions and their emotions. Written in a highly accessible style, that conveys something of the excitement of this groundbreaking theory, Mirrors in the brain is the definitive account of one the major scientific discoveries of the past 50 years.
Nets, Trees, and Lies
Authors: Higgins Peter M
Published: November 2023

The importance of networks has taken everyone by surprise. So much of modern mathematics is about how one thing is related to another, or more widely, how objects within a collection are interrelated, and this idea is captured in the notion of a network. And networks are just what you would imagine them to be—they can be pictured as an array of dots on the page, called nodes or vertices, with some of the dots joined to others by lines that we call edges or arcs. These links could stand for physical connections by bridges, roads, or wires, or less tangible connections by radio signals, or abstract personal connections such as friendship or enmity, or even the ancestral relationships of a family tree. This book reveals something of the surprising and subtle nature of networks, or nets as they can sometimes be called. Like nets themselves, it does not have a linear structure but, as you read on, the overall picture will become progressively clearer and the many sides of the subject will begin to coalesce.
Establishment
Authors: Davis Mark A
Published: November 2023

For an individual to successfully establish, defined as persisting long enough in the new environment to reproduce, it needs to accomplish four tasks. It needs to find an environment with abiotic conditions (e.g. temperature, salinity, moisture) it can tolerate. It needs to be able to access resources necessary for its maintenance, growth (if a juvenile or a species with indeterminate growth), and reproduction.
Evolution
Authors: Davis Mark A
Published: November 2023

It is frequently argued that one of the distinguishing features of invasions is that newly introduced species have experienced an evolutionary history separate from that of the long-termresi-dents (Cox 2004). While it is often true that the new species did not interact with the species in its new environment prior to its arrival, it may have shared an evolutionary history with species phylogenetically related to some of the native species, e.g. congeners. Even in instances where the phylogenetic interactions may be new, the newly introduce species may have interacted with ecologically similar species.
Multinomial and Poisson response data
Authors: Aitkin Murray , Francis Brian , Hinde John , Darnell Ross
Published: November 2023

The dataset faults gives the number n of faults in 32 rolls of material of length l metres; the data come from Bissell (1972), and are reproduced in Table 5.1.

The number of faults is a non-negative integer, and is naturally modelled by the Poisson distribution, the standard model for count data.
Survival data
Authors: Aitkin Murray , Francis Brian , Hinde John , Darnell Ross
Published: November 2023

Over the last 30 years there has been a rapid development of probability models and statistical analysis for technological and medical survival data. Many studies have been made of the length of life or of periods of remission of animal or human subjects being treated for serious diseases. These studies have used probability models for duration of life which originated in engineering reliability studies of the operating lifetimes of electrical and mechanical systems. We will use the terms ‘death’ and ‘failure’ interchangeably to represent the events and ‘survival time’ to represent the times to these events. In this chapter we give an account of the main probability models and their use in data analysis.
Random effect models
Authors: Aitkin Murray , Francis Brian , Hinde John , Darnell Ross
Published: November 2023

In Chapter 5 we found overdispersion in the fabric fault data; the Poisson GLM did not fit or represent the data adequately. The failure of a generalized linear model to fit may be due to several causes. The distribution of Y may not be the specified exponential family member, or the regression model fitted may be mis-specified. A fruitful way of expressing the problem, which unifies these two possibilities,is through omitted variables from the regression model: the full model we have fitted is missing one or more important variables. If these have been recorded then they can be added to the model and fitted in the usual way (e.g. interactions). The common reality however, especially in survey or observational studies, is that we do not know what variables should have been recorded or measured to construct an adequate model.
Variance component models
Authors: Aitkin Murray , Francis Brian , Hinde John , Darnell Ross
Published: November 2023

In this chapter we consider GLMs with shared random effects arising through variance component or repeated measures structure, for example, in two-stage sample designs, or longitudinal data. As we will see, the analysis of these models parallels closely that for overdispersion models, with slightly greater complexity in the EM algorithm. The range of possible models in this category is surprising.
Singular Filtering
Authors: Xiong Jie
Published: November 2023

In this chapter, we consider the filtering problem when the magnitude of the observation noise depends on the signal itself. Such a situation arises from many application problems, such as the stochastic volatility model in mathematical finance and the general filtering problem with the Ornstein–Uhlenbeck process as the observation noise. Since the covariance matrix of the observation noises is completely observable by using the quadratic covariation process, the optimal filter becomes a probability measure supported on the surface (manifold) on which the covariance matrix of the observation noises is constant. Thus, the optimal filter is singular. In this chapter, we will demonstrate how to transform this singular filtering problem to the classical one that we studied in the previous chapters.
Farey Series And A Theorem of Minkowski
Authors: Hardy G H , Wright E . M
Published: November 2023

The definition and simplest properties of a Farey series. In this chapter we shall be concerned primarily with certain properties of the ‘positive rationals’ or ‘vulgar fractions’, such as 1 or 7 . Such a fraction may be regarded as a relation between two positive integers, and the theorems which we prove embody properties of the positive integers.
The theory of risk
Authors: Anderson Raymond
Published: November 2023

Risk is part and parcel of any business endeavour. It arises from different sources that require different data and models to assess it, and different tools to control—and even play—with it. While this textbook focuses specifically upon credit risk, it is only one of many possible risks that companies face. This chapter covers a broader risk framework, which is treated under three headings:
Development management issues
Authors: Anderson Raymond
Published: November 2023

The scorecard development process has now been covered, and the next steps are strategy setting, implementation, and use—all covered in the next module. For the moment though, some development management issues need to be highlighted, which are covered under the headings of: (i) scheduling, prioritisation, when there are multiple developments; and (ii) streamlining, means of speeding up the development and implementation process.

22.1 Scheduling

Many credit providers, especially banks, have a number of different portfolios where credit scoring is applied—cheque accounts, personal loans, credit cards, home loan and motor vehicle finance, small-business lending, and so on. They may also be using different types of scorecards for each—application, behavioural, attrition, etc. When scheduling scorecard developments, consideration should be given to:
Monitoring
Authors: Anderson Raymond
Published: November 2023

Now comes mention of that dirty word, monitoring! Unfortunately, it has to be done! Its purpose is to determine how well the models are working, and what is happening within the processes in which they are being used. The following discussion relates mostly to bespoke application scorecards, but other situations must be considered.
Know your customer (KYC)
Authors: Anderson Raymond
Published: November 2023

In 1957, Eliot Ness published his memoirs, which were presented both as a TV series (1959 to 1963, starring Robert Stack; and 1993/1994, starring Tom Amandes), and a movie (1987, starring Kevin Costner). This was The Untouchables, set during the 1930s prohibition, which told the story of a small band of Chicago policemen, whose primary nemesis was Al Capone— one of the most infamous gangsters of that era. Capone was finally indicted on tax evasion charges in 1931, and sentenced to 11 years in prison. The case was a precedent, because a hardened mobster, who was involved in practically every type of racketeering and organised crime possible during that era, was jailed for a crime that many consider acceptable.
Mycenaean Greek
Authors: Colvin Stephen
Published: November 2023

At the beginning of our historical survey, c.1500 BC, we find two civilizations occupying a dominant position in the Aegean area. These have become known in modern times as the ‘Minoan’ civilization in Crete and the ‘Mycenaean’ in southern and central Greece. The non-Greek Minoan was the older of the two: the Mycenaeans were heavily influenced by Minoan culture, and Mycenaean civilization at its height was essentially a fusion of the Minoan and the native (‘Helladic’) culture of the Greek mainland. Between the sixteenth and the twelfth centuries BC, Mycenaean power and influence expanded at the expense of the Minoans, and the Mycenaeans seem to have taken control of Crete itself in the fifteenth century. Mycenaean power was at its height between 1400 and 1200, with the establishment of great palatial centres at Pylos, Mycenae, and Tiryns in the Peloponnese, and Thebes and Orchomenos in Boeotia. Mycenaean settlement is attested in the Cycladic Islands, the Dodecanese, and on the west coast of Asia Minor. There is also evidence for Mycenaean trading activity around the Mediterranean, with Cyprus and the Levant in particular, and with Sicily and southern Italy in the West.
Syllabification
Authors: Colvin Stephen
Published: November 2023

Linear B signs denote a vowel (V) or consonant + vowel (CV). In a very few cases a sign denotes two consonants followed by a vowel (CCV), but in general consonant clusters have to be written either by inserting extra vowels, or by omitting consonants: Most syllables of the pattern CCV have to be written either
Vocabulary
Authors: Colvin Stephen
Published: November 2023

The vocabulary of Mycenaean Greek is more or less the same mixture of Indo-European, substrate, and borrowed items that we find in later Greek. Myc. words with well-established IE origins include: Other words apparently lack IE cognates: Certain words ending in -(i)nthosand -(s)soshave traditionally been associated with the substrate language(s) of Greece, i.e. the language (which may or may not have been Indo-European) spoken by the inhabitants of Greece before the arrival of the ‘Greeks’ (§1.3 above). In addition, some words are clearly loans from Semitic or other neighbouring languages: As one would expect, some changes in meaning are detectable between the Mycenaean period and Homeric Greek:
The Alphabetic Period
Authors: Colvin Stephen
Published: November 2023

The passing of Mycenaean civilization was followed by a dramatic decline in population, disintegration of trading links, and in general a much poorer material culture. This transformation has been connected with movements of population in Greece in the centuries following the Mycenaean collapse. There were also far-reaching migrations from Greece to the coast of Asia Minor and the offshore islands during this period, no doubt triggered to some extent by unsettled conditions in Greece. The Greek settlers who occupied Lesbos and the most northerly part of Asia Minor called the region they inhabited ‘Aeolis’: these Aeolians seem to have migrated from Thessaly. To the south of Aeolis lay Ionia, which was settled for the most part by migrants from Attica; most of the central Aegean islands between Attica and Ionia were also settled by Ionic-speakers. The Asiatic coast south of Ionia, and the southern Aegean islands (Crete, Carpathos, Rhodes, and Cos) were occupied by Dorians from southern Greece.