bluuebunny/crossref_metadata_2025_split huggingface dataset:
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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 &gt; 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) &gt; 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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
The Marginalization Paradox and Probability Limits*
Authors: Wallstrom Timothy C 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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.