bluuebunny/crossref_metadata_2025_split huggingface dataset:
Topology and analysis in the complex plane
Authors: Priestley H A 
Published: November 2023

Abstract
Complex analysis has a vital geometric facet, from which it derives much of its character. The geometry of the plane is inextricably bound up with its topological structure, defined by the open sets we introduce below, and this structure provides the key to the analysis of complex sequences and series and of complex-valued functions defined on subsets of ℂ, in particular the study of convergence, continuity, and differentiability.
This section introduces notions which are topological in nature. We shall assume no prior acquaintance with topology and include the bare minimum for our immediate needs. Those who have studied the rudiments of topology in Euclidean spaces or in the more general setting of metric spaces should find much here that is familiar. For an introduction to topology we recommend [7].
Complex series and power series
Authors: Priestley H A 
Published: November 2023

Abstract
We begin this chapter with some introductory remarks to motivate the study of complex power series. As we shall see in Chapter 14, such series turn out to be fundamental in the theory of holomorphic functions.
We should like to have complex analogues of these. In the complex case, geometric ways of defining trigonometric functions are no longer available. We shall therefore wish to use series expansions to define functions such as sine and cosine.
Host-plant selection: when to accept a plant
Authors: Schoonhoven Louis M , Loon Joop J A van , Dicke Marcel 
Published: November 2023

Abstract
One of the most notable features of herbivorous insects that has emerged from the previous chapters is that most species are very selective feeders and meticulously choose the plants on which they deposit their eggs. Recent research on several species has shown that they select not only certain plant species but also specific plant organs.
Spatial analysis of ERP and EEG data
Authors: Strik Werner K , Koenig Thomas 
Published: November 2023

Abstract
The extended scalp potential differences that are measured by electroencephalography (EEG), magneto encephalography (MEG), and event related potentials (ERPs) result directly from the coherent firing of large, predominantly cortical, neural populations. Theoretically, EEG and ERPs, therefore, offer views on brain functions that no other non-invasive technique can provide; these include different modes of oscillation (frequency analysis), transient functional coupling of brain regions (event related synchronization and desynchronization), or temporal sequencing of brain events in the sub-second time domain (microstates). Each of these views might be relevant for the understanding of brain functions during schizophrenia.
Bayesian Inference for Elliptical Linear Models: Conjugate Analysis and Model Comparison
Authors: Arellano-Valle Reinaldo B , Iglesias Pilar L , Vidal Ignacio 
Published: November 2023

Abstract
Bayesian inference for normal regression models, including sensitivity analysis, model comparison and error in variables under non-informative and conjugate prior for the model parameters has received considerable attention in the last decades. From a distributional point of view the results can be extended in several directions. One is by considering a wider class of prior distributions for the parameters of the model. Another, is by considering alternative distributions for the error terms. Usually, the results with non-conjugate priors rely heavily on MCMC methods. On the other hand, many extensions has been obtained by considering the so called dependent elliptical model, which is often used in linear regression analysis to accommodate the kurtosis of the error terms and to accommodate outliers. Bayesian inference with multivariate elliptical models was initially presented in Chu (1973). Posteriorly, Meinhold and Singpurwalla (1989) consider a robustification of Kalman filters by using the multivariate Student-t distribution. This distribution was also used by Zellner (1976), who considered a Bayesian treatment of linear regression models under non-informative prior distributions.
On Inferring Effects of Binary Treatments with Unobserved Confounders
Authors: Chib Siddhartha 
Published: November 2023

Abstract
One of the most pervasive problems in statistics is the following. Suppose x is a binary {0,1} indicator of a treatment (where the term treatment is intended to embrace a covariate of interest, not necessarily one arising in a medical or epidemiological setting) and y is a response and the objective is to isolate the effect (“treatment effect” ) of x on y. To fix ideas, x may be an indicator of smoking status taking the value one if the subject is a current smoker and the value zero otherwise and y may be some measure of subject health. For simplicity we assume that both the treatment and response are univariate although this can obviously be relaxed. It is well understood that outside of the experimental setting inferring effects of this kind raise a multitude of challenges that are not easy to address (even in a randomized treatment setting, inference is difficult when human subjects are involved due to dropouts, non-compliance and other such complications). The problem is that when the treatment intake is non-random, as in an observational setting where subjects self-select into a treatment state, the choice of treatment may be influenced by unmeasured or unmeasurable or unobservable covariates that also affect the response.
Discrimination Based on an Odds Ratio Parameterization
Authors: Linde Angelika Van Der , Osius Gerhard 
Published: November 2023

Abstract
It is argued that the association of any two random elements with positive joint probability density function is characterized by its odds ratio function. The impact of this fundamental result is explored in two applications. In Bayesian analyses it is the association between an observable random variable and a random parameter that is of primary interest. In multivariate analysis it is the association between two random vectors that is investigated. If two random elements are strongly related the corresponding conditional distributions can well be separated. A concept of dependence therefore implies an approach to solving problems of discrimination. Discrimination based on the characterization of association by the odds ratio function is exemplified in Bayesian inference and in multivariate analysis.
Robust Analysis of Salamander Data, Generalized Linear Model with Random Effects
Authors: Chan S T Boris , Choy. Jennifer S K , Yam Carrie H K 
Published: November 2023

Abstract
The salamander mating data reported by McCullogh and Nelder (1989) have been analyzed by many researchers using both classical and Bayesian approaches. The study design in the data is crossed rather than nested. This imposes great computation difficulties when using the classical approach because the likelihood function cannot be factorized. Moreover, the likelihood function will become very complicated when non-normal random effects distributions are adopted. Hence, previous researches have always assumed normal distributions for the random effects. In this paper, we adopt a Bayesian approach and choose the Students distribution as an alternative to the normal distribution in order to allow for the possible thick tail behavior of the random effects and hence to provide a robust analysis. To identify possible outlying random effects, we represent the Students distribution as a scale mixtures of normal distribution within the Bayesian framework and the models are implemented using the Markov chain Monte Carlo method, in particular, the Gibbs sampler. Finally, we highlight the novel and interesting features of this data set.
A Relationship Between Randomized Manipulation and Parameter Independence
Authors: Daneshkiiah Alireza , Smith Jim Q 
Published: November 2023

Abstract
We argue that a Bayesian will usually need to specify a joint prior density of the conditional probabilities of a Causal Bayesian network (CBN). We show that in order to do this, under very mild conditions it will be necessary to demand that this joint prior density exhibits the properties of local and global independence. To make the connection between prior independence and causality, it is first necessary to strengthen slightly the assumptions of factorization invariance under manipulation which induces randomized intervention. We introduce the hypercausal BN (HCBN) that asserts a set of factorizations of densities which are invariant to a class of “do” operations larger than those considered by Pearl. We show that if a BN is assumed to be hypercausal, then the prior distributions on the probabilities of the idle system must exhibit local and global independence.
Direct Bayes for Interest Parameters
Authors: Fraser Don A S , Wong Augustine , Reid Nancy , Yi Grace Y 
Published: November 2023

Abstract
For an interest parameter ψ (θ) the Bayesian method eliminates the nuisance parameter ψ (θ) by integrating with respect to a conditional prior for A given ψ. This conditional prior may be difficult to specify in both the subjective and objective Bayesian contexts. We propose the use of results from likelihood theory that give highly accurate third-order determinations of various marginal distributions in the continuous case. The appropriate conditional prior exists as part of the calculations for the marginal distributions and corresponds to an integration used in the marginalization. To third order, however, the integrated likelihood for the interest parameter can be obtained directly; it needs no model information beyond that commonly available for accurate analyses of likelihood. Simple examples are given where the steps are analytically available to illustrate this direct Bayesian calculation.
Dynamic Lattice-Markov Spatio-Temporal Models for Environmental Data
Authors: Garside Linda M , Wilkinson Darren J 
Published: November 2023

Abstract
This paper is concerned with the modelling of the latent structure of a Bayesian spatio-temporal model with a view to improving parameter inference, smoothing and prediction. The equilibrium distribution of a time stationary system will be examined, paying particular attention to edge-effects and the effect of grid-coarsening. In order to develop an effective MCMC algorithm, the latent process is integrated out of the model. These techniques will be illustrated using North Atlantic ocean temperature data.
Compatible Priors for Causal Bayesian Networks
Authors: Lcucari Valentina , Consonni Guido 
Published: November 2023

Abstract
We consider discrete causal DAG-models (or Bayesian Networks) wherein the ordering of the variables is fixed across model structures. Given a prior on the parameter space of a model we describe a method for deriving a compatible prior on the parameter space of a submodel. This allows to generate automatically compatible priors for model parameters starting from a single prior relative to the largest entertained model. Our method makes use of a general procedure for constructing compatible priors for causal DAG- models, named reference conditioning, which is invariant within a suitable class of re-parameterizations and is model intrinsic. We show that if the generating prior satisfies global parameter independence, so does the compatible prior; in addition, prior modularity holds. Further results are obtained when the starting prior is product Dirichlet. A simple illustration of the methodology, and comparisons with alternative methods, are presented.
Modelling Bivariate Extremes in a Region
Authors: Smith Elizabeth L , Walshaw David 
Published: November 2023

Abstract
Practitioners of extreme value methodology have been slow to accept the Bayesian paradigm, and the initial work that has been carried out in recent years has reflected the history of the classical approach, in concentrating solely on univariate problems. In this paper we take a first step towards balancing the substantial frequentist literature on multivariate extreme value inference by considering problems of bivariate inference from a Bayesian point of view. We relate the bivariate case to inference problems for extremes of environmental variables recorded at a number of locations in a spatial region. We show how inference for bivariate extreme value models can be implemented using an MCMC scheme, and compare two popular model families. We then select one of these families for use in a practical example involving rainfall data. We employ prior information on marginal behavior of extremes constructed from carefully elicited expert beliefs, while prior beliefs about the dependence parameter relate the strength of dependence inversely to the distance between locations, thus exploiting the spatial aspect inherent in the inference problem. We briefly discuss how our ongoing work in this area will lead to a spatial model which enables inference at a particular location of interest to be improved through the model for bivariate extremal dependencies with other locations. We conclude with a pointer to inference for max-stable process models, which are being developed by the authors to address the problems involved in truly multivariate inference.
The FEM for stochastic structures: A review and improvement
Authors: Elishakoff Isaac , Ren Yongjian 
Published: November 2023

Abstract
Computational stochastic mechanics involves the numerical solution of stochastic mechanics problems, typically by the finite element method. Since early 1980 ‘s, this field has received increasing attention and presently is an active area of research—A. Der Kiureghian (1994). Many different interpretations are possible for the terminology: stochastic finite element analysis—E. Vanmarcke, M. Shinozuka, S. Nakagiri, G. I. Schuëller, and M. Grigoriu (1986).
Element-level flexibility-based FEM for stochastic structures
Authors: Elishakoff Isaac , Ren Yongjian 
Published: November 2023

Abstract
In Chapters 3 and 5 we proposed two non-perturbative FEMs for stochastic structures, namely the exact inverse based FEM for simple stochastic structures and the variational principle based FEM for stochastic beams. These two approaches encounter difficulties when they are generalized as a widely applicable tool for two-or three-dimensional structures. This chapter presents an element-level flexibility-based FEM for stochastic problems. The unconventional step in the new formulation is to divide the element-level finite element equilibrium equation by the element stiffness so that the reciprocal of the stiffness (the flexibility) appears on the right side of the equation, and thus becomes uncoupled from the unknown displacement.
A comparison of stochastic and interval finite elements
Authors: Elishakoff Isaac , Ren Yongjian 
Published: November 2023

Abstract
In this chapter, structural uncertainties are modeled by using both the stochastic and interval methods to quantify the uncertainties in the response quantities. Through a suitable discretization, stochastic and interval FEMs are constructed. A comparison of these methods is illustrated using a shear frame with uncertain stiffness properties. Response quantities, in the form of internal forces, stresses, displacements, and strains, are needed to evaluate the safety and serviceability of structures. In many real-life structural engineering problems neither the initial conditions, nor external forces, nor the parameters of the constitutive relations used in the procedures to calculate response quantities can be perfectly described because of the lack of detailed knowledge and also due to the inherent uncertainties.
Lotteries
Authors: Haigh John 
Published: November 2023

Abstract
Mathematicians become accustomed to requests for good strategies to play the Lottery. One main hope is that statistics can be used to predict which numbers will be drawn in the future. The autobiography of Len Shackleton, one of my boyhood heroes, includes a celebrated chapter headed ‘What the average director knows about football’: the chapter was simply a blank page. Any chapter from me entitled ‘How to win more often’ would also be a blank page, apart from the single line ‘Buy more tickets’. But there are ways in which a mathematical approach to the Lottery can help gamblers, as I shall show.
One coin, many games
Authors: Haigh John 
Published: November 2023

Abstract
It may be just a SOP piece to you, but to a probabilist a coin is also a convenient randomizing device. No-one uses paper money or credit cards to settle a family argument over which set of parents to visit at Christmas, or which TV programme shall be watched. Faced with two alternatives, you can allocate Heads to one of them, Tails to the other: if, when Tails appears, your instinct is ‘Make it best of three’, you know which one you really prefer. You do not have to obey the coin’s whim, it might just help you make up your mind. Many recreational games are based round the easy availability of a coin which will yield two outcomes that can plausibly be taken as equally likely.
Games with few choices
Authors: Haigh John 
Published: November 2023

Abstract
You and I require one ordinary coin each to play the following game. Each of us decides, in secret, whether to show Heads or Tails. We may reach our decision by any means we want: we could toss our coin, to let it make its own decision, or we may use whatever criterion we like to make a deliberate choice. When we have decided, we compare choices. If they are the same, you win two units from me; if they are different, I win two units from you. What these units are will be agreed before the game-they may be counters, pence, Euros, or whatever. Is this game fair, or is it advantageous to one of us?
Waiting, waiting, waiting
Authors: Haigh John 
Published: November 2023

Abstract
The common theme here is that there is a sequence of opportunities for something to happen. In some problems, we want to know how long we have to wait, in others it is how many ‘somethings’ are going to occur. As each problem is introduced, you are invited to make your assessment of the appropriate answer. Be honest: pause before you read on, and make your best guess. Award yourself gold stars for good guesses-provided your reasoning was valid-and suffer some suitable penance otherwise. Do not simply read on to discover the answer and then persuade yourself you would have got it about right. Be active.
Let’s play best of three
Authors: Haigh John 
Published: November 2023

Abstract
If two people, or two teams, compete for a prize, how many matches should they play? Once, the world snooker champion defended his title over a series of 143 frames; in modern times, up to 35 frames are used. The finals of the World Series at baseball, and the Stanley Cup at ice hockey, are played as best of seven matches, split four to three between the home venues of the contesting teams. Test cricket, in which drawn games occur frequently, is played over a series of from two to six matches. Chess world championships are seldom played under exactly the same rules each time, but ‘best of 24’ has been common recently. A single game at lawn tennis does not have a fixed number of points: to win, you must score at least four points, and you must also be at least two points ahead of your opponent.
Casino games
Authors: Haigh John 
Published: November 2023

Abstract
The main purpose of the Betting and Gaming Act, 1960, was to provide a legal framework for off-course betting on horse-racing, but it also led to the opening of some UK casinos. The 1968 Gaming Act brought stricter controls over casino operation, including rules on where they may be sited. A Gaming Board determines what games are permitted, advises the local magistrates who actually grant the licences, and carries out checks on the character of employees. The annual ‘drop’-the amount of money exchanged for gambling chips-is some £2.6 billion, of which £470 million stays with the casinos. London, with more than 20 casinos, accounts for 80% of the UK turnover.
Probability for lawyers
Authors: Haigh John 
Published: November 2023

Abstract
It is now common that in crimes such as rape and murder, blood or semen samples from the crime scene and from a suspect are compared. An expert may testify that the chance of a match between the crime sample and a random innocent person is as low as one in a billion. Less dramatic figures, one in mere tens of thousands, may be offered for comparisons of fibres from clothing, fragments of glass from broken windows, or footprints in the garden. But whatever the figure, the precise way in which it is given during a trial is of crucial importance: what may seem to be just finicky changes in wording can make all the difference between a fair and an unfair trial.
The Early Universe
Authors: Weinberg Steven 
Published: November 2023

Abstract
We have been exploring the period in the history of the universe when the radiation temperature dropped from a little over 10 K down to its present value of 2.725 K. We now want to look back to the era when the temperature was greater than about 10 K, well before the energy density in radiation fell below that of baryons and cold dark matter. We will carry the story back to when the temperature was above 10 K, when electron–positron pairs were abundant and neutrinos were in equilibrium with these pairs, and even farther back, as far as our current knowledge of the laws of physics will take us.
Inflation
Authors: Weinberg Steven 
Published: November 2023

Abstract
We can have some confidence in the story of the evolution of the universe from the time of electron–positron annihilation to the present, as told in the previous three chapters. About earlier times, so far we can only speculate. In the past quarter century these speculations have centered on the idea that before the period of radiation domination√, during which the Robertson–Walker scale factor a(t) was growing as t , there was an earlier period of inflation , when the energy density of the universe was dominated by a slowly varying vacuum energy, and a(t) grew more-or-less exponentially. The possibility of an early exponential expansion had been noticed by several authors, but at first it attracted little attention. It was Alan Guth who incited interest in the possibility of inflation by noting what it was good for. Guth noticed that, in a model of grand unification he was considering (with Henry Tye), scalar fields could get caught in a local minimum of the potential, which in his work corresponded to a state with an unbroken grand unified symmetry. The energy of empty space would then have remained constant for a while as the universe expanded, which would produce a constant rate of expansion, meaning that a(t) would have grown exponentially. Eventually this inflation would be stopped by quantum-mechanical barrierpenetr ation, afterw hich the scalarfield would start rolling down the potential toward a global minimum, corresponding to the present universe. In itself this would have been a result of no great immediate importance.
Evolution of Cosmological Fluctuations
Authors: Weinberg Steven 
Published: November 2023

Abstract
We will now apply the formalism developed in the previous chapter to work out the evolution of cosmological fluctuations, from a temperature 10 K when electron positron annihilation is substantially complete and neutrinos have decoupled from matter and radiation, down to the relatively recent time when the matter fluctuations become too large to be treated as firstorder perturbations. Our results will be applied to analyze the observed fluctuations in the cosmic microwave background in the next chapter, and large scale structure in Chapter 8.