bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized linear models for longitudinal data
Authors: Diggle Peter J , Heagerty Patrick J , Liang Kung-yee. , Zeger Scott L
Published: November 2023

This chapter surveys approaches to the analysis of discrete and continuous longitudinal data using extensions of generalized linear models (GLMs). We have shown in Chapter 4 how regression inferences using linear models can be made robust to assumptions about the correlation, especially when the number of observations per person, ni, is small relative to the number of individuals, m. With linear models, although the estimation of the regression parameters must take into account the correlations in the data, their interpretation is essentially independent of the correlation structure. With non-linear models for discrete data, such as logistic regression, different assumptions about the source of correlation can lead to regression coeficients with distinct interpretations. The data-analyst must therefore think even more carefully about the objectives of the analysis and the source of correlation in choosing an approach.
Local Ring Theory
Authors: Boffi Giandomenico , Buchsbaum David A
Published: November 2023

The development of the first five sections of this chapter is guided by the desire to establish a string of inequalities for local rings (always assumed to be noetherian here) which lead to the result, in Section II.5, that a local ring is regular if and only if its global dimension is finite. The development here is very close to that used in the notes of Reference [19] and rests on the work found in References [7] and [8].
Generalized Koszul Complexes
Authors: Boffi Giandomenico , Buchsbaum David A
Published: November 2023

In the preceding chapter, we saw the fundamental role that the Koszul complex played in the study of certain aspects of local ring theory. One of the main ideas tied up with that complex is that of regular sequence, with the Cohen–Macaulay Theorem one of the major results obtained through its use.
Structure Theorems for Finite Free Resolutions
Authors: Boffi Giandomenico , Buchsbaum David A
Published: November 2023

In the previous chapter, we saw a whole class of complexes associated with a given map, f , of finite free modules. We proved that all of them were sensitive to the depth of the ideal generated by the maximal minors of f , and gave a necessary and sufficient condition for them to be finite free resolutions of the cokernels of the exterior powers of f in terms of the depth of the ideal generated by the maximal minors of f .
Topology and analysis in the complex plane
Authors: Priestley H A
Published: November 2023

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

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

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

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

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

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

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

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

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

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

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

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

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.
Prologue
Authors: Elishakoff Isaac , Ren Yongjian
Published: November 2023

Engineering mechanics has been flourishing thanks to modern computers and updated computer codes... Today, computational mechanics is able to carry out various structural analyses, provided that the relevant input data are at hand�S. Nakagiri (1987).
The FEM for stochastic structures: A review and improvement
Authors: Elishakoff Isaac , Ren Yongjian
Published: November 2023

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

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

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

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

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

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

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

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

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

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

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

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

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.
The Growth of Structure
Authors: Weinberg Steven
Published: November 2023

In Chapter 6 we followed the evolution of small perturbations through the radiation and matter dominated eras, up to the time of decoupling, when radiation no longer interacted effectively with matter. Now we will continue the story past the time of decoupling. In Section 8.1 we will follow the perturbations while they remained small, continuing our linear analysis. This era is increasingly becoming accessible to observation, as studies of the cosmic matter distribution are pushed to larger redshifts. As we shall see, data on the distribution of matter fluctuations already provides an important extension of results from cosmic microwave background anisotropies to smaller wavelengths, and it is hoped that eventually it may provide information of the effect of dark energy on cosmic expansion.
Gravitational Lenses
Authors: Weinberg Steven
Published: November 2023

In 1979 Walsh, Carswell, and Weymann noticed a pair of quasars at the same redshift, about 1.4, separated by just 6. The similarity of the spectrum of the two quasars suggested to them that there was really just one quasar, now known as Q0957+561, split into two images by the deflection of light in the gravitational field of an intervening massive body. This suggestion was verified with the discovery of a galaxy with a redshift 0.36 between the lines of sight to the quasar. Such gravitational lenses had already been studied theoretically by many authors, and now a serious search for them was put in train. Many more lensing galaxies were discovered, generally elliptical field galaxies, and also some lensing clusters of galaxies, which generally produce arc-like images.
Inflation as the Origin of Cosmological Fluctuations
Authors: Weinberg Steven
Published: November 2023

The most exciting aspect of the inflationary cosmological theories described in Chapter 4 is that they provide a natural quantum mechanical mechanism for the origin of the cosmological fluctuations observed in the cosmic microwave background and in the large scale structure of matter, and that may in the future be observed in gravitational waves. We have seen in Chapter 6 that the magnitude and wavelength dependence of adiabatic scalar and tensor fluctuations depend on initial conditions only through the quantities R° and D° , respectively.
Karl Jaspers and General Psychopathology
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

In this chapter we turn from the broad history of psychopathology to one of its most important exponents in the twentieth century, Karl Jaspers. Jaspers set out his psychopathology in the first edi- tion of his monumental Allgemeine Psychopathologie or General Psychopathology, published in 1913. We will be looking at a short passage from Allgemeine Psychopathologie towards the end of the chapter. We will be focusing, however, on two papers that Jaspers published at about the same time as Allgemeine Psychopathologie; one (Jaspers, 1913a) on the importance of meanings as well as causes in psychopathology, an idea that Jaspers in turn derived from the ‘Methodenstreit’ (a nineteenth century debate in Germany on methods in the natural and human sciences), the other (Jaspers, 1912) on the distinctive role of phenomenology as a methodology for psychopathology. Taken together, these two papers will give us important insights into some of the key guiding ideas behind Jaspers’ Allgemeine Psychopathologie. The topics with which the two papers deal will be taken up in more detail later, phenomenology in Chapters 9 and the Methodenstreit in Chapter 10.
Diagnosis, explanation, and tacit knowledge
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

In this chapter we move from symptoms of mental disorder and their classification to the diagnostic process: how we come to explain or claim knowledge of someone’s condition. Diagnostic explanation in medicine, as we saw in Chapter 3, is partly in terms of syndromes (identifying a patient’s symptoms with a recognized pattern that carries implications for treatment and prognosis) and partly in terms of aetiology (causal information). In general medicine, diagnostic explanations are more in terms of aetiology; in psychiatry and nosology, they are more in terms of symptoms and syndromes (they are ‘descriptive’, in the sense of that term used in ICD and DSM, see Chapter 13). Either way, though, diagnostic explanations are perceived as a species of scientific explanation. This prompts the question, therefore, just what a sound scientific explanation consists in. This question, as we will see, has been the subject of close scrutiny in the philosophy of science, and, although no definitive answers have been given, a number of key points have been established which are relevant to our understanding of the nature of scientific explanation in general and hence of diagnostic explanation in particular.
Chapter 16
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

Like other areas of medicine, treatment and management within psychiatry has increasingly been influenced by the growth of evidence-based medicine or evidence-based practice. A recent review article in the British Journal of Psychiatry starts with this observation. Clinical effectiveness, evidence-based medicine (EBM) and related terms were the politically correct medical slogans of the 1990s. For many they are ‘buzz-words’ conveying a modern progressive approach and in some circles it is unwise to express scepticism. Evidence-based medicine is being embraced by all specialities and there has been a strong signal that psychiatry is joining the movement by the introduction in 1998 of a psy- chiatric journal dedicated to evidence-based practice.
It’s the law! Rationality and consent as a case study in values and mental health law
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

In this chapter we shall be examining the concepts of rationality and consent from a medico-legal viewpoint. These concepts have been central to the way the English courts have tried to reconcile the perception that the patient has a right to decide what happens to him with the perception that the doctor has a duty to try her best to heal her patient. The tension between these two perceptions, as we have seen in Chapters 17 and 18, is central to the ethical issues raised specif- ically by involuntary psychiatric treatment. In common law the English courts, like most courts around the world, have repeatedly affirmed that an adult patient of ‘sound’ mind has an absolute right to accept or reject medical treatment. Corres- pondingly, therefore, the courts will sometimes override this right where the patient is of ‘unsound’ mind. The Mental Health Act, as we saw in Chapter 17, gives statutory authority to this autonomy override in respect of mental disorders, albeit not on the same incapacity basis applied by common law. Other legis- lation covers contexts, such as the patient being a child, or where the welfare of a viable foetus is at stake.
The mind–body problem and mental health, a philosophical update
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

The previous chapter provided an historical introduction to the mind–body problem. In this chapter we will return to the issue of the relation of mind and body and examine some of the rival contemporary approaches within the philosophy of mind. The aim of the chapter will be to shed light on the range of different ways that mind and body might be related and the kind of argu- ments, both based on a priori reasoning and on very general empirical evidence, that can be brought to bear on the issue. It will do this by examining a small sample of views and indicating the range of other choices that might be defended.
Reasons and the content of mental states: 2. Antireductionism and discursive psychology
Authors: Fulford K W M , Thornton Tim , Graham George
Published: November 2023

Chapter 24 examined the kind of approach to meaning and inten- tionality implicit in cognitive neuropsychology and cognitive neuropsychiatry. The underlying approach was characterizable using a term from the philosophy of thought and language as repres- entationalism. Such an approach aims to shed light on how our mental states can have the meaning or content they do using a cog- nitivist model drawing heavily on an analogy with computing. A key idea is that the fact that people can have mental states such as beliefs can be explained at a lower subpersonal level in terms of information processing using inner mental representations: struc- tural configurations in their brains. Because the intentionality—the world-involving nature—of the mental states of whole people is explained in terms of the causal processes acting on lower level parts of their brains, such an approach can be thought of as ‘bottom up’.
Free boundary problems
Authors: Ockendon John , Howison Sam , Lacey Andrew , Movchan Alexander
Published: November 2023

This chapter is the most unconventional in the book. Whereas hyperbolic, elliptic and parabolic problems have been studied over many decades, and many texts are devoted to each, the subject of free boundary problems has attracted few specialised publications despite its importance in modern applied mathematics. In fact, we have already encountered several examples of this type of problem, although we have not classified them as such. For example, the thin film flows described in Chapter 1, the shock waves in Chapter 2, the contact problem in Chapter 5, and the porous medium equation of Chapter 6 could all be posed as problems involving the solution of partial differential equations in domains that are unknown a priori; not only the solution of the equations but also the domain of definition of the equations must be determined.
Spatial and temporal resolution in FMRI
Authors: Menon Ravi S , Goodyear Bradley G
Published: November 2023

Most functional MRI studies to date have used relatively low resolution, both in space and time, to interrogate brain function. Typically, an in-plane resolution of 3-4 mm is used, in conjunction with slice thicknesses of 5-10 mm. This means that the typical volume element (voxel) being interrogated is on the order of 100 mm3• Additionally, a temporal resolution of several s is usually employed, due to the need to allow for Tl signal recovery between acquisitions and because of the sluggish nature of the haemodynamic response. Many brain processes occur on spatial scales that are smaller than can be readily accessed with fMRI and with temporal scales that are much faster than the haemodynamic response time. This chapter addresses the limitations imposed by the fMRI technique and suggests some strategies to improve both resolutions.
Effective paradigm design
Authors: Donaldson David I , Buckner Randy L
Published: November 2023

Advances in functional magnetic resonance imaging (fMRI) are affording numerous new ways to design and analyse brain-imaging studies. A major driving force for these advances has been the widespread use of MRI scanners capable of ultra-fast imaging. For example, MRI scanners in many laboratories and clinical settings typically can acquire whole-brain images once every 2 s or even faster (see Chapter 4). However, the temporal resolution of fMRI is limited by the underlying physiological signals through which neuronal activity is indirectly measured (see Chapter 2). The optimal choice of an MRI experimental paradigm is determined by an interaction between methodological limitations key concepts or strategies rather than to provide a review of the literature. It also should provide a guide to the chapters that follow. We hope that it will help to place them in context. In doing of MRI technology and of the underlying physiology that constrain paradigm design for functional brain imaging.
The scanner as a psychophysical laboratory
Authors: Savoy Robert
Published: November 2023

The use of magnetic resonance imaging (MRI) for mapping human brain function has naturally required the presentation of stimuli, and recording of behavioural and physiological responses in the challenging MRI environment. The earliest human studies used very simple visual stimulation systems, such as goggles with blinking light-emitting diodes (Belliveau et al. 1991), or depended on the brain activity needed for simple motor tasks that did not require any extra simulation or recording equipment (e.g. Bandettini et al. 1993). There has been steady progress, both in individual laboratories and in the development of integrated commercial systems, for the sophisticated control of stimulus presentation and response recording during MRI. Some of this progress (and the general considerations for anyone establishing a functional MRI research environment) is articulated in the present chapter.
Affine varieties and finite morphisms
Authors: Geck Meinolf
Published: November 2023

In this chapter, we come to those results on affine varieties and algebraic groups which rely in an essential way on the hypothesis that the ground field k is algebraically closed. We will see that, under this hypothesis, the image of a morphism between affine varieties is a relatively ‘thick’ subset, more precisely, it contains an open subset of its closure. This fact will turn out to be a key tool.
The Evolution of Human Neocortex: Is the Human brain fundamentally Different than that of other Mammals?
Authors: Krubitzer Leah , Kahn Dianna M
Published: November 2023

The neocortex is composed of areas that are functionally, anatomically, and histochemically distinct. In comparison to most other mammals, humans have an expanded neocortex, with a pronounced increase in the number of cortical areas. This expansion underlies many complex behaviors associated with human capabilities, including perception, cognition, language, and volitional motor responses. We consider data from comparative studies as well as from developmental studies to gain insight into the mechanisms involved in arealization, and discuss how these mechanisms may have been modified in different lineages over time to produce the remarkable degree of organizational variability observed in the neocortex of mammals.
Time as Coding Space in the Cerebral Cortex
Authors: Singer Wolf
Published: November 2023

Evidence is reviewed which suggests that the cerebral cortex applies, in parallel, complementary strategies to enhance the saliency of neuronal responses selected for further joint processing and to encode relations among the activities of distributed neurons. Saliency is enhanced by increasing discharge rate and/or by synchronizing the discharges of neurons. Relations between distributed neurons are encoded by integrating their responses in conjunction with specific neurons or by associating the neurons in functionally coherent cell assemblies that are distinguished by synchronous firing. It is proposed that selecting responses and encoding relations through synchronization is particularly well suited for the processing of rare or novel relations for which no conjunction-specific neurons have been implemented.
Plasticity and Functional Brain Development: The Case of face Processing
Authors: Johnson Mark H
Published: November 2023

This commentary addresses the issue of how specialization for visual— cognitive functions arise in the human cortex. Three viewpoints on this issue are reviewed: a maturational view, a skill-learning view, and an ‘interactive specialization’ approach. In considering the example of specialization for face processing, it appears that the interactive specialization view can potentially explain the widest range of phenomena. Many of the chapters in this book concern the extent and nature of specialization of perceptual and attention functions within the human adult cerebral cortex. This contribution, and some of those preceding it (see Chapter 2), focus on the more basic question of how such specialization of function within the cortex arises in the first place.
The Convection-Diffusion Equation
Authors: Elman Howard C , Silvester David J , Wathen Andrew J
Published: November 2023

This equation arises in numerous models of flows and other physical phenomena.
Solution of Discrete Navier-Stokes Problems
Authors: Elman Howard C , Silvester David J , Wathen Andrew J
Published: November 2023

In this final chapter of the book, we bring together our ideas underlying fast solvers for convection-diffusion and Stokes problems to develop effective strategies for solving the discrete systems that arise in the solution of the Navier-Stokes equations.
Community ecology
Authors: Gibson David J
Published: November 2023

Community ecology considers an assessment of all the species in an area and their interactions and is thus a hierarchical step up from population ecology (Chapter 5). To understand the community ecology of grasslands we need to consider the temporal and spatial patterns exhibited by the species and the processes involved in their interactions with each other and their environment. The history of seeking to understand pattern and process in grassland can be traced back to the pioneering field work of ecologists including Cowles (1899), Clements (1936), and Weaver (see Chapter 1), and the theoretical ideas of Gleason (1917; 1926). The ideas from these early studies were brought together by Alex S. Watt in his Presidential Address to the British Ecological Society (Watt 1947). In his address, Watt described how plant communities, including the acidic Breckland grassland in the UK that he studied for over 30 years (Watt 1940; 1981a), are dynamic in time and space reflecting the growth of the different species. He described plant communities as being patchy and a mosaic of different species at various growth stages; a series of small-scale cyclic replacements.
World grasslands
Authors: Gibson David J
Published: November 2023

Grasslands cover a vast area, occupying 41–56 X 106 km2, or 31–43% of the earth’s land surface (Chapter 1). Spread across every continent except Antarctica, grasslands vary in composition and physiognomy depending upon regional and local variations in climate, underlying geology, soil moisture, and disturbance regime (principally grazing and fire regimes). The term encompasses the sparse open communities of desert grasslands as well as the lush ‘sea of grasses’ of the South American Pampas. Summarizing this variation adequately is a challenge.
Disturbance
Authors: Gibson David J
Published: November 2023

Disturbance, defined as ‘any relatively discrete event in time that disrupts ecosystem, community, or population structure and changes resources, substrate availability, or the physical environment’ (White and Pickett 1985) is an integral and import- ant natural phenomenon in grasslands worldwide. The importance of disturbance is that it changes fundamental properties of grasslands at a variety of spatial and temporal scales. Disturbance resets secondary succession (see § 6.2.2). Together, the different types and frequencies of disturbance that characterize grassland define the disturbance regime. Each type of disturbance varies in its spatial distribution, frequency and intensity, predictability, area or size affected, and interaction with other disturbances. Consequently, characterizing and understanding disturbances are critical for understanding grasslands.
Does the perception of moving eyes trigger reflexive visual orienting in autism?
Authors: Swettenham John , Condie Samantha , Campbell Ruth , Milne Elizabeth , Coleman Mike
Published: November 2023

Does movement of the eyes in one or another direction function as an automatic attentional cue to a location of interest? Two experiments explored the directional movement of the eyes in a full face for speed of detection of an after coming location target in young people with autism and in control participants. Our aim was to investigate whether a low-level perceptual impairment underlies the delay in gaze following characteristic of autism. The participants’ task was to detect a target appearing on the left or right of the screen either 100 ms or 800 ms after a face cue appeared with eyes averting to the left or right.
The pathogenesis of autism: insights from congenital blindness
Authors: Hobson R Peter , Bishop Martin
Published: November 2023

There is substantial heterogeneity in the aetiology and clinical presentation of autism. So how do we account for homogeneity in the syndrome? The answer to this question will be critical for any attempt to trace the links between brain pathology and the psychological disabilities that characterize autism. One possibility is that the source of homogeneity in autism is not to be found ‘in the child’, but rather in dysfunction of the system constituted by child-in-relationto- other. We have been exploring this hypothesis through the study of congenitally blind children, among whom features of autism, and the syndrome of autism itself, are strikingly common. To justify such an approach, one needs to establish that the clinical features in blind children have qualities that are indeed ‘autistic-like’. We conducted systematic observations of the social interactions of two matched groups of congenitally blind children who do not have autism, rating their social engagement, emotional tone, play and language during three sessions of free play in the school playground. The qualities of social impairment in the more disabled children were similar to those in sighted children with autism. Additional evidence came from independent ratings of the children in a different play setting: on the childhood autism rating scale (CARS), the socially impaired children had ‘autistic-like’ abnormalities in both social and non-social domains. If we can determine the way in which congenital blindness predisposes to features of autism, we shall be in a better position to trace the developmental pathways that lead to the syndrome in sighted children.