bluuebunny/crossref_metadata_2025 huggingface dataset:
Fermion Fock space
Authors: Neretin Yu. A , Gould G G
Published: November 2023

In this chapter we shall generalize the constructions in Chapter 1 to the infinite dimensional case.
Functions on locally compact abelian groups
Authors: Reiter Hans , Stegeman Jan D
Published: November 2023

We define here certain auxiliary functions, on arbitrary locally compact abelian groups; they are basic tools in later developments.
Wiener’s theorem and locally compact abelian groups
Authors: Reiter Hans , Stegeman Jan D
Published: November 2023

First, we establish the theorem of Wiener-Levy for 1oca11y compact abelian groups, recalling from Section 4.4 thatFG) is the algebra of Fourier transforms of the functions in L1(G).
Degree Theory in Analysis and Applications
Authors: Fonseca Irene , Gangbo Wilfrid
Published: November 2023

In this book we study the degree theory and some of its applications in analysis. It focuses on the recent developments of this theory for Sobolev functions, which distinguishes this book from the currently available literature. We begin with a thorough study of topological degree for continuous functions. The contents of the book include: degree theory for continuous functions, the multiplication theorem, Hopf`s theorem, Brower`s fixed point theorem, odd mappings, Jordan`s separation theorem. Following a brief review of measure theory and Sobolev functions and study local invertibility of Sobolev functions. These results are put to use in the study variational principles in nonlinear elasticity. The Leray-Schauder degree in infinite dimensional spaces is exploited to obtain fixed point theorems. We end the book by illustrating several applications of the degree in the theories of ordinary differential equations and partial differential equations.
Properties Of The Degree For Sobolev Functions
Authors: Fonseca Irene , Gangbo Wilfrid
Published: November 2023

In this chapter we present a generalization of Sard’s Lemma for Sobolev functions and the following change of variables formulae. Let D ⊂ ℝ𝒩 be open and bounded and assume that either p >N or N −1 < p  ≤  N and Jϕ (x) > 0 ℒN a.e. x ∈ D.
Restoration of 3D Real Images using Projection onto Convex Sets
Authors: Razaz M , Lee R A , Shaw P J
Published: November 2023

The projection onto convex sets (POCS) is a powerful iterative approach for the solution of inverse problems. One can easily incorporate into this approach a variety of useful constraints for image restoration which would otherwise be difficult to implement using the traditional image restoration techniques. We present the application of POCS for restoration of 3D real images. The underlying principle of the method is discussed in detail, and optical microscopy images restored by this method are presented and analysed. It will be shown that POCS is a versatile image restoration method and can produce high quality 1estored images if an appropriate set of constraints are used.
Jigsaws and Faster Fractal Pictures
Authors: Hoggar S G , Menzies L
Published: November 2023

This paper presents a method for accelerating the computation of fractal images using the idea of a jigsaw. The algorithmic details of this technique are presented together with a range of examples.
Analysis of Colour-Level Distribution 1n Filter Backwashing Videos
Authors: Fitzpatrick C S D
Published: November 2023

Granular media filters used in water treatment become dogged due to the accumulation of removed particles on the media grains. Periodic cleaning is required and is achieved by backwashing the filter with upflowing water with or without air scour. Backwashing efficiency can be improved by increasing bed agitation and reducing clean water consumption during cleaning. This is achieved using combined air and water upflow.
Open Problems
Authors: Forster T E
Published: November 2023

Does NF prove that there are infinitely many infinite cardinals’? This is an old question of Specker's, and has resisted protracted assaults by Forster and Pétry. At present it still seems to be consistent with NF that NCI, the set of infinite cardinals, should be finite.
Axisymmetric Black-Hole Collisions At The Speed Of Light: Reduction To Two Independent Variables And Calculation Of The Second-Order News Function
Authors: D'eath P D
Published: November 2023

Here further progress will be described concerning the gravitational radiation emitted in the axisymmetric collision of two black holes at the speed of light. The preceding chapter was concerned with describing the problem and with setting up an analytical treatment using a perturbation approach. In this chapter we describe analytical simplifications which make feasible the numerical calculation of the second-order news function, which gives partial information about the angular distribution of gravitational radiation. Results and conclusions concerning the radiation emitted and consequent mass loss are presented in Chapter 8.
Homotopy Type and Homology
Authors: Baues Hans-Joachim
Published: November 2023

Research mathematicians in algebraic topology will be interested in this new attempt to classify homotopy types of simply connected CW-complexes. This book provides a modern treatment of a long established set of questions in algebraic topology. The author is a leading figure in this important research area.
Introduction
Authors: Baues Hans-Joachim
Published: November 2023

The dimension of Δn is n. The name simplex describes an object which is supposed to be very simple; indeed, natural numbers and simplexes both have the same kind of innocence. Yet once the simplex was created, algebraic topology had to emerge.
Eilenberg-Mac Lane and Moore Functors
Authors: Baues Hans-Joachim
Published: November 2023

We consider three types of Eilenberg–Mac Lane functors given by homology, cohomology, and pseudo-homology of Eilenberg–Mac Lane spaces. While the homology and cohomology of Eilenberg-Mac Lane spaces is extensively studied (see Eilenberg and Mac Lane [I], [II], Cartan [HC], and Decker [IH]), the pseudo-homology of Eilenberg-Mac Lane spaces is not treated in the literature. In our theory of boundary invariants, however, the pseudohomology arises naturally in the same way as the cohomology in the theory of k-invariants. For this reason we describe the cohomology and pseudohomology of Eilenberg- Mac Lane spaces along parallel lines.
Compactness
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall consider the notion of compactness in topological spaces. In particular, we shall characterize compact subsets in metric spaces. Also, for later application, we will present the Arzelà-Ascoli, Stone-Weierstrass and Tychonoff theorems. The reader could skip this chapter and return to it when needed.
Normed spaces
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall consider the notion of (complete) normed spaces which is fundamental in all of functional analysis.
Orthonormal systems
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall concern ourselves with orthonormal systems and orthonormal bases in Hilbert spaces. In order to be able to do this in the specified framework we shall briefly deal with summable families and convergent series in normed spaces.
The Banach spaces Lp(X, µ) and C(X)′;
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we will use the notations and statements from integration theory presented in Appendix A. Unless otherwise stated, we agree that in the sequel X is a locally compact, σ-compact, topological space andµ is a measure on X. Thus we considerµ on one side as a positive linear functional on Cc(X, ℝ) and on the other as a σ-additive set function on the σ-algebra :F of µ-measurable subsets of X (cf. A.25 and A.26). Further, we denote by ℳ, ℳ (X), L1 resp.Nall 𝕂-valued functions on X which are µ-measurable, Borel measurable, µ-integrable, resp. µ-null functions.
Banach algebras
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we give an introduction to the theory of Banach algebras as they allow a simple and elegant derivation of the results in spectral theory in their framework.
Unbounded operators between Hilbert spaces
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

The spectral theory of normal and self-adjoint operators in Hilbert spaces treated thus far has a manifold of beautiful applications in dealing with integral equations. However, it is not suitable for dealing with (partial) differential equations and as a framework for classical quantum mechanics. The theory presented in the following three chapters will achieve this.
Projective and injective topologies
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall generate new locally convex spaces from given ones. For this we shall familiarize ourselves with new concepts and the first applications of the duality theory. In particular, we generalize the closed graph and open mapping theorems of chapter 8. We begin with the two simplest situations, namely the product and the direct sum of locally convex spaces.
Codes
Authors: Curtis Robert T , Morris Tony R
Published: November 2023

In this chapter adjacency matrices of graphs are used to generate binary codes. By placing suitable conditions on the graph, we can ensure that the resulting code has certain desirable properties. In particular, we use the method to construct explicitly all binary self-dual doubly-even codes of length less than or equal to 24. In a recent paper [4], it was shown how the binary Golay code can be obtained from the graph of the icosahedron. In this chapter we exploit the technique of generating codes from graphs and show how, by imposing various conditions on the graph, we can ensure that the resulting code has certain desirable properties. In particular, we are able to produce all self-dual doubly-even binary codes of lengths 8, 12 and 24, simply by writing down a collection of graphs satisfying the conditions.
Topology
Authors: Beineke Lowell W
Published: November 2023

The primary focus of this chapter involves putting graphs on surfaces. Questions that we discuss include the following. Which graphs are planar; that is, which graphs can be drawn in the plane without any edges crossing? If a graph is not planar, what is the smallest number of crossings in any drawing of it? How many planar graphs are needed to form a given graph? In what surfaces can a non-planar graph be embedded? There are many links between graph theory and topology, but the strongest is that of drawings and embeddings of graphs on surfaces. Our survey of this area of mathematics is divided into two parts, the first (Sections 11.2-11.4) on graphs in the plane, including the topics of crossing number and thickness, and the second (Sections 11.5-11.8) on embeddings in other surfaces, both orientable and non-orientable.
Artificial Neural Networks
Authors: Anthony Martin
Published: November 2023

‘Artificial neural networks’ are machines (or models of computation) based loosely on the ways in which the brain is believed to work. In this chapter, we discuss some links between graph theory and artificial neural networks. We describe how some combinatorial optimization tasks may be approached by using a type of artificial neural network known as a Boltzmann machine. We then discuss ‘learning’ in neural networks, where we focus on the amount of training data required and the computational complexity. There has recently been intense, and fast-growing, interest in ‘artificial neural networks’. These are machines (or models of computation) based loosely on the ways in which the brain is believed to work. Neurobiologists are interested in using these machines as a means of modelling biological brains, but much of the impetus comes from their applications. For example, engineers wish to create machines that can perform ‘cognitive’ tasks, such as speech recognition, and economists are interested in financial time series prediction using such machines. Inevitably, there is a certain amount of hype associated with the subject, particularly in relation to neurobiological modelling.
Fungal Populations and Species
Authors: Burnett John
Published: November 2023

Recognizing and discriminating between fungal populations and the genetical processes that accompany them, including speciation is now a rapidly developing field that is heavily dependent upon the use of molecular markers. There was no basic text on this subject, John Burnett has provided such an account. The text describes the methodologies employed and, for the benefit of those without a background in mycology, a brief introduction to basic fungal biology. Recent findings relating to processes in fungal populations—mutation, migration, recombination, heterokaryosis, hybridization, polyploidy, and the operation of selective forces are combined with traditional fungal biology. Finally the taxonomic problems raised by fungal species are discussed, together with the processes of speciation.
Change in gene frequency in fungal populations-I. General considerations: selection for oligogenically determined traits
Authors: Burnett John
Published: November 2023

No organisms, fungi included, are exempt from the process of natural selection (Darwin 1859). The ways in which selection operates and affects fungal populations will be considered in this and the next chapter. Direct evidence of selection operating in natural situations is sparse, although some information is available from agricultural situations and experimental investigations of economically important characters of pathogens of crop plants in growth rooms, glasshouses or, less frequently, the field.
Speciation in fungi
Authors: Burnett John
Published: November 2023

Speciation is a population phenomenon, namely the process or sequence of processes that result in the origin of a new species. Characteristically, all species are adapted more or less effectively to particular habitats, and show either very limited or no gene flow between populations of other species. Therefore the basic processes to understand are as follows.
CW complexes
Authors: Lawson Terry
Published: November 2023

In Section 3.8, where we discussed homotopic equivalences, we showed that if we had a handle decomposition of a surface with one 0-handle and k 1-handles, then we could find a deformation retraction of this surface down to a wedge of k circles. This much of the space can be thought of as being built up from a central point corresponding to the 0-handle and then attaching intervals corresponding to the 1-handles where their end points are all identified to the central point. When the 2-handles are attached, we could compose their attaching maps with this homotopic equivalence and get a space which is built up from a point, some 1-disks attached, and then some 2-disks attached. It turns out that the original surface is homotopic equivalent to this space, which is an example of a two dimensional CW complex. In this chapter we will develop the concepts of CW complexes and apply them to fundamental group calculations as well as discuss homotopy-theoretic ideas concerning them. Our discussion will include finite CW complexes of any dimension, but we will emphasize two-dimensional complexes where the geometry is easier to visualize. We will also discuss important special cases of simplicial complexes and -complexes.
Homology
Authors: Lawson Terry
Published: November 2023

The first homology measures when certain one-dimensional objects such as loops which have no boundary are the boundaries of some two-dimensional objects. As an example, it measures when a loop in a surface is the boundary of a subsurface with boundary, such as how the equator in a sphere bounds the upper hemisphere or the circle where a connected sum in formed bounds the two summands. In general, n-dimensional homology measures when n-dimensional objects which have no boundary are boundaries of (n + 1)-dimensional objects. This is admittedly very vague, and making it precise requires introducing the notion of a chain complex and its homology as well as determining chain complexes which are associated to topological spaces, A-complexes, or CW complexes. In this section we introduce the basic ideas of a chain complex. In succeeding sections, we will look at specific chain complexes related to topology and do some fundamental calculations. We then look at some properties that characterize homology for an important class of topological spaces and use these properties to do more calculations. We will give a number of important applications of homology. It turns out that although homology is somewhat complicated to define, it obeys some properties which make it relatively easy to compute.
Sheaves On A Locale
Authors: Johnstone Peter T
Published: November 2023

In this chapter, our main aim is to describe the ‘geometric’ origins of topos theory, by setting up the topos of sheaves on a topological space, and indicating how topological properties of spaces and continuous maps may be translated into properties of toposes of sheaves and geometric morphisms between them. However, there is a significant ‘generalization’ of the notion of topological space, namely the notion of locale, which is of importance in the topos-theoretic context, and almost everything that can be said about toposes of sheaves on spaces carries over without extra effort to toposes of sheaves on locales. Since the notion of locale may not be familiar to the reader, we therefore begin with a couple of sections setting up the category of locales, and describing its relation to the category of spaces.
Toposes As Groupoids
Authors: Johnstone Peter T
Published: November 2023

The title of this chapter perhaps needs a few words of explanation. Our general thesis throughout Part C has been that the notion of (Grothendieck) topos is a generalization of the notion of topological space (or, better, of the notion of locale). In particular, toposes (or geometric morphisms between them) can be ascribed topological properties such as (local) compactness or (local) connectedness, as we saw in Chapter C3; and the theory of exponentiability for toposes, which we explored in Chapter C4, also has close parallels with that for spaces (or locales). Nevertheless, we know from the examples of toposes we have seen (in Section A2.1 and elsewhere) that, even if we restrict our attention to Grothendieck toposes, there are many which (in their origins, at least) do not appear at all ‘spatial’ in character. So one is tempted to ask whether this generalization is perhaps too large to be genuinely useful.
Aspects Of Finiteness
Authors: Johnstone Peter T
Published: November 2023

The definition and some of the basic properties of natural number objects in a topos were introduced in Section A2.5. However, there were some important properties which could not be developed there because they required the ability to interpret higher-order logic in a topos. Having developed the techniques for this in the previous chapter, we are now ready to return to the study of natural number objects and complete what we left unfinished in Section A2.5.
The general theoretical framework
Authors: Balucani Umberto , Zoppi Marco
Published: November 2023

Since their introduction in the 1960s (Zwanzig 1961; Mori 1965a), projection operators and memory functions pervade many theoretical approaches dealing with the dynamics of strongly interacting systems. In particular, their presence is nearly ubiquitous in the microscopic treatments of liquid state dynamics. Indeed, the idea of describing a many-body system by a limited number of ‘relevant’ variables characterized by a relatively simple dynamics appears to be extremely appealing. Moreover, an analysis of the formally exact expressions of the memory functions can shed light on the nature of the physical processes involved and their relative importance.
Single-particle properties
Authors: Balucani Umberto , Zoppi Marco
Published: November 2023

In Section 3.3 we have seen that the dynamical processes underlying the velocity autocorrelation function in the liquid range cannot be accounted for by a simplified memory-function analysis. In particular, the assumption that the decay of the memory function is ruled by a single relaxation time must be significantly revised in view of the results of the kinetic framework developed in the last chapter.
Angular Momentum
Authors: Brink D M , Satchler G R
Published: November 2023

This book introduces the quantum theory of angular momentum to students who are unfamiliar with it and develops it to a stage useful for research. The first part contains the basic theory of rotations and angular momentum. As the book aims to emphasize applications, mathematical details are avoided and difficult theorems stated without proof. The second part contains examples of applications to a wide range of physical phenomena and presents a collection of results helpful in solving problems.
Crossover from localized moment to local fermi or non-fermi liquid
Authors: Kuramoto Y , Kitaoka Y
Published: November 2023

A fundamental theoretical model that can deal with the Kondo effect is called the Anderson model [1]. In the simplest version of the model, one considers an impurity with a nondegenerate localized orbital in a metallic environment which has a single conduction band with the spectrum ϵ  k The localized orbital has the on-site Coulomb repulsion U, and the electron with spin a is annihilated by the operator f σ.
Experimental trends in bonding and structure
Authors: Pettifor D G
Published: November 2023

The crystal structures of the elements display well-known trends within the periodic table. On a broad scale the close-packed structures that are characteristic of the metallic bond on the left-hand side give way to the more open structures of the covalent bond on the right-hand side. On a finer scale, specific trends are observed such as the hcp → bcc → hcp → fcc sequence across the transition-metal series or the 3-fold coordinated graphitic → 4fold coordinated diamond → 12-fold coordinated fee sequence down group IV from C to Pb. The crystal structures of isostoichiometric binary compounds also display well-defined trends when the experimental data base is presented within a two-dimensional structure map. In addition to structural domains reflecting close-packed metallic or open covalent bonding, ionic domains of stability appear, such as the NaCl and CsCl regions amongst the alkali halides.
Bonding of molecules
Authors: Pettifor D G
Published: November 2023

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH.
Founding Father
Authors: Davison Sydney G , Stęślicka Maria
Published: November 2023

At the beginning of 1932, the journal Physik Zeitschrift der Sowjetunion published the paper ‘On the possible bound states of electrons on a crystal surface’ which indicated, for the first time, the existence of specific electron states (later to be called ‘Tamm states’) localized near the crystal boundary. Subsequently, this article played an important role in the development of the theory of surface and contact properties of solids and their numerous applications.
Mathieu Potential Model
Authors: Davison Sydney G , Stęślicka Maria
Published: November 2023

The first analysis of surface states on the basis of the Mathieu potential was provided by Statz (1950). However, because of the importance of the location of the surface in the first unit cell of the crystal, Levine (1968) carried out a more detailed analysis of the Mathieu problem for conditions of arbitrary termination. It is this latter approach which is adopted here.
Historical Development
Authors: Davison Sydney G , Stęślicka Maria
Published: November 2023

After discussing the mathematical aspects of the theory of surface states, it is worthwhile to spend some time tracing their evolution from both a theoretical and experimental point of view. However, a comprehensive review will not be attempted here, but merely an overview, highlighting the various periods of progress. In this way, it is hoped that the reader will gain some historical perspective of the subject. It is interesting to note that, although the theoretical work of Tamm in 1932 predicted the existence of surface states, fifteen years had to elapse before any experimental evidence was uncovered confirming the possibility of their existence.
Charge Exchange at Relativistic Energies
Authors: Bransden B H , McDowell M R C
Published: November 2023

In ion-atom collision theory relativistic effects enter from two directions. If the nuclear charges ZA or Z8 are sufficiently large, the mean velocity of an electron in an atomic bound state (ve = Z/n) can become comparable with the velocity of light c. Accordingly relativistic corrections, which are negligible for small Z, rxZ ≤ 0.1, where rx is the fine structure constant, become significant for large Zand theatomic or molecular orbitals employed must be based on solutions of the single- or two-centre Dirac equation, or approximations to these. A different source of relativistic effects arises when the collision velocity is large compared with c, the velocity of light. Relativistic kinematics must then be employed, and, in addition, even for small values of ZA and Z8, relativistic atomic orbitals must be used since the momentum distribution of the bound electron, on which high-energy charge exchange depends explicitly, is very different in the relativistic and non-relativistic cases.
Psychotherapy Of Somatoform Disorders
Authors: Lipsitt Don R , Escobar Javier
Published: November 2023

Since medicine’s earliest beginnings, physicians have been perplexed and vexed by patients whose symptoms seem medically unexplainable and who respond poorly to treatment.
‘Cluster A’ Personality Disorders
Authors: Williams Paul , Haigh Rex , Fowler David
Published: November 2023

‘Cluster A’ comprises paranoid personality disorder (PPD), schizoid personality disorder (SPD), and schizotypal personality disorder (StPD). These disorders affect 2%, slightly less than 1%, and 4% of the Western population, respectively, and can be highly disabling.
‘Cluster B’ Antisocial Disorders
Authors: Cordess Christopher , Davidson Kate , Morris Mark , Norton Kingsley
Published: November 2023

Antisocial personality disorder (ASPD) (DSM–IV–R, 1997), dyssocial personality disorder (ICD–10 WHO, 1992), and psychopathy are overlapping terms that are each more or less unsatisfactory in their own particular ways.
Dependent Personality Disorder
Authors: Perry J Christopher
Published: November 2023

Dependency includes universal personality traits, expressed in different ways to some degree over the life span. Like other mammals, humans start out being very dependent upon adults for care and protection, then evolve through maturation and learning into more self–regulating and autonomous individuals.
Psychotherapy For Medical Patients
Authors: White C A , Trief P M
Published: November 2023

Physical illnesses are associated with an increased risk of experiencing psychological problems and disorders. People who are medically ill often have to endure debilitating treatments that can further contribute to this increased risk. Deterioration in quality of life and family functioning can also occur.
Dynamics of the batch MG with fake memory
Authors: Coolen A C C
Published: November 2023

One of the main tools for analyzing the dynamics of disordered stochastic many-particle systems is generating functional analysis. This formalism allows one to carry out the disorder average (which in MGs is an average over all strategies) of dynamic macroscopic observables and take the N →∞ limit exactly.
An introduction to the concept of stereotypy and a historical perspective on the role of brain dopamine
Authors: Cooper Steven J , Dourish Colin T
Published: November 2023

Psychosis associated with the use of amphetamine (benzedrine) was first described by Young and Scoville (1938). Following the Second World War, amphetamine abuse became prevalent, and it was not uncommon for individuals to take large doses of the drug. Cases of amphetamine-induced psychosis ceased to be rarities, and Connell highlighted the problem with the publication of his now classic monograph (Connell 1958). Connell put forward the important proposal that the clinical features of amphetamine psychosis were difficult to distinguish from acute or chronic paranoid schizophrenia. Subsequently, Ellinwood (1967) provided a detailed behavioural description of amphetamine psychosis in individuals who had been taking large daily doses of the drug, and identified the presence of paranoid psychosis, with hallucinations and thought disorder.Attempts were made to discover if amphetamine abuse exacerbated symptoms in predisposed individuals, or could provoke psychotic reactions in non-schizophrenic individuals. Griffith and his colleagues made the first attempt to induce amphetamine psychosis in non-schizophrenic volunteer subjects in a controlled hospital setting (Griffith et al.1968). 10 mg of o-amphetamine was administered hourly, and an abrupt onset of paranoid delusions occurred, but in the absence of thought disorder or hallucinations.
Aspects of stereotyped and nonstereotyped behaviour in relation to dopamine receptor subtypes
Authors: Waddington John L , Molloy Anthony G , O’boyle, Ka Thy M , Pugh Markt.
Published: November 2023

The rise of interest in stereotyped behaviour since the 1960s has occurred in close temporal contiguity with recognition of the important role for the neurotransmitter dopamine in motor function, and identification of the action of various drugs to influence dopaminergic activity. This relationship is often perceived as being of such intimacy that, at least in certain disciplines, stereotypy is in common usage equated automatically with dopaminergic function and drug action on that function. We are reminded in this volume that stereotypy is a broad, long-standing neuropsychological concept with general applicability to behaviour and cognition. It is often overlooked that, in animals, the induction of stereotyped motor behaviour by apomorphine, the involvement of striatal function in its manifestation, and its sensitivity to antagonism by neuroleptic drugs had all been recognized by 1960. At the time of each of these individual studies, it was not yet known that apomorphine was a direct dopamine receptor agonist, that the striatum was a major terminal field of ascending dopaminergic neurones, or that neuroleptics were potent dopamine receptor antagonists (Neumeyer eta/.1981).
Neuropeptides and the issue of stereotypy in behaviour
Authors: Isaacson Robert L , Gispen Willem H
Published: November 2023

When reviewing our research on excessive grooming elicited by the direct administration of neuropeptides or their fragments into the cerebral ventricles or into the brain, itself, in the context of behavioural stereotypy, we were forced to think about the nature and the significance of stereotypy itself. This, in turn, led us to a further step: the consideration of the adaptive significance of the mechanisms underlying excessive grooming-those neural systems that assist members of a species to survive and prosper in their environment.Stereotypy is not simply the reproduction of identical motor responses. This definition is clearly insufficient, even though such behaviour does occur in animals after the administration of large doses of certain drugs, especially dopaminergic agonists. As Douglas emphasized some years ago (1967) and as reinforced by Gaffan and his associates (1984a,b), responses should be considered in terms of their consequences, their outcomes, and what they accomplish. Accordingly, behaviours, even though varied, that all lead to the same, less-than-optimal results or consequences should be regarded as stereotyped.
Graphs and hypergraphs
Authors: Lauritzen Steffen L
Published: November 2023

A graph, as we use it throughout this book, is a pair 𝒢 = (V, E), where V is a finite set of vertices and the set of edges E is a subset of the set V x V of ordered pairs of distinct vertices. Thus our graphs are simple, i.e. there are no multiple edges and they have no loops.
Quasi-likelihood, stochastic processes, and optimal estimating functions
Authors: Desmond A F
Published: November 2023

Recent work on inference for stochastic processes via estimating functions is reviewed. The connections between the notions of quasi-likelihood (Wedderburn 1974) and quasi-scores (Godambe 1985) are outlined in a general semi¬ parametric framework. The emphasis is on obtaining optimal estimating functions within the martingale structure of Godambe and Heyde (1987). By focusing on properties such as linearity and unbiasedness, applied to estimating functions, rather than estimators, finite sample optimality properties similar in spirit to classical ideas such as the Gauss Markov theorem are obtained. There are close connections also with the work of McCullagh (1983), who emphasizes local unbiasedness and local linearity and the asymptotic properties of maximum quasi-likelihood estimates.
Tests of Goodness of Fit, Independence and Homogeneity; with Table of 𝒳2
Authors: Fisher R A , Yates F
Published: November 2023

In the last chapter some use has been made of the 𝒳2 distribution as a means of testing the agreement between observation and hypothesis 𝒳in the present chapter we shall deal more generally with the very wide class of problems which may be solved by means of the same distribution. The element common to these tests is the comparison of the numbers actually observed to fall into any number of classes with the numbers which upon some hypothesis are expected.
Tests of Significance of Means, Differ-Ences of Means, and Regression Coefficients
Authors: Fisher R A , Yates F
Published: November 2023

23. The Standard Error of the Mean The fundamental proposition upon which the statistical treatment of mean values is based is that-If a quantity be normally distributed with variance σ 1, then the mean of a random sample of n such quantities is normally distributed with variance σ2/n. The utility of this proposition is somewhat increased by the fact that even if the original distribution were not exactly normal, that of the mean usually tends to normality, as the size of the sample is increased; the method is therefore applied widely and legitimately to cases in which we have not sufficient evidence to assert that the original distribution was normal, but in which we have reason to think that it does not belong to the exceptional class of distributions for which the distribution of the mean does not tend to normality.
Introduction to glim
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

GLIM is an acronym for Generalized Linear Interactive Modelling. It is a program specially designed to facilitate the fitting of generalized linear models (GLMs). Here we give a brief introduction to the data types handled by GLIM and to the types of statistical model which can be fitted. An outline of the structure of the User Guide is provided together with a brief description of the new facilities in GLIM.
Data structures: definition and input
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

In Chapter 2, we saw that numeric data can be stored in different types of structure: scalars, vectors (consisting of variates and factors), and arrays. We now consider how these structures are defined and how values are given to these structures. We also introduce lists, which are structures in GLIM that are used to store collections of identifiers, and show how lists can be used and manipulated.
Calculations on data
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

GLIM allows calculations to be performed using arrays, vectors, vector elements, scalars, and constants with the result of a calculation being stored or immediately printed out. Various facilities exist for specific statistical and modelling calculations to be performed, for example, GLIM will calculate summary statistics or model parameter estimates when appropriate directives are used. This chapter is concerned with arbitrary calculations and manipulations on data structures under the user’s direct control. Some directives such as GFACTOR and TABULATE perform special-purpose calculations or data manipulations, and are described in the relevant chapters. The most general data structure manipulation directive is CALCULATE which performs vector or vector/scalar arithmetic and includes a number of useful functions. ASsIGN is most useful when an arbitrary sequence of values is to be stored in a vector. The PICK directive may be used to extract values from vectors. There are two directives, GROUP and MAP, for recoding data, and the EDIT directive may be used to alter specific elements of vectors.
Macros
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

Macros in GLIM have two functions: (a) storing text; (b) storing collections of GLIM statements. These statements may then be executed, possibly repeatedly, at appropriate points in the analysis. In either case, the macro is stored in the workspace as text. It may be printed, edited, used as input to other directives (such as GRAPH or PLOT), and substituted as part of the command line. If it contains GLIM statements, it may also be executed, with optional argument passing. If the GLIM statements in the macro fail to achieve the desired effect, it may be traced and debugged interactively. A simple macro editor is provided to change the contents of macros.
User-Defined Models
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

The model specification described in [8] allows those error and link specifications that provide models which are the most commonly used in practice. The specification of a GLM, however, is more general than this, as explained in the Modelling Guide [11]. GLIM has facilities for specifying any model within this more general framework, by users specifying their own error distribution or their own link or both, though the fitting procedure is slightly less efficient than for the standard models. These models are referred to here as OWN models.
Guide to statistical modelling with GLIM
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

This chapter gives a description of the general principles of statistical modelling using the GLIM package. A theoretical treatment is deferred to Chapter 11. Standard models that are subsumed in the GLM family and which can be routinely analysed with GLIM are treated first. Later sections describe many examples of non-standard models that can also be analysed with GLIM. The user may need to refer to the User Guide for more detail. Case studies of analyses for many of these models are given in Chapter 12.
Applications of GLIM
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

This chapter of the Modelling Guide is intended to give a set of more or less complete analyses covering a range of practical problems for which GLIM is useful. The examples are also intended to convey how the various facilities of GLIM, especially the high-resolution graphics, may be used with practical problems, and to provide a useful reference for users with similar problems. The examples given here are designed to cover the most common problems that arise for which univariate modelling is appropriate. They are grouped, mainly, according to the type of response variable of which the main types of interest are continuous (measured), dichotomous (two categories), and counted (frequencies). However there is some overlap so it was not possible to keep rigidly to this scheme.
Faults and Error Handling
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

The sections in [15] describe the normal behaviour of GLIM, that is, when the statements presented are syntactically correct and specify valid operations. In this chapter we describe how GLIM handles exceptions. Such exceptions occur when GLIM detects a potentially dangerous occurrence ([16.1] on warnings), or is presented with a syntactically or semantically incorrect statement or encounters the FAULT directive ([16.2] on faults), or is interrupted by the user while executing a statement ([16.3] on break-ins), or is interrupted by the operating system when detecting a floating point error [16.4], or finds an inconsistency within its own data structures ([16.5] on system faults), or finds a FORTRAN inconsistency which GLIM cannot handle ([16.6] on FORTRAN level faults).
Properties of the Inverse Gaussian Distribution
Authors: Seshadri V
Published: November 2023

For a comprehensive survey of the basic properties of the inverse Gaussian law it is essential to have a clear understanding of the fundamentals of exponential families. The seeds of exponential families were first sown by Fisher (1934) who argued that families of one-dimensional distributions admitting a sufficient reduction have to be exponential. This idea got Dar mois (1935), Koopman (1936), and Pitman (1936) on the trail while some early development can be found in Lehmann (1959) where the details of some basic results on exponential families are introduced. These early ex positions merely scratched the surface until Barndorff-Nielsen (1970) began a systematic study of the exact theory of exponential families culminating in his doctoral dissertation (1973) on exponential families and condition ing (see also Chentsov 1966 for a detailed study of exponential families). The panorama of their structure is portrayed in his classic work (1978a) and complemented in some areas by Johansen (1979). Efron (1978) has provided a new dimension by exploring the geometry of exponential fam ilies. The monograph of Brown (1986) contains a theoretical examination of exponential families with emphasis on decision theory.
Public Health Decision Making: a Sequential Vaccine Trial
Authors: Berry Donald A , Wolff Mark C , Sack David
Published: November 2023

A vaccine for Hcemophilus injluenzce type B is compared in a randomized trial with a placebo vaccine. ‘The trial should end and the vaccine should be abandoned when it becomes clear that it is not sufficienlly effective. And the trial should end when the available information makes it clear that the vaccine is sufficiently effective to be approved for general use by regulatory authorities and recommended for general use by medical authorities. We take a decision-theoretic point of view in which the objective is to minimize the expected number of cases of H. infiuenzce among Navajo Indians during the next several years. We use the available historical information in determining the trial’s design, and update this information as data accumulates from the trial. An important type of information to be assessed is that concerning actions the regulatory and medical authorities will take based on data from the trial. ‘The data that accumulate during the trial includes the time each subject has spent at risk. The design of the trial is sequential; we find optimal designs by numerical calculations using backwards induction. We evaluate optimal designs in an actual trial and compare them with nonsequential designs and with the frequentist design that was actually used in the trial.
Non-informative Priors
Authors: Ghosh Jayanta K , Mukerjee Rahul
Published: November 2023

This paper reviews non-informative priors based on considerations of (i) entropy, (ii) matching what a frequentist might do and (iii) weak minimaxity. Some new results have also been presented. The best way to think of a non-informative prior is, as Bernardo (1979) has argued, as a sort of origin or reference point against which any given p1ior reflecting some subjective opinion can be judged. In fact, it would be quite appropriate to call all candidates for non-informative priors reference priors. However, in what follows, the term reference prior will be used only for the p1iors proposed by Bernardo (1979) and Berger and Bernardo (1989) and the traditional terminology will be used for the other non-informative priors.
The Elusive Concept of Statistical Evidence
Authors: Royall Richard M
Published: November 2023

We examine the fundamental rule for interpreting statistical data as evidence, the Law of Likelihood. The Law’s rationale and implications are sketched, and its limitations are explored via an attempt to extend its scope to include composite hypotheses. Our fundamental question is this: When is it correct to say that one statistical hypothesis is better-supported than another by a given body of observations?. Than is, when is the fact that a random variable x takes on a specific value x properly interpreted as evidence supporting hypothesis H0 in favor of H1? A second question concerns quantifying this evidence: Can we measure its strength? These questions lie at the heart of many applications of statistical methods in scientific inference. Questions of calibrating and revising degrees of belief and problems of choosing from a list of available actions are also important, but analyses aimed at objectively representing and interpreting the data as evidence are central to much of scientific research. A conspicuous example is the practice of using significance tests (p-values) to measure the strength of evidence.
Warranties
Authors: Singpurwalla N D , Wilson S P
Published: November 2023

Consumer products, such as automobiles, often carry warranties such as 5 years or 50,000 miles, whichever comes first. There are two issues of interest, the first being a specification of an optimum price-warranty combination, and the second the forecast of a reserve fund to meet warranty claims. The former involves a consideration of the item’s reliability and the competitors’ actions, and the latter involves the analysis of a time series in two dimensions for which the use of Bayesian methods is natural. In this expository paper we overview the warranty problem and suggest strategies for addressing the ensuing issues.
Advances in Bayesian Experimental Design
Authors: Verdinelli Isabella
Published: November 2023

In this paper, current issues and recent advances in the Bayesian design of experiments are outlined. The unifying view of Bayesian decision theory is emphasized in order to include old and new optimality criteria derived from suitable utility functions. A special case is considered to illustrate the behavior of different designs and to show their sensitivity to the particular features of the experiment. Further research topics are briefly outlined and future directions to be taken are also described.