bluuebunny/crossref_metadata_2025_split huggingface dataset:
CW complexes
Authors: Lawson Terry 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
‘Cluster B’ Antisocial Disorders
Authors: Cordess Christopher , Davidson Kate , Morris Mark , Norton Kingsley 
Published: November 2023

Abstract
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.
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.