bluuebunny/crossref_metadata_2025 huggingface dataset:
Action planning affects spatial localization
Authors: Jordan Jerome Scott , Stork Sonja , Knuf Lothar , Kerzel Dirk , Müsseler Jochen
Published: November 2023

Abstract. When observers are asked to indicate the 1nal position of a moving stimulus, their localizations are reliably displaced beyond the 1nal position, in the direction the stimulus was traveling just prior to its offset. Recent experiments indicate that these localization errors depend on whether or not observers track the moving stimulus with eye-movements. If they track, there is a localization error; if not, the error reduces to zero. The present series of experiments investigated whether localization error might be due, in part, to the binding of the moving stimulus in an action plan. Experiment 1 utilized circular stimulus trajectories, and the eye tracking/ no-tracking discrepancy revealed in previous studies was replicated. Experiment 2 required central 1xation by all observers, and either the computer program (i.e. induction) or a button press by the observer (i.e. intention) produced the stimulus offset.
Variation in extinction risk and species richness
Authors: Bennett Peter M , Owens Ian P F
Published: November 2023

In the previous sections we investigated how living birds have evolved a diversity of solutions to the problems of growing, surviving, mating, and providing parental care for their offspring. These problems have engaged biologists from Darwin onwards and were those tackled by David Lack in Ecological adaptations for breeding in birds. In recent years, however, the increasing threat posed by human disturbance to natural environments has brought a series of new challenges for biologists.
The Combinatorics of some Abstract Data Types
Authors: Atkinson M D , Tulley D
Published: November 2023

Abstract data types (ADTs) may be regarded as abstract machines and then a program for an ADT is any sequence of operations allowed by its speciflcation. The effect of such programs on container ADTs is captured by the relationship between each input sequence and the set of possible output sequences that can result from it. This relationship is studied principally in the case of dictionaries, stacks and priority queues and a distinction is drawn between ADTs of unbounded and bounded capacity. Abstract machines have a long and honourable history in Computer Science. Turing machines, push-down automata, and flnite-state machines are three well known types; they have been used to study general purpose computers, compilers, and string manipulation although their importance goes well beyond these three applications. The central theoretical issue for these (and other) machines is the characterisation of the languages associated with them. The aim of this paper is to study some abstract data types in the same spirit.
The Regular Coloration of Graphs
Authors: Everett M G , Borgatti; S P
Published: November 2023

A regular coloration of a graph is an assignment of colours to the vertices which obeys the rule that if two vertices are coloured the same then their neighborhoods have the same set of colours. If the graph represents a social system then vertices which are coloured the same can be thought of as playing the same role. We investigate the concept of regular coloration and present some results which allow for the development of algorithms which can be used to analyze social network data. Graph theory has been extensively used as a model in the social sciences. The vertices of a graph represent individuals or groups of individuals. The groups can be as diverse as political parties, countries or family groups. The edges represent interpersonal or intergroup relations, for example “likes”, “hates”, “agrees”, “communicates with”, “married to”, “allied with”, “trades with” etc. Clearly this model can give rise to both digraphs and graphs.
A Constructive Algorithm for Neural Network Design with Application to Channel Equalization
Authors: Sweatman* Catherine Z W Hassell , Gibson; Gavin J , Mulgrew* Bernard
Published: November 2023

We describe a deterministic algorithm for designing a multilayer perceptron (MLP) [11] for the solution of a two-state classiflcation problem. This algorithm is illustrated in the context of channel equalization [4], but is more generally applicable. Attention is restricted to MLPs with one hidden layer of nodes and a single output node (see [3] and Figure 1). The outputs of the nodes in the flrst (hidden) layer are the inputs to the output node.
Multi-Function Coding and Modulation for Spread Spectrum and CDMA with Inherent Security
Authors: Smith D H
Published: November 2023

Currently, spreading sequences for spread-spectrum communications and sequences for CDMA (code division multiple access) systems typically use codes whose auto- and cross-correlation properties are optimized for the characteristics of the channel in question. If security is desired, this is added as a further layer of coding. Sequences exist, however, which combine both desirable modulation characteristics and strong cryptographic properties. The most promising of these appears to be the sequences produced by the Blum Generator, which has been shown to possess a very high degree of randomness [l]. This generator has already been used to provide the key sequence for a public key stream cipher radio scheme [2] and so a natural extension of this is the use of such sequences as spreading codes, which as well as offering the advantages of spread spectrum communications,
Physical principles of field ion microscopy
Authors: Miller M K , Cerezo A , Hetherington M G , Smith G D W
Published: November 2023

In this chapter, the basic physical processes involved in field ion microscopy and atom probe analysis are discussed. For reasons of space, full derivations are given only for the most important relationships. References are given for more advanced mathematical treatments. 2.1 Electric Field Distribution Knowledge of the distribution of the electric field and potential within the FIM is of fundamental importance, since the potential distribution between the specimen and the imaging screen determines the overall trajectories of the gas ions, the nature of the image projection and the magnification in the FIM. It also dictates the rate of ion acceleration in the atom probe and the trajectories of the field evaporated ions. Regional differences over the specimen surface control the local gas supply function and affect the local rates of field ionization and evaporation. Atomic scale variations of the field determine image contrast and also influence the initial stages of the field evaporation process, producing small aberrations in ion trajectories which limit the spatial resolution attainable in atom probe analysis.
Statistical analysis of atom probe data
Authors: Miller M K , Cerezo A , Hetherington M G , Smith G D W
Published: November 2023

In this chapter, the statistical methods for analysing conventional and three-dimensional atom probe data are presented. Most of the statistical methods that are applicable to atom probe data are based on probability theory and the analysis of time series (an ordered set of observations of a phenomenon which moves through time or space such as a composition profile). The main focus is on the characterization of fine-scale microstructures for which the atom probe is uniquely appropriate. Several worked examples are presented to illustrate the various statistical methods. 5.1 Introduction The goal of the analysis of atom probe data is the characterization of a threedimensional microstructure from the sequence of detected ions. However, the interpretation of the data is not necessarily straightforward and has to be performed with an awareness of the common pitfalls. Obvious questions which may be posed in estimating the scale or magnitude of a composition variation are what is the best method to make the estimate, how accurate is this estimate, is the estimate biased or unbiased, how dependent is the estimate on any implicit or explicit model of the microstructure and to what degree are the estimated parameters characteristic of the scale and magnitude of composition fluctuations in the bulk materialã There is no single or simple answer to these questions; the answer depends on the correct formulation of the problems with the use of appropriate models.
Dynamics Of A Black Hole In A Background Universe
Authors: D'eath P D
Published: November 2023

The perturbation theory described in Chapter 2 is concerned with linear perturbations superimposed on an asymptotically flat Kerr solution, thereby ignoring the presence of the rest of the universe. However, one sometimes needs to understand the way in which a black hole fits into the surrounding space-time. For example, the rotating black hole may be interacting with matter of comparable or much greater mass, as in a galaxy or in cosmology, in which case the perturbation approach just mentioned is inadequate, and one should take into account the perturbations of the black hole produced by the matter, the perturbations of the external geometry produced by the black hole, and the motion of the black hole relative to the matter. A technique is presented here for dealing with this type of situation (D’Eath 1975a). This problem was also studied in the case of a Schwarzschild black hole by Manasse (1963) and Demianski and Grishchuk (1974). The ‘external universe’ may also be the geometry produced by another massive object, such as a black hole, neutron star, or other compact body. The case of two black holes in nearly Newtonian orbit around each other is described in the following Chapter 4 (D’Eath 1975b). These matching ideas are still viable for compact bodies which are not black holes (Kates 1980a; Damour and Taylor 1992).
Gravitational Radiation From High-Speed Black-Hole Encounters
Authors: D'eath P D
Published: November 2023

Let us turn now to the gravitational radiation emitted in black-hole encounters, which becomes more and more significant as one increases the approach velocity. A review which covers the subject of gravitational wave generation is given by Thorne (1987). As described in Chapter 4, one can study the interaction of two black holes using perturbation theory in various different regimes. First, one can take, as in Chapter 4, the case of a low-velocity quasi-Newtonian interaction, where the black holes’ paths are either approximately bound or unbound Newtonian orbits. Second, one can take the case of a distant encounter of two black holes at relativistic speed (but not too close to the speed of light), with deflection by a small angle (Thorne and Kovacs 1975; Kovacs and Thorne 1977; 1978; D’Eath 1979b). If the relativistic encounter is close, then the usual perturbation methods will break down, as strong-field effects will appear. Third, one can take an encounter of two black holes with relative velocity close to the speed of light. Here, instead of taking (for example) the masses as small parameters, one uses γ−1 as a small parameter, where ‘Y is a typical Lorentz factor (measured in a centre-of-mass frame) of an incoming black hole. This leads to a new type of perturbation theory, which is valid even for head-on collisions (Chapters 6, 7, and 8), giving the gravitational radiation emitted near the forward and backward directions (D’Eath 1978; D’Eath and Payne 1992a-c). The results on gravitational radiation for all three regimes merge smoothly together. The first two regimes will be summarized briefly in Section 5.2. The third regime is the topic of the rest of this chapter, and is related to the work on collisions at the speed of light described in the following Chapters 6, 7 and 8.
Conclusion
Authors: D'eath P D
Published: November 2023

The examples of black-hole interactions treated in this book show the power gained by the use of matched asymptotic expansions in general relativity. This technique, in fact, seems very well suited to a variety of problems involving the interaction of strongly self-gravitating systems, and in one case—as in Chapters 5-8—to a strong-field interaction between strong-field systems, namely the collision or close encounter of two black holes at or near the speed of light.
Dual maps
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall characterize, with the help of the bipolar theorem, those continuous linear maps between Banach spaces which have a closed range. For this, we shall next introduce the notion of a dual map.
Hilbert spaces
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall show that those Banach spaces whose norms are induced by a scalar product have particularly elegant properties. A scalar product is defined as follows.
The spectral theorem for normal operators
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter H denotes a non-trivial complex Hilbert space. Then, by 17.15(4), L(H) is a C*-algebra. Thus we can apply to L(H) the notions and results from Chapter 17. In particular, it is clear what self-adjoint, normal and unitary operators in L(H) are.
The spectral theorem for unbounded self-adjoint operators
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall prove the spectral theorem for self-adjoint (unbounded) operators A in Hilbert spaces. It says that for each A there exists a unique spectral measure E on a(A), so that A = ∫ t dE. In the sequel H is a complex Hilbert space.
Nuclear spaces
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

In this chapter we shall consider the class of nuclear spaces introduced by Grothendieck. We prove their fundamental properties and show that many important spaces in analysis are nuclear.
A Boundary Value Problem for the Laplacian in a Multi-Structure
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander
Published: November 2023

In the present chapter we consider a multi-structure ‖;ε defined as a union of a three-dimensional domain and a number of thin cylinders of normalised thickness ε parallel to each other (see Fig. 2.1). We deal with the asymptotic analysis of a solution u of a mixed boundary value problem for the Laplacian operator in ∂‖;ε.The Dirichlet data are prescribed on the bases of thin cylinders; on the remaining part of the surface ∂Ωε we have the Neumann boundary condition. We note that the solution of this problem describes the temperature field in the multistructure for the case when the heat flux is specified on the boundary surface outside the base regions of the thin cylinder, where the values of the temperature are given.
International Finance
Authors: Biggs Norman
Published: November 2023

Exchanges among a given set of currencies define a graph, and the rates of ex- change satisfy a condition which can be described in terms of a potential function on the graph. Using this approach, the matrix-tree technique is applied to show that the balance of payments determines a unique system of exchange rates. Let V be a set of currencies and E the set of pairs of currencies that can be exchanged directly. Clearly, there is a corresponding graph G = (V,E). The aim of this chapter is to explain how such a network of exchange rates can be studied in graph-theoretic terms. If every pair of currencies is exchangeable, then the graph is a complete graph, but this will not generally be the case, and the theory is not restricted to complete graphs. However, for our purposes it is reasonable to assume that the graph is connected, which means that any two currencies can be converted indirectly, by a sequence of exchanges involving other currencies.
Introduction
Authors: Burnett John
Published: November 2023

The majority of plant or animal populations studied exist as groups of diploid individuals of limited growth that reproduce sexually. In contrast, the majority of true fungi are haploid, are capable of potentially unlimited growth provided nutrients are available for them to absorb and can reproduce sexually, or propagate clonally, by means of genetically identical mitotically produced spores.
Genetic markers for population studies-I Morphological, physiological, and cytological markers
Authors: Burnett John
Published: November 2023

Traditionally, quantitative and morphological traits have been employed most frequently in the description of species, variants and variation. For population studies, however, there is a need for discrete characters which vary within the species that can be used as markers to recognize or differentiate populations. It is especially useful if the markers used have a known genetic basis, and, indeed, the use of genetic markers-discrete differences in genetic information possessed by different individuals within a species-is the preferred option.
The generation of variation-Ill Recombination through heterokaryosis, parasexuality, hybridization and polyploidy
Authors: Burnett John
Published: November 2023

Hybridization and polyploidy are not uncommon amongst diploid Eukaryota, although the significance accorded to them as evolutionary processes continues to be debatable, but these processes are poorly documented in fungi. In contrast, hetero karyosis and para sexuality are much less common in diploid Eukaryota but well documented in Eumycota where they are seen to be a reflection of the structure and biology of the fungal mycelium. However, all four of these processes in fungi are far better known and studied in the laboratory than in natural conditions where the question of how they affect populations of both Eumycota and Straminipila is still far from clear.
Ethologist in the 1930s
Authors: Kruuk Hans
Published: November 2023

The Tinbergens returned to Holland on a high; many people knew about the expedition and admired the pluck of Niko and Lies. Their arrival back home in September 1933 was soon followed by articles in the Dutch popular press and pieces written by Niko himself,1 and obviously they could capitalize on their stories for a long time. In the world of birdwatchers Niko’s tales of phalaropes, snow buntings, and gyr-falcons made news, and as far as his Dutch friends were concerned, he had become an ornithological world authority. There was the fabulous collection of Eskimo art and utensils, and his first-hand knowledge of life in the cold. It was something like fame, with all its time-consuming trimmings.
Niko’s two worlds: Oxford in the 1960s
Authors: Kruuk Hans
Published: November 2023

Looking back at the 1950s, one gets an impression of Niko’s life as hectic, confused, and torn in many directions. But at the beginning of the next decade it gained stability, and he appeared to come to terms with his niche in Britain. At least he seemed to settle down, into two separate existences, related but firmly apart, literally racing from one to the other. One of these worlds was in the field, in his wide-open spaces, in the dunes somewhere in the north of England, or in the Serengeti in Africa. His other world was in the Zoology Department in Oxford.
The fundamental group and its applications
Authors: Lawson Terry
Published: November 2023

In this chapter we study, through the example of the fundamental group, the general method of algebraic topology. We give a means of associating to a geometric problem a (hopefully easier) algebraic problem to solve. Consider the problem of distinguishing between two surfaces. How can we tell, for example, that there is no homeomorphism between the sphere and the torus? According to algebraic topology, to solve this problem we should transform it into an algebraic problem that is readily solved. To each topological space X, associate to it some algebraic object, say a group g(X). Do this in such a way that homeomorphic spaces have isomorphic groups associated to them. Thus one way of telling that X is not homeomorphic to Y is by showing that g(X) is not isomorphic to g(Y). Of course, this works only when we can readily compute g(X) and g(Y) and decide whether or not they are isomorphic. This method is successful in distinguishing between surfaces.We now formalize the informal discussion above. In this section, we start by discussing briefly the concept of a group. Readers with a previous course in abstract algebra should just skim over the group theory material in this section to become familiar with our notation and viewpoint. We then apply these ideas to discuss how algebraic topology uses group theory to answer topological questions. In later sections and chapters, we will introduce more sophisticated results from group theory as it is needed.
Classes Of Geometric Morphisms
Authors: Johnstone Peter T
Published: November 2023

Our aim in this chapter is to revisit some of the ‘topologically inspired’ classes of geometric morphisms which we introduced in Section C1.5, in the context of morphisms between localic toposes, and to investigate their properties in the more general context of morphisms between Grothendieck toposes. As in Section C2.4, we shall henceforth interpret ‘Grothendieck topos’ loosely as meaning any topos defined and bounded over a base to pos 𝒮 having a natural number object; but we shall often treat 𝒮 notationally as if it were the classical category Set of sets, relying on the reader to translate our arguments as required into the language of 𝒮-indexed categories as developed in Part B.
Reversible and irreversible work processes
Authors: Carrington Gerald
Published: November 2023

In this chapter we introduce some basic results deriving from the second law. These concern the work performed on systems undergoing reversible and irreversible work processes. We shall also introduce work processes on systems other than fluids. The reversible process theorems (Haywood 1980) are analogous to the Carnot theorem, but they apply to non-cyclic processes, whereas the Carnot theorem applies to cyclic processes. We shall use the Kelvin-Planck expression of the second law in order to establish these theorems.
Electric and magnetic work processes
Authors: Carrington Gerald
Published: November 2023

Several different types of work process may be identified when matter is subject to electric and magnetic fields. Consequently there are a number of expressions for the work performed. Each is useful in a particular physical situation. This chapter provides an introduction to these work processes and to the thermodynamic functions associated with them. While we shall refer to this material in subsequent chapters it may be passed over on a first reading without loss of continuity.
Fundamental properties of electrons in solids
Authors: Kuramoto Y , Kitaoka Y
Published: November 2023

Electrons in metals have an effective mass m* which is in general different from the mass in vacuum, mo= 9.1 ×1028g Experimentally, m* can be measured by such methods as cyclotron resonance, de Haas-van Alphen (dHvA) effect, specific heat, and so on.
Metallic and insulating phases of heavy electrons
Authors: Kuramoto Y , Kitaoka Y
Published: November 2023

In the previous chapters, we have seen that the magnetic and thermal properties of heavy electrons are determined basically by strong local correlations. A signature of the local nature is that the susceptibility and specific heat are approximately proportional to the concentration of Ce in systems such as CexLa1-xCu6 or CexLa1-xBu6 The RKKY interaction is operative in bringing about magnetic ordering. Its energy scale is given by JRKKY × J2Pc, where J is the exchange interaction between f and conduction electrons and Pc is the density of conduction band states per site. The RKKY interaction competes with the Kondo effect which points to the nonmagnetic singlet ground state. There exists a rather detailed balance bel\veen these two tendencies. It is expected that the magnetic transition temperature TM, if it exists, is lowered due to the Kondo effect. In the opposite case, TK » J2Pc, no magnetic order should occur.
Anomalous magnetism
Authors: Kuramoto Y , Kitaoka Y
Published: November 2023

In this chapter, we discuss magnetically ordered or nearly ordered states of heavy electrons. In describing heavy-electron magnetism, there are two complementary pictures one can consider. First, one can regard a heavy-electron system as a lattice of Kondo centres coupled to each other by the RKKY interaction. Of central interest is the competition between the RKKY interaction toward magnetic order and the Kondo screening toward the nonmagnetic singlet state. The RKKY interaction is mediated by conduction band electrons which are only weakly renormalized.
Introduction
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco
Published: November 2023

Nuclear physics with electromagnetic probes has its roots deep in the early years of modem physics. Soon after the discovery of the Dirac (1928) equation for the relativistic electron, Mott (1929) derived the cross-sectional formula for the scattering of Dirac particles by point nuclei. Just two years after the discovery of the neutron by Chadwick (1932), which indicated the composite nature of nuclei in terms of nucleons, the photodisintegration of the deuteron by Chadwick and Goldhaber (1934) may be considered the first photonuclear experiment.
Two-Nucleon Emission
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco
Published: November 2023

The occurrence of two-nucleon emission processes induced by electromagnetic probes gives an unambiguous signature of nucleon-nucleon correlations in nuclei. The available data, obtained by making either inclusive (e,é) or coincidence experiments, have provided strong evidence that these processes play a relevant role in extended kinematical regions. The depletion of the occupancy of various shells, observed throughout the periodic system in recent high-resolution (e,ép) experiments in the quasifree region (see Chapter 7), suggests a considerable hole strength at large missing energy, which, according to the results of many-body calculations, is the effect of shortrange NN correlations (SRC). Moreover, the results of they-scaling analysis of (e,é) data (see Section 10.3) in the low-energy-loss tail of the quasielastic peak and the (e,ép) cross sections measured at large recoil momentum and missing energy clearly show the existence of high-momentum components in the nuclear wave function, owing to strong NN correlations.
Bonding of transition metals and semiconductors
Authors: Pettifor D G
Published: November 2023

The only elements with cohesive energies greater than 7 eV per atom are sp-valent carbon (7.37 eV) and the sd-valent transition metals niobium (7.57 eV), tantalum (8.10 eV), tungsten (8.90 eV), rhenium (8.00 eV), and osmium (8.17 eV), as can be seen from Fig. 1.7. Interestingly, carbon with its saturated covalent <J bonds does not have the highest cohesive energy, this honour belonging to the transition metal, tungsten. The transition metals are not describable by the conventional NFE model of the metallic bond since their valence d electrons remain relatively tightly bound to their parent atoms, forming unsaturated covalent bonds with their neighbours. These d bonds are responsible for the structural and cohesive properties of transition metals.
Structural trends within solids
Authors: Pettifor D G
Published: November 2023

Elemental solids and binary compounds display numerous well-defined structural trends. We saw in chapter 1 that we would like theory to be able to explain at least the following: 1) the change from close-packed structures on the left-hand side of the periodic table to the more open structures on the right-hand side;

(2) the 8-N rule which gives the number of neighbours expected for N ~ 4,and exceptions to the rule such as graphitic carbon and dimeric nitrogenand oxygen; In this chapter we will show that the tight binding (TB) description of the covalent bond is able to provide a simple and unifying explanation for the above structural trends and behaviour.
Diffuse scattering theory
Authors: Nield Victoria M , Keen David A
Published: November 2023

In the previous chapter an introduction to neutron scattering formalism was given. This formalism can be used directly to calculate the diffuse scattering for various specific models of disorder, provided an atomic model reflecting this disorder can be produced. An example of this is given in §3.2 below. The equations can also be modified to be applied more easily to certain specific types of material, such as molecular materials with orientational disorder (§3.3 and §3.4). In both these cases the calculated diffuse scattering can then be compared with the experimental data. In other cases theoretical methods are used to extract meaningful information directly from the experimental diffuse scattering data.
Diffuse scattering from molecular materials
Authors: Nield Victoria M , Keen David A
Published: November 2023

In Chapter 3 the underlying theory of diffuse scattering from orientationally disordered materials was considered. In studying these materials the relative positions of the molecules, and the reorientations that they undergo, are usually the features under study. The internal structure of the molecule can also be studied, and often details of the intra-molecular structure are necessary to explain the orientational information. This is particularly the case if the orientations are affected by the orientations of neighbouring molecules for steric reasons (as shown in Fig. 3.1, and discussed in §3.1.1).
Nearly-Free Electron Approach
Authors: Davison Sydney G , Stęślicka Maria
Published: November 2023

Although Maue (1935) was the first to use the nearly-free electron approximation (NFE) to study surface states, and their effect on the electrical conductivity of a metal, it was the subsequent generalization of the method by Goodwin (1939a) that eventually brought it into prominence. Unlike Goodwin's three-dimensional treatment, a one-dimensional one is developed here, for the sake of simplicity.
Inelastic Ion-Atom Collisions - Coupled Channel Models
Authors: Bransden B H , McDowell M R C
Published: November 2023

In this chapter we shall begin to develop the quantum theory of inelastic ion atom collisions. In order to discuss the basic concepts without inessential complication, the theory will be developed for a simple system composed of a single electron and two inert singly charged ions A+ and B +. This will allow us to discuss charge exchange reactions like H+ + H( 1s) -+ H(n/m) + H + and H + + Li0 -+ H(n/m) + Li+ where, in the second example, Li+ is treated as an inert core interacting with the electron through an effective potential. The restriction to singly charged cores and one-electron systems will be removed later.
Applications of the Coupled Channel Impact Parameter Model
Authors: Bransden B H , McDowell M R C
Published: November 2023

In this chapter a number of illustrative examples of the application of the coupled channel impact parameter model introduced in Chapter 3 and developed in Chapter 5 will be discussed. First let us recollect the conditions under which this model can be applied. A basic assumption is that the internuclear motion can be described by a single classical trajectory determined by an effective potential W(R) at an energy in the centre-of-mass system of E = µv6/2. The resulting coupled equations for the probability amplitudes A/b, t) are of the form (3.205). The conditions for the validity of these equations, or the equivalent set of equations (3.131), were analysed in Section 3.6. They can be summarized as follows.
Intermediate Energies
Authors: Bransden B H , McDowell M R C
Published: November 2023

The full coupled channel model in which the direct and exchange channels receive equal representation in the wave function is the principal method for calculating ion atom cross sections at low velocities, v0/ve :s; I, where ve is the Bohr velocity of the active electron in the target. This model can also be employed at arbitrarily high velocities, provided the continuum is sufficiently well represented in the eigenfunction expansions; but at high velocities, for example v0/ve ;::: 2, it is natural to consider perturbation and distorted wave methods. Perturbation methods based on the coupled equations have been discussed in Chapter 7, and the topic will be taken up in a more general way in Chapter 10. Leaving aside such true high-energy methods, there are a number of approximations which are particularly suitable for the computation of cross sections outside the low-velocity region, up to moderate, but not extremely high, velocities. In this intermediateenergy interval possible approaches, described in this chapter, are to employ a simplified coupled channel model, based on single-centre expansions, to develop appropriate optical potentials, and, very different in spirit, to apply classical mechanics to the three-body problem presented by the two heavy particles and the active electron.
Non-Relativistic Models at High Energies
Authors: Bransden B H , McDowell M R C
Published: November 2023

In this chapter, we shall be concerned with charge exchange at high impact velocities for which methods based on perturbation or distorted wave series are appropriate, but for which a non-relativistic formulation remains accurate. This high-velocity region cannot be precisely defined, but as a guide we can take v0/ve 3 4 where v0 is the incident velocity and ve the Bohr velocity of the active electron in the target. Relativistic corrections for collisions between light ions become significant when v0 ≤ 60 a.u. and we shall consider the modifications required to the theory to take account of these in the next chapter. It is interesting to consider the mechanisms which allow the capture of an electron from a target atom (B + -e ) by a very fast ion A. (A very full analysis has been given by Shakeshaft and Spruch (1979)). In a reference frame centred on the ion A, the initial electronic energy (kinetic) of V6/2 is large, while the final electronic energy, after capture, of the atom (A+ e-) is small. The different mechanisms for capture correspond to different means of effecting this change of energy. The first possibility is radiative capture, A + (B + e-) -> (A + e-) + B + hv. At sufficiently high energies, the ion B acts as a spectator and the cross section is effectively that for radiative capture of a free electron by the moving ion A. This process will be discussed in Chapter 11. All that needs to be noted here is that although the cross section for radiative capture is small at low impact velocities it decreases less rapidly (like E- i or v0 2) than non-radiative capture cross sections and is the dominant process at high energies. This occurs at impact energies in excess of ~ 10 MeV/a.m.u. for collisions between light ions.
Paraphilias
Authors: Fagan Peter J , Lehne Gregory , Strand Julia G , Berlin Fred S
Published: November 2023

Individuals with paraphilia entering psychotherapy often have led a very secret sexual life for many years. Therapy may be their first opportunity to speak with another about impulses, urges, and behaviors that may have been at best a curiosity and at worst a torment. Therapy can be rewarding as therapist and patient speak about thoughts, feelings, and behaviors that have heretofore been shrouded in secrecy, often regarded with shame, a source of pleasure as well as a possible source of suffering for the self or others.
Sexual Orientation and Psychotherapy
Authors: Phillips Sidney H , Richardson Justin , Vaughan Susan C
Published: November 2023

Setting aside a chapter to explore the implications of our patient’s sexual orientation on their psychotherapy suggests that the treatment of gay, lesbian, and bisexual patients differs from the work we do with our heterosexual patients. In many ways, of course, it doesn’t.
Ethics and Psychotherapy
Authors: Adshead Gwen
Published: November 2023

The term ‘ethics’ can be defined in many ways. In the context of mental health care, any discussion about an ethical dilemma involves a special type of dialog; the discourse of ‘ought’ and ‘should’ in interpersonal relationships.
Stereotyped motor phenomena in neurological disease
Authors: Stoessl A J
Published: November 2023

Stereotyped behaviour can be regarded as that which is repetitive, purposeless, and involuntary, often interfering with normal behaviour. Such behaviour is generally a consequence of disruption of the normal chemical milieu of the central nervous system and, in humans, stereotypy is usually seen as an unwanted side-effect of medications or, in the context of primary disease of the nervous system, as one of the so-called movement disorders. The taxonomy of the movement disorders is controversial and often confusing even to those well versed in neurology. One approach is to divide the disorders into those in which motor activity is either increased (hyperkinetic) or decreased (hypokinetic) or those predominantly affecting tone (i.e. the resistance to passive movement). Even this classification has its difficulties, since Parkinson’s disease, for example, one of the commonest movement disorders, is characterized simultaneously by too little motor activity (bradykinesia), excessive movement (tremor), and increased muscular tone or rigidity. For the purposes of this chapter, we will first deal with primary hyperkinetic disorders, and then discuss drug-induced involuntary movements. The hyperkinetic disorders can be subclassified into tremor, chorea, tic, myoclonus, and dystonia.
Introduction
Authors: Lauritzen Steffen L
Published: November 2023

Graphical models have their origin in several scientific areas. One of these is statistical physics. Here the ideas can be traced back to Gibbs (1902). The object of interest is a large system of particles, possibly the atoms of a gas or solid. Each particle is occupying a site where it can be in different states. The total energy of the system is composed by an external potential plus a potential due to interaction of groups of particles. It is usually assumed that only particles at sites close to each other interact.
Models for mixed data
Authors: Lauritzen Steffen L
Published: November 2023

In this chapter we unify the graphical models developed for contingency tables and for the multivariate normal distribution. At the same time we extend the theory and methodology to deal with variables of which some are qualitative - as discussed in the chapter on contingency tables - and some are quantitative - as in the chapter on multivariate normal models. The results in this chapter will eventually contain many of the results already described.
On optimal estimating functions for partially specified counting process models
Authors: Greenwood P E , Wefelmeyer W
Published: November 2023

Consider a semimartingale with predictable characteristics depending on a one-dimensional parameter&. Suppose that the associated martingale problem does not have a unique solution. We are interested in efficient estimation of &. Thavaneswaran and Thompson (1986) and Heyde (1987) give versions of Godambe’s optimality concept based on estimating functions in this setting. For a counting process model, we compare their concepts with asymptotic efficiency based on the partially specified likelihood process. We give conditions under which the notions are asymptotically compatible.
Tests based on an optimal estimate V
Authors: Thavaneswaran A
Published: November 2023

A general framework for constructing test statistics in stochastic models based on an optimal estimate is developed. Martingale limit theorems are used to prove the asymptotic normality and strong consistency of the optimal estimate.
Estimating functions in semi-parametric models
Authors: Ritov Ya’ acov
Published: November 2023

Suppose we have a random sample from a distribution which is only known to belong to some non-parametric family and we wish to estimate some parameter of this distribution. Under some regularity conditions this parameter can be estimated in a rate.
Introductory
Authors: Fisher R A , Yates F
Published: November 2023

1. The Scope of Statistic The science of statistics is essentially a branch of Applied Mathematics, and may be regarded as mathematics applied to observational data. As in other mathematical studies, the same formula is equally relevant to widely different groups of subject-matter. Consequently the unity of the different applications had usually been overlooked, the more naturally because the development of the underlying mathematical theory had been much neglected. We shall therefore consider the subject-matter of statistics under three different aspects, and then show in more mathematical language that the same types of problems arise in every case. Statistics may be regarded as (i) the study of populations, (ii) as the study of variation, (iii) as the study of methods of the reduction of data.
Diagrams
Authors: Fisher R A , Yates F
Published: November 2023

7. The preliminary examination of most data is facilitated by the use of diagrams. Diagrams prove nothing, but bring outstanding features readily to the eye ; they are therefore no substitute for such critical tests as may be applied to the data, but are valuable in suggesting such tests, and in explaining the conclusions founded upon them.8. Time Diagrams, Growth Rate, and Relative Growth Rate The type of diagram in most frequent use consists in plotting the values of a variable, such as the weight of an animal or of a sample of plants against its age, or the size of a population at successive intervals of time. Distinction should be drawn between those cases in which the same group of animals, as in a feeding experiment, is weighed at successive intervals of time, and the cases, more characteristic of plant physiology, in which the same individuals cannot be used twice, but a parallel sample is taken at each age. The same distinction occurs in counts of microorganisms between cases in which counts are made from samples of the same culture, or from samples of parallel cultures.
Distributions
Authors: Fisher R A , Yates F
Published: November 2023

II. The idea of an infinite population distributed in a frequency distribution in respect of one or more characters is fundamental to all statistical work. From a limited experience, for example, of individuals of a species, or of the weather of a locality, we may obtain some idea of the infinite hypothetical population from which our sample is drawn, and so of the probable nature of future samples to which our conclusions are to be applied. If a second sample belies this expectation we infer that it is, in the language of statistics, drawn from a different population; that the treatment to which the second sample of organisms had been exposed did in fact make a material difference, or that the climate (or the methods of measuring it) had materially altered. Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first.
The Correlation Coefficient
Authors: Fisher R A , Yates F
Published: November 2023

30. No quantity has been more characteristic of biometrical work than the correlation coefficient, and no method has been applied to such various data as the method of correlation. Observational data in particular, in cases where we can observe the occurrence of various possible contributory causes of a phenomenon, but cannot control them, have been given by its means an altogether new importance. In experimental work proper its position is much less central; it will be found useful in the exploratory stages of an inquiry, as when two factors which had been thought independent appear to be associated in their occurrence ; but it is seldom, with controlled experimental conditions, that it is desired to express our conclusion in the form of a correlation coefficient.
Intraclass Correlations and the Analysis of Variance
Authors: Fisher R A , Yates F
Published: November 2023

38. A type of data, which is of very common occurrence, may be treated by methods closely analogous to that of the correlation table, while at the same time it may be more usefully and accurately treated by the analysis of variance, that is by the separation of the variance ascribable to one group of causes from the variance ascribable to other groups. We shall in this chapter treat first of those cases, arising in biometry, in which the analogy with the correlations treated in the last chapter may most usefully be indicated, and then pass to more general cases, prevalent in experimental results. in which the treatment by correlation appears artificial, and in which the analysis of variance appears to throw a real light on the problems before us. A comparison of the two methods of treatment illustrates the general principle, so often lost sight of, that tests of significance, in so far as they are accurately carried out, are bound to agree, whatever process of statistical reduction may be employed.
Further Applications of the Analysis of Variance
Authors: Fisher R A , Yates F
Published: November 2023

We shall in this chapter give examples of the further applications of the method of the analysis of variance developed in the last chapter in connexion with the theory of intraclass correlations. It is impossible in a short space to give examples of all the different applications which may be made of this method ; we shall therefore limit ourselves to those of the most immediate practical importance, paying especial attention to those cases where erroneous methods have been largely used, or where no alternative method of attack has hitherto been put forward.
Model fitting and assessment
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

The theory of Generalized Linear Models has been introduced in [1] and covered in more detail in the Modelling Guide [10]. However a brief summary is given here to help make this chapter relatively self-contained. In simple terms models are algebraic structures to summarize the patterns of systematic variation seen in the mean or expected values of y (response/outcome /dependent) variables in terms of quantitative (variates or covariates) or qualitative (factors) explanatory variables. The unknown constants or parameters in the models have to be estimated from data values, which include random variation, using some criterion to determine which are the best. GLIM uses the principle of maximum likelihood which makes an assumption that, given the probability distribution and form of model, the sample is the most likely to have occurred.
The language
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 defines the general features of the GLIM language. At its lowest level, a GLIM session consists of the input to GLIM of a sequence of characters from a given character_set, together with the output from GLIM of another sequence of characters from the same set.
Structures
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl
Published: November 2023

Various kinds of object are recognized by the system, and have names by which the user can refer to them; these names are known as identifiers. (See [13.2] for a discussion of the syntax of identifiers.) Identifiers refer to either data structures or subfiles. When a data structure is created it is associated with an identifier, by which the user can refer to it. An identifier is said to be defined when it has been associated with a data structure; otherwise it is said to be undefined. A defined identifier has the same type as the associated data structure. An undefined identifier has unknown type. The identifier remains defined until the associated data structure is deleted, when it becomes undefined again. An identifier is declared as a global identifier by default, unless is is specifically declared as a local identifier to a macro via the LOCAL option to the MACRO  directive [15.50].