bluuebunny/crossref_metadata_2025 huggingface dataset:
Introduction To Connections, Curvature And Holonomy Groups
Authors: Joyce Dominic D
Published: November 2023

In this chapter we will introduce the theory of connections, focus sing in particular on two topics, the curvature and the holonomy group of a connection. Connections can be defined in two different sorts of bundle, that is, vector bundles and principal bundles. Both definitions will be given in §2.1.
Quasi-Ale Metrics With Holonomy Su(M) And Sp(M)
Authors: Joyce Dominic D
Published: November 2023

Let G be a finite subgroup of U(m) and suppose (X,π) is a resolution of Cm/G. In the case in which G acts freely on Cm\ (0), so that Cm/G has an isolated quotient singularity at 0, Chapter 8 defined a special class of Kähler metrics on X called ALE Kähler metrics, and proved an existence result for Ricci-flat ALE Kähler metrics. We will now generalize these ideas to the case when G does not act freely on Cm \(0) , so that the singularities of Cm/G are not isolated.
Construction Of Compact 7-Manifolds With Holonomy G
Authors: Joyce Dominic D
Published: November 2023

In this chapter we explain how to construct examples of compact 7-manifolds with holonomy G. Here is a sketch of the method. We begin with a torus T equipped with a flat G-structure (ϕ0, g0), and a finite group r of automorphisms of T preserving (ϕ0, g0). Then T /r is an orbifold with a flat G-structure (ϕ0, g0).
Construction Of Compact 8-Manifolds With Holonomy Spin(7)
Authors: Joyce Dominic D
Published: November 2023

In this chapter we explain how to construct compact 8-manifolds with holonomy Spin(7), following the G2 case in Chapter 11 closely. We begin with a torus T 8 equipped with a flat Spin(7)-structure (Q0, g0), and a finite group r of automorphisms of T 8 preserving (Q0, g0). Then T 8/r is an orbifold with a flat Spin(7)-structure (Q0, g0).
Methods for studying nucleic acid structure
Authors: Neidle Stephen
Published: November 2023

Our knowledge of DNA and RNA three-dimensional structures has advanced immeasurably since the elucidation of the first such structure, that of the DNA double helix, in 1953 by Watson and Crick in conjunction with the X-ray fibre diffraction data of Franklin and Wilkins. Fibre diffraction methods subsequently enabled the morphologies of a whole range of nucleic acid double-helical types to become established. More recently, the relationships between DNA primary sequence and fine details of molecular structure have become increasingly understood, in large part from single-crystal and nuclear magnetic resonance (NMR) structural studies on defined-sequence oligonucleotides. DNA structure itself continues to surprise with its ability to exist in a wide variety of forms, such as left-handed and multiple-stranded helices. The study of RNA structure has a more recent history, which reveals that RNA can fold in a variety of complex ways as well as occur in a double-helical form. There is also now a very large body of experimental information on the structures of protein-DNA and drug-DNA complexes.
Assumptions and modelling philosophy
Authors: Buckland S T , Anderson D R , Burnham K P , Laake J L , Borchers D L , Thomas L
Published: November 2023

This section provides material for a deeper understanding of the assumptions required for the successful application of distance sampling theory. The validity of the assumptions allows the investigator assurance that valid inference can be made concerning the density of the population sampled. Before we address the assumptions, we note that the design and conduct of the survey must pay due regard to good survey practice, as outlined in Chapter 7. If the survey is poorly designed or executed, the estimates may be of little value. Sound theory and analysis procedures cannot make up for poor sampling design or inadequate field protocol.
The Boundary Layer On A Flat Plate
Authors: Sobey I J
Published: November 2023

This chapter and the next are concerned with a simple boundary layer problem of flow past a flat plate aligned with the stream. In the present chapter we will follow developments up to 1969. Boundary layer theory development had followed two avenues, on one hand seeking to describe finite Reynolds number flows over bodies such as cylinders and airfoils, flows which involved separation, whilst on the other hand finding greater analytic success with the geometrically simpler flat plate where separation was absent. Even with the simplification of geometry, the development of an analysis for a flat plate boundary layer saw two periods of activity before 1969.
Separated Flow About A Cylinder
Authors: Sobey I J
Published: November 2023

There are many qualitative observations of flow about a circular cylinder but the ones we shall concentrate on here are those which give quantitative information about the surface pressure distribution, the surface velocity and steady separation. The difficulty in taking reliable measurements should not be under estimated.
Prediction Of Separation From A Cylinder
Authors: Sobey I J
Published: November 2023

The length scales needed to resolve the singularity at the trailing edge of plate were simultaneously applied to separation in a compressible flow by Stewart son and Williams (1969) and Neiland (1969). In compressible flow separation can occur ahead of the place where an oblique shock interacts with a wall and the spontaneous nature of this upstream separation was something of a puzzle since the mechanism by which a disturbance could be propagated upstream of the wall-shock interaction in a supersonic flow was unclear, see, for example, Reyhner and Flilgge-Lotz (1968).
Coanda Effect
Authors: Sobey I J
Published: November 2023

Amongst many interesting phenomena in fluid dynamics, one of the simplest illustrations of unexpected physical complexity in fluid flow is the Coanda effect. It is an effect named after H.Coanda (1886-1972) who observed that a jet of air flowing parallel but near a wall (in his case, the fuselage of an aircraft) would deflect so as to flow closer to the wall, appearing to ‘attach’ to the wall. One explanation for this comes from consideration of the pressure distribution.
The Cauchy problem for systems
Authors: Bressan Alberto
Published: November 2023

This chapter is concerned with the global existence of solutions to the Cauchy problem
Power semiconductors
Authors: Holmes-Siedle Andrew , Adams Len
Published: November 2023

The power subsystems of large space equipment, radiation-generating equipment, and nuclear power sources are required to handle high currents and voltages in the kilowatt range. Local regulation is by, amongst other devices, power transistors, thyristors, and large rectifiers. CERN, for example, will employ power diodes for the Large Hadron Collider (Berland et al. 1995) and power ASICs (see Section 6.14). Silicon power devices of the type described operate on the same general principles as junction devices discussed earlier, but their construction is often different: the chip is larger and may even be in the form of a ‘pellet’ having the full diameter of the source ingot. Epitaxial growth is used more extensively in power devices, while special doping (e.g. neutron transmutation) and unusual geometry are required to achieve a high junction breakdown voltage, low ‘ON’ resistance and good heat removal. In general, locally low levels of doping are required for high-voltage devices. In radiation-effects engineering, this is significant because carrier removal due to particle irradiation will be more noticeable. Also, in order to accommodate large depletion regions, large values of base width are required in the design of power transistors and thyristors. This can impart unusually high sensitivity to degradation of gain (see Chapter 5). In some respects, the power MOS device is also structurally different from its low-power relatives (see, for example, VMOS and HEXFET construction). Nevertheless, the response of the gate oxide layer-a dominant effect in space and gamma radiation–can still be predicted by the methods described earlier. One IC supplier has issued a ‘rad hard power management ICs Handbook’ (Intersil 2000). BICMOS is discussed in Section 4.8.9.
Conclusions
Authors: Holmes-Siedle Andrew , Adams Len
Published: November 2023

The overall scientific conclusion from the reviews given in this handbook must be that, in the millennium, microelectronics and the newer nano-and optoelectronics, when operating in a radiation environment, exhibit sometimes alarming misbehaviour. Without a doubt, this situation continues to provide the engineer/designer with a wide range of challenges in applied science. Our job herein is to highlight these problems, explain them where possible and then lead the engineer towards a balanced solution. Explanations, we feel, require proper scientific review. Topics must include a description of the radiation environment and the theory of how radiation interacts with effects in solids, especially solids of the electronic variety. This method, deriving from the style of the original ‘design handbook’ for ESA, is different from the textbook style of some competitors. We gather from readers, however, that such a handbook still serves, in addition, as a grounding for students. Now, preparing a second edition, we look backward and forward. First, colleagues tell us that the first edition was helpful and not too difficult to read and that the indexing was good. We have worked to give a smoother and even better cross-referenced scientific and engineering review.
The adaptive brain
Authors: Tweed Douglas
Published: November 2023

To cope with an uncertain, changing world, the brain must be able to reprogram itself on the fly. Its sensorimotor systems will do their jobs only if they are correctly tuned, their synapses set to appropriate values. The right setting for each synapse depends on how the other synapses are set, and on the state of the sense organs and the muscles. If a muscle weakens, the neural signals driving it must strengthen to achieve the same motion. But then how does a sensorimotor system stay accurate over a lifetime, as the sensors and muscles, and the body parts moved by the muscles, change with growth, injury, aging, and disease? And how does it tune itself in the first place, in the fetal and infant brain, when the neural circuits encounter the newly formed sensors and muscles for the first time? There is only one way. It manages all this by constantly monitoring and calibrating itself, adjusting its own internal structure to optimize its performance.
Thoughts running in circles
Authors: Tweed Douglas
Published: November 2023

During the Second World War a mathematician named Norbert Wiener was recruited to lend his special talents to the American military effort. His secret mission: to design automatic aiming mechanisms for anti-aircraft guns. As he toiled over his sinister engines, with their sensors, motors, and electronic brains, he reflected that their operating principles applied equally to living organisms. After the war he presented his ideas in the influential book Cybernetics: or Control and Communication in the Animal and the Machine.127 Wiener’s central message in Cybernetics was the crucial role of feedback guidance, the process where a system’s output loops back and affects its input to steer it to some goal. In this chapter I discuss why this sort of feedback is crucial to brain function.
Plane geometry
Authors: Silvester J R
Published: November 2023

We shall assume that the set of real numbers, ℝ, is a familiar object on which we can perform the usual arithmetic operations.
Beyond isometry
Authors: Silvester J R
Published: November 2023

Most of this book has been about the transformations called isometries, the distance preserving maps on ℝ2 ( or ℝn). These transformations form a group, I(ℝ2), and we have been studying the properties preserved by the transformations in this group: distance, angle, collinearity, etc., and for a conic (in the last chapter), eccentricity and axis length.
Complex geometry
Authors: Silvester J R
Published: November 2023

In elementary school algebra, before we meet complex numbers, we are faced with the necessity to distinguish those quadratic equations like x2 - 1 = 0 that have solutions, from those like x2 + 1 = 0 which do not.
The size of a group
Authors: Krause Jens , Ruxton Graeme D
Published: November 2023

The last two chapters discussed the mechanisms by which being in a group can affect an individual. Of course, these mechanisms are often not mutually exclusive, and being in a group will affect an individual in several different ways simultaneously. Further, the different costs or benefits that an individual derives from these different mechanisms will change differentially with changes in group size. Section 4.1 will outline the idea that this differential change in costs and benefits will often lead to the existence of a unique group size that allows individuals to maximize fitness, the ‘optimal group size’. Deviations from this group size will be disadvantageous to group members.
Heterogeneity and homogeneity of group membership
Authors: Krause Jens , Ruxton Graeme D
Published: November 2023

Until now, this book has discussed groups as if they were composed of intrinsically identical individuals. Of course, this is often a poor approximation of reality. Even in cases where there is marked similarity between individuals in a group, we must consider if individuals have chosen to assort non-randomly. The next sections look at assortment in the context of both anti-predatory behaviour and foraging in groups. However, other factors, such as transport costs or disease transmission, although much less studied, are also likely to have a considerable influence on the composition of groups.
Environmental effects on grouping behaviour
Authors: Krause Jens , Ruxton Graeme D
Published: November 2023

We discussed in the preceding chapter how grouping behaviour can evolve in a population, and how the tendency for grouping can change over evolutionary time as an adaptation to environmental selection pressures. However, there are also many ways in which the behaviour of an individual animal can be affected by the environment during its lifetime. Phenotypic plasticity as a short-term response of the organism to its environment is particularly common during the early stages of development when tissues and organs and their nervous control are in the process of differentiation. Such plasticity should be specially selected for in changeable environments where conditions fluctuate within a generation.
GPCR superfamily and its structural characterization
Authors: Schöneberg Torsten
Published: November 2023

The diversity of receptor groups within the GPCR superfamily is the result of a long evolutionary process. It has been suggested that serotonin (5-HT) receptors have existed for more than 750 million years (Peroutka and Howell 1994). The tendency towards protein diversification depends upon gene duplications and the continuous accumulation of mutations. The maintenance of vital functions in organisms, however, strictly requires enough structural conservation to ensure the functionality of the corresponding proteins. Despite the remarkable structural variety of natural GPCR agonists, hydropathy analysis, biochemical, and immunological data suggest that all GPCRs share a common molecular architecture consisting of seven transmembrane domains (TMDs) connected by three extraand three intracellular loops. Interestingly, this global architecture is maintained in all GPCRs discovered so far, despite a rather low amino acid sequence homology.
Transcriptional regulation of GPCR expression
Authors: Buckley Noel J , Garriga-Canut Mireia
Published: November 2023

G protein coupled receptors (GPCRs) represent the largest family of signalling molecules present in the organism and are found in all phyla from viruses through yeast to mammals. This sequence diversity is reflected in their expression patterns which invariably show that each transcript has a unique distribution. As anticipated, this diversity of gene type and distribution is most manifest in the CNS. This poses both problems and opportunities. On the one hand, such unique distributions offer potential for highly specific therapeutic targets. On the other hand, they present a problem of phenotypic regulation: How are these expression patterns established and maintained? It is this latter aspect that is the focus of this review.
Structural mechanics of GPCR activation
Authors: Rasmussen Søren G F , Gether Ulrik
Published: November 2023

The majority of hormones, neurotransmitters, and other chemical signalling molecules in the human body exert their effects via G protein coupled receptors (GPCRs) (Strader et al. 1994; Ji et al. 1998; Gether 2000). Evidently, this extreme functional diversity raises some fundamental questions in relation to the function of GPCR at the molecular and cellular level. What are, for example, the molecular mechanisms underlying the ability of this broad variety of molecules to bind and activate receptors that presumably share a preserved overall tertiary structure? Or more specifically, what are the physical changes linking binding of an agonist to activation of intracellular signalling cascades? During the last few years our insight into these fundamental mechanisms have improved considerably. An important breakthrough has been the application of biophysical approaches that has allowed direct insight into the conformational changes that accompany activation of a GPCR (see Gether 2000; Hubbell et al. 2000).
Characterization of orphan GPCRs
Authors: Fidock Mark
Published: November 2023

Bioinformatic analysis of sequence databases to identify new GPCR family members based on homology and conserved ‘motifs’ to known GPCRs suggests that the total number of GPCRs is likely to be around 350 (this does not include olfactory, taste or opsin receptors, see chapter 1). Of these 350, the number which are currently classified as ‘orphans’ (that is receptors without a defined physiologically relevant ligand) is in the region of 175. These ‘orphans’ typically show low sequence identity (< 40%) to known receptors and are distributed throughout the entire GPCR phylogenetic tree. A large number show greater sequence identity to each other than to any known GPCR suggesting they are new subfamilies with distinct, possibly novel ligands.
Introduction And Overview
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

The interplay between partial differential equations (PDEs) and the theory of mappings has a long and distinguished history, and that connection underpins this book. Gauss’s practical geodesic survey work stimulated him to develop the theory of conformal transformations, for mapping figures from one surface to another. For conformal transformation from plane to plane he used a pair of equations apparently derived by d’ Alembert, who first related the derivatives of the real and imaginary part of a complex function in 1746 in his work on hydrodynamics (31], p. 497. These equations have become known as the Cauchy–Riemann equations. Gauss developed the differential geometry of surfaces around 1827, emphasizing the intrinsic geometry, with Gaussian curvature defined by measurements within the surface. If a surface is deformed conformally (preserving angles), then the Gaussian curvature is unchanged, and hence the intrinsic geometry of the surface is unaffected by such deformations. Gauss also considered geodesic curves within surfaces. In 1829 Lobachevsky constructed a surface (the horosphere) within his non-Euclidean space, such that the intrinsic geometry within that surface is Euclidean, with geodesic curves being called Euclidean lines. For the converse process, he could only suggest tentatively that, within Euclidean space, the intrinsic geometry of a sphere of imaginary radius was Lobachevskian. But imaginary numbers were then regarded with justifiable suspicion, and he did not propose that as an acceptable model of his geometry within Euclidean space. In his most famous work, Beltrami [32] showed that Lobachevsky’s geometry is the intrinsic geometry of a surface of constant negative curvature, with geodesic curves being called lines in Lobachevsky’s geometry. Beltrami illustrated various surfaces with constant negative curvature, the simplest of which is the pseudosphere generated by revolving a tractrix around its axis. Beltrami’s paper convinced most mathematicians that the geometries of Euclid and of Lobachevsky are logically equivalent. In that work Beltrami used a differential equation corresponding to Gauss’s equation. This has come to be known as Beltrami’s equation, and later in this book we shall present the most recent developments in this area, solving Beltrami’s equation at the critical point. where uniform ellipticity bounds are lost. This will necessitate the development of some considerable technical machinery to enable us to move away from the classical setting of uniformly elliptic PDEs to the case of degenerate elliptic equations. Beltrami’s equation and its solutions, the quasiconformal mappings, have found a home in virtually all aspects of modern complex analysis, from the theory of Riemann surfaces and Teichmüller and Moduli spaces to more recent developments such as holomorphic dynamics and three-dimensional hyperbolic geometry. We hope the developments presented in this book encourage new applications of quasiconformal mappings in these areas.
Conformal Mappings
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

This chapter is intended as a gentle introduction to the basic notions of conformal geometry. In this way we are able to introduce and discuss some concepts from differential geometry which we will need later. We meet Möbius transformations and then prove Liouville’s celebrated rigidity theorem of 1850, that conformal diffeomorphisms of ℝ,. n2: 3, are Möbius transformations. This proof serves as a model for our subsequent proof of this theorem in much greater generality.
Stability Of The Mobius Group
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

Liouville’s theorem demonstrates the strong rigidity of conformal mappings in dimensions n≥ 3. An important point to note from the previous chapter is the global injectivity of nonconstant solutions to the Cauchy–Riemann system. It is natural to ask if this property is still true for “nearly” conformal mappings. In order to answer this question we shall need to examine fairly general classes of mappings defined on subdomains of ℝn. Naturally the classes of mappings in question should remain invariant under elementary changes of variables, such as scaling and translation, since the Möbius group is. We shall show that if these classes are close to the Mobius class in a well-defined sense, then they inherit some of the rigidity properties, in particular local injectivity. (Indeed, they will be shown to consist of locally quasiconformal mappings).
Differential Forms
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

There are important applications of the L-theory of differential forms in nonlinear analysis. In particular, many recent developments in the areas of quasiconformal mappings and non-linear elasticity are founded on the framework provided by non-linear Hodge theory. When p= 2, the theory is fairly well understood and presented in many textbooks. However for p≠ 2, the LP-theory of differential forms has yet to be fully developed. In this chapter we expose many of the standard techniques used when p= 2 and add critical new techniques for p≠ 2.
Riesz Transforms
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

Singular integrals have played an important role in the theory of partial differential equations from the very beginning, largely pertaining to the higher integrability theory of the gradient of weak solutions. It is only recently that we have become fully aware of the importance of computing, or at least obtaining good estimates for the p-norms of such operators – for example, in determining the exact degrees of improved regularity and other geometric properties of solutions for both linear and non-linear PDEs in higher dimensions.
Conformal Structures
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

In the next few chapten; we are going to need to have at hand some facts concerning conformal structures on domains in ℝn and the mappings between them. The aim in this brief chapter is to present this material. It is in this differential-geometric setting that many ideas crystallize, and further generalizations become apparent.
Advances in Bayesian image analysis
Authors: Hurn Merrilee , Husby Oddvar , Rue Havard
Published: November 2023

Statistical interest in data in the form of images really took off in the 1980s following the papers by Geman and Geman (1984) and Besag (1986), although in fact Grenander had been working in the area of pattern recognition for some considerable time by then (Grenander 1976, 1978, 1981).
Discharging
Authors: Wilson Robert A
Published: November 2023

In order to prove the four-colour theorem, we need a good method for producing unavoidable sets.
Perspectives on the timing of events and actions Introduction to Section II
Authors: Summers Jeff
Published: November 2023

Time perception in terms of the temporal properties of environmental events and time production in terms of the execution of self-generated sequences of precisely timed movements are abilities that are essential for successful interactions with the world around us. Furthermore, coordinating our actions in time to coincide with an external event, that is, perception–action coupling, is a feature of many everyday activities, from pressing a key on a piano, to shaking someone’s hand or hitting a squash ball. Unfortunately the study of the perception of event structure (i.e. the motional and rhythmic properties of events) and the study of movement timing have progressed somewhat independently, leaving the crucial question of how perceptual variables map onto motor variables largely neglected. In this section four papers are presented dealing with different aspects of timing.
Action representation and the inferior parietal lobule
Authors: Gallese Vittorio , Fadiga Luciano , Fogassi Leonardo , Rizzolatti Giacomo
Published: November 2023

Abstract. From birth onwards, primates’ cognitive development depends heavily on being able to observe and interact with other individuals. How can individuals assign a meaning to the actions performed by other conspeci1cs? A possible neural correlate of the mechanism allowing action understanding could be represented by a class of neurons (mirror neurons) that we have discovered in area F5 of the ventral premotor cortex of the macaque monkey. We proposed that mirror neurons could be part of a cortical system that, by matching action observation with action execution, enables individuals to ‘understand’ the behavior of others. The present study is aimed at better clarification of the nature and the properties of such a cortical matching system. Neurons responding to the observation of complex actions have been described by Perrett and co-workers in the cortex buried within the superior temporal sulcus (STS). These neurons could be a particularly well-suited source of visual input for F5 mirror neurons. However, area F5 does not receive direct projections from the STS region. One of its major inputs comes from the inferior parietal lobule and in particular from area PF (7b).
Coordination and integration in perception and action Introduction to Section V
Authors: Ward Robert
Published: November 2023

Integration of perception and action systems is necessary for survival. A perceptual system which can’t guide action is literally useless, and an action system which isn’t guided by perception is probably dangerous. So how are perception and action systems linked to allow effective behaviour? The chapters in this section address many aspects of this question, but at least two important themes emerge. One is the increasing variety of approaches that develop and even replace traditional notions about the way perceptual analyses are dynamically linked to responses. A second crucial issue is the way that associations between stimuli and response are structured by experience and by task demands.
Green’s equivalences; regular semigroups
Authors: Howie John M
Published: November 2023

The notion of ideal mentioned in the last chapter leads naturally to the consideration of certain equivalence relations on a semigroup. These equivalences, first studied by J. A. Green (1951), have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group.
Completely regular semigroups
Authors: Howie John M
Published: November 2023

It is well known that a group (G, μ) can alternatively be regarded as having three operations, namely the binary operation μ : (a, b)  ⟼ab, the unary operation a ⟼a-1, and the 0-ary operation (the constant) 1.
Inverse semigroups
Authors: Howie John M
Published: November 2023

In planning the chapter on inverse semigroups the main problem has been one of selection. As long ago as 1961, Clifford and Preston offered the opinion that inverse semigroups were the most promising class of semigroups for future study, and the intervening years have amply justified their forecast. It is inappropriate in a general introductory book to attempt a comprehensive updating of Petrich’s (1984) very complete account. Rather I shall cover the basic ideas and attempt to explore one or two avenues in more detail.
Degree Theory For Continuous Functions
Authors: Fonseca Irene , Gangbo Wilfrid
Published: November 2023

In the first three chapters, unless the contrary is explicitly stated, D is a bounded, open subset of ℝN. Also, in the sequel we will use the following notation:
Degree Theory In Finite-Dimensional Spaces
Authors: Fonseca Irene , Gangbo Wilfrid
Published: November 2023

In this chapter we prove those properties of d(φ, D,p) that we consider to be most useful in applications.

The first theoremtheorem. is the basis of many of the applications of degree theory in analysis.
Computer-based Radiological Training and Education
Authors: Jeffery* N P , Teather* D A , Teather* D , Sharples** M , Boulay** D Du , Boulay† G H Du
Published: November 2023

In teaching radiology residents and medical students, there is now the problem of transmitting a larger amount of material in what appears to be an increasingly inadequate time span. Despite the fact that the length of radiology training has heen extended, it is no longer possible for finishing residents and fellows to know all that they need to know if they are going to enter the practice of radiology. There is therefore a need for professional updating and supplementary teaching. Training and education in radiology depend to a large extent on visual pre sentation [l]. The transfer of information in radiology, as in all of medicine, has traditionally been in standard teaching formats such as an instructor lecturing to a group of students, one-to-one discussions, and direct hands on experience.
Constructive truth in practice
Authors: Bridges Douglas S
Published: November 2023

In this chapter, which has evolved over the last ten years to what I hope will be its perfect Platonic form, I shall first discuss those features of constructive mathematics that distinguish it from its traditional, or classical, counterpart, and then illustrate the practice of that distinction in aspects of complex analysis whose classical treatment ought to be familiar to a beginning graduate student of pure mathematics.

My experience shows that a typical mathematician believes that constructive mathematics is characterized by either a rejection of the law of excluded middle from logic or else a rejection of the full axiom of choice from set theory. In fact, although some authors (notably Richman (1996)) seem to endorse the former characterization, the pioneers of constructivism—Brouwer, Markov, Bishop-all arrived at their rejection of the law of excluded middle (and hence, implicitly, at a rejection of the axiom of choice—see later in this chapter) as a consequence of their insistence that the phrase there exists be interpreted strictly as we can construct.
The mathematician as a formalist
Authors: Dales H G
Published: November 2023

The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is ‘true’. This debate began at least 2500 years ago, and will presumably continue at least well into the next millennium; it would be implausible and perhaps presumptuous to suppose that even the union of the talented and distinguished speakers that have been assembled here in Mussomeli will approach any solution to the problem, or even arrive at a consensus of what a solution would amount to.
True to the pattern
Authors: Oliveri Gianluigi
Published: November 2023

The aim of this chapter is to sharpen and defend the view advocated by Wittgenstein in Philosophical Investigations that an aspect is not ‘[…] a property of the object, but an internal relation between it and other objects’.

This conception of aspects is philosophically very important for the following reasons.

First, it provides a view of experience which differs from that inherited by a large part of the post-Kantian tradition.
NF and Related Systems
Authors: Forster T E
Published: November 2023

The first question in the mind of newcomers to NF concerns the paradoxes. We have seen in section 1.4 how NF avoids Russell’s paradox. Our first task here is to show that a version of Cantor’s theorem can nevertheless be proved: all sets have fewer singleton subsets than subsets.
Church-Oswald Models
Authors: Forster T E
Published: November 2023

In [1974) Church showed us a consistency proof for an axiomatic system of set theory containing inter alia an axiom to the effect that there is a set of all sets. This bore no relation to any previously published set theories with such an axiom, and naturally involved a new construction.
Black Holes Gravitational Interactions
Authors: D'eath P D
Published: November 2023

Black Holes are regions of space-time where the gravitational field is so strong that not even light can escape. There has been much written on black holes, however in most cases they are treated as isolated objects. In this important new book, the author has found a number of cases in which the interaction of a black hole with another strong-field system (such as the background universe or another black hole) could be treated analytically. This includes using the powerful method of matched asymptotic expansions, and these wider ranging problems and examples are considered here for the first time. In addition to a thorough treatment of the equations of motion for a pair of black holes, the book provides a useful treatment of the standard theory for these objects. It will be widely read by all those working in gravitation, along with post-graduate students in mathematical physics.
Invariants of Homotopy Types
Authors: Baues Hans-Joachim
Published: November 2023

The classical algebraic invariants of a simply connected homotopy type (X) are the homotopy groups σn(X) and the homology groups Hn(X), n ≥ 2.
On the Homotopy Classification of (N − 1)-Connected (n + 3)-Dimensional Polyhedra, n≥4
Authors: Baues Hans-Joachim
Published: November 2023

J.H.C. Whitehead in 1948 classified (n −1)-connected (n + 2)-dimensional homotopy types. Since then it has been a challenging problem to consider the next step in the classification of (n − 1)-connected (n + 3)-dimensional homotopy types. Various authors have worked on this problem in the stable range n≥ 4, for example Shiraiwa [HT], Uehara [HT], Chang [PI], [HT], [AS], [NH], and Chow [HG]. They use a complicated method of primary and secondary cohomology operations; compare Section 8.5 below. We here apply the new method of boundary invariants which, via the classification theorem 3.4.4, yields fairly simple classifying data for (n − 1)-connected (n + 3)-dimensional homotopy types. In this chapter we deal only with the stable case n≥ 4. In Chapters 9 and 12 we describe the considerably more intricate unstable cases, n = 3 and n = 2.
Partial Orders
Authors: Brightwell Graham
Published: November 2023

We explore several connections between graphs and partially ordered sets. We define various graphs and digraphs associated with a partially ordered set, and explore how the properties of the partial order are reflected in these graphs. We consider the incidence order of a graph, and prove Schnyder’s Theorem, that a graph is planar if and only if its incidence order has dimension at most 3. It is possible, and only moderately perverse, to think of a graph as a special kind of partially ordered set. Then again, a partially ordered set can be regarded as nothing more than a special kind of directed graph. One should be wary of concluding that the concerns of one subject are similar to those of the other, or that results from one area are necessarily of use in the other, but it is not unreasonable to expect that there will be connections. This chapter is devoted to some of those links that have proved interesting.
Statistics
Authors: Wild Peter
Published: November 2023

In this chapter we give several examples of the close connection between statistical design and graph spectra. Focusing on block designs, we describe measures of efficiency of an experimental design in terms of certain functions of eigenvalues of the Fisher information matrix. The most efficient designs correspond to graphs with some extreme spectral behaviour. One of the main aims of mathematics is to model problems that arise in the real world–that is, to represent a real-life situation as a mathematical system. By this means, many different instances of the same problem can be tackled using a single theory. This theory may be descriptive, providing a clearer understanding of the problem. It may also be a tool that can be used to prove previously unsuspected results that may be applied to the real-life situation to make predictions about its behaviour.
Local Compactness And Exponentiability
Authors: Johnstone Peter T
Published: November 2023

Our principal goal in this chapter is to establish the characterization of exponentiable objects in the 2-category ℬℐℴ𝓅/𝒮, for a general base topos 𝒮, as those which are ‘locally compact’ in an appropriate sense. We have already made some observations about exponentiability in ℬℐℴ𝓅/𝒮 in Section B4.3; and we shall assume that the reader of this chapter is familiar with them. In this and the next section we shall take our base topos to be Set, in order to simplify the notation; but virtually all that we do can be extended to a general base topos S with a natural number object, using an appropriate internal finiteness notion in S to interpret the finiteness conditions which appear below.
Cognitive–Behavioral Group Interventions
Authors: Coon David W , Shurgot Gia Robinson , Gillispie Zoë , Cardenas Veronica , Gallagher–Thompson Dolores
Published: November 2023

This research was supported through the Resources for Enhancing Alzheimer’s Caregiver Health (REACH) project, which is funded by the National Institute on Aging (grant no. AG 13289) to DGT, Principal Investigator at this site.
Psychotherapy Integration
Authors: Trijsburg Rutger Willem , Colijn Sjoerd , Holmes Jeremy
Published: November 2023

In this chapter we shall consider psychotherapy integration not just as a specific therapeutic modality, but also as a theoretical and research viewpoint that encompasses several of the distinct psychotherapeutic approaches reviewed in this section.
Hierarchical Models for Ranking and for Identifying Extremes, with Applications¹
Authors: Morris C N , Christiansen C L
Published: November 2023

We address the problem of ranking and of identifying the best or worst of several individuals or groups, e.g., athletic teams or medical practitioners (called “profiling” in medicine, an increasingly important topic in US health policy). Satisfactory statistical approaches must account for covariates that might indicate that the degree of difficulty differs for the individuals being compared, and they also must account for random variation, especially for regression to the mean. Hierarchical Bayesian (multi-level) methods permit one to model and then to account for differing amounts of sampling information, usually due mainly to different sample sizes, in the groups being compared. This can lead to “crossover” effects, which do not occur in standard ranking and selection theory. We review here the relevant theories and compare existing and new methods and criteria for doing this in several applications.
Bayes Posteriors for Scalar Interest Parameters
Authors: Fraser D A S , Reid N
Published: November 2023

The posterior distribution for an interest parameter is usually obtained by integrating the nuisance parameters out of a full posterior distribution. For this, considerable attention has focused on finding a prior that is noninforrnative for the interest parameter and yet allows the effective elimination of the nuisance parameters; of course this needs model structure beyond the likelihood function. As a paradigm for generalizing this, we take a location model for the interest parameter and a separate model for the nuisance parameter. Then for a general asymptotic model we use recent third order asymptotics to determine location model structure relative to a scalar interest parameter; we thus obtain a posterior for the interest parameter based on a flat or diffuse prior for only the interest parameter.
Protoplasmic pantheism
Authors: Mazzarello Paolo
Published: November 2023

At the beginning of the 1890s, support for Golgi’s diffuse neural net was confined to the circle of his direct or indirect pupils. Gerlach’s version of the reticular theory continued to be much more popular in Italy and elsewhere. There were also other reticular theories, sometimes touching on the bizarre. The Lithuanian, Alexander Stanislavovich Dogiel, for example, wishing to mix oil and water, maintained that in the retina there existed a double intercellular reticulum; one was inter-cylindraxial (similar to that of Golgi); the other inter-dendritical (similar to that of Gerlach). And then there was even a suggestion that there might be three reticula, with the third consisting of a connection between dendrites and axons.1 The most important scientists, however, were embracing the theory of the neuron with more and more conviction.
The laboratory where a discovery is made every day
Authors: Mazzarello Paolo
Published: November 2023

By the end of the century, the Laboratory of General Pathology had became an institution of world-renown and was considered the most important centre of biological research in Italy. In its new location in Palazzo Botta it was better equipped than ever and could host a considerable number of researchers.
Working unto death
Authors: Mazzarello Paolo , Buchtel Henry A , Badiani Aldo
Published: November 2023

The last years of Golgi’s life were set in a period of dramatic events for Italy and Europe. On 28 June 1914 Archduke Francis Ferdinand of Austria-Este and his morganatic wife, the Duchess of Hohenberg, were assassinated by a Serbian nationalist in Sarajevo. After a century of optimistic faith in technical, scientific, and moral progress, Europe plunged into the abyss of the First World War; a war that was expected to be over in a few months and instead lasted five years, devastating the youth of the continent.
Stem Cells and their Gliogenic Potential
Authors: Brustle O , Dubois-Dalcq M
Published: November 2023

A detailed understanding of the lineage relationships between the three principal cell types of the central nervous system (CNS)—neurons, astrocytes and oligodendrocytes-is a central issue in the study of CNS development and repair. The discovery that in vitro type 2 astrocytes and oligodendrocytes can develop from a common, self-renewing progenitor established the existence of a bipotential precursor for CNS glia (Raff et al., 1983; Bögler et al., 1990). These experiments also showed that the decision of a progenitor cell to differentiate into an oligodendrocyte or a type 2 astrocyte is influenced by the culture medium, indicating that the fate of neural precursor cells can be modulated by extrinsic factors. While type 2 astrocytes are rarely encountered in vivo, subsequent in vivo lineage analyses with retroviral vectors established the presence of a common progenitor for type-I astrocytes and oligodendrocytes (Levison and Goldman, 1993). These studies also provided evidence for the existence of neuron-astrocyte and neuron-oligodendrocyte precursors (Galileo et al., 1990; Williams et al., 1991). However, it was the discovery of a multipotential neural precursor cell for neurons, astrocytes and oligodendrocytes which established the neural stem cell (NSC) concept (for reviews, see Weiss et al., 1996b; McKay, 1997).
Introduction
Authors: Diggle Peter J , Heagerty Patrick J , Liang Kung-yee. , Zeger Scott L
Published: November 2023

The definning characteristic of a longitudinal study is that individuals are measured repeatedly through time. Longitudinal studies are in contrast to cross-sectional studies, in which a single outcome is measured for each individual. While it is often possible to address the same scientfic questions with a longitudinal or cross-sectional study, the major advantage of the former is its capacity to separate what in the context of population studies are called cohort and age effects. The idea is illustrated in Fig. 1.1. In Fig. 1.1(a), reading ability is plotted against age for a hypothetical cross-sectional study of children. Reading ability appears to be poorer among older children; little else can be said. In Fig. 1.1(b), we suppose the same data were obtained in a longitudinal study in which each individual was measured twice. Now it is clear that while younger children began at a higher reading level, everyone improved with time. Such a pattern might have resulted from introducing elementary education into a poor rural community beginning with the younger children. If the data set were as in Fig. 1.1(c), a different explanation would be required. The cross-sectional and longitudinal patterns now tell the same unusual story – that reading ability deteriorates with age.
Paths
Authors: Priestley H A
Published: November 2023

In this chapter we start systematically to study curves in the complex plane. To regard a curve, such as a circle, simply as a subset of the plane will not suffice for our purposes. Instead, we adopt a dynamic approach and think of a curve as the route traced out by a moving point, the route being specified by a suitable function of some real parameter.

We shall need a few of the ideas from this chapter when we consider elementary conformal mapping in Chapter 8 and multifunctions in Chapter 9. Readers seeking the quickest possible route to the theory at the heart of complex analysis, in particular to Cauchy’s theorem, may wish to proceed straight from this chapter to Chapter 10, in which we discuss integrals along paths.
Applications of contour integration
Authors: Priestley H A
Published: November 2023

This chapter is devoted to applications of Cauchy’s residue theorem to the evaluation of definite integrals and the summation of series. The method will handle quite baroque examples. If we seem to have included some examples of this sort, especially in the final section (advanced track), it is because these give valuable technical experience. Very few of the integrals we consider can be evaluated by more elementary methods such as substitution.