bluuebunny/crossref_metadata_2025 huggingface dataset:
Attentional Functioning in Alzheimer’s Disease
Authors: Parasuraman Raja
Published: November 2023

The population of older adults afflicted with Alzheimer’s disease (AD) continues to grow rapidly. New techniques for preventing, slowing the onset of, and treating AD are therefore urgently needed. Such efforts would be boosted if this progressive disease could be detected early in its course, before irreversible brain changes occur. Consequently, many research groups have investigated cognitive changes in the early stages of AD, particularly memory (Albert 1998; Becker 1988; Morris 1996a; Nebes 1992) and attention (Morris 1996b; Parasuraman and Haxby 1993; Perry and Hodges 1999). Changes in these functions may also occur in the preclinical stage, before individuals show symptoms that meet the diagnostic criteria for AD (Bondi et al.1999; Greenwood et al.2000).
Executive Functions in Alzheimer’s Disease
Authors: Collette Fabienne , Van Der Linden Martial
Published: November 2023

It has long been widely recognized that episodic memory impairment is a hallmark of Alzheimer’s disease (AD), present in the first stages and even in the prodromal period. On the other hand, until relatively recently, executive dysfunction was not considered as an important characteristic of AD. For example, Pillon et al.(1986) indicated that executive dysfunction tends to be mild and usually occurs relatively late in the disease. A number of recent studies have nevertheless demonstrated that individuals with AD are impaired on a variety of tasks that are commonly considered as measures of executive control and that these executive deficits are present relatively early in AD (in association with episodic memory disorders). The purpose of this chapter is to review these studies and also to present the researches which have attempted to relate executive impairment in AD patients to neuropathological modifications.
Information Processing Defects in Episodic Memory in Alzheimer’s Disease
Authors: Overman Amy A , Becker James T
Published: November 2023

Alzheimer’s Disease (AD) is the clinical manifestation of a degenerative neuropathological disorder that typically affects older individuals. The primary presenting symptom of the disease, indeed its defining characteristic, is the profound and progressive loss of memory. AD patients lose their knowledge of day-to-day events, and their fund of knowledge and concepts deteriorates. Although clearly a multi-system disease, the neuropathological changes focus in the temporal and parietal lobes, and progress to the rest of the cerebral cortex. Subcortical structures (e.g. thalamus, striatum) are less affected, and typically do not become involved until later in the natural history of the disease.
Language in Alzheimer’s Disease
Authors: Kertesz Andrew
Published: November 2023

Interest in language function in Alzheimer’s disease (AD) has increased exponentially in the last two decades. On the other hand, language deficits have been submerged in the general cognitive decline in many clinical and epidemiological studies. Alzheimer’s (1907) original case had impaired comprehension and paraphasic responses later in the course of the illness. Pick (1892) emphasized aphasia in the description of frontotemporal lobar atrophy.
Neurobiological Abnormalities in Alzheimer’s Disease: Structural, Genetic, And Functional Correlates Of Cognitive Dysfunction
Authors: Morris Robin G
Published: November 2023

The neurobiological changes that result in the cognitive impairment in AD are now much better understood. These span the different levels, including studies that explore gross morphological and histological changes, as well as those to do with abnormalities at the molecular, biochemical, or cellular level. Whilst the neurobiological aspects are covered in much greater depth elsewhere (e.g. Dawnbarn and Allen 2001; Iqbaal et al.1999), this chapter relates some of the neurobiological findings more directly to the neuropsychology of AD. What emerges is a reasonably good correspondence between the two aspects, indicating that AD is a true neuropsychological disorder, with the different features of brain neurodegeneration broadly predicting the pattern of cognitive impairment.
Chaos and Time-Series Analysis
Authors: Sprott Julien Clinton
Published: November 2023

This text provides an introduction to the exciting new developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics are discussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations. While many books on chaos are purely qualitative and many others are highly mathematical, this book fills the middle ground by giving the essential equations, but in the simplest possible form. It assumes only an elementary knowledge of calculus. Complex numbers, differential equations, and vector calculus are used in places, but those tools are described as required. The book is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in a practical setting. It is written at a level suitable for advanced undergraduate and beginning graduate students in all fields of science and engineering.
Spatiotemporal chaos and complexity
Authors: Sprott Julien Clinton
Published: November 2023

Most of the previous discussion has concerned low-dimensional chaotic systems, governed by simple iterated maps or ordinary differential equations. By contrast, natural systems such as economic, ecological, social, neural, and meteorological, are inherently high-dimensional, involving many interacting variables. Even relatively simple nonlinear interactions between a limited number of variables can lead to complex behavior.
Uniformly Quasiregular Mappings
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

The interesting question of which compact Riemannian manifolds admit rational maps has been considered in [218] as a generalization of the Lichnerowitz conjecture. This conjecture states that only the n-sphere admits a non-compact group of homeomorphic conformal mappings and was solved affirmatively by Lelong-Ferrand [200]. The general question is in turn related to the notion of
Analytic Continuation For Beltra1h Systems
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

This chapter is devoted to proving the following theorem which, as a corollary, establishes the uniqueness of homeomorphic solutions of general Beltrami systems.
The Solo Performer’s Identity
Authors: Davidson Jane w.
Published: November 2023

The previous chapter explored how self-identity is formed and how young people come to define themselves as musicians. The current chapter moves on from where the previous chapter concluded, accepting the definition of the musician’s identity which emerged. The central topic for consideration here is the notion of ‘being a performer’, in particular the question: ‘what makes a performer?’ The chapter concentrates on the soloist, for it is well documented that soloists typically are more exposed to performance pressures —they do not have co-performers with whom to collaborate. Furthermore, in popular, folk and classical Western traditions, the soloist is often regarded as a person who needs to possess very high-level communicative abilities in order to engage the audience’s attention and foster a sense of participation (see Davidson, 1997, for more discussion of solo versus co-performance). The discussion in this chapter reflects on the environmental circumstances, patterns of behaviour and personality traits that might influence the development of an individual’s performance abilities. In particular, what makes a ‘good’ solo performance is considered.
Covariate Effects On Continuous And Ordinal Tests
Authors: Pepe Margaret Sullivan
Published: November 2023

In Chapter 3 we discussed factors that can affect the result of a diagnostic test beyond disease status. The need to identify such factors is as relevant for continuous and ordinal tests as it is for binary tests. However, as we will see in this chapter, conceptual and technical approaches are more complex.
Phenomenological treatments of transport coefficients
Authors: Egelstaff P A
Published: November 2023

It will have been noticed that the diffusion constant was expressed frequently in terms of velocities, distances, and times rather than in terms of the pair potential and the pair correlation function. The method of calculation adopted in the last two chapters has differed from that used earlier, in that statistical mechanics was not used extensively. This points out a basic difference between the usual methods of calculating the equilibrium properties and the transport properties. As an illustration of these differences, Fig. 13.1 shows the main steps in the mathematical procedures. For equilibrium properties, classical mechanics and the pair potential provide the starting point and the calculation proceeds via equilibrium statistical mechanics. Along this route the information regarding the time variation of positions is lost. In contrast, for transport coefficients the calculation proceeds via a detailed molecular dynamics method. Such a calculation may be accomplished in one of two ways: either the equations of motion for each atom may be written down and solved (nearly) continuously on a large computer (Chapter 6); or a model for the liquid may be assumed and the dynamical consequences of the model worked out. Several examples of the latter method were given in Chapters 11 and 12.
The difficult years 1665–7
Authors: Hall Marie Boas
Published: November 2023

The hard winter of 1664–5 brought with it a series of catastrophes for England and immense difficulties for Oldenburg personally, most of them arising directly from the national disasters. Those years were so full of dire events that many invoked the milleniarist tradition of prophetic numerology that turned the year 1666 (1000 + 666) into the herald of, possibly, the end of the world foretold in the Book of Daniel, and at least presaged great turmoil and chaos in the social and political world. Certainly England was to be beset with enough catastrophes to satisfy the prophets: a lengthy and on the whole disastrous war, a devastating outbreak of plague, and the Great Fire of London. And all these in different ways affected Oldenburg himself if not disastrously at least for the worse.
Causality and graphical models in time series analysis
Authors: Dahlhaus Rainer , Eichler Michael
Published: November 2023

Over the last few years there has been growing interest in graphical models and in particular in those based on directed acyclic graphs as a general framework to describe and infer causal relations (Pearl 1995, 2000; Dawid 2000; Lauritzen 2001). This new graphical approach is related to other approaches to formalize the concept of causality, such as Neyman and Rubin’s potential-response model (Neyman 1935; Rubin 1974; Robins 1986) and path analysis or structural equation models (Wright 1921; Haavelmo 1943). The latter concept has been applied in particular by economists to describe the equilibrium distributions of systems that typically evolve over time.
Spatial hierarchical Bayesian models in ecological applications
Authors: Penttinen Antti , Divino Fabio , Riiali Anne
Published: November 2023

The spatial distribution of species, the suitability of sites, and association between species are matters of importance in biological and ecological research. These issues have entered also into modern forest research where the objectives of planning strategies are not only in timber production but increasingly in the multi-purpose use of forest areas, including the ability to host plant and animal species.
Statistical approaches to genetic mapping
Authors: Stephens David A
Published: November 2023

The analysis of genetic data, specifically in relation to the modelling of population-level variation in disease, is one of the most challenging areas for statisticians. Advances in molecular technology have now facilitated routine, large-scale genetic screening, and such data will provide key information in the study of diseases such as hypertension and cardiovascular disease, helping to quantify purely genetic and gene-environment components of variation and risk.
The genealogy of a neutral mutation
Authors: Griffiths R C , é Simon Tavar
Published: November 2023

Technological advances in molecular biology have made it possible to survey DNA sequence variation in natural populations. These data include restriction fragment length polymorphisms, microsatellite repeats, single nucleotide polymorphisms, and complete DNA sequences of many loci; for more details, we refer to Chapter 2 of Hartl and Jones (2001).
Asymptotics of non-parametric posteriors
Authors: Vaart Aad van der
Published: November 2023

Nils Hjort is to be congratulated on his interesting overview of issues in nonparametric Bayesian statistics. He discusses a wide range of topics. Perhaps it is somewhat biased toward his own work to be a true overview of the field.
Applications of Euler’s formula
Authors: Wilson Robert A
Published: November 2023

You may have met Euler’s formula for regular polyhedra: if <V is the number of vertices, E the number of edges, and <F the number of faces, then <V −E +<F = 2. There are five such regular polyhedra, and you can check this equation in the five cases (see Table 3.1).
Kempe’s approach
Authors: Wilson Robert A
Published: November 2023

Kempe (pronounced ‘kemp’) published his ‘proof’ of the four-colour theorem in 1879, and for a decade it was accepted as a valid proof, and an ingenious solution to the problem. It contained several clever ideas, which we now present. For historical reasons, we describe his arguments in the face-colouring form, as Kempe himself did. He also mentioned duality and the translation of the problem into the vertex-colouring form. We discuss this translation in Section 4.4.
Kuratowski’s theorem
Authors: Wilson Robert A
Published: November 2023

We have looked at problems of colouring graphs of different genus, but how do we know what genus a given graph has? In general, this is a hard problem. The genus O case is obviously of special interest to us, as a good characterization of genus O (i.e. planar) graphs might help us to attack the four-colour theorem. The most famous characterization of planar graphs is Kuratowski’s theorem, which gives us a practical way of showing that a given graph is non-planar. On the other hand, the easiest way to show that a given graph is planar is to draw a plane graph which is isomorphic to it.
Overview
Authors: Wilson Robert A
Published: November 2023

The overall strategy of the proof of the four-colour theorem does not differ greatly from that adopted by Kempe in his 1879 paper. If we consider the vertex colouring form of the theorem, then the proof goes by induction on the number of vertices. Clearly, the induction starts, as any graph with at most four vertices is 4-colourable.
Common mechanisms in perception and action Introductory remarks
Authors: Prinz Wolfgang , Hommel Bernhard
Published: November 2023

The contributions to this volume discuss a classical theme in human-performance research, and they do so under some new perspectives that have emerged in recent years. The classical theme refers to the interplay between perception and action—a theme that is, and has ever been, one of the core issues in the 1eld of attention and performance. For instance, in the classical work inspired by linear stage theory, notions like stimulus–response translation and/or response selection have been introduced to account for putative operations underlying the transition from stimulusto response-related processing, and a number of factors affecting these operations have been identi1ed. Yet, despite their supposed central function, the study of translation mechanisms has always played a somewhat marginal role. Instead, research has tended to emphasize stimulusover response-related processing, and there has been rather little interest in response-related processing mechanisms and the way they are linked to those dealing with stimulus information.
Several ‘vision for action’ systems: a guide to dissociating and integrating dorsal and ventral functions (Tutorial)
Authors: Rossetti Yves , Pisella Laure
Published: November 2023

Abstract. There is a well-established argument for a double-dissociation between vision for action and vision for conscious identi1cation. The distinction between these two visual systems applies to both the attributes being processed and the outputs of the processing. However, numerous direct and indirect interconnections and convergence have been described between cortical and subcortical visual pathways as well as between the dorsal and the ventral streams.
The perception and representation of human locomotion
Authors: Rieser John J , Pick Herbert L
Published: November 2023

Abstract. Locomotion is both a class of actions and a class of perceptible events. As a class of actions it is embedded in its environmental context and participates in 1ght, 2ight, and many functional behaviors. As a class of perceptible events, it is central to dynamic spatial orientation, that is, keeping up-to-date on the changes in self-to-object distances and directions that occur during locomotion. This chapter is focused on locomotion and on spatial orientation when people walk without vision and without access to nonvisual information about their surroundings. The thesis is that even when walking without vision, people perceive their locomotion relative to the remembered environment as a frame of reference. This environment-centered perception of locomotion accounts for how they keep up-to-date on their changing spatial orientation relative to features of the remembered surroundings. And the resulting representation is used to steer their ongoing locomotion and control all other environmentally directed actions.
Interaction between feature binding in perception and action
Authors: Stoet Gijsbert , Hommel Bernhard
Published: November 2023

Abstract. To explain how coherent representations can be formed of information that is distributed throughout the brain, binding mechanisms have been hypothesized that temporarily hold together or bind such distributed information. Evidence of temporary feature binding has been reported from tasks requiring perceptual integration and action planning, and there is some evidence that action planning affects perception. The present study provides further evidence that binding-related effects cross borders between perceptual and motor domains by demonstrating that perceptual integration affects action planning. Results from 3 psychophysical experiments suggest that if a particular perceptual feature is bound into an object representation, it is less accessible for concurrent action planning. Furthermore, our results support the idea that the formation of object representations goes through two phases: feature activation and feature integration. Feature sharing between perception and action is bene1cial during the feature activation, but leads to mutual interferences in feature integration. Wider implications of these 1ndings are discussed, especially with regard to feature binding as a general mechanism of cognitive representation as well as the relationship between perception and action.
Selection-for-perception and selection-forspatial-motor-action are coupled by visual attention: a review of recent findings and new evidence from stimulus-driven saccade control
Authors: Schneider Werner X , Deubel Heiner
Published: November 2023

Abstract. The topic of this paper is how selection-for-visual-perception (usually identified with visual attention) and selection-for-spatial-motor-action are related. The later process refers to the fact that simple actions such as grasping an object usually imply the need to select one movement target among other potential targets. In the 1rst part of the paper, a theoretical framework for understanding the relationship between selective perception and motor target selection will be introduced, namely the ‘Visual Attention Model’ (VAM, Schneider 1995). The main hypothesis of VAM is that of a tight coupling between selection-for-perception and selection-for- spatial-motor-action, which is assumed to be mediated by a common visual attention mechanism. Recent behavioral evidence supporting this claim is reviewed in the second part. The basic experimental paradigm (Deubel and Schneider 1996) required subjects to discriminate briefly presented target stimuli while they were preparing a saccadic eye movement or a manual pointing movement. The data revealed a spatially selective (possibly object-specific) coupling of motor programming and visual perception. In the third part of the paper, three new experiments are reported which investigated whether this coupling also holds when the motor action is directed in a stimulus-driven way. A discrimination judgment had to be made about a letter object that was brie2y presented during the preparation of a saccade guided by a peripheral cue. All three experiments showed a tight, spatially specific coupling between the intentionally controlled perceptual discrimination and the stimulus- driven saccade programming. Additionally, the third experiment addressed the question of whether this result is the consequence of an obligatory attraction of attention by peripheral cues per se. The data show that a nonrelevant peripheral cue attracted attention automatically only when cue and discrimination target appeared in the same hemifield. We conclude that visual attention is not obligatorily coupled to peripheral cues, rather, the spatial relationship between cue and the goal-driven attentional focusing has to be taken into account. Implications of the new findings for theories of attentional control in visual perception and motor action are discussed.
Visible and invisible structures on infinite-dimensional groups
Authors: Neretin Yu. A , Gould G G
Published: November 2023

This·chapter is by way of an introduction. No formal reference will be made to it in the subsequent chapters. Anybody who is not acquainted with the topic could well skip this chapter. It is a commentary on a theory which will not be too interesting to those without a suitable background.
Classical Harmonic Analysis and Locally Compact Groups
Authors: Reiter Hans , Stegeman Jan D
Published: November 2023

A revised and expanded second edition of Reiter's classic text Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press 1968). It deals with various developments in analysis centring around the fundamental work of Wiener, Carleman, and especially A. Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study of certain general function algebras, and then discusses functions defined on locally compact groups. The aim is, firstly, to bring out clearly the relations between classical analysis and group theory , and secondly, to study basic properties of functions on abelian and non-abelian groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. In the new edition relevant material is added that was not yet available at the time of the first edition.
Applications of Combinatorial Mathematics
Authors: Mitchell Chris
Published: November 2023

In the last thirty years, combinatorial mathematics has found itself at the heart of many technological applications. The aims of the conference on which this book is based were to stimulate combinatorial mathematicians to pursue new lines of research of potential practical importance, and to uncover the breadth of applications of the subject. Topics covered include neural networks, cryptography, radio frequency assignment for mobile telecommunications, coding theory, sequences for communications applications, interconnection networks, data types, knot theory, radar, parallel processing, network reliability, formal specification of programs and protocols, and combinatorial optimisation.
The Use of Combinatorial Structures in Communication Signal Design
Authors: Golomb S W
Published: November 2023

For many kinds of communication channels, the optimum detection system is a correlation detector, which computes the cross-correlation between the actual (noisy) received signal and locally generated models of the various waveforms which might have been sent. The waveform with the largest correlation is the maximum likelihood estimate of what was sent. It is this fact which motivates the search for sets of signals (waveforms) which are as mutually uncorrelated as possible for use as the “codewords” in reliable communication systems, and for signals which are as uncorrelated as possible with all non-zero time-shifts of themselves for use in radar, sonar, and synchronisation applications.
Numerical Solution of Differential-Algebraic Equations
Authors: Petzold Linda R
Published: November 2023

Many physical systems are naturally described as systems of differential-algebraic equations (DAEs). These types of systems occur in the modeling of electrical networks, flow of incompressible fluids, control, mechanical systems subject to constraints, and in many other applications. This class of problems includes systems which are in many ways quite different from ODEs. In these notes we outline some of the theory and available software for the numerical solution of DAE systems, and explore some challenging applications.
Other classes of regular semigroups
Authors: Howie John M
Published: November 2023

The success of inverse semigroup theory has naturally prompted the study of more general regular semigroups, very often quite explicitly defined as generalizations. In the Exercises and in the Notes at the end of the chapter we make brief reference to one or two pieces of work of this kind, but in the text we shall confine ourselves to three fairly natural types of regular semigroup.
Free semigroups
Authors: Howie John M
Published: November 2023

In Chapter 1 we came across the notion of the free semigroup A+and the free monoid A* on a set A. While the emphasis of this book is unquestionably on the study of various classes of regular semigroups, it would be wrong in a general introduction not to include a short chapter on free semigroups, for in the wide and growing applications of semigroup theory to automata, languages and machines it is the free semigroups that play the major role.
Introduction
Authors: Fonseca Irene , Gangbo Wilfrid
Published: November 2023

The degree d( ϕ, D,p) is a tool that describes the number of solutions for the equation ϕ (x) =p in a given open set D ⊂ X, whereϕ  : D ⊂ X → X is a continuous function, p ∉  ϕ(  ∂D), and X is a topological space, often a metric space. As it turns out, the degree is a generalization of the winding number of [ineq] when we identify the complex plane ℂ to ℝ (see Chapter 2).
The Evolution of an Image Processing Language
Authors: Saxton W O
Published: November 2023

The image processing program Semper, still in widespread use in many laboratories across the world, was originally produced twenty years ago with very limited resources, to provide the tools that were needed to address the serious problems of image interpretation arising in high resolution electron microscopy of a range of specimens of physical, chemical and biological interest. This paper records the main stages of software development in the context of successive hardware improvements and the main applications within electron microscopy: the phase problem, image averaging, image restoration, averaging and three-dimensional reconstruction of distorted crystals, microscope control, and aperture-synthesis microscopy.
Probabilistic Resolution Criterion for Imaging in Scattering Media
Authors: Appel R K , Hopcraft K I , Somekh M G
Published: November 2023

This paper presents a. probabilistic resolution criterion for quantifying imaging performance in scattering media. This criterion incorporates an explicit description of the noise and is therefore superior to standard resolution criteria such as those introduced by Rayleigh and Sparrow. The probabilistic resolution criterion is applicable to imaging systems with generalised noise distributions. As an illustrative example, a simple optical imaging system is considered, whe1e the illumination is coherent and the scattering assumed to be Gaussian. The analysis requires a description of the intensity statistics at the detector plane, which in this case is described by two correlated Ricean distributions. This is derived and then used to determine the probabilistic resolution criterion. Results are presented for two variants of the probability criterion, which are modifications of the standard Sparrow and Rayleigh resolution criteria.
Truth and the foundations of mathematics. An introduction
Authors: Dales H G , Oliveri G
Published: November 2023

The concept of truth occupies a central position both in mathematics and in its philosophy. As we shall see in what follows, different conceptions of what it means to say of a mathematical statement that it is true give rise to different and mutually incompatible mathematical theories and to mutually exclusive positions on whether there are such things as mathematical knowledge and reality and on how these ought to be characterized.

The purpose of this introduction is to guide the reader to an appreciation of the importance of the theme of the book through: a preliminary clarification of the historical background relevant to the contemporary debate on the concept of truth in mathematics; a brief discussion of the mathematical and philosophical importance of such a concept; and a sketch of the applicability of the concept of truth in set theory.
Truth and objectivity from a verificationist point of view
Authors: Prawitz Dag
Published: November 2023

Truth in mathematics is a very appropriate theme for a conference on what mathematics is about. Questions of truth often work as a catalyst in bringing out contrasts between different positions concerning the nature of a given field. For instance, the question of the applicability of truth is a main issue in discussions on the position known as mathematical formalism, a position that occurs in many versions. Hilbert’s variant of formalism is based on the idea that so-called real sentences are true or false while all other sentences lack truth values. In his chapter in this volume, Dales (1998) seems to advocate a more radical formalism. Challenging the realist conception of mathematics by saying that it takes truth as a key notion but leaves unanswered how truth is established, he takes the merit of formalism to be that it accounts for the nature of mathematics without relying upon any notion of truth. The critics of such a strict formalism typically claim that in the end even the formalist account will depend on some notion of truth. I think that such a criticism can be rightly levelled also against Dales’s formalism. He proposes that a mathematical theorem is to be understood as asserting that a certain formula follows logically from certain axioms, but if fallows logically is understood as follows according to the rules of predicate calculus, then the proposal reduces mathematics to a body of truths about a certain calculus, a certain formal game if you want. This makes mathematics a science that still pursues truths, although truths of a special kind, and we are left with explaining the nature of such truths.
Truth, rigour, and common sense
Authors: Manin Yu. I
Published: November 2023

The main difficulty of discussing the nature of mathematical truth in 1995 as I see it is that no new insights into it have been gained since the epoch of deep discoveries crowned by Godel’s results of the late thirties.

To avoid repetition and to enliven the discourse one can try to put the matter into a broader context and add a personal note. Both solutions tend to divert the reader’s attention to vaguely related topics, and I offer my apology for choosing these dubious tactics.musings on the history of mathematics perceived as a genre of symbolic (or semiotic) games; a discussion of truth and proof in the context of contemporary research (centering on a recent controversy prompted by a letter by A.
Mathematical definability
Authors: Slaman Theodore A
Published: November 2023

One might fairly say that the mathematical analysis of definability began in 1931, with the appearance of Gödel’s Incompleteness Theorem (Gödel 1931). Gödel showed that, for sufficiently strong formal systems T, there exist undecidable statements φ such that there is no proof of φ or of φ within T. This theorem pointed to an intrinsic incompleteness within the formal notion of proof.

The method of computation by algorithm is more general than that of verification by formal proof. It too was shown to be incomplete, but it took some time to develop the technical apparatus needed to state this incompleteness correctly. (Kleene 1987), in his biographical memoir of Gödel, recalls this development and we summarize some of his remarks. Kleene describes the intuitive notion of an algorithm as follows.
Black Holes
Authors: D'eath P D
Published: November 2023

One of the major applications of general relativity is to the study of black holes formed by the gravitational collapse of a massive body (Misner et al. 1973) or in the early universe by the collapse or collision at high speeds of regions containing large amounts of energy (Barrow and Carr 1978). Black holes are an intrinsically non-linear phenomenon, depending on the strong-field behaviour of the gravitational field. In a black hole, the gravitational field is so strong that even light cannot escape. Black holes should be contrasted with another generic feature of the vacuum gravitational field-gravitational waves. There one solves approximately linear perturbation equations, perhaps about a nontrivial background space-time, to describe the waves. Indeed, at least in the noncosmological case, one might conjecture that a generic vacuum gravitational field could be built up by ‘superposing’ in a non-linear way the fields of various black holes and gravitational radiation. This superposition is described in Chapters 3 and 4. One can also extend this to the case in which there is matter in the space-time.
The Homotopy Category of (n − 1)-Connected (n + 1)-Types
Authors: Baues Hans-Joachim
Published: November 2023

We have to consider the hierarchy of categories and functors (n≥ 2) where types is the full category of (n -−1)-connected (n + k)-types, that is, of CW-spaces Y with πiY = 0 for i < n and i > n + k. The functor P is the Postnikov functor which carries an (n + k)-type to its (n + k − 1)-type, k ≥l. Since (n -−1)-connected n-types are the same as Eilenberg–Mac Lane spaces K(A, n), we can identify them with abelian groups.
Decomposition of Homotopy Types
Authors: Baues Hans-Joachim
Published: November 2023

In this chapter we describe explicit results on the classification of homotopy types. For example we give a complete list of (n -−1)-connected (n + 3)dimensional homotopy types X, n≥ 4, for which all homology groups Hi(X) are cyclic. We also obtain a complete list of all homotopy types X for which πn X, πn+ 1  X, πn+2 X, nɥ 4, are cyclic groups and for which π  i  X is trivial otherwise. These results are obtained by describing the corresponding indecomposable homotopy types. The indecomposable (n − 1)-connected (n + 3)dimensional polyhedra were found in Baues and Hennes [HC]. The complete solutions of classification problems in this chapter show that the prospect of homotopy types is not so dim.
Homotopy Groups in Dimension 4
Authors: Baues Hans-Joachim
Published: November 2023

The computation of the homotopy groups πn X, n≥ l, of a connected space X is a fundamental problem of algebraic topology. It is well known how to determine the fundamental group πnX in terms of the attaching maps of 2-cells in X. For n ≥2 we may assume that X is simply connected since πn X coincides with the corresponding homotopy group of the universal cover of X.
Dual spaces and the Hahn-Banach theorem
Authors: Meise Reinhold , Vogt Dietmar
Published: November 2023

The elements of E ′are called continuous linear forms or continuous linear functionals on E. In this chapter we will show that for every normed space E, the space E′ is so plentiful that E′ can be used to investigate properties of E. The richness of E′ results from the Hahn-Banach theorem which will be proved with the help of Zorn’s lemma.
Matroids
Authors: Oxley James
Published: November 2023

A matroid consists of a collection of subsets of a finite set which, loosely speaking, behave like the edge sets of cycles in a graph. Matroids also arise naturally from matrices and projective geometries. This chapter provides some examples, mainly in the context of connectivity, of how the interplay between graphs and matroids has led to new results for both matroids and graphs. Matroids were introduced by Hassler Whitney [22] in 1935, with the aim of capturing the fundamental properties of dependence that are common to graphs and matrices.
Basic point set topology
Authors: Lawson Terry
Published: November 2023

We will also discuss more precisely the “geometrical objects” in which we are interested (called topological spaces), but our viewpoint will primarily be to understand more familiar spaces better (such as surfaces) rather than to explore the full generalities of topological spaces. In fact, all of the spaces we will be interested in exist as subspaces of some Euclidean space Rn. One of the methods of mathematics is to abstract central ideas from many examples and then study the abstract concept by itself. Although it often seems to the student that such an abstraction is hard to relate to in that we are frequently disregarding important information of the particular examples we have in mind, the technique has been very successful in mathematics. Frequently, the success is rooted in the following idea: knowing less about something limits the avenues of approach available in studying it and this makes it easier to prove theorems (if they are true). Of course, the measure of the success of the abstracted idea and the definitions it suggests is frequently whether the facts we can prove are useful back in the specific situations which led us to abstract the idea in the first place. Some of the most important contributions to mathematics have been made by those who have figured out good definitions. This is difficult for the student to appreciate since definitions are usually presented as if they came from some supreme being. It is more likely that they have evolved through many wrong guesses and that what is presented is what has survived the test of time.
The Gibbs formulation
Authors: Carrington Gerald
Published: November 2023

We shall initially consider only simple systems, which we identify as follows. First, a simple system is homogeneous, having no internal walls or partitions. Second, we assume that its equilibrium state is identified by the value of U, the amount of each of its chemical components, expressed as mol numbers, N1, N2, … , Nr and the deformation variables for the system.
Symmetry in Physical Laws
Authors: Brink D M , Satchler G R
Published: November 2023

A THEORETICAL investigation of a physical problem may come upon difficulties of two kinds. The exact physical laws govern¬ing the behaviour of a system may not be known, making it impossible to arrive at a complete theoretical description of the system. Problems of fundamental particle structure and reactions present this first difficulty in an acute form. More often the situation is analogous to that encountered in prob¬lems of atomic and molecular structure, where the inter¬ actions (Coulomb forces) are well-known, but where the struc ture in a particular problem may be so complicated that no exact solution can be found.
Tensors and Tensor Operators
Authors: Brink D M , Satchler G R
Published: November 2023

WE are accustomed to deal with certain physical quantities such as mass and energy which are in no way connected with the orientation of our coordinate system and which have no directional properties. Such quantities a.re sea.la.rs, or tensors of rank zero. ‡ Other quantities, such as the position of a point in space or the velocity of a particle, have associated with them a direc¬tion as well as a magnitude. These quantities are vectors or tensors of rank one and in order to specify them we must give the direction as well as the magnitude.
Matrix Elements of Tensor Operators
Authors: Brink D M , Satchler G R
Published: November 2023

WE are now in a position to calculate those parts of any physical problem which are concerned with angular integrations, the coupling of angular momentum vectors, or our choice of coordinate system-in fact general rotational symmetries-which we might call the ‘geometrical’ parts. The basic technique is to exploit the simplest matrix reduction which we have, already met in Chapter IV, namely the WignerEckart theorem for the matrix elements of spherical tensors.
Dynamics of Heavy Electrons
Authors: Kuramoto Y , Kitaoka Y
Published: November 2023

Heavy electrons are found among a number of lanthanide and actinide compounds, and are characterized by a large effective mass which becomes comparable to the mass of a muon. Heavy electrons exhibit rich phenomena such as unconventional superconductivity, weak anti- ferromagnetism, or pseudo meta-magnetism. This book is intended not only as a monograph, but can readily serve as an advanced textbook on theoretical and experimental physics of strongly correlated electrons. Over the last two decades, heavy electrons have been the focus of very active experimental and theoretical studies. Many established ideas and techniques have been insufficient to describe and understand heavy electrons and their impact properly. On the theoretical side, quantum fluctuations make mean-field theories difficult to handle, while on the experimental side, extreme conditions such as strong magnetic fields and pressure at ultra-low temperatures may be required. Heavy electron systems as described in this book offer a case study for applying and testing most of the major tools in theoretical and experimental condensed matter physics. Graduate students and researchers working on strongly correlated condensed matter systems will find in this book a comprehensive introduction and many examples how conventional concepts of solids may work or not work, and how they can be refined and sharpened in the context of heavy electron systems.
Preface
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.
The Electromagnetic Interaction
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco
Published: November 2023

In this introductory chapter we give the basic formalism to describe the electromagnetic field and its interaction with hadronic matter for both real and virtual photons. The formalism is developed for the use of an electromagnetic probe to investigate the single-particle (s.p.) properties of atomic nuclei and to study the many-body effects which are particularly important in nuclear structure. A number of formulae will be found in this chapter: they will be useful in the treatment of the problems discussed in all sections of the book. Moreover, they will give a general framework suitable for providing a clear starting point to understand the different situations one has to face when working in the field and to find the appropriate solutions. After a brief reminder of the general properties of the electromagnetic field, with particular attention to the gauge invariance of the electromagnetic potential, the one-photon exchange approximation is discussed for electron scattering. This approximation is the fundamental basis of the whole treatment and essentially relies upon the relative weakless of the electric force. In the few cases where a better approximation is necessary, specific sections will be devoted to these refinements. Attention will be focused on the longitudinal and transverse components of the electromagnetic interaction with respect to the momentum transfer q, since a clear comparison between the electron and the photon probe can be made in this way. Moreover, in different situations this separation produces several observable quantities that can clarify some aspects of the reaction mechanism or of nuclear structure, which are averaged and therefore obscured in the global response.
Form Factors of Excited Baryons
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco
Published: November 2023

The finding that the nucleon is an extended object (Hofstadter and McAllister 1955; Chambers and Hofstadter 1956; Hofstadter 1956) with an internal structure (Bloom et al. 1969; Breidenbach et al. 1969; Miller et al. 1972; Friedman and Kendall 1972) immediately calls for an understanding of its excitation spectrum. The excitation spectrum of the nucleon has been extensively studied by pion scattering and a large number of states have been discovered after the pioneering work of Fermi and coworkers (Anderson et al. 1952). Baryon states are classified by the Particle Data Group (Montanet et al. 1994) according to a quark model based on SU(6) spin-flavour symmetry. The structure and dynamics of hadrons have to be understood in terms of a theoretical description of strong interactions ultimately derived from QCD, but in a regime where the underlying QCD dynamics cannot be treated perturbatively. Thus the complexity of hadrons requires the development of soluble models not only retaining the basic symmetries of QCD but at the same time also containing the relevant dynamical features of interacting quarks and gluons. The electromagnetic excitation of nucleon resonances (N*) gives important complementary information on the internal dynamics of baryons since it provides constraints on theoretical models by determining the photocoupling amplitudes associated with the-γNN* vertex at different four-momentum transfers Q2•
One-Nucleon Knockout Reactions
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco
Published: November 2023

abstract

This chapter is devoted to the analysis of the experimental data of direct knockout reactions with one-nucleon emission. The interest will be addressed mainly to complex nuclei, without considering, in general, the few-body systems. A choice of the available data will be presented, in order to provide a review of typical transitions and to stress the mechanism and the fundamental properties of the process. Attention will be focused on the reactions where the residual nucleus is left in a discrete state. The energy region above the two-nucleon emission threshold will be treated in Chapter 8. The one-particle mechanism, presented and discussed in the preceding chapter, reproduces very well the experimental data of one-nucleon knockout from valence states. This is due to the relatively weak electromagnetic interaction and to the fact that electron scattering can transfer a rather low energy combined with a large momentum, which favours the direct interaction with a single nucleon.