bluuebunny/crossref_metadata_2025_split huggingface dataset:
The velocity correlation function
Authors: Egelstaff P A 
Published: November 2023

Abstract
The diffusion models described in Chapter 11 arc not valid for the shortperiod modes of single-particle motion, which will be discussed in this chapter through the velocity correlation function. This function relates the velocity of an atom at a time τ = 0, with its velocity at a later time. It has a simple relation to the diffusion constant (Section 12.2), and it is of unique physical importance in liquid state theory if the self correlation function Gs(r, τ) is approximately Gaussian in r. The reason for this is that if Gs is Gaussian, the higher-order velocity correlations (that is, the correlation of four or more time points) may be shown to be simply related to the ‘two-time’ velocity correlation discussed in this chapter. Conversely, if Gs(r, τ,) is markedly non-Gaussian in r, the higher-order velocity correlations will have a marked influence on the single-particle modes in addition to the effects covered by the simple two-time correlation.
Graphical models for stochastic processes
Authors: Didelez Vanessa 
Published: November 2023

Abstract
Graphical models have proven to be a valuable concept in various fields of multivariate data analysis, as underpinned by several contributions to this book. However, the pure definition of conditional independence graphs is not satisfactory for the representation of two closely related dependence concepts: causal and dynamic dependence - both sharing for instance the property of being asymmetric, as opposed to conditional dependence. In graphical models directed edges symbolize specific sets of conditional independence hypotheses.
MCMC methods for stochastic epidemic models
Authors: ‘Neill Philip D O 
Published: November 2023

Abstract
The previous article highlighted some of the challenges involved in performing statistical inference using stochastic models for infectious diseases. These challenges arise due to both the inherent features of infectious disease outbreak data, for instance a high level of dependency in such data and a lack of complete observational information, and also the relative mathematical intractability of even very simple stochastic epidemic models.
A predictive point of view on Bayesian non-parametrics
Authors: Petrone Sonia 
Published: November 2023

Abstract
Professor Hjort touches upon many topics, and gives many ideas and suggestions to be developed. In my discussion, rather than making a long list of comments on the many aspects touched upon, I would like to start with an example, which raises some questions and, I think, underlines some open issues in Bayesian nonparametric inference.
Processing mechanisms and neural structures involved in the recognition and production of actions Introduction to Section III
Authors: Rumiati Raffaella Ida 
Published: November 2023

Abstract
Interest in the recognition and imitation of actions has grown considerably in the last ten years among neuroscientists, as testi1ed by the very ample review of related theories and empirical studies made available by Bekkering and Wohlschläger (this volume, Chapter 15). First, the authors stress the importance of imitation in the 1eld of social and developmental psychology. Second, they provide the reader with several conceptualizations of imitation and, by comparing the research on humans and non-human primates or on other species in this 1eld, they try to answer the question of who can and who cannot imitate. Finally, after discussing the most in2uential theories of imitation, Bekkering and Wohlschläger illustrate their own view on the mechanisms involved in imitation. In short, their theory of goal-directed imitation holds that, when humans imitate an action, for instance touching an ear, they map the goal of the action irrespective of the effector used for performing the movement (e.g. the left or right hand), and of the movement path (e.g. ipsior contralateral).
Content-specific interactions between perception and action Introduction to Section IV
Authors: Eimer Martin 
Published: November 2023

Abstract
Of the numerous factors involved in the control of perceptuo-motor links, perhaps the most widely studied is the similarity (or compatibility) between speci1c stimuli and responses. S–R compatibility has important effects on the quality of behavioural performance. Some stimulus–response mappings are more compatible than other mappings, and variations in S–R compatibility affect both the speed and the accuracy of responses. Such compatibility effects are content-speci1c, because they do not re2ect general processing limitations in perceptuo-motor interactions, but are determined by particular features of stimuli and responses, and by speci1c stimulus–response mappings. Recent research has provided numerous insights into the mechanisms underlying S–R compatibility effects. Detailed hypotheses have been put forward about ways in which stimulus and response properties can be compatible or incompatible, and about the nature of the perceptuo-motor links that are affected by S–R compatibility (see Kornblum and Stevens, this volume, Chapter 2).
Comparative methods
Authors: Bennett Peter M , Owens Ian P F 
Published: November 2023

Abstract
Bird species exhibit enormous diversity in morphology, behaviour, and ecology. In this book we attempt to explain why variability in life-history traits, mating systems, and extinction patterns exists across a wide range of bird species. We do this by making comparisons among taxa to test hypotheses about the adaptive significance of variation in these traits. In this section we present the theoretical and methodological basis for our work.
Ecological basis of sexual dimorphism
Authors: Bennett Peter M , Owens Ian P F 
Published: November 2023

Abstract
The traditional explanation for interspecific variation in the extent of sexual dimorphism among birds is that it is a consequence of variation among species in social mating system and the pattern of parental care (from Darwin 1871 and Wallace 1889 onwards; reviewed in Lack 1968; Butcher and Rohwer 1988; Andersson 1994). For example, social polygamy leads to the competitive sex being larger and more ornate than the choosy sex, whereas large sex differences in parental care leads to the caring sex developing more cryptic plumage. Recently, however, two empirical observations have challenged this traditional view. First, many extremely polygamous species in which one sex cares for the offspring alone are, in fact, largely monomorphic with respect to both size and plumage colour (Hoglund 1989; Trail 1990; but see Oakes 1992). But even more strikingly, many apparently monogamous species that display classic biparental care are, in fact, highly dimorphic (Moller 1986; Harvey and Bradbury 1991).
Explaining variation in species richness
Authors: Bennett Peter M , Owens Ian P F 
Published: November 2023

Abstract
Why do some bird families contain so many more species than other families? This deceptively simple question has proved difficult to answer. We examined this question in a series of analyses in collaboration with Paul Harvey (Owens et al. 1999). There are two major types of explanation. The first simply states the fact that uneven taxonomic species distributions may arise through chance alone and do not, therefore, require complex explanations (e.g. Raup et al. 1973; Raup 1985). Explanations of the second type predict that chance alone is not responsible for the extent of variation in species richness and attempt, therefore, to identify the factor(s) that predispose certain lineages to being species-rich and other lineages to being species-poor (see Cracraft 1982, 1985; Slowinski and Guyer 1989; 1993; Guyer and Slowinski 1995; Nee et al. 1992, 1996; Purvis 1996; Barraclough et al. 1998a,b).
Categories of Symmetries and Infinite-Dimensional Groups
Authors: Neretin Yu. A , Gould G G 
Published: November 2023

Abstract
There are many types of infinite-dimensional groups, most of which have been studied separately from each other since the 1950s. It is now possible to fit these apparently disparate groups into one coherent picture. With the first explicit construction of hidden structures (mantles and trains), Neretin is able to show how many infinite-dimensional groups are in fact only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers.
The Weil representation: finite-dimensional case
Authors: Neretin Yu. A , Gould G G 
Published: November 2023

Abstract
In work on mathematical physics from the 1950s to the beginning of the 1960s it was discovered that the real symplectic group Sp(2n,ℝ.) has a representation that is strikingly similar to the spinor representation S0(2n, ℂ). By a freak of mathematical terminology which is difficult to explain, this representation is called the Weil (or Segal-Shale-Weil) representation, although the correct terminology should be ‘Friedrichs-Segal-Berezin representation’, see §6.2. In this and the following chapter we carry out the same programme with regard to the Weil representation as has already been carried out with regard to the spinor representation. Here (in contrast to Chapter 2) we leave out the motivation leading up to it and go straight into the theory.
Representations of the group of diffeomorphisms of a circle with highest weight
Authors: Neretin Yu. A , Gould G G 
Published: November 2023

Abstract
This section contains the simple definitions relating to the group of diffeomorphisms of a circle, as well as a brief introduction to the algebraic theory of representations of a Virasoro algebra with highest weight. Unfortunately, there are no standard texts on the theory of representations of a Virasoro algebra with highest weight (if I am not mistaken). In spite of the fact that in the 1980s this theory was one of the most fashionable in mathematics, real progress in this area has not been too great. Answers have been obtained to a number of natural questions (such as reducibility conditions, the structure of submodules, and unitarizability conditions); however, in the majority of cases no ‘natural’ proofs are known at present. Also there are no known answers to many reasonable questions which to all appearances are not insoluble.
Some algebraic constructions of measure theory
Authors: Neretin Yu. A , Gould G G 
Published: November 2023

Abstract
Let K be a real Hilbert space, and let IsomR(K) be the group of affine isometries of K, Then IsomR(K) acts in F(Kc) by formula (10.1.1). In view of (10.1.2), this action is linear.
Function algebras and the generalization of Wiener’s theorem
Authors: Reiter Hans , Stegeman Jan D 
Published: November 2023

Abstract
Here we shall discuss, in considerable generality, algebras of functions and their ideals. The concrete basis for our study is the Fourier algebraF (IRv) (Definition L1.13) we want to develop methods for extending Wiener’s approximation theorem to groups and for generalizing it The abstract approach will make the proofs simpler and more lucid.
Locally compact groups and the Haar measure
Authors: Reiter Hans , Stegeman Jan D 
Published: November 2023

Abstract
In this section some notation and terminology to be used later is outlined, mainly in those cases where there are several choices in the literature; some of the relevant facts are also mentioned, for later reference. For classical complete expositions see Montgomery and Zippin ( f955), Weil (1953), Bourbaki (1960, Chapter III), and Pontryagin (1966). See also Chevalley ( I 946, pp. 26-32) and the exposition in Kaplansky (1957, Chapters IV and VIII); an historical discussion is given in Freudenthal (1940). In Appendix B some more modern references are given.
0-simple semigroups
Authors: Howie John M 
Published: November 2023

Abstract
The chapter begins with some elementary results on simple and 0-simple semigroups. A decomposition theorem for semigroups in general then indicates why an understanding of simple and 0-simple semigroups is important. The main result of the chapter is due to Rees (1940), and applies to 0-simple semigroups containing primitive idempotents. The Rees Theorem, strongly motivated by the Wedderburn-Artin Theorem for rings (see, for example, Cohn (1989)) has played a dominant role in the development of the subject.
Semigroup amalgams
Authors: Howie John M 
Published: November 2023

Abstract
The use of module theory in the study of rings is long established, but only in relatively recent years has serious use been made in semigroup theory of the non-additive analogue of a module. Perhaps surprisingly for such a simple structure, what we shall call S-systems (where S is a monoid) have proved a useful tool in the study of monoids and semigroups. The particular use that we shall highlight in this chapter is the application to amalgamation theory and related topics. The technique is available only for monoids, but, as we shall see, it is usually possible to extend the results to semigroups in a fairly straightforward way.
Degree In Infinite-Dimensional Spaces
Authors: Fonseca Irene , Gangbo Wilfrid 
Published: November 2023

Abstract
We define the Leray-Schauder degree in a linear normed space of infinite dimension, X. Let D ⊂ X be an open, bounded set, let ϕ:D¯ → X be a continuous mapping, and let p ∈ X\ φ (∂D). We want to defined(φ, D,p), expecting that
Nonstandard Methods in Image Processing
Authors: Hoskins R F 
Published: November 2023

Abstract
In March 1994 the IMA held a Conference on The Mathematical Education of Engineers at Loughborough University, United Kingdom. The theme was the increasingly difficult problem of deciding what mathematics is essential to a specific engineering audience, and how best to teach it. The problem is compounded by the fact that students are often handicapped by an inadequate background of basic mathematical equipment. In the particular case of Image Processing there is an obvious need for a reasonably comprehensive knowledge of Harmonic Analysis, and this in turn demands some acquaintance with the theory of Gener alised Functions, at least in so far as delta functions are concerned. In principle, a rigorous theory of delta functions has been in existence since the publication of Laurent Schwartz’s Theory of Distributions [1], in 1950/51. However, this was fairly difficult for the non-mathematician when it first appeared and, broadly speaking, has remained so ever since, despite attempts to make it more accessible to a broadly-based audience.
Algebraic Solutions to the Non-stationary Deconvolution Problem
Authors: Blackledge J M , Lezeau P A 
Published: November 2023

Abstract
Discrete non-stationary deconvolution in both one- and two-dimensions is approached as a linear algebraic problem and some numerical results presented. The discrete non-stationary convolution operation is modelled and expressed in terms of a linear system of algebraic equations. Exploiting its spa1sity, this system is then solved using two iterative methods: (i) a Successive Under-Relaxation Scheme (SUR); (ii) the Conjugate Gradient Method. It is found that these algorithms are numerically stable for signals. For images, they are useful provided the blurring is not too extensive. The choice of the best method to use is related to the structure of the convolution kernel. Sensitivity to additive noise is also investigated and partially resolved. Finally, some details on the computer implementation of the methods are given.
Faster Block Coding of Images using the Truncation Method
Authors: Anguh M M , Martin R R 
Published: November 2023

Abstract
Image compression is widely used in computer graphics; one main method is transform coding of images [l]. For example, the JPEG standard [2] uses Discrete Cosine Transform coding, while the Slant Transform [3] has been used for coding television signals. Other applications have also used Fourier and Walsh Transforms for image compression.
Fractal Dimension Segmentation
Authors: Blackledge J M , Foxon B , Mikhailov S 
Published: November 2023

Abstract
This paper discusses the use of fractal geometry for segmenting digital images. A method texture segmentation is introduced which uses the Fractal Dimension to measure image texture. Using this approach, variations in texture across an image can be characterised in terms of variations in the fractal dimension. By imaging the spatial fluctuations in fractal dimension obtained using a conventional moving window approach, a digital image can be texture segmented-this is the principle of Fractal Dimension Segmentation.
Images of the Earth’s Surface and Atmosphere
Authors: Rycroft M J 
Published: November 2023

Abstract
Two-dimensional analogue or digital images are obtained, with appropriate spatial resolution, from aircraft or satellites by remote sensing of radiation in the ultraviolet, visible, infrared and microwave parts of the electromagnetic spectrum. These images are used for cartography or for studies of geology, glaciology, hydrology, flooding, vegetation (crops and forestry, including forest fires) and volcanoes. Over the oceans they give physical information on subocean features, sea surface temperatures, currents, waves and shipping; they also provide valuable information on the ocean’s biological productivity—phytoplankton and nutrient rich areas that are good for fishing. Regarding the atmosphere, information is gained on clouds, winds, cyclones, hurricanes and rainfall as well as air pollution, temperature structure and ozone content. The aurora australis and borealis are well studied from satellites in eccentric orbits. Thus, such images on local, regional and global scales are used for a variety of purposes for the benefit both of the peoples of the Earth and of the Earth itself.
Spatial Data Representation for Rotation Invariant Correlation
Authors: Blackledge J M , Sapounas D 
Published: November 2023

Abstract
Rotation invariant image processing is an old problem with many applications in commercial and military systems, ranging from quality control and machine vision to automatic object recognition. A rotation invariant data representation is proposed and a method for performing image correlation of areas (sensed images) extracted from overl1ead images (reference images), invariant to position and rotation, is developed. The process, based on artificial neural network (ANN) concepts, wavelet theory and current digital image processing techniques, reduces the spatial data to a linear representation suitable for training an ANN to obtain the coordinates of a sensed image within a reference image. A step by step description of the process and performance results for various levels of Gaussian noise are provided.
Application of Some Image Processing Techniques to the B-scan Analysis of Two-Phase Flows
Authors: Blackledge J M 
Published: November 2023

Abstract
This paper discusses some of the latest results of a research project based at Schlumberger Cambridge Research being undertaken by the Imaging Research Centre at De Montfort University. The project is concerned with the application of a commercial ultrasound scanner (originally designed for medical imaging-a “Brightness” or B-scanner) to study two-phase flows. Operating at a frequency of 7.5 MHz, the scanner provides a real-time image formed by the scattering of ultrasound from a stream of microbubbles in a predominantly single-phase (water) flow and/or the air-water interface characteristic of a two-phase flow proper. The probe consists of a linear array of transducers aligned along the direction of the flow. Experiments have been conducted using the two-phase flow systems available at Schlumberger Cambridge Research which are consistent with industrial scale flows occurring in a wide range of process engineering industries. The types of B-scan images studied so far have all been of horizontal flows through 3 inch internal diameter reinforced plastic pipes.
Estimating Fractal Dimension and Number of Degrees of Freedom for Multiphase Flow Regime Identification
Authors: Rawes W , Oddie G , Yeung H 
Published: November 2023

Abstract
At present, flow regime identification is based on methods which involve a certain amount of subjectivity. Air-water flows have been analysed in a. 50 mm diameter pipe in an attempt to objectively classify the flow regimes. Signals have been collected from three different types of non-invasive sensors. The fractal properties of these signals have been investigated using power spectra decay. The number of degrees of freedom of the system producing such signals has been investigated using singular value decomposition and properties of the correlation integral.
Mathematics as language
Authors: Effros Edward G 
Published: November 2023

Abstract
According to an anecdote popular among physicists, it is easy to tell when you are speaking to a mathematician: if you should ask him ‘do you or do you not own an umbrella’, it is likely that after some thought he will answer ‘yes’.
Ever since mathematics was codified in terms of symbolic logic in the early part of this century, it has been understood that all of mathematical discourse consists of tautologies of the above variety. Owing to the seemingly absolute precision of axiomatic deduction, few mathematicians are concerned with the grammatical truth of their subject. Thus despite the fact that they recognize that the axioms of logic are necessarily incomplete, and even possibly inconsistent, most mathematicians are confident that any future difficulties will yield to technical adjustments. This complacency has been reinforced by the remarkable progress that logicians have made in delineating the limits of the axiomatic method.
Set Theory with a Universal Set
Authors: Forster T E 
Published: November 2023

Abstract
Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by other sets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science. The second edition still concentrates largely on Quine's New Foundations, reflecting the author's belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the set theories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.
Introduction
Authors: Forster T E 
Published: November 2023

Abstract
It is often assumed that Russell’s paradox shows that the universe cannot be a set, but this follows only if every subclass of a set is a set. So, if we want the universe to be a set (hereafter “V E V”), we must somehow forestall the application of comprehension-like schemes to big2 sets, lest we enable the diagonal construction to go through. This does not exclude the possibility that, for some suitable notion of “small”, the small sets in such a system form a model of ZF. In some of the systems described here this possibility is made explicit in an axiom whose relative consistency can be proved. Thus the extra generality of V E V need not cost anything.
Permutation Models
Authors: Forster T E 
Published: November 2023

Abstract
The first thing to say about this permutation method is that it is not the permutation method of Fraenkel and Mostowski. It is due to Rieger [1957] and Bernays [1954] and was first applied to NF by Scott [1962]. It is familiar to students of ZF as the technique used in the standard proof of the independence of the axiom of foundation.