bluuebunny/crossref_metadata_2025 huggingface dataset:
Cannabinoid receptors
Authors: Kendall D A , Alexander S P H
Published: November 2023

Cannabinoid receptors are seven transmembrane receptors that mediate the central and peripheral actions of extracts from the cannabis plant. Although many endogenous agonists of cannabinoid receptors have been described, a categorical role of these (mainly fatty acid derived) molecules as the endogenous ligand for cannabinoid receptors is currently lacking. Putative endogenous ligands of the cannabinoid receptors, which have been termed endocannabinoids, include anandamide, 2-arachidonylethanolamide, homoγ-linolenylethanolamide, docosatetra-7,10,13,16-enylethanolamide and 2-arachidonyl glyceryl ether. It should be pointed out, however, that the putative endocannabinoid anandamide is also a full agonist at the VR1 vanilloid receptor (Smart et al . 2000). This is a Ca2+-gating ion channel receptor that is located on the central and peripheral terminals of sensory nerves as well as in a number of different brain regions (Guo et al . 1999).
Dopamine receptors
Authors: Gazi Lucien , Strange Philip G
Published: November 2023

Dopamine is one of the major neurotransmitters in the central nervous system. Central dopaminergic systems participate in a number of important physiological functions. These systems control voluntary as well as involuntary motor movements, execution of learned motor programs, and regulate the secretion of prolactin and corticotrophin. In addition, central dopaminergic systems mediate reward, enhance mood, and are important for functions like working memory and goal-oriented behaviour. The effects of dopamine tend to be relatively slow so that it may be considered to be a modulator of fast synaptic transmission. The physiological functions of dopamine are mediated by several receptors, which belong to the superfamily of G protein-coupled receptors (GPCRs). Here, we present the main features of these receptors, from their molecular and pharmacological properties to the clinical perspective.
Galanin receptors
Authors: Kahl U , Langel Ü , Bartfai T
Published: November 2023

Galanin was discovered in 1983 by Tatemoto et al . who isolated the 29 amino acids long neuropeptide from porcine intestine, by using a chemical method for detection of amidated C-terminals of peptides (Tatemoto et al . 1983). Since then, the galanin sequence from a large number of species has been determined (Table 16.1). In all species so far, apart from man, galanin has 29 amino acids and is C-terminally amidated. In humans the galanin sequence is 30 amino acids long, without C-terminal amidation, and instead has a free carboxyl group in its C-terminal end. The N-terminal 14 amino acids of the molecule are 100 per cent homologous in all species, with the exception of galanin from tuna fish, where the ordinary serine in position 6 is exchanged for a proline. The first 13 amino acids of galanin also constitute the part of the molecule that has been shown to be crucial for binding of galanin to galanin binding sites in the central nervous system (CNS) (Table 16.2) (Land et al . 1991).
Histamine receptors
Authors: Hough Lindsay B , Leurs Rob
Published: November 2023

Histamine [2-(4-imidazolyl)ethylamine, HA] is an endogenous biogenic amine synthesized in and released from several kinds of cells, and involved in many kinds of biological signalling (Uvnas 1991). Mast cells (a family of bone marrow-derived secretory cells) store much of the body’s HA in very high concentrations. These cells respond with HA release to a myriad of diverse signals (including tissue damage, antigen exposure, and some kinds of drugs), yet the significance of mast cell HA under strictly physiological conditions remains unknown. In contrast, HA in the gastric mucosa is stored in and released from specialized cells resembling enterochromaffin cells, where it plays a vital physiological role as a mediator of normal gastric acid secretion.
Tachykinin receptors
Authors: Medhurst Andrew D , Hay Douglas W P
Published: November 2023

The mammalian tachykinins, also known as neurokinins, are a family of small peptides that share the common COOH-terminal sequence, Phe-X-Gly-Leu-Met-NH2, whereX isa Val or Phe residue, and NH2 represents amidation of the COOH-terminus which is important for biological activity (Maggio 1988; Maggi et al . 1993; Otsuka and Yoshioka 1993). The name ‘tachykinin’—from the Greek words tachys (‘swift’) and kinesis (‘movement’)—originally referred to the fast onset of action of these peptides compared to the slower acting peptide bradykinin (Maggio and Mantyh, 1994). Tachykinin peptides exert their major biological effects through activation of 7TM spanning tachykinin receptors (Simon et al . 1991; Strader et al . 1994).
GABAB receptors
Authors: Bowery Norman G
Published: November 2023

The GABAB receptor was originally described based on pharmacological observations. In studies focusing on GABA control of transmitter release it was noted that the GABA receptor responsible for modulating the evoked release of transmitters, in a variety of isolated tissue preparations, appeared to have different pharmacological characteristics from that of the receptor responsible for the Cl− dependent preand post-synaptic action of GABA. The modulatory action of GABA could not be blocked by bicuculline, was not mimicked by isoguvacine, was activated by only high concentrations of the normally potent agonist, muscimol and was not dependent on [Cl−] but was dependent on [Ca2+] or [Mg2+]. Most striking of all was that the therapeutic agent, baclofen (β-chlorophenyl GABA), which had already been introduced into therapeutics as an antispastic agent on the basis that it would mimic the effect of endogenous GABA (Bein 1972; Keberle and Faigle 1972), was stereospecifically active at this novel receptor.
Bioinformatic mining for GPCRs
Authors: Duckworth D Malcolm , Michalovich David
Published: November 2023

The advent of large-scale cDNA and genome sequencing efforts has revolutionized how we identify new genes and has also helped established the discipline of bioinformatics as a major component of both academic and industrial research programs. The mining for novel GPCRs is a good case in point with both industrial and academic researchers utilizing expressed sequence tag (EST) and genomic sequence data (see later) as their starting point to hunt for new receptors. In recent years bioinformatic search strategies have yielded the second GABAB receptor subunit (Jones et al . 1998; Kaupmann et al . 1998; see chapter 28), the human orexin receptors (Sakurai et al . 1998) and the third and fourth histamine receptors [reviewed by (Hough 2001); see chapter 17] to name just a few examples.
Sobolev Theory And Function Spaces
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

This chapter contains a brief review of a number of facts concerning Sobolev spaces that will be repeatedly used throughout the text. Most of the unreferenced results in this section can be found in basic real analysis texts; see, for instance, [350].
Mappings Of Finite Distortion
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

In this chapter we introduce the classes of mappings whose study will occupy the majority of the remainder of this book. A first point of departure from our earlier discussion and from the extant texts in the area [336, 283, 289, 342] is that these monographs discuss mappings which have uniformly bounded distortion. We will relax this assumption by only requiring that the distortion is finite almost every-where and shall see that in this greater generality many important facts are more transparent and even easier to prove. Of course there is the additional advantage that the results have wider applicability. However, much of our motivation and many subsequent results come from the classical setting of bounded distortion.
Compactness
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

In this chapter we discuss the compactness properties of the various families of mappings which will be of interest to us in particular, those mappings of finite distortion with prescribed bounds on the volume integral and the distortion function. Such families of mappings will turn out to be normal and closed under local uniform convergence or, equivalently, under weak convergence of the derivatives. In order to establish these claims we will first need to answer a number of questions concerning the convergence of ,Jacobians.
Topics From Multilinear Algebra
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

This chapter is dedicated to establishing notation and an exposition of the sometimes cumbersome technical details associated with exterior algebra and our forthcoming analysis of mappings of bounded distortion via the LP-theory of differential forms. Some useful references for this topic are [60, 122].
The Gehring Lemma
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

The theory of a PDE usually begins with estimates in the norms of its natural Sobolev space. These estimates are called energy estimates. The important point to note is that energy estimates imply a higher degree of integrability of the derivatives of a solution. This is something we have already seen in the solution to the Liouville theorem and also in our discussion of the complex Beltrami equation. In higher dimensions this idea goes back at least to F.W. Gehring [102] who proved that the differential of a quasiconformal mapping of a domain ft C R” is locally integrable with a power greater than n. Gehring’s ideas have been greatly extended to treat more general non-linear problems arising in the theory of PDEs, including non- injective mappings of bounded distortion (that is, quasiregular mappings).
The Governing Equations
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

This chapter is devoted to the study of the governing partial differential equations for the theory of mappings of finite distortion. We have already met a number of these equations, principally the Cauchy-Riemann system and the Beltrami system. Here, the goal is to put these equations in a more general framework and discuss them from a number of perspectives. For instance, when lifted to the level of exterior algebra, the Beltrami system takes on a somewhat nicer form indeed, in special cases it linearizes. Studying these equations at the level of differential forms has led to major new advances in the theory of quasiregular mappings and conformal geometry. Also there is a close connection between mappings of finite distortion and the minima of certain variational integrals. We shall outline this connection and set up the associated Euler—Lagrange equations. This leads to the non-linear potential theory which we mention only briefly; the book [134] contains a detailed study of this area.
Topological Properties Of Mappings Of Bounded Distortion
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

One of the great motivations for the development of geometric function theory in IRn has been its use as a tool to explore variational methods and the properties, both topological and analytic, of solutions to problems such as minimizing energy integrals. As noted earlier, geometric problems that arose from attempts to generalize aspects of the theory of holomorphic functions led naturally to the Beltrami system,
PainlevÉ’S Theorem In Space
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

We have already seen how the Caccioppoli estimate (14.29) witJ1 the exponent s= n,together with Gehring’s lemma, implies higher integrability results for quasiregular mappings. Although a little surprising, it is the Caccioppoli estimate below the dimension which will be the basic tool of this chapter.
Even Dimensions
Authors: Iwaniec Tadeusz , Martin Gaven
Published: November 2023

The equations governing mappings of finite distortion are, in general, quite difficult to deal with because they are non-linear and not uniformly elliptic if the distortion function is unbounded. However it is in just this setting that the modern geometric theory of mappings finds its most important connections with harmonic analysis and non-linear elasticity.
Estimating The Roc Curv
Authors: Pepe Margaret Sullivan
Published: November 2023

Having defined the ROC curve and explored some of its properties in the previous chapter, we turn now in this chapter to statistical methodology for making inferences about the ROC curve from data. We consider three approaches for estimating the ROC curve and its summary indices. The first is to apply non-parametric empirical methods to the data to obtain the empirical ROC curve, from which empirical summary measures can be calculated. Empirical methods have been the popular choice for settings involving continuous test results.
One hundred years of the design of experiments on and off the pages of Biometrika
Authors: Atkinson Anthony C , Bailey R A
Published: November 2023

The earliest important papers on planned experiments in Biometrika appeared within a year of each other in 1917 and 1918. Roughly speaking, one was concerned with design optimality and industrial experiments, the other with agricultural trials and blocking. We find this approximate division of the subject into two parts helpful in describing its development and growth. As a result of the hostility between Fisher and Karl Pearson, much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of Biometrika. Despite this, we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and Bayesian versions of design optimality.
Biometrika Centenary: Survival analysis
Authors: Oakes David
Published: November 2023

Although papers relating to survival analysis have appeared in Biometrika since the very first issue, the current emphasis on the topic in this journal is fairly new, especially as it relates to applications in biostatistics. This survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of Biometrika, focusing primarily on work published since 1980.
Biometrika Centenary: Sample surveys
Authors: Smith T M F
Published: November 2023

Despite Karl Pearson’s stated aim that the ‘evolutionist has to become in the widest sense of the words a registrar-general for all forms of life’, the papers published in Biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s. There has been little work on sampling in the life sciences, with the exception of capture-recapture methods. The major areas have been in variable probability designs, the foundations of inference for finite populations, analytic surveys and the role of selection mechanisms in inference. In recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory, with interesting consequences for both areas.
Notes on Bias in Estimation
Authors: Quenouille M H
Published: November 2023

1. One of the commonest problems in statistics is, given a series of observations x  1, x  2, … , x  n, to find a function of these, tn(x  1, x  2, … , x  n), which should provide an estimate of an unknown parameter θ.The desirable properties of estimation procedures have been discussed fully elsewhere. They are:(a) That the estimator should be efficient according to some .definition of efficiency previously arranged. Most commonly, the reciprocal of the variance of the estimates is taken as a measure of its efficiency, as this is most useful where central limit theory may be relevant.
Studies in the History of Probability and Statistics. XX
Authors: Pearson E S
Published: November 2023

Letters or extracts from letters which passed between W. S. Gosset, R. A. Fisher and Karl Pearson during the years 1912-20 are reproduced. They throw light on the start of Fisher’s statistical career. In the notes accompanying the correspondence, attention is drawn to the problems in estimation and significance testing which were brought to the front at that date by the unusual character of the sampling distribution of the correlation coefficient. An early disagreement between Pearson and Fisher on estimation through minimizing χ and maximizing likelihood is covered.
Monte Carlo sampling methods using Markov chains and their applications
Authors: Hastings W K
Published: November 2023

A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.
G
Authors: Dodge Yadolah
Published: November 2023

g-statistics The sample values of standardized cumulants. See gamma coefficients. There are a variety of other meanings in specific applied fields.
J
Authors: Dodge Yadolah
Published: November 2023

J-shaped distribution An extremely asymmetrical frequency distribution with the maximum frequency at the initial (or final) frequency group and a declining or increasing frequency elsewhere. The shape of this distribution roughly resembles the letter J or its reverse. Among theoretical curves referred to as J-shaped are the Pareto and certain of the Pearson system of frequency curves.
L
Authors: Dodge Yadolah
Published: November 2023

L-estimator Any estimator that is a linear function of the ordered sample values, with coefficients determined by the order. The trimmed mean and the interquartile range are examples.
O
Authors: Dodge Yadolah
Published: November 2023

oblique factor In educational or psychological testing a factor which is correlated with one, or more, other factors is said to be oblique. In one geometrical representation of the situation the vectors which represent them are no longer orthogonal one to another. The use of oblique factors is confined largely to psychology. [See also factor analysis, factor pattern.]
R
Authors: Dodge Yadolah
Published: November 2023

R A flexible and powerful software environment for statistical data analysis and graphical display (Ihaka and Gentleman, 1996). It is a freely available clone of S-PLUS, and has replaced the latter as the primary statistical programming tool at many research and academic institutions around the world.
U
Authors: Dodge Yadolah
Published: November 2023

Ultimate cluster The aggregate of ultimate or final stage units included in a primary unit. ultrametric inequality An inequality implying that all triangles are isosceles with the equal sides longer than the other. It applies to the distances at which items combine in hierarchical cluster analysis, and to the geometry of the dendrogram.
W
Authors: Dodge Yadolah
Published: November 2023

waiting time In the theory of queues this term is self-explanatory, but in renewal theory residual waiting time is the period from a given point in time t to the next renewal point. Spent waiting time is the time elapsed since the last renewal. The sum of the two waiting times is the length of recurrence interval. In the theory of random walks residual waiting time is called ‘point of first entry’ or ‘hitting point’ for the interval (t, ∞).
Y
Authors: Dodge Yadolah
Published: November 2023

Yates, Frank (1902–1994) A British statistician. After reading mathematics at Cambridge, he worked for some years in Africa on surveying. He was then appointed to Rothamsted Experimental Station, initially to work with R.A. Fisher, and he remained there until his retirement. He made major contributions to the design of experiments, to sampling methods and to the systematic use of computers in statistics.
Z
Authors: Dodge Yadolah
Published: November 2023

z-core A term used by some writers in connection with educational and psychological testing as an alternative to standardized scores. A z-score for an observation is the score expressed as a deviation from the sample mean value in units of the sample standard deviation.
Measurement of distribution functions
Authors: Egelstaff P A
Published: November 2023

An introductory account of the methods used and information obtained via radiation scattering experiments was given in Sections 1.8 and 1.9. It was seen that some distribution functions could be obtained from the Fourier transformation of intensity data. In this chapter we consider this subject in greater detail, beginning with a discussion (Section 3.2) of scattering using the examples listed in Table 1.4. This is the foundation for the treatment of scattering by fluids. The treatment given here is divided into sections on atomic liquids (class 1 in Section 1.1), on molecular fluids (e.g. classes 2 or 4) and on liquid metals (class 3). However, at this stage the discussion will be restricted to the static structure factors and to the distribution functions discussed in Chapter 2.
Properties and models of the dynamic structure factor
Authors: Egelstaff P A
Published: November 2023

In this chapter we begin the discussion of non-equilibrium properties. The vehicle used for this purpose will be the van Hove space-time distribution function, that is, the generalization of the pair distribution function to the time-dependent case. As a starting point we shall discuss some general questions that affect the understanding of the liquid state, beginning with a discussion of the classical limit to S(Q, ω) and its limiting behaviour as Q → ∞ or Q → 0. Another problem of importance is the relation between macro- and microscopic properties, and therefore the way macroscopic properties may be obtained from microscopic correlation functions will be discussed. Part of the discussion of transport properties (Chapter 11 onwards) will be concerned with the macroscopic limiting behaviour of the liquid, and, as a prelude, this chapter includes a discussion of the size of the region in (ω, Q) space to which macroscopic properties may be applied.
Diffusion and single-particle motion
Authors: Egelstaff P A
Published: November 2023

Chapters 11 and 12 are concerned with one of the basic phenomena occurring in a liquid —the allowed motion of a single atom. This chapter deals with the scale (in distance and time) of the diffusion process, and is thus concerned with those motions that are observed on a relatively long time scale. In contrast, Chapter 12 deals with motion on a relatively short time scale. For that discussion the important quantity is the velocity correlation function, and some methods of measuring or calculating it will be described in Chapter 12. Chapter 11 commences with a discussion of the random walk theory of diffusion and continues with accounts, from several points of view, of the basic step in the random walk. To conclude this chapter a brief discussion of rotational diffusion, for the case of spherical molecules, will be given.
The velocity correlation function
Authors: Egelstaff P A
Published: November 2023

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.
Analysing social science data with graphical Markov models
Authors: Wermuth Nanny
Published: November 2023

The term graphical Markov models has been suggested by Michael Perlman, University of Washington, for multivariate statistical models in which a joint distribution satisfies independence statements that are captured by a graph.
Graphical models for stochastic processes
Authors: Didelez Vanessa
Published: November 2023

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

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.
Towards Bayesian inference in epidemic models
Authors: Auranen Kari
Published: November 2023

Estimation in epidemic models involving unidentifiable types of heterogeneous individuals requires observations of appropriate contrasts. It is well understood that under variability in susceptibility, the more frail individuals tend to contract infection earlier during an epidemic or earlier in life in endemic situations.
A predictive point of view on Bayesian non-parametrics
Authors: Petrone Sonia
Published: November 2023

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

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

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

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

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

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

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

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.
The Weil representation: infinite-dimensional case
Authors: Neretin Yu. A , Gould G G
Published: November 2023

It is worth considering whether (6.1.9) and (6.1.11) can be interpreted literally as integrals with respect to a Gaussian measure. This is not exactly the case, as we shall now see.
Representations of the group of diffeomorphisms of a circle with highest weight
Authors: Neretin Yu. A , Gould G G
Published: November 2023

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

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

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

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.
The spectrum and its applications
Authors: Reiter Hans , Stegeman Jan D
Published: November 2023

This chapter is devoted to the spectrum of functions and ideals. We start with a definition. Definition 7.1.1 Let G be a locally compact abelian group.
Introductory ideas
Authors: Howie John M
Published: November 2023

In this chapter certain basic definitions and results are presented. Reference will be made to these throughout the book, though it should be noted that Section 1.8 is referred to only in Section 3.5.
0-simple semigroups
Authors: Howie John M
Published: November 2023

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

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

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

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

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

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

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

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

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

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

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.
Optoelectronic ESPI
Authors: Tatam R P
Published: November 2023

Electronic speckle pattern interferometry (ESPI) is a non-contact optical technique that enables measurement of static and dynamic deformation and surface shape to be measured over an extended area of view [1]. The technique was first demonstrated nearly thirty years ago.
Digital Image Processing in Medicine
Authors: Reading N .G
Published: November 2023

This paper discusses the use of digital image processing techniques for medical imaging in general. The role that image processing plays in different fields of radiology is stressed including Computed Tomography, Magnetic Resonance imaging, Radiography, Angiography, Nuclear Medicine and Ultra. sound.
Mathematics as language
Authors: Effros Edward G
Published: November 2023

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

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.