bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Graph Theoretic Solution to the Interface Equation
Authors: Pengelly A D , Ince D C 
Published: November 2023

Abstract
The synthesis and subsequent generation of protocol converters can be a time consuming and tedious affair. An automatic means of generating these converters, given a formal description of the interfacing protocols, has been researched by a number of academics and industrialists. While there is a strong standards movement within the protocol community, the output from that process is likely to be slow in terms of its dissemination to the communications world at large. Hence, the development of convertors will be a key issue for many years to come. The work in this paper can be seen as a natural extension of the earlier work of Norris, Martin and Shields. The theory developed adopts a completely novel approach - moving the problem into the domain of graph theory and topology. The resulting theory has spawned a number of interesting results, which include extensions to CCS, further development of the quotient machine concept, the notion of symmetric validation and a further uniflcation between automata and graph theory.
Boundary Element Methods
Authors: Sloan Ian H 
Published: November 2023

Abstract
What are boundary element methodsã They are methods for the approximate solution of two- or three-dimensional boundary value problems, which rely on casting the problem into the form of an integral equation over the boundary; then chopping the boundary into pieces (‘elements’), on each of which a low-degree polynomial approximation is assumed; and then approximating the resulting discrete problem numerically. Approximate solutions to the original problem can then be obtained by carrying out a suitable approximate integration over the boundary.
Fractal Image Compression
Authors: Barnsley M , Barnsley L 
Published: November 2023

Abstract
What is multimedia? It is a special publication or “title”; it can be “read” inter actively on a computer screen and it is made up of text, pictures and probably sound and motion video as well. Early multimedia titles ran on microcomputers such as the Apple Mac or IBM PCs and popular sources of material for such early titles were the text and pictures in old-fashioned, paper-based encyclopaedias. These days however, multimedia titles do not need to be tied to one computer; they can be stored on company-wide networks or even on the information super-highway.
Logical completeness, truth, and proofs
Authors: Lolli Gabriele 
Published: November 2023

Abstract
When discussing such topics as ‘truth in mathematics’, it would be culpable negligence to ignore what logic has to say on the subject. What logic has to offer are theorems, not speculations. We teach these theorems in logic classes, out apparently to no avail, since the teaching does not seem to leave any trace in grown-up mathematicians. Perhaps this is due to the fact that when proving cheorems their significance is seldom discussed; only their mathematical usefulness, as opposed to general wisdom, is stressed. Theorems are admittedly not a detailed description of reality; they refer to idealized models; logic deals only with models of reasoning; but mathematicians, and scientists in general, should know what a tremendous amount of reliable and useful information is conveyed by properties of abstract models. We should sometimes pause to reflect on theprems, besides proving new ones, especially when, as is the case in logic, they concern our own activity.
A credo of sorts
Authors: Jones V F R 
Published: November 2023

Abstract
Let me begin by claiming to be quite ordinary among mathematicians in my attitude to my subject, with little understanding of its philosophical underpinnings. I remember being worried by Russell’s paradox as a youngster, and am still worried by it, but I hope to demonstrate, by a series of anecdotes and musings, that it is not at all difficult to live with that worry while having complete confidence in one’s mathematics. Let us start on very very solid ground.
Foundations of set theory
Authors: Tait W W 
Published: November 2023

Abstract
The topic of our conference is truth in mathematics, and certainly the implied question is in part: what constitutes truth in mathematics where, in contrast to the natural sciences, there are no phenomena to be saved? In the fourth century BC, Plato answered this question by observing that we begin with the idea of a certain structure, perhaps derived from experience, and, by analysis (which he called ‘dialectic’), we arrive at the principles which define this structure. What is true of the structure then is what can be derived from those first principles. This prescription works very well in the cases of Euclidean geometry, the theory of real numbers, and the theory of finite sets (or of sets of rank less than the least inaccessible cardinal, etc.), where we have ultimately agreed on certain (second-order) axioms which characterize the structures in question to within isomorphism. However, even in these cases, the status of certain propositions about these structures — for example, the Continuum Hypothesis — remains undetermined, pointing to an incompleteness of the laws of the underlying higher-order logic and, in particular, the laws governing the logical notion of set (to use the term of (Shapiro 1991)) implicit in the second-order comprehension axiom. In another direction, Godel’s incompleteness theorems yield propositions in predicate logic of any order which are not provable in that system, but which are provable l?y passing to logic of still higher-order. In this direction we are led to the theory of transfinite ordinals and to set theory; in particular, we are led to the question of the existence of large cardinals. However, in this case, as opposed to the case of Euclidean geometry et al., there does not seem to be just one generally accepted idea of the universe of set theory and of the laws defining it. Thus, perhaps there is no one notion of truth in this subject; there may be different conceptions, each carrying its own notion of truth-as in the case of different geometries.
Which undecidable mathematical sentences have determinate truth values?
Authors: Field Hartry 
Published: November 2023

Abstract
I will begin by contrasting three metaphysical pictures about mathematics. The first, about which I will have little to say in what follows, is the fictionalist picture. This says that strictly speaking, there are no mathematical entities; still, we can perfectly well reason from premises that postulate such entities, and systematic reasoning from such premises is both intrinsically interesting and highly useful in our practical affairs. On this view, mathematical theories are not literally true. Of course, a fictionalist needs to say something about why these theories are useful if they are not true: in disciplines other than mathematics, the utility of a theory is generally taken as good reason to believe that the theory is at least approximately true, and, if it is not a good reason in the mathematical case, then we need to know what the relevant differences between the mathematical and the non-mathematical are. Myself, I think that there are such relevant differences, and that the fictionalist view can be defended,1 but I will almost completely ignore it in what follows.
Metric and topological spaces
Authors: Meise Reinhold , Vogt Dietmar 
Published: November 2023

Abstract
In order to be able to cruise through functional analysis one needs, in the general set up of metric or topological spaces, the notions of continuity and convergence learnt in earlier analysis courses. The relevant notions, definitions, and facts are briefly introduced here and it is recommended that the reader carries out the simple proofs unless they are already known.
Projections
Authors: Meise Reinhold , Vogt Dietmar 
Published: November 2023

Abstract
In this chapter we shall consider the question: When does it happen that for a subspace E0of a metric linear space E there exists a subspace E1, with the property that + : E0 × E1 → E is an isomorphism? It is closely tied to the following question: For a given surjective continuous linear map A between metric linear spaces, when can one find a solution x = x(y), to the equation Ax = y, which is linearly and continuously dependent on y? Next, we recall a few notions from linear algebra.
Asymptotic Analysis of Fields in Multi-Structures
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander 
Published: November 2023

Abstract
The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.
Introduction to Compound Asymptotic Expansions
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander 
Published: November 2023

Abstract
This chapter contains an introduction to the technique of compound asymptotic expansions. We demonstrate the main features of this method by examples of several comparatively simple singularly perturbed boundary value problems. By ‘singularly perturbed’ we mean that the problem involves a small parameter ε, and it degenerates in some sense as ε → 0: for example, the equation reduces its order or a part of the boundary reduces its dimension.
Elastic Multi-Structure
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander 
Published: November 2023

Abstract
In this chapter we analyse a mixed boundary value problem for the Lame system in an elastic multi-structure which consists of a union of a three-dimensional domain and thin cylinders and has the same geometry as in Chapter 2. In addition, we assume that the number of thin cylinders exceeds two and that the junction points do not belong to the same straight line. Just for the sake of simplicity of presentation we assume that the cylinders have the same cross-sections.
Spectral Analysis for 3d–1d
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander 
Published: November 2023

Abstract
The asymptotic analysis developed in previous chapters can be applied to the study of spectral properties of boundary value problems in multi-structures. In this chapter we show this for the multi-structure depicted in Fig. 2.1, which was studied in Chapters 2 and 4. Here, we obtain asymptotic formulae for the first eigenvalues of the Laplace and Lame operators with the same boundary conditions as before.
Introduction
Authors: Wilson Robin J 
Published: November 2023

Abstract
We present those definitions and theorems in graph theory that are assumed throughout this book. Further explanation of these terms, together with the proofs of stated results, can be found in the standard texts listed below, although not all of the terminology is standardized. Definitions and results not included here are introduced later, as needed. A graph G consists of a finite non-empty set V (G) of elements called vertices and a finite set E(G) of distinct unordered pairs of distinct elements of V(G) called edges (see Fig. 1.1). We call V(G) the vertex set of G and E(G) the edge set of G; these are sometimes abbreviated to V and E, respectively. The number n of vertices of G is the order of G, and the number of edges of G is denoted by m. The edge {v, w} (where v and w are vertices of G) is often denoted by v w.
Covering spaces
Authors: Lawson Terry 
Published: November 2023

Abstract
This chapter elaborates upon the ideas used in Chapter 3 to compute the fundamental group of the circle using the covering space p ; JR -+ 81 to develop the theory of covering spaces. We will show that there is an intimate connection between the covering spaces of B and the subgroups of the fundamental group 1r1 ( B, b). As before, we are assuming that the spaces A, B in a covering space p ; A -+ B are each path connected and locally path connected. We start with some basic examples and properties. We can also take the product of a covering space with itself and get a new covering space. For example, we can take the product of the covering space of the reals over the circle with itself and get the covering space of the plane over.
Generalized kinetic theory
Authors: Balucani Umberto , Zoppi Marco 
Published: November 2023

Abstract
Up to the early 1970s, a ‘kinetic approach’ to the time-dependent properties of fluids was synonymous with a framework based on statistical mechanics in which a central role is played by those dynamical events referred to as uncorrelated binary collisions. Although the details of these collisional events depend on the specific form of the interatomic potential, in most cases the relevant effects are due to the harsh repulsion prevailing at small separations, often modelled as a ‘hard sphere’ interaction. As a consequence, a collision may usually be considered as an event strongly localized both in space and time. Because of this character, it seems reasonable to assume that two subsequent collisions are mutually uncorrelated. This assumption is actually one of the cornerstones of the traditional kinetic frameworks since their invention by Boltzmann more than a century ago. If we explore at a deeper qualitative level the physical content of the uncorrelated-collisions assumption, we arrive at the conclusion that this ansatz is indeed justified for dilute fluids, where the collisional events are comparatively rare so that, in a sense, a particle has available an amount of space and time sufficient to ‘forget’ a collision before the occurrence of another one.
The Impact Parameter Model
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
In the last chapter the theory of ion-atom scattering at very low energies was discussed in terms of an angular momentum decomposition of the quantum mechanical coupled equations. As we saw in Chapters 2 and 3, the number of partial waves required for convergence becomes very large when the initial relative velocity v0 is greater than a few tenths of an atomic unit of velocity (as shown in Table 3.1). Also, as v0 is increased the kinetic energy of the heavy particle motion becomes large compared with changes in electronic energy. Under these conditions the impact parameter model is accurate and is more convenient to use than the partial-wave method. In the impact parameter model we have to solve the time-dependent Schrodinger equation (3.163a).
Approximate Solutions of Coupled Equations
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
Most of the theoretical descriptions of inelastic ion-atom collisions, discussed in the preceding chapters, have resulted in sets of coupled equations, either for radial functions in partial-wave models or for probability amplitudes in the case of the impact parameter model. These equations have to be solved numerically. However, under certain conditions, usually rather restrictive, approximate analytical solutions have been developed, which provide rapid means of calculating cross sections and which may also illuminate the general nature of the theory. In this chapter two rather different groups of approximation will be discussed. The first group is concerned with the approximate solutions of the two-state coupled equations, particularly in situations where a transition is dominated by a curve crossing between two molecular states, and the extension of these solutions to systems which exhibit multiple crossings. The second group is different in character and is based on perturbation and distorted wave methods, which apply in cases of weak coupling.
Introduction
Authors: Coolen A C C 
Published: November 2023

Abstract
Minority Games (MGs) are relatively simple mathematical models that were initially designed to increase our understanding of the cooperative phenomena and fluctuations that are observed in financial markets. They apply in fact more generally to any situation where a large number of selfish decision-making ‘agents’ all try to achieve individual gain by predicting (inductively, on the basis of incomplete public information, and often with an element of irrationality) and anticipating the decisions to be taken by their competitors. Such situations arise quite frequently, e.g. in queuing and traffic problems, in politics, sociology, etc. Not just in markets. Although there is a considerable history of mathematical studies aimed at understanding the interaction between agents in socio-economic systems, such as game theory, the key advantage of models such as MG is that in the latter one does not assume or rely on the participants in these systems to act fully rationally.
Preparing the stage for statistical mechanics
Authors: Coolen A C C 
Published: November 2023

Abstract
We seem to have collected most of the information needed to launch a statistical mechanical analysis of the MG. We have established that the key control parameter in the MG should be α = 2M /N , and that for infinte α we may expect the limit N∞ to give well-defined statistics for the overall bids A(.e). We know which quantities to inspect, e.g. the volatility and the fraction of frozen agents. However, there remain issues that have not yet been resolved, such as the scaling with N of the characteristic timescales of the process (which do influence theory and simulations); these will be dealt with in the present chapter.
Dynamics of MGs with true market history
Authors: Coolen A C C 
Published: November 2023

Abstract
Except for the early chapters of this book, where we just presented numerical simulations in order to appreciate the phenomenology of the standard versions of MG, we have in all theoretical chapters so far carefully steered away from having to analyze MG models with true market history, and instead analyzed exclusively the mathematically more manageable Markovian ‘fake history’ versions. This was at least partly justified by the earlier observation in numerical simulations that the differences in behaviour between MGs with true market history and those with ‘fake’ history’ were surprisingly small.
Variations and generalizations
Authors: Coolen A C C 
Published: November 2023

Abstract
The initial motivation to introduce and study MG was largely to increase our under-standing of the collective effects of inductive decision making by large numbers of agents in (financial) markets. It is therefore no surprise that the model’s conception subsequently generated a large body of generalizations, variations, and spin-off models, which all tried to introduce further details into the basic MG in order to bring the model closer to economic reality. It is neither possible nor helpful to give an exhaustive overview of all such variations and generalizations which have been published. Instead, here we will limit ourselves to a selection that has been made largely on the basis of whether the proposed variation not only makes sense but also allows for the resulting model to be solved and understood mathematically with the techniques presently available.
Disintegration into stereotypy induced by drugs or brain damage: a microdescriptive behavioural analysis
Authors: Teitelbaum Philip , Pellis, Sergio M , Devietti Terry L 
Published: November 2023

Abstract
Implicit in the phenomenon of stereotyped behaviour is a puzzle: the term stereotype applies to a behavioural act that is repeated again and again, but unlike a motivated act, it makes no sense because it does not seem to achieve an adaptive outcome: Drug-induced stereotypy, such as that produced by high doses of central stimulants, has that character. The wide variety of seemingly unrelated independent stereotypies generated by central stimulants is also puzzling. In rodents, for instance, drugs such as apomorphine and amphetamine have been reported to elicit climbing, jumping, rearing, prancing, running, walking, circling, revolving, pivoting, gnawing, licking, nose-poking, sniffing, verticalization, side-to-side head and paw movements, backward locomotion, and underwater swimming without surfacing (e.g. Alander etal.1983; Cole 1977; Costall and Naylor 1973; Decsi et al.1979; Fray et al.1980; Janssen et al.1960; Jerussi and Glick 1976; Kokkinidis and Anisman 1979; Schijljrring 1971; Schoenfeld et al.1975; Segal et al.1980; Szechtman et al.1982; Teitelbaum 1986; Thomas and Handley 1978; Voigtlander eta/.1975). What do they have in common?
Elements of bivariate time-series analysis
Authors: Diggle Peter J 
Published: November 2023

Abstract
In this final chapter we give a brief introduction to the analysis of data in the form of a pair of possibly inter-dependent time series. Our notation for this will be {(xt,Yt): t = l, ... , n }. For motivation, consider Example 1.4 involving monthly numbers of male and female deaths in the UK due to bronchitis, emphysema, and asthma. Both series show an obvious seasonal pattern. Might there also be a more subtle form of inter¬ dependence, for example arising out of a common response in both series to unusually harsh or mild weather conditions? How should we analyse the data to see if this is indeed the case? Our theoretical model will be a pair of random processes, which we write as {(Xt, Yt)}.
Use of a quadratic exponential model to generate estimating equations for means, variances, and covariances
Authors: Zhao Lue Ping , Prentice Ross L 
Published: November 2023

Abstract
A quadratic exponential family model has been shown (Gouricroux et al., 1984) to be unique in quite generally yielding consistent ‘pseudo-maximum likelihood’ e timates of parameters in the marginal means, variances and covariances even if sampling takes place from outside this family. Furthermore, this class of models can be shown to generate simple score-estimating equations for mean, variance and covariance parameters that extend standard equations for mean parameters arising as solution to score equations from generalized linear models. In fact, these equations are quite similar to those that have been proposed on ad hoc grounds for marginal means and correlations.
Statistical Methods, Experimental Design, and Scientific Inference
Authors: Fisher R A , Yates F 
Published: November 2023

Abstract
R.A. Fisher has had more influence on the development of statistical theory and practice than any other twentieth-century statistician. His writings (both in paper and book form) have proved to be as relevant to present-day statisticians as they were when first published. This book brings together as a single volume three of Fisher's most influential textbooks: Statistical Methods for Research Workers, The Design of Experiments , and Statistical Methods and Scientific Inference . In this new edition Frank Yates has provided a foreword which sheds fresh light on Fisher's thinking and on the writing and reception of each of the books. He discusses some of the key issues tackled in the three books and reflects on how the ideas expressed have come to permeate modern statistical practice.R.A. Fisher has had more influence on the development of statistical theory and practice than any other twentieth-century statistician. His writings (both in paper and book form) have proved to be as relevant to present-day statisticians as they were when first published. This book brings together as a single volume three of Fisher's most influential textbooks: Statistical Methods for Research Workers, The Design of Experiments , and Statistical Methods and Scientific Inference . In this new edition Frank Yates has provided a foreword which sheds fresh light on Fisher's thinking and on the writing and reception of each of the books. He discusses some of the key issues tackled in the three books and reflects on how the ideas expressed have come to permeate modern statistical practice.