bluuebunny/crossref_metadata_2025 huggingface dataset:
Island hopping in Drosophila: genetic patterns and speciation mechanisms
Authors: Hollocher Hope
Published: November 2023

Islands have always been attractive systems for the study of evolution, and in particular speciation, for a wide variety of reasons, the most obvious being that they tend to harbour numerous and splendidly diverse arrays of species not typically found in continental areas. These arrays are characterized by high levels of endemism. Therefore, it follows that islands represent conditions that are extremely conducive for repeated speciation. If we can understand which evolutionary processes are important for speciation on islands, we may be able to define general principles that are applicable to a number of different biological situations.
Radiations, communities, and biogeography
Authors: Grant Peter R
Published: November 2023

The preceding chapters discussed causes and mechanisms of speciation. The remaining chapters extend the discussion of speciation on islands and in island-like habitats to questions about the evolution of many species from the same ancestral stock. There is a change of scale in this transition; from the evolution of two species from one to the evolution of many species from one or a few.
Single-mode quantum optics
Authors: Loudon Rodney
Published: November 2023

The theory of the electromagnetic field quantization developed in Chapter 4 simplifies considerably for applications Lo many of the key experiments in quantum optics. Thus many experiments use plane parallel light beams whose transverse intensity profiles are not important for the measured quantities. Again, it is often sufficient in interpreting the data to consider the light beams as exciting a single mode of the field. The present chapter begins with the specialization of the quantization to single-mode excitations. The quantum theory is illustrated by its application to several varieties of single-mode state and the main features of number Cates, coherent states, chaotic statistical mixtures and squeezed states are derived.
Resonance fluorescence and light scattering
Authors: Loudon Rodney
Published: November 2023

The basic components of a light-scattering experiment include a scattering region, with the atoms of interest illuminated by a parallel beam of light, and a detector that measures the scattered intensity at some finite angle to the direction of the incident beam. The scattering at small angles is usually difficult to resolve from the transmitted incident beam itself, and it is convenient in many experiments to measure the light scattered at right angles. In high-resolution studies, the atoms may be injected into the scattering region in the form of a beam in the third mutually perpendicular direction, to minimize the Doppler broadening of the scattered light.
Nonlinear quantum optics
Authors: Loudon Rodney
Published: November 2023

The book so far is almost entirely concerned with linear optical processes, where the response of a material to incident light is described by its linear susceptibility and the rates of optical processes are proportional to the incident intensity. However, examples of nonlinear behaviour occur in the saturation of atomic transitions, discussed in §1.7, and in the power-broadened susceptibility, derived in eqn (2.8.6). Atomic saturation is also an important component in the laser theory of§§t.10 and 7.3. The expressions derived in these examples contain the electromagnetic energy density or photon number in denominators whose expansions include terms proportional to all positive powers of the optical energy. The higherorder, or nonlinear, terms are normally much smaller than the linear term for conventional light sources but their influence is often significant in experiments that use laser sources. The present chapter treats the effects of the nonlinear terms in modifying the properties of incident light beams.
Physical Overview
Authors: Monk Kathryn A , Fretes Yance de , Reksodiharjo-Lilley Gayatri
Published: November 2023

Nusa Tenggara and Maluku (NT&M) is unlike any other region in Indonesia. It encompasses innumerable volcanic and coral reef islands scattered through some of the deepest seas in the world, and has no large islands such as Java or Sumatra. The area of Java, 132,000 km, is six and one-half times that of the largest island in NT&M, Halmahera, at 20,000 km. This region occurs at the heart of the complex crossroads of two continents, Asia and Australia, and two oceans, the Indian and Pacific. While this strategic position is a result of geological history, the climate, hydrology, and soils must also be considered if the biological, social, and economic life of the region is to be understood. An excellent review of the physical features of NT&M is supplied by the Regional Physical Planning Programme for Transmigration (RePPProT) in both Indonesian and English, but this is not widely available (RePPProT l 989a,b). However, every Regional Development Planning Board (Badan Perencanaan Pembanguan Daerah: BAPPEDA) in each provincial capital should hold a complete set of the relevant RePPProT reviews and maps.
Land Resource Use: Agriculture
Authors: Monk Kathryn A , Fretes Yance de , Reksodiharjo-Lilley Gayatri
Published: November 2023

Agriculture is the mainstay of the economy of Nusa Tenggara and Maluku (NT&M), with more than 80% of the population dependent on cultivation or animal husbandry (RePPProT 1989a). This necessarily means that understanding agricultural systems within NT&M is essential for the management of nearly 40% of the land and for improving the lives of most of the people of the region.
Introduction and basic concepts
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

In this introductory chapter, we first give a sample of the problems and questions to be treated in the book. Then we explain some basic notions and techniques, mostly fundamental and simple ones common to most branches of mathematics. We assume that the reader is already familiar with many of them or has at least heard of them. Thus, we will mostly review the notions, give precise formal definitions, and point out various ways of capturing the meaning of these concepts by diagrams and pictures. A reader preferring a more detailed and thorough introduction to these concepts may refer to the book by Stewart and Tall [8], for instance.
Generating functions
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

In this chapter, we are going to present a useful calculation technique. The basic idea, quite a surprising one, is to consider an infinite sequence of real numbers and associate a certain continuous function with it, the so-called generating function of the sequence. Problems about sequences can then be solved by calculations with functions. In this introductory text, we will only get to simpler examples, whose solution can mostly be found also without generating functions. In some problems, various tricks can reach the goal even quicker than the method of generating functions (but it may not be easy to discover such tricks). This should not discourage the reader from learning about generating functions, since these are a powerful tool also for more advanced problems where other methods fail or become too complicated.
Applications of linear algebra
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

Linear algebra is a part of algebra dealing with systems of linear equations, matrices, determinants, vector spaces, and similar things. We have already seen several proofs using linear algebra in previous chapters, most notably in Section 7,5. Here we will demonstrate few more methods and applications. First, we present two problems, one concerning the existence of so-called block designs and the other about covering a complete graph by complete bipartite graphs. Hardly anyone would suspect that these problems are related to matrices, and yet an elegant solution can be given based on the notion of rank of a matrix. An interested reader can find much more about similar proofs in the very vividly written textbook by Babai and Frankl [12]. In the subsequent two sections of this chapter, we assign several vector spaces to each graph; this leads to a com pact and insightful description of seemingly very complicated sets. Finally in Section 11.6, we consider two elegant algorithms where linear algebra blends with a probabilistic method.
Inner product spaces
Authors: Kaye Richard , Wilson Robert
Published: November 2023

In this chapter we consider ways of ‘multiplying’ two vectors in a vector space V to give a scalar. Such a product is called an inner product, or scalar product, and the theory is based initially on a familiar example (sometimes called the dot product) on three-dimensional vectors in ℝ3. To begin with, we consider real vector spaces, but we will consider complex vector spaces later on. The scalar product, inner product, or dot product, of two vectors in ℝ2 or ℝ3 is rather well known. We start this chapter with its definition and description of its main properties. Throughout this section, llvll will denote the length of the vector v in ℝ2 or ℝ3
Orthogonal bases
Authors: Kaye Richard , Wilson Robert
Published: November 2023

One important use of the standard inner product of ℝ 3 is that it allows us to distinguish between ‘nice’ bases such as the usual one where the basis vectors are orthogonal to each other and each has length 1, and others such as (1, 0, 0)T, (1, 1, 0)T, (1, 1, 1)T where this is not true. The main objective of this chapter is to show how to find such nice (or, as we shall call them, orthonormal) bases for a given finite dimensional vector space with an arbitrary inner product, and to study the properties of these orthonormal bases. This chapter concerns inner products on vector spaces, and all our vector spaces are over ℝ or ℂ throughout.
Self-adjoint transformations
Authors: Kaye Richard , Wilson Robert
Published: November 2023

This chapter combines material concerning quadratic forms with material from the previous chapter on diagonalization. Throughout, V is a finite dimensional vector space over ℝ or ℂ with an inner product <|>. The main goal in this chapter is to understand the nature of quadratic forms, symmetric bilinear forms and conjugate-symmetric sesquilinear forms on a finite dimensional inner product space V—in particular, how the form relates to the inner product on V. It turns out that the key to describing such a form is an associated linear transformation on V. The linear transformations here are of interest in their own right, and have the property of being self-adjoint (as defined below). They can be diagonalized using methods in the last chapter, and this diagonalization provides a complete description of the bilinear or sesquilinear form we are interested in.
Patterns
Authors: Ball Philip
Published: November 2023

There was always something a little different about meteorite ALH84001, found in 1984 on the icy Allan Hills of Antarctica. For one thing, it came from Mars---like only 11 other meteorites found around the world. But unlike these others, ALH84001 was old-and I mean four-and-a-half billion years old. The rock was formed when the Red Planet was newly born. But the most extraordinary aspect of this little lump of Mars did not emerge until August 1996, when scientists from NASA announced that it might contain signs of fossil life from our cosmic neighbour. Maybe my years at Nature magazine have exposed me to too many amazing ‘discoveries’ that vanish like morning mist under close scrutiny; but I felt in my bones that this claim would not stand the test of time. If I’m wrong (and I rather hope I am), this is one of the most significant discoveries of the twentieth century.
Principles
Authors: Ball Philip
Published: November 2023

I hope you have not been holding your breath in anticipation that in this final chapter I will disclose a grand; unifying picture of pattern formation. I had better start out by saying that I shall not be presenting one, since I don’t know that such a thing exists. Some physicists have in recent years encouraged an unfortunate aspiration towards grand unified pictures, but I fear we must accept that the world that we encounter, the world of real stuff that we see and touch, is far too messy for that. At the same time, it is far more beautiful. Perhaps it is a matter of taste, but I feel that there is much more wonder in a world that weaves its own tapestry using countless elegant and subtle variations, combinations and modifications of a handful of common processes than one in which the details become irrelevant, in which a few recondite equations are supposed to provide us with all we need.
Genetic diversity: do marker genes tell us the whole story?
Authors: Tregenza T , Butlin R K
Published: November 2023

To understand the variety of life and, more urgently, to decide how best to conserve it, biological diversity must be measured. Such an endeavor has two prerequisites: first, that we decide what we mean by diversity, and secondly that we are able to quantify the differences between organisms, concentrating on those differences we believe to be most relevant. Because species are the units ecologists are best able to count (Magurran 1988), they are frequently used as a practical measure of diversity. This ought to mean that the still unresolved search for a universal species concept (Claridge et al.1997) should be placed at the center of ecological debates about biodiversity. However, practising ecologists usually cannot devote the time needed to tackle this thorny issue: they necessarily make pragmatic use of the species defined by systematists. There are essentially three classes of species concepts which can be applied to real situations. These are based either on diagnosability, reproductive isolation or ecological distinctiveness. When measuring alpha-diversity (the number of species within a community), which of these concepts is used is unlikely to affect estimates of diversity, except with a minority of species which present problems either of asexual reproduction or of hybridisation. Clones within asexual ‘ species ‘ may have different ecological roles (Vrijenhoek 1994), so if it is ecological distinctiveness which interests us, these clones may be more appropriate units than diagnosable species.
Sexual selection and natural selection 1n bird speciation
Authors: Price Trevor
Published: November 2023

Natural selection, sexual selection and random drift have all been postulated to play roles in the origin of species. Natural selection has the strongest empirical support, because rapid speciation is best documented in adaptive radiations: the more or less simultaneous divergence of numerous lines from a common ancestor to exploit new adaptive zones (Simpson 1953, p.223; Schluter 1998). Artificial selection experiments, mimicking natural selection, often produce reproductive isolation as a correlated response (Rice and Hostert 1993). Comparisons of sister clades with differing numbers of species have been used to identify traits which accelerate speciation rates. Heard and Hauser (1994) reviewed 47 proposed ‘key innovations ‘. Thirty-five (74%) were traits enabling exploitation of new resources (such as phytophagous habit in insects; Mitter et al.1988), 10 (22%) affected dispersal, and just two (4%) were related to sexual selection.
Sexual conflict and speciation
Authors: Partridge L , Parker G A
Published: November 2023

We discuss here the role of sexual conflict (or antagonism)-the different evolutionary interests of males and females- as a force regulating the potential for speciation. Although there has been awareness of sexual conflict and its ramifications for many years (e.g. Trivers 1972; Dawkins and Carlisle 1976; Dawkins and Krebs 1978, 1979; Parker 1979) there has been relatively little consideration of its possible implications for speciation (but sec Parker 1974a, 1979; Wilson and Hedrick 1982). Our emphasis will be on the evolution of reproductive isolation, because of its central importance in the speciation process. We shall consider the potential role of sexual conflict in the evolution of both pre and post-zygotic isolation. Conflict between the sexes can occur through two genetic routes (Chapman and Partridge 1996a). Sexual conflict within gene loci occurs when allelic variation at one locus affects a trait in both males and females, there are different trait optima for the sexes, and hence selection for sexual dimorphism. There will then be a genetic correlation between trait values in the two sexes through pleiotropycffccts of the same alleles on males and on females. The difference between selection on the alleles when in females and in males can therefore result in one sex constraining the evolution of the other (Slatkin 1984; Rice 1984; Lande 1987). For instance, high levels of re-mating in females may be of no direct benefit to females themselves, and may instead occur as a result of a pleiotropic genetic correlation between the sexes for mating frequency, and a correlated response in females to selection for frequent re-mating in males (Halliday and Arnold 1987).
Population differentiation without speciation
Authors: Magurran Anne E
Published: November 2023

It is conventional to view biological diversity as synonymous with species richness and/or species abundance (Magurran l 988; Rosenzweig 1995). In recent years, however, the concept of biological diversity has been extended to embrace the rich seam of diversity within species themselves (Barbault et al.1995; Gaston 1996; Mallet 1996; Butlin and Tregenza 1998). Such diversity can be cryptic and only apparent once appropriate techniques are applied, an example being the use of allozymes to uncover levels of heterozygosity (Butlin and Tregenza 1998), or it may be expressed phenotypically and manifest itself as variation in behaviour, or morphology, or life histories (Mallet 1996; Foster and Endler 1999).Current conservation practice recognises that intraspecific diversity is worth preserving in its own right. This is partly because the viability of a species may in some way be related to its variability (Bisby 1995, but see also Amos and Harwood 1998). An additional consideration is that intraspecific diversity is perceived as the raw material for evolution (Barba ult and Sastrapradja 1995; Mallet 1996). It stands to reason that populations that are highly differentiated are the precursors of new species. Thus it is not simply variation as such, but also the potential to generate new species and even more biological diversity, that must be conserved (Myers 1997). However, as evolutionary biologists have been discovering, the relationship between population divergence and speciation is not straightforward. Although population differentiation can be an important step on the path to speciation, speciation is by no means the inevitable outcome of even the most marked population differentiation. This chapter illustrates the issue by reviewing recent work on a little fish that is increasingly being cited as a classic case of evolution in action.
Gulliver ‘s further travels: the necessity and difficulty of a hierarchical theory of selection
Authors: Gould Stephen Jay
Published: November 2023

For principled and substantially philosophical reasons, based largely on his reform of natural history by inverting the Paleyan notion of overarching and purposeful beneficence in the construction of organisms, Darwin built his theory of selection at the single causal level of individual bodies engaged in unconscious (and metaphorical) struggle for their own reproductive success. But the central logic of the theory allows selection to work effectively on entities at several levels of a genealogical hierarchy, provided that they embody a set of requisite features for defining evolutionary individuality. Genes, cell lineages, demes, species, and clades -as well as Darwin ‘s favored organisms-embody these requisite features in enough cases to form important levels of selection in the history of life. R. A. Fisher explicitly recognized the unassailable logic of species selection, but denied that this real process could be important in evolution because, compared with the production of new organisms within a species, the origin of new species is so rare, and the number of species within most clades so low. I review this and other classical arguments against higher-level selection, and conclude (in the first part of this chapter) that they are invalid in practice for intergenic selection, and false in principle for species selection. Punctuated equilibrium defines the individuality of species and refutes Fisher ‘s classical argument based on cycle time. In the second part of the chapter, I argue that we have failed to appreciate the range and power of selection at levels above and below the organismic because we falsely extrapolate the defining properties of organisms to these other levels (which arc characterized by quite different distinctive features), and then regard the other levels as impotent because their effective individuals differ so much from organisms.
Battling The Authorities And The Muses
Authors: Parshall Karen Hunger
Published: November 2023

The years from 1850 to 1855 had been explosively productive for Sylvester mathematically, witnessing as they had his fundamental contributions to the theory of invariants as well as his subsequent exploration of ideas suggested by them. This mathematical success, however, had made him increasingly aware of where his real interests and loyalties lay—in mathematics and not in the day-to-day duties of the actuary. How could he get more time to pursue his true calling and still earn his way in the world? Academe seemed to hold the only answer, but it presented him with the same impediments in the mid-1850s as it had in the late-1830s.
Returning Home
Authors: Parshall Karen Hunger
Published: November 2023

Sylvester left Baltimore and The Johns Hopkins on 21 December, 1883 following a day of fanfare and farewells. The entire university had turned out for a reception in his honor on the twentieth, and, not surprisingly, the mathematician had taken a turn at the podium. His remarks were classically Sylvesterian—long-winded, exuberant, humorous, heart-felt. He praised the University for the high standards it had set for higher education in the United States; he lauded individual faculty members for their contributions to their respective fields; and he extolled the University’s guiding light, its President Daniel Coit Gilman, for his vision. He was not, however, uncritical.
Introduction
Authors: Pier Jean-Paul
Published: November 2023

In mathematics there is a method to seek after truth, that Plato is claimed to have invented, that Theon called analysis and defined in the following way: Consider the thing looked for as if it were given, and step from conclusions to conclusions until one recognizes the thing looked for as being true.
Lie groups
Authors: Pier Jean-Paul
Published: November 2023

Lie’s work comes out of problems related to differential equations, partial differential equations, and differential geometry; the subject was to become increasingly one of the busiest intersections of algebra, analysis, and geometry.
Theory of functions and analytic geometry
Authors: Pier Jean-Paul
Published: November 2023

In studying functions of complex variables the analyst, besides the geometrical image that is his usual instrument, finds several physical images which he can make use of as successfully.
Algebraic geometry
Authors: Pier Jean-Paul
Published: November 2023

I believe that the numbers and functions of analysis are not the arbitrary product of our mind; I think that they exist outside of us, with the same character of necessity as things of objective reality, and we meet them or discover them, and study them, like physicists, chemists, and zoologists.
Tha estronomical Background
Authors: Richards E G
Published: November 2023

Our interpretation of what we see of the heavens is very different from that of the ancients. We believe, following Copernicus, that the earth revolves around the sun and rotates about its own axis. The ancients believed, following Ptolemy and common sense, that the earth was stationary and that the stars and sun and moon moved in cycles above it. If we were to observe the solar system looking down on it from the north, we would see the earth spinning on its axis in an anticlockwise direction and moving in its orbit in the same sense. Ptolemy, again looking south, would say that the sun and the stars rotated above the earth in a clockwise direction from east to west.
Writing and Libraries
Authors: Richards E G
Published: November 2023

Some 12ooo years ago, the glaciers were starting to recede for the last time. A few thousand years later, at the start of the Neolithic Age, man had learnt to grow crops and domesticate animals, rather than lead a hand-to-mouth existence, hunting and gathering food. His tribe and community still remained small but where the land, irrigated by great rivers, was particularly fertile, the supply of food increased. The size of communities grew, and some 6000 years ago the first cities and civilizations were established: in the land between the Tigris and the Euphrates called Mesopotamia, in Egypt by the Nile, in north ern India in the Indus valley, and in China by the Yellow River. There was, in these places, sufficient surplus food to support an army (for protection or depredation) and workers (to build dams and canals and monuments to gods or kings).Travellers and merchants moved from one centre to another, spreading news of any discoveries. The keeping of records and in turn writing, became a necessity; with writing, the calendar became possible.
Numbers and Arithmetic
Authors: Richards E G
Published: November 2023

The possibility of a calendar just did not exist before the invention of counting and a system to express numbers. Without such an intellectual tool, there is no way of assessing the days in a month or a year, and a calendar is impossible. For calendrical purposes we have the day, the month, and the year, and the passage of time can be marked by counting these events. When man’s ability to count had become sufficiently sophisticated, one supposes that people attempted to assess the number of days in a month, of months in a year, and of days in a year.
The Reform of the Calendar
Authors: Richards E G
Published: November 2023

Calendars are resistant to change. The kings of Egypt had to swear before they took office that they would not change the calendar; any change in the Jewish calendar requires a meeting of the Great Sanhedrim; the reform of the Christian calendar in 1582 required a papal bull. One possible reason for this apparent sanctity is that calendars are religious objects; they define the times of rites and fasts and festivals. Where there is a calendar there is a religion more often than not; where there is a religion, there is a calendar.
ThCealendars of Babylon and the Near East
Authors: Richards E G
Published: November 2023

Cities and civilization probably first arose in Mesopotamia, in the region fer tilized by the great rivers of the Tigris and Euphrates. Sometime in the fourth millennium BC, the Sumerians in Mesopotamia and the surrounding fertile crescent started to build cities: Eridu, Ur, Babylon, and others.This area, now part oflraq, was ruled by a succession of dynasties from at least 4000 BC.Itis convenient to refer to the inhabitants as Babylonians, though the area extended far beyond that city.
ThCealendars of China and East Asia
Authors: Richards E G
Published: November 2023

People have been living in settlements in China since at least 3500 BC. Although there is a traditional story that the invention of writing is as old, the earliest known writing dates from the Shang period (c. 1600 BC).
Calendar Conversions
Authors: Richards E G
Published: November 2023

The problem of converting dates from one calendar to another has often been solved by using tables. This is still the only method if the calendar is so ill defined that recourse must be made to contemporary records, as is the case for strictly empirical calendars in which the start of a month or a year, or the deci sion of whether an intercalation is to be made, is determined by observation of the heavens, the seasons, or nature itself Some astronomical calendars (see Chapter 6), such as the Chinese and many Indian calendars, depend on a detailed theory of the behaviour of heav enly bodies, and some, like the Chinese calendar, have suffered innumerable modifications. These theories and modifications are usually not available, and it is beyond the scope of this book to provide algorithms for conversions of these: recourse must again be made to conversion tables.
Mathematical Notes
Authors: Richards E G
Published: November 2023

The descriptions of the algorithms presented in this section are unavoidably mathematical in character. Nevertheless, I have aimed to keep the algebra and arithmetic as simple as possible. All the numbers involved are whole numbers or integers (with one exception in algorithm H); these may be combined in various ways to yield further integers by addition, subtraction, multiplication, division, and remaindering. The evaluation of the equations requires some comment. First you should evaluate expressions within brackets starting with the innermost bracket. To avoid an excessive number of these, a rule of precedence (familiar to computer programmers) has been used: first evaluate multi plications and divisions; only when this has been done should you evaluate additions and subtractions. Multiplication is usually implied in the usual way by writing the symbols for two or more quantities next to one another (but note that in deference to tradition I have used SOL and LUN to stand for single quantities). Invariably in the algorithms, and sometimes elsewhere, multiplication is denoted by*.
ToCalculate the Day of the Week
Authors: Richards E G
Published: November 2023

There are several ways in which you can work out the day of the week of any date in either the Julian or Gregorian calendar. These are generally arithmetic and require us to specify the day of the week by a number. We shall use the tra ditional numbering as shown in TABLE 24.1 (although other numberings have been used from time to time).
The Jewish Calendar
Authors: Richards E G
Published: November 2023

The Jewish calendar has an undeserved reputation of being hard to under stand. In reality it is not so difficult and is much more comprehensible than the rules for the calculation of the date of Easter or the intricacies of the Mayan calendar round. The important thing to grasp is the difference between the highly regular astronomical calendar and the civil calendar with its postponements.
AShort History of Easter
Authors: Richards E G
Published: November 2023

Easter is the time when Christians celebrate their central mystery of the Cru cifixion and Resurrection ofJ esus Christ. The word ‘Easter’ (German, ‘Oster’) itself derives from the name of the old Northern god of the spring, Eostre, but a different word, deriving from the Hebrew for Passover, ‘Pesah’, is used in almost all other European languages and in the English adjective, ‘paschal’. There is no etymological connection between paschal and Christ’s Passion on the Cross.
ThDeate of Easter Sunday
Authors: Richards E G
Published: November 2023

I am reminded of the author who, wishing to know how to calculate the date of Easter, telephoned the Royal Observatory at Greenwich. He was told that those august astronomers consulted the tables at the back of the Prayer Book. This not altogether satisfactory, albeit apocryphal, response prompted this chapter, in which I discuss how the date of Easter Sunday is calculated first according to the Dionysian canon in the Julian Calendar and then according to the Gregorian canon. This involves a discussion of golden numbers and epacts and how these and dominical numbers are used in the calculation. (Dominica! letters and numbers have already been described at length in Chapter 24.)
ABook of Hours
Authors: Richards E G
Published: November 2023

St Benedict founded his order of monks in the sixth century. His ‘rule for monks’ required that the praises of God be sung seven times a day-an idea which probably originated from ancient Jewish practices. The times, the canonical hours, at which this should be done came to be known as matins and lauds, prime, tierce, sext, none, vespers and compline. Matins and lauds were sung without break in the middle of the night, with prime following at dawn; tierce, sext, and none followed at regular intervals during daylight (none even tually gave its name to noon); and vespers and compline were executed in the evening. The result was a near continuous hymn of praise. The actual texts to be sung at the canonical hours were taken from, or at least inspired by, the Book of Psalms and copied into the Divinum Officium (the book of the Divine Office).
Energy, environment and economy
Authors: Chan C C , Chau K T
Published: November 2023

Energy is the source of our lives, environment is the reliance of our lives, and economy is the operation of our lives. EVs can contribute to energy, environment and economy, hence beneficial to our lives (Chan, 2000). Their contributions are due to the improvement in energy security and energy efficiency for transportation, the alleviation of air pollution and noise pollution caused by ICEVs, and the creation of new businesses for supplementing or even replacing ICEVs. In fact, the first impetus for the redevelopment of EVs was due to the energy crisis in the 1970s, whereas the second impetus for the promotion of EVs was due to the goal of environmental protection in the 1990s. It is anticipated that the third impetus for the commercialization of EVs will be due to the economic opportunity in the 2000s.
The Basic Model Of Virus Dynamics
Authors: Nowak Martin A , May Robert M
Published: November 2023

Traditional epidemiology describes the spread of infectious agents within populations of individuals. Here we turn to the population dynamics of infection at a different level, which happens within the body of an infected individual; we describe how viruses spread from cell to cell. This micro-epidemiology opens up a completely new perspective for understanding infectious diseases. The aim is to reveal the basic laws that govern the spread of infectious agents within individuals, their interaction with the immune system and their response to treatment.
Dynamics Of Hepatitis B Virus
Authors: Nowak Martin A , May Robert M
Published: November 2023

Hepatitis is a general term denoting infection or inflammation of the liver. The most notable sign of liver disease, jaundice, is already described in ancient medical sources such as the Babylonian Talmud or the writings of Hippocrates. There are several different viruses that can cause hepatitis. In this chapter, we focus on the hepatitis B virus (HBV).
How Fast Do Immune Responses Eliminate Infected Cells?
Authors: Nowak Martin A , May Robert M
Published: November 2023

In order to understand the role of the immune system in limiting HIV-1 replication, it is critical to know to what extent the rapid turnover of productively infected cells is caused by viral cytopathicity or by immune-mediated lysis. In this chapter, we show data that many HIV-1 infected patients contain cytotoxic T lymphocytes (CTL) that lyse target cells in vitro  – at plausible CTL to target ratios – with half-lives of less than 1 day. In 23 patients with CD4 counts ranging from 10 to 900 per µl, the average rate of CTL mediated lysis corresponds to a target cell half-life of0.7 days. We develop mathematical models to calculate the turnover rate of infected cells subjected to immune-mediated lysis and viral cytopathicity and to estimate the fraction of cells which are killed by CTL as opposed to virus. The models provide new interpretations of drug treatment dynamics and explain the otherwise puzzling fact that the observed rate of virus decline is roughly constant for different patients. We conclude that in HIV-1 infection CTL-mediated lysis can reduce virus load by limiting virus production, with small effects on the half-life of infected cells.
What Is A Quasispecies?
Authors: Nowak Martin A , May Robert M
Published: November 2023

The word quasispecies is a mystery for most biologists, possibly because it was invented by chemists. In the 1970s, Manfred Eigen and Peter Schuster developed a chemical theory for the origin of life. They described how populations of RNA molecules could reproduce themselves. They noted that the spontaneous chemical reproduction of such comparatively simple molecules was much less accurate than the genetic replication of any organism currently alive. The first proliferation of biological information was thus an extremely error-prone process, compared to the more accurate replication mechanisms which appear in modern cells. Random events would lead to mutations. The reproduction of such molecules by base-pairing is not completely accurate, so a certain degree of mismatching is to be expected. Consequently a population of RNA molecules that was the result of such an inaccurate replication process would not be absolutely homogeneous, but a mixture of RNA molecules with different nucleotide sequences.
Advanced Antigenic Variation
Authors: Nowak Martin A , May Robert M
Published: November 2023

In this chapter, we discuss more complicated models of antigenic variation. In the simple models of Chapter 12, all viral strains had the same kinetic parameters. Now we assume that strains may differ in all their characteristic parameters, such as replication rate, immunological properties and cytopathicity. This leads to important new insights.
Multiple Epitopes
Authors: Nowak Martin A , May Robert M
Published: November 2023

The previous two chapters described antigenic variation in a single epitope. In this chapter we develop mathematical models of antigenic variation in multiple epitopes. The resulting ‘Multiple epitope theory’ leads to significant refinements in our understanding of the dynamical interaction between genetically variable pathogens and the immune system.
Applications to Integral Equations
Authors: Ng Michael K
Published: November 2023

Problems in many fields lead to integral equations of the form whereg()anda(,)are given functions.
Wigglers and undulators
Authors: Wille Klaus
Published: November 2023

It was mentioned in Chapter 2 that particularly intense and tightly collimated synchrotron radiation can be produced by special magnets consisting of a periodic series of short bending magnets (Fig. 2.7). Such magnets are termed ‘wigglers’ and ‘undulators’. In Section 8.2 we will discuss when a magnet of this kind is a wiggler and when it is an undulator, but to begin with we will not make any distinction between the two types and will talk generally about W/U magnets.
Introduction
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

Pour a bottle of beer. Restraining your thirst for the moment, admire its lively performance. One by one, bubbles of gas are nucleated, rise and crowd together at the surface. A foam, or froth, is quickly formed.1 Most of the liquid drains away, leaving the bubbles packed closely together in the form of elegant polyhedral cells. If you wait long enough you may see the structure change, as gas diffuses between the cells. This gradual change is punctuated by sudden local rearrangements. In most brands of beer it is quickly overtaken by the collapse of the foam, as its individual films burst. Drink it in time, and you can feel that the foam is not quite a liquid. Paradoxically, it is a very soft solid, creamy in texture if the bubbles are small. Cheers †.
Quantitative description of foam structures
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

All of nature is tetrahedrally coordinated.

Buckminster Fuller

We will develop here some of the essential notation relating to structure. Writing the volume of a cell or bubble as Vb, we may define its effective diameter d
Making foams
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

I do not suppose that there is any one in this room who has not occasionally blown a common soap bubble, and while admiring the perfection of its form, and the marvellous brilliancy of its colours, wondered how it is that such a magnificent object can be so easily produced.

Boys’ comment aptly extends to the making of foams. While their production − the subject of this chapter − is a simple matter, the result is of fascinating complexity.
Electrical conduction in a foam
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

Things should be made as simple as possible but not any simpler.

A. Einstein

The electrical conductivity σf of a liquid foam is a good measure of its liquid fraction. If it is divided by the conductivity of the bulk liquid, σ1, the resulting relative conductivity σ is found to be primarily a function of Φl
Forces, energies, and timescales in condensed matter
Authors: Jones R A L
Published: November 2023

Condensed matter is held together by intermolecular forces; the strength and range of these forces determine the bulk, macroscopic properties of matter. In a solid, each molecule is locked into a definite location on a crystal lattice as a result of these intermolecular bonds; there is a direct relationship between the energy of the bonds and the stiffness of the material. In a liquid, molecules are also held together by intermolecular forces in a state of high density, but in contrast to a solid the molecules are not locked rigidly into well-defined positions on a lattice. Instead, a mol cule’s position relative to its neighbours changes on a certain characteristic relaxation time which itself is determined by the way the random, thermal motion of the molecules is modified by the intermolecular forces. It is this relaxation time that determines how easily the liquid will flow when a stress is applied. In this chapter we will discuss the relationship between the bulk properties of matter, such as its response to an externally applied stress, and the forces acting between its component molecules. One of our main tasks in this chapter is to establish the difference between solids and liquids. This difference is clear for many simple substances, but we shall see that in soft matter the distinction may be less clear-cut. Characteristic relaxation times for soft matter often fall into a range of values easily discernible to the human senses, and these materials seem to behave in a way that is neither entirely solid-like or entirely liquid-like–they are viscoelastic. In many systems, as the temperature is lowered the relaxation times increase dramatically, with the appearance of tending to infinity at some finite temperature. This divergence of the relaxation time leads to a non-equilibrium state of matter–a glass–in which a liquid-like lack of order is combined with solid-like elastic properties.
Phase transitions
Authors: Jones R A L
Published: November 2023

Soft matter often has a very rich and complicated morphology; rather than having a simple structure its components can be arranged in a complicated way, involving features at length scales intermediate between the atomic and the macroscopic. Examples will be discussed in detail in later chapters, and include block copolymer morphologies, soap morphologies, and emulsions. The remarkable feature of these structures is that they put themselves together in very complicated arrangements without outside assistance – they self-assemble. Understanding self-assembly involves understanding phase transitions and their kinetics. This is important for soft condensed matter, but much of what we need to know applies also to simpler kinds of matter too, and our discussion and examples will not be restricted to soft matter.
Gelation
Authors: Jones R A L
Published: November 2023

A gel is a material composed of subunits that are able to bond with each other in such a way that one obtains a network of macroscopic dimensions, in which all the subunits are connected by bonds. If one starts out with isolated subunits, and successively adds bonds, one goes from a liquid – a sol – to a material with a non-zero shear modulus – a gel. A gel has the mechanical properties characteristic of a solid, even though it is structurally disordered and indeed may contain a high volume fraction of liquid solvent. If the gel consists of linear segments joined together at cross-link points, and the linear sections are flexible and long enough to be considered as random walks, the mechanical properties of the gel may be described by the theory of rubber elasticity described in the last chapter. Gels may also go through a glass transition; gels with a high density of short rigid segments are likely to be glassy. Within this broad framework there are many different types of gel, with different classes of subunit, and with different types of bonding between them. For example, the subunits may be multi-functional monomers, which are connected together by covalent bonds to form a three-dimensional network. An example would be an epoxy resin. Alternatively, the subunits may themselves be linear polymers, which are connected together by covalent cross-links to form a rubber. Linear polymers may be connected by physical, rather than chemical, bonds, giving a thermoreversible gel such as gelatin. The subunits themselves may be colloidal aggregates of many molecules, which then are linked together by physical interactions.
Supramolecular self-assembly in soft condensed matter
Authors: Jones R A L
Published: November 2023

One of the most spectacular properties of soft matter systems is their ability to self-assemble on a hierarchy of length scales: molecules arrange themselves in supramolecular assemblies, and these assemblies in tum pack in structures that may be highly ordered, even though the units that are being packed are noncrystalline and of dimensions considerably bigger than atomic scales. The most common examples of these self-assembled phases are found in soap and other materials that are formed by mixing water with a class of molecules known as amphiphiles, which have the property that part of the molecule has an affinity to water and another part of the molecule is repelled from water. When such molecules are dissolved in water, the way the system attempts to satisfy these two irreconcilable tendencies leads to a rich array of possible structures. Many amphiphilic molecules are relatively small, but polymers too can display this tendency if they are composed of two or more chemically different blocks covalently linked together. In solution such block copolymers behave in very similar ways to small-molecule amphiphiles. However, the large size of polymer molecules has important consequences for the thermodynamics of mixing. Even when the chemical units making up a pair of polymers are relatively similar, and the unfavourable energies of interaction between them small, the entropy of mixing is usually not large enough to promote mixing and the polymers will phase separate. If the two polymers are linked together covalently, this constraint prevents them from phase separating on a macroscopic scale and the result is microphase separation, an ordered arrangement of domains of the two polymer types on mesoscopic length scales. This is another example of self-assembly-complex ordered structures arising solely from the requirement that the system minimises its free energy.