bluuebunny/crossref_metadata_2025 huggingface dataset:
Properties of first-order logic
Authors: Hedman Shawn
Published: November 2020

We show that first-order logic, like propositional logic, has both completeness and compactness. We prove a countable version of these theorems in Section 4.1. We further show that these two properties have many useful consequences for first-order logic. For example, compactness implies that if a set of first-order sentences has an infinite model, then it has arbitrarily large infinite models. To fully understand completeness, compactness, and their consequences we must understand the nature of infinite numbers. In Section 4.2, we return to our discussion of infinite numbers that we left in Section 2.5. This digression allows us to properly state and prove completeness and compactness along with the Upward and Downward Löwenhiem–Skolem theorems. These are the four central theorems of first-order logic referred to in the title of Section 4.3. We discuss consequences of these theorems in Sections 4.4–4.6. These consequences include amalgamation theorems, preservation theorems, and the Beth Definability theorem. Each of the properties studied in this chapter restrict the language of first-order logic. First-order logic is, in some sense, weak. There are many concepts that cannot be expressed in this language. For example, whereas first-order logic can express “there exist n elements” for any finite n, it cannot express “there exist countably many elements.” Any sentence having a countable model necessarily has uncountable models. As we previously mentioned, this follows from compactness. In the final section of this chapter, using graphs as an illustration, we discuss the limitations of first-order logic. Ironically, the weakness of first-order logic makes it the fruitful logic that it is. The properties discussed in this chapter, and the limitations that follow from them, make possible the subject of model theory. All formulas in this chapter are first-order unless stated otherwise. Many of the properties of first-order logic, including completeness and compactness, are consequences of the following fact: Every model has a theory and every theory has a model. Recall that a set of sentences is a “theory” if it is consistent (i.e. if we cannot derive a contradiction). “Every theory has a model” means that if a set of sentences is consistent, then it is satisfiable.
Models of countable theories
Authors: Hedman Shawn
Published: November 2020

We define and study types of a complete first-order theory T. This concept allows us to refine our analysis of Mod(T). If T has few types, then Mod(T) contains a uniquely defined smallest model that can be elementarily embedded into any structure of Mod(T). We investigate the various properties of these small models in Section 6.3. In Section 6.4, we consider the “big” models of Mod(T). For any theory, the number of types is related to the number of models of the theory. For any cardinal κ, I(T, κ) denotes the number of models in Mod(T) of size κ. We prove two basic facts regarding this cardinal function. In Section 6.5, we show that if T has many types, then I(T, κ) takes on its maximal possible value of 2κ for each infinite κ. In Section 6.6, we prove Vaught’s theorem stating that I(T, ℵ0) cannot equal 2. All formulas are first-order formulas. All theories are sets of first-order sentences. For any structure M, we conveniently refer to an n-tuple of elements from the underlying set of M as an “n-tuple of M.” The notion of a type extends the notion of a theory to include formulas and not just sentences. Whereas theories describe structures, types describe elements within a structure. Definition 6.1 Let M be a ν-structure and let ā = (a1, . . . , an) be an n-tuple of M. The type of ā in M, denoted tpM(ā), is the set of all ν-formulas φ having free variables among x1, . . . , xn that hold in M when each xi in is replaced by ai. More concisely, but less precisely: If ā is an n-tuple, then each formula in tpM(ā) contains at most n free variables but may contain fewer. In particular, the type of an n-tuple contains sentences. For any structure M and tuple ā of M, tpM(ā) contains Th(M) as a subset. The set tpM(ā) provides the complete first-order description of the tuple ā and how it sits in M.
The incompleteness theorems
Authors: Hedman Shawn
Published: November 2020

In this chapter we prove that the structure N = (ℕ|+, · , 1) has a first-order theory that is undecidable. This is a special case of Gödel’s First Incompleteness theorem. This theorem implies that any theory (not necessarily first-order) that describes elementary arithmetic on the natural numbers is necessarily undecidable. So there is no algorithm to determine whether or not a given sentence is true in the structure N. As we shall show, the existence of such an algorithm leads to a contradiction. Gödel’s Second Incompleteness theorem states that any decidable theory (not necessarily first-order) that can express elementary arithmetic cannot prove its own consistency. We shall make this idea precise and discuss the Second Incompleteness theorem in Section 8.5. Gödel’s First Incompleteness theorem is proved in Section 8.3. Although they are purely mathematical results, Gödel’s Incompleteness theorems have had undeniable philosophical implications. Gödel’s theorems dispelled commonly held misconceptions regarding the nature of mathematics. A century ago, some of the most prominent mathematicians and logicians viewed mathematics as a branch of logic instead of the other way around. It was thought that mathematics could be completely formalized. It was believed that mathematical reasoning could, at least in principle, be mechanized. Alfred North Whitehead and Bertrand Russell envisioned a single system that could be used to derive and enumerate all mathematical truths. In their three-volume Principia Mathematica, Russell and Whitehead rigorously define a system and use it to derive numerous known statements of mathematics. Gödel’s theorems imply that any such system is doomed to be incomplete. If the system is consistent (which cannot be proved within the system by Gödel’s Second theorem), then there necessarily exist true statements formulated within the system that the system cannot prove (by Gödel’s First theorem). This explains why the name “incompleteness” is attributed to these theorems and why the title of Gödel’s 1931 paper translates (from the original German) to “On Formally Undecidable Propositions of Principia Mathematica and Related Systems” (translated versions appear in both [13] and [14]). Depending on one’s point of view, it may or may not be surprising that there is no algorithm to determine whether or not a given sentence is true in N.
Non-Stoichiometric Compounds Derived From Extended Defects
Authors: Kosuge Koji
Published: November 2020

The non-stoichiometric compounds that we describe in this chapter are closely correlated with the classical non-stoichiometric compounds derived from point defects discussed in Chapter 1. For the past twenty years precise structural analyses on complex binary and ternary compounds have been carried out using X-ray and neutron diffraction techniques. Moreover, owing to the striking development of the resolving power of the electron microscope crystal structures can be seen directly as structure images. As a result, it has been shown that most complex structures can be derived by introducing extended defects regularly into a mother structure. A typical example is a ‘shear structure’, which is derived by introducing planar defects of anion rows into the mother lattice. A ‘block structure’ is derived by introducing two groups of planar defects. ‘Vernier structures’, ‘micro-twin structures’, ‘intergrowth structures’, and ‘adaptive structures’ are also described in detail in this chapter. At the beginning of 1950, Professor A. Magnéli’s group in Sweden started a systematic study of the crystal structures of the oxides of transition metal elements such as Ti, V, Mo, and W, mainly by X-ray diffraction techniques. As a result, they confirmed the existence of the homologous compounds expressed by VnO2n–1; TinO2n–1 etc. (n = 2, 3, 4, . . .) and also predicted that the crystal structure of these compounds could be derived from a mother structure, ‘rutile’. Figure 2.1 shows the X-ray powder diffraction patterns (CuKα) of compounds TiOx between Ti2O3 (x = 1.5) and TiO2 (x = 2.0).3 This clearly indicates the convergence of the diffraction patterns to that of TiO2 (rutile) with increasing x, which is why the Magnéli school predicted the mother structure to be rutile. This prediction was verified by the structure determinations of Ti5O95 and VnO2n–1.6 These compounds are called Magnéli phases after the main investigator, and similar compounds have been discovered.
Using text in Sequence Analysis
Authors: Raychaudhuri Soumya
Published: November 2020

Text about genes can be effectively leveraged to enhance sequence analysis (MacCallum, Kelley et al. 2000; Chang, Raychaudhuri et al. 2001; McCallum and Ganesh 2003; Eskin and Agichtein 2004; Tu, Tang et al. 2004). Most of the emerging methods utilize textual representations similar to the one we introduced in the previous chapter. To analyze sequences, a numeric vector that contains information about the counts of different words in references about that sequence can be used in conjunction with the actual sequence information. Experienced biologists understand the value of using the information in scientific text during sequence searches, and commonly use scientific text and annotations to guide their intuition. For example, after a quick BLAST search, a trained expert might quickly look over the hits and their associated annotations and literature references and assess the validity of the hits. The apparently valid sequence hits can then be used to draw conclusions about the query sequence by transferring information from the hits. In most cases, the text serves as a proxy for structured functional information. High quality functional annotations that succinctly and thoroughly describe the function of a protein are often unavailable. Defining appropriate keywords for a protein requires a considerable amount of effort and expertise, and in most cases, the results are incomplete as there is an evergrowing collection of knowledge about proteins. So, one option is to use text to compare the biological function of different sequences instead. There are different ways in which the functional information in text could be used in the context of sequence analysis. One possibility is to first run a sequence analysis algorithm, and then to use text profiles to summarize or organize results. Functional keywords can be assigned to the whole group of hit sequences. Additionally, given a series of sequences, they can be grouped according to like function. In either case, quick assessment of the content of text associated with sequences offers insight about exactly what we are seeing. These approaches are particularly useful if we are querying a large database of sequences with a novel sequence that we have very little information about.
Text-Based Analysis of a Single Series of Gene Expression Measurements
Authors: Raychaudhuri Soumya
Published: November 2020

In this chapter we begin to address the issue of the analysis of gene expression data with the scientific literature. Here we describe methods for the analysis of a single experiment—one where a single expression measurement has been made for many genes within the same organism. In Chapter 7 we will address the analysis of larger data sets with multiple expression measurements for each of the genes; the questions that occur in that setting are often more complex and utilization of scientific text in that setting can be more useful. But focusing on a single series of expression measurements is an effective starting point in understanding the scientific literature and how it can be used with experimental data. The lessons here can be applied to a wide array of genomic assays besides gene arrays. These methods can be applied to any assay that assigns a single value to each gene In addition, many investigators generate single-condition expression data sets, and these methods are widely applicable. One of the great difficulties in analyzing a single expression series is that context is lacking. That is, we have a large set of isolated measurements. Each measurement corresponds to the log of the relative ratio of a single gene’s expression in an experimental condition compared to its expression in a control condition. These measurements represent a single snapshot of a cell’s physiologic status. One of the great challenges is sorting out the physiologically important expression changes compared to random experimental and physiologic aberrations and fluctuations. Gene expression measurements are subject to a great amount of noise and distinguishing true positives from genes that are not truly induced or repressed is a great challenge. Typically, investigators use their knowledge of biology to prioritize likely positives. In this chapter we argue that text-mining approaches can be used to help prioritize these genes instead. Another equally important challenge is to discern broadly what biological functions are active in a given experiment.
Zonation and succession
Authors: Maun M. Anwar
Published: November 2020

There is ample evidence that a progressive change in the intensity of an important environmental factor leads to the formation of zones or belt-like communities in which the plant species reflect a fairly distinct range of tolerance for that factor (Daubenmire 1968). Zonation has been defined as a sequence of vegetation in space and succession as a sequence of vegetation in time (McIntosh 1980). A zone is an area occupied by a plant community that is distinctly different from other zones and can be readily recognized by a change in dominant vegetation. Striking examples of zonation are found in salt marshes, mountain slopes and ponds because of soil salinity in salt marshes, decrease in temperature on mountain slopes and increase in water depth in ponds (Daubenmire 1968; Chapman 1976; Partridge and Wilson 1988). Similarly, it has long been known (Beck 1819) that sand dunes along sea coasts exhibit a zonation pattern extending from the beach to inland dunes. The zones are discrete and occur in parallel series with distinctly different species composition that is related to the ability of plant species to withstand the environmental factors prevailing in that zone (Doing 1985). Many later studies using transects from the shoreline to the inland dunes have confirmed that the taxa are not randomly distributed; they peak at definite distances from the beach (Oosting and Billings 1942; Boyce 1954; Martin 1959; Barbour 1978; Barbour et al. 1985). Succession in coastal dunes is an example of primary succession because the sandy material deposited on the shoreline by waves is inert. The term is generally used to denote a directional change in species composition and physiognomy of vegetation at the same site over time (Drury and Nisbet 1973). However, only the very early stages of dune succession can be observed during the life time of a plant ecologist and the later stages are usually inferred from plant communities represented on older sand dunes. It is hypothesized that the autogenic influence of early colonizers alters environmental conditions in the habitat and facilitates the establishment of new species better adapted to live in the altered habitat.
Public policy towards catastrophe
Authors: Posner Richard A.
Published: November 2020

The Indian Ocean tsunami of December 2004 focused attention on a type of disaster to which policymakers pay too little attention – a disaster that has a very low or unknown probability of occurring, but that if it does occur creates enormous losses. The flooding of New Orleans in the late summer of 2005 was a comparable event, although the probability of the event was known to be high; the Corps of Engineers estimated its annual probability as 0.33% (Schleifstein and McQuaid, 2002), which implies a cumulative probability of almost 10% over a thirty-year span. The particular significance of the New Orleans flood for catastrophic-risk analysis lies in showing that an event can inflict enormous loss even if the death toll is small – approximately 1/250 of the death toll from the tsunami. Great as that toll was, together with the physical and emotional suffering of survivors, and property damage, even greater losses could be inflicted by other disasters of low (but not negligible) or unknown probability. The asteroid that exploded above Siberia in 1908 with the force of a hydrogen bomb might have killed millions of people had it exploded above a major city. Yet that asteroid was only about 200 feet in diameter, and a much larger one (among the thousands of dangerously large asteroids in orbits that intersect the earth’s orbit) could strike the earth and cause the total extinction of the human race through a combination of shock waves, fire, tsunamis, and blockage of sunlight, wherever it struck. Another catastrophic risk is that of abrupt global warming, discussed later in this chapter. Oddly, with the exception of global warming (and hence the New Orleans flood, to which global warming may have contributed, along with manmade destruction of wetlands and barrier islands that formerly provided some protection for New Orleans against hurricane winds), none of the catastrophes mentioned above, including the tsunami, is generally considered an ‘environmental’ catastrophe. This is odd, since, for example, abrupt catastrophic global change would be a likely consequence of a major asteroid strike.
Super-volcanism and other geophysical processes of catastrophic import
Authors: Rampino Michael R.
Published: November 2020

In order to classify volcanic eruptions and their potential effects on the atmosphere, Newhall and Self (1982) proposed a scale of explosive magnitude, the Volcanic Explosivity Index (VEI), based mainly on the volume of the erupted products (and the height of the volcanic eruption column). VEI’s range varies from VEI = 0 (for strictly non-explosive eruptions) to VEI = 8 (for explosive eruptions producing ∼1012 m3 bulk volume of tephra). Eruption rates for VEI = 8 eruptions may be greater than 106 m3s−1 (Ninkovich et al., 1978a, 1978b). Eruptions also differ in the amounts of sulphur-rich gases released to form stratospheric aerosols. Therefore, the sulphur content of the magma, the efficiency of degassing, and the heights reached by the eruption column are important factors in the climatic effects of eruptions (Palais and Sigurdsson, 1989; Rampino and Self, 1984). Historic eruptions of VEI ranging from three to six (volume of ejecta from <1 km3 to a few tens of km3) have produced stratospheric aerosol clouds up to a few tens of Mt. These eruptions, including Tambora 1815 and Krakatau 1883, have caused cooling of the Earth’s global climate of a few tenths of a degree Centigrade (Rampino and Self, 1984). The most recent example is the Pinatubo (Philippines) eruption of 1991 (Graf et al., 1993; Hansen et al., 1996). Volcanic super-eruptions are defined as eruptions that are tens to hundreds of times larger than historic eruptions, attaining a VEI of 8 (Mason et al., 2004; Rampino, 2002; Rampino et al., 1988; Sparks et al., 2005). Super-eruptions are usually caldera-forming events and more than twenty super-eruption sites for the last 2 million years have been identified in North America, South America, Italy, Indonesia, the Philippines, Japan, Kamchatka, and New Zealand. No doubt additional super-eruption sites for the last few million years exist (Sparks et al., 2005). The Late Pleistocene eruption of Toba in Sumatra, Indonesia was one of the greatest known volcanic events in the geologic record (Ninkovich et al., 1978a, 1978b; Rampino and Self, 1993a; Rose and Chesner, 1990).
Biotechnology and biosecurity
Authors: Nouri Ali , Chyba Christopher F.
Published: November 2020

Biotechnological power is increasing exponentially, reminiscent of the increase in computing power since the invention of electronic computers. The cofounder of Intel Corporation, Gordon Moore, pointed out in 1965 that the number of transistors per computer chip – a measure of how much computation can be done in a given volume – has doubled roughly every 18 months (Moore, 1965). This exponential increase in computing power, now called ‘Moore’s Law’, has continued to hold in the decades since then (Lundstrom, 2003) and is the reason that individuals now have more computing power available in their personal computers than that was available only to the most advanced nations only decades ago. Although biotechnology’s exponential lift off began decades after that of computing, its rate of increase, as measured, for example, by the time needed to synthesize a given DNA sequence, is as fast or faster than that of Moore’s Law (Carlson, 2003). Just as Moore’s Law led to a world of personal computing and home appliance microprocessors, so biotechnological innovation is moving us into a world where the synthesis of DNA, as well as other biological manipulations, will be increasingly available to small groups of technically competent and even individual users. There is already a list of well-known experiments – and many others that have received less public attention – that illustrates the potential dangers intrinsic to modern biological research and development. We review several examples of these in some detail below, including: genetic manipulations that have rendered certain viruses far more deadly to their animal hosts (Jackson et al., 2001); the synthesis of polio virus from readily purchased chemical supplies (Cello et al., 2002) – so that even if the World Health Organization (WHO) succeeds in its important task for eradicating polio worldwide, the virus can be reconstituted in laboratories around the world; the reduction in the time needed to synthesize a virus genome comparable in size to the polio virus from years to weeks; the laboratory re-synthesis of the 1918 human influenza virus that killed tens of millions of people worldwide (Tumpey et al., 2005); the discovery of ‘RNA interference’, which allows researchers to turn off certain genes in humans or other organisms (Sen et al., 2006); and the new field of ‘synthetic biology’, whose goal is to allow practitioners to fabricate small ‘biological devices’ and ultimately new types of microbes (Fu, 2006).
Stability of Navier–Stokes Equations
Authors: Chemin Jean-Yves , Desjardins Benoit , Gallagher Isabelle , Grenier Emmanuel
Published: November 2020

In this chapter we intend to investigate the stability of the Leray solutions constructed in the previous chapter. It is useful to start by analyzing the linearized version of the Navier–Stokes equations, so the first section of the chapter is devoted to the proof of the well-posedness of the time-dependent Stokes system. The study will be applied in Section 3.2 to the two-dimensional Navier–Stokes equations, and the more delicate case of three space dimensions will be dealt with in Sections 3.3–3.5.
The Periodic Case
Authors: Chemin Jean-Yves , Desjardins Benoit , Gallagher Isabelle , Grenier Emmanuel
Published: November 2020

This chapter deals with the rotating-fluid equations (NSC) in a purely periodic setting. Let a1, a2 and a3 be three positive real numbers and define the periodic box unlike the previous chapter where T3 denoted the unit periodic box in R3. In this chapter the size of the box will have some importance in the analysis. The system we shall study is the following. where P is the Leray projector onto the space of divergence-free vector fields. Let us recall its definition in Fourier variables.
Ekman Boundary Layers for Rotating Fluids
Authors: Chemin Jean-Yves , Desjardins Benoit , Gallagher Isabelle , Grenier Emmanuel
Published: November 2020

In this chapter, we investigate the problem of rapidly rotating viscous fluids between two horizontal plates with Dirichlet boundary conditions. We present the model with so-called “turbulent” viscosity. More precisely, we shall study the limit when ε tends to 0 of the system where Ω = Ωh×]0, 1[: here Ωh will be the torus T2 or the whole plane R2. We shall use, as in the previous chapters, the following notation: if u is a vector field on Ω we state u = (uh, u3). In all that follows, we shall assume that on the boundary ∂Ω, uε0 · n = uε,30 = 0, and that div uε0 = 0. The condition u30 = 0 on the boundary implies the following fact: for any vector field u ∊ H(Ω), the function ∂3u3 is L2(]0, 1[) with respect to the variable x3 with values in H−1(Ωh) due to the divergence-free condition.
Stability of Horizontal Boundary Layers
Authors: Chemin Jean-Yves , Desjardins Benoit , Gallagher Isabelle , Grenier Emmanuel
Published: November 2020

Let us now detail the stability properties of an Ekman layer introduced in Part I, page 11. First we will recall how to compute the critical Reynolds number. Then we will describe briefly what happens at larger Reynolds numbers. The first step in the study of the stability of the Ekman layer is to consider the linear stability of a pure Ekman spiral of the form where U∞ is the velocity away from the layer and ζ is the rescaled vertical component ζ = x3/√εν. The corresponding Reynolds number is Let us consider the Navier–Stokes–Coriolis equations, linearized around uE The problem is now to study the (linear) stability of the 0 solution of the system (LNSCε). If u=0 is stable we say that uE is linearly stable, if not we say that it is linearly unstable. Numerical results show that u=0 is stable if and only if Re<Rec where Rec can be evaluated numerically. Up to now there is no mathematical proof of this fact, and it is only possible to prove that 0 is linearly stable for ReRe2 with Re1<Rec<Re2, Re1 being obtained by energy estimates and Re2 by a perturbative analysis of the case Re=∞. We would like to emphasize that the numerical results are very reliable and can be considered as definitive results, since as we will see below, the stability analysis can be reduced to the study of a system of ordinary differential equations posed on the half-space, with boundary conditions on both ends, a system which can be studied arbitrarily precisely, even on desktop computers (first computations were done in the 1960s by Lilly).
An Impasse
Authors: Weiner J. S. , Stringer Chris
Published: November 2020

Dawson had received widespread recognition, but died too soon to be given any special award from a scientific body. Twenty years later his achievement was commemorated by the erection of a memorial stone at the site of the gravel pit at Barkham Manor. Sir Arthur Smith Woodward had taken the initiative in this and borne most, if not all, of the expense. The unveiling was done, at his request, by his old friend Sir Arthur Keith at the well-attended ceremony on 22 July 1938. Keith gave a brief but eloquent oration. He dwelt on the wonderful achievement of the keen-sighted amateur Dawson, an achievement which he likened in the history of discovery to that of the French lock-keeper, Boucher de Perthes—the first man, three-quarters of a century ago, to recognize clearly the human workmanship of the Ice Age flint hand-axes of the Somme. The discovery at Piltdown ranked worthily, too, with that of Neanderthal man discovered in 1857, the first known of all fossil men. These discoveries had encountered tremendous opposition before acceptance was won. The claims of Perthes had brought incredulity and set the scientific world a momentous problem, and only after years of stormy argument were these claims conceded; the discovery of Neanderthal man likewise brought disagreement and controversy. But this fossil form was accepted in the end. As Keith said, then came Dawson’s discovery, and this brought the greatest problem of all. But Keith did not go on to claim that all was now well with ‘the earliest known representative of man in Western Europe’, of which he had just finished a laborious re-study. A puzzle it had always been and a puzzle it was still. Keith could not hide his underlying doubt, and ten years later he expressed it again in the Foreword which he wrote at Lady Smith Woodward’s request to Woodward’s own book, The Earliest Englishman, published posthumously in 1948. He declared: ‘The Piltdown enigma is still far from a final solution.’ Why should Keith still express such doubt and bewilderment? But it was no longer surprising.
The Sussex Wizard
Authors: Weiner J. S. , Stringer Chris
Published: November 2020

It is common knowledge that Dawson did not command high esteem in the archaeological circle of Lewes. Some local archaeologists, on the basis of their personal feelings about Dawson as well as on their long-held, rather low opinion of his archaeological reliability, came to invest the Piltdown discovery with extreme scepticism from the start; objective evidence to back this up, such as St. Barbe, Morris, or Marriott might have offered, there seems to have been none. It is perhaps as well to indicate how Dawson came to acquire his reputation for ‘unreliability’, since it has a bearing both on the standard of his archaeological work and on the quality of his scientific writing on the Piltdown material, activities which we saw provided grounds for genuine surprise in their vagueness and inaccuracy. The local reasons for Dawson’s unpopularity should be assessed as objectively as possible, for it should not be forgotten how solid a reputation Dawson had made with his Wealden collections at the British Museum and how good his standing was with such men as Keith and Woodward. The deliberate avoidance of the great Piltdown discovery in official local circles is quite undeniable. On my first visit of inquiry in August 1953, I had fully expected to see much made of Piltdown in the local museums. The Borough Museum contained nothing but a small picture of an imaginary Eoanthropus presented by Dr. S. Spokes and some Piltdown eoliths presented by Harry Morris. The Barbican Museum, the home of the Sussex Archaeological Society, hard by the Castle keep, is in the street where once lived the famous Dr. Mantell; and in the same street is Dawson’s home, Castle Lodge. Here, too, there were no specimens of Charles Dawson’s on view, but more flints of Harry Morris, including eoliths from Piltdown. A cast of the well-known reconstruction of Piltdown man was displayed along with three enlarged models of teeth—one the molar from Piltdown II and, for comparison, chimpanzee and human molars. The cast and models (and also the picture in the Borough Museum) had all been presented by Dr. S. Spokes in 1928—fifteen years after the world-famous discovery.
Ancestors
Authors: Mitchell Peter
Published: November 2020

In Greek myth the winged horse Pegasus was actually ridden by the hero Bellerophon rather than by Perseus, yet Shakespeare’s words neatly capture the striking combination of supernatural power and tractability that is the horse. This chapter picks up these themes by developing three topics: it describes the evolution of the modern horse, Equus caballus, identifies key features of its biology relevant to subsequent discussions, and reviews the history of human–horse interaction in the Old World, emphasizing the horse’s domestication and subsequent spread. Horses and their relatives, the wild asses and zebras, were once seen as an almost paradigmatic example of how evolution works, although more recent research has shown that their history is more complex and multi-branched than originally thought. Along with tapirs and rhinoceroses, they belong to the taxonomic order Perissodactyla, the odd-toed division of the ungulates or hoofed mammals. The superficial similarities that they share with even-toed antelopes, which belong to the order Artiodactyla, are thus largely the result of evolution converging on similar body plans. In fact, some genetic studies suggest that perissodactyls are closer to carnivores than to the artiodactyls. Like modern tapirs and rhinoceroses, the earliest horses were three-toed, but for the past 40 million years or so all have borne their weight on just the third toe, with ligaments, rather than a fleshy pad, for support. Subsequently, the central metapodial (the bones connecting the digits to the wrist or ankle) was considerably elongated to form a long, slender lower limb and the second and fourth digits were minimized, though still giving support when galloping and jumping. Beginning around 10 million years ago, in the late Miocene period, the remaining side toes were reduced to splints and the animal’s weight came to be carried entirely on a single enlarged hoof. The first perissodactyls were browsers, not grazers. Some 45–34 million years ago, however, temperatures fell at higher latitudes and climate became more seasonal: successful ungulates evolved new adaptations, including the first appearance of both ruminants (which ferment their food in a specialized foregut) and new kinds of ancestral horses such as Mesohippus and its successor Miohippus.
A Prodigal Return
Authors: Mitchell Peter
Published: November 2020

It is one of the great ironies of history—equine and human—that the continent on which the horse was born was also the continent on which it died out. For after more than 40 million years, sometime between 12,000 and 7,600 years ago, the last truly wild horse in North America was no more. And yet, as it turned out, that animal’s last breath marked not an end, but only a hiatus, one that ended when Columbus—on his second trans-Atlantic voyage—brought horses to the Caribbean island of Hispaniola. This chapter therefore looks at four interrelated questions: the initial arrival of people in the Americas over 13,000 years ago; the variety of horses that they encountered there; how far their interactions with those horses contributed to the latter’s extinction; and how the horse returned to North America following Columbus’s voyage. When, where, and how people first arrived in the Americas remain some of archaeology’s most hotly contested topics, but we do know that horses were there to welcome them. Before considering how these two different mammals—the bipedal newcomer and the quadrupedal native—interacted, we need to answer the questions with which this paragraph began. Almost certainly humans entered the Americas from Siberia: early settlers in the western Pacific reached no further east than the Solomon Islands, while arguments that eastern North America was reached from Europe by Upper Palaeolithic hunters moving by boat and across ice around the North Atlantic fly in the face of both technology and chronology. But if the ancestors of Native Americans did indeed arrive in the New World from Asia (something that all genetic analyses of both modern and ancient populations confirm), when and how did they do so? Until recently the archaeological consensus—especially among Anglophone scholars in North America—was that this occurred around 13,000 years ago and was effected by people taking advantage of the globally depressed sea levels of the Last Ice Age to cross the Bering Straits when they formed part of a much broader landmass, Beringia.
Disease control and lesion prevention
Authors: Banerjee Avijit , Watson Timothy F.
Published: November 2020

From the previous chapter it can be seen that in all cases of caries and tooth wear, minimum intervention disease control and lesion prevention are key aspects of the management strategy, often commencing in the stabilization phase of the care plan, but continuing throughout the full course of treatment and beyond in order to maintain lifelong oral health. Neither the dentist, as part of the oral healthcare team, nor the patient has the power to prevent the caries or tooth-wear process. These ubiquitous processes occur at the ionic, metabolic, and microscopic level at the tooth surface/biofilm interface, and are made pathological by other factors in combination. If these factors are controlled or modified by the patient (with help from the oral healthcare team), then the processes can be regulated. The term primary prevention is sometimes used in this context. The term prevention has been commonly used, but actually it is only the manifestation of the pathological process (i.e. the lesion in caries or tooth wear) that can be prevented if the disease process is controlled. The term secondary prevention has been used in this context to slow down or stop (arrest) incipient, progressing lesions. Tertiary prevention is a term sometimes used to describe the care offered to the patient in an attempt to control or reduce the pattern of future disease. On the basis of the history and examination, the patient may be allocated to one of the following in terms of caries activity/risk status:… • Caries inactive/caries controlled/low risk: no active lesions and no history of recurrent active restorations in the past 2 to 3 years. A level of control (maintenance) is still required to remain in this stable condition. • Caries active/modifiable risk factors/moderate risk (plaque control, fluoride, diet): presence of active lesions and a yearly increment of more than two new/progressing/filled lesions in the preceding 2 to 3 years. Caries control may be achieved by changing/ modifying risk factors. • Caries active/unmodifiable or unidentifiable risk factors/ high risk (dry mouth, medications): this category will always be high risk, although it may still be possible to control caries by optimal moderation of such risk factors. Presence of active lesions and a yearly increment of more than two new/progressing/filled lesions in the preceding 2 years.
Shortness of breath
Authors: Farne Hugo , Norris-Cervetto Edward , Warbrick-Smith James
Published: November 2020

Shortness of breath essentially means either that not enough oxygen is getting around the body or that there is a cause for increased respiratory drive. This could be due to many causes, as shown in Figure 10.1: • Timing of onset? This is crucial because vascular (e.g. PE) and mechanical (e.g. pneumothorax, foreign body) pathologies present suddenly. At the other end of the spectrum, it may take weeks or months before diseases such as lung cancer or pulmonary fibrosis cause sufficient dyspnoea for the patient to present. • Alleviating or exacerbating factors? Most shortness of breath will be worse on exertion. However, heart failure will also be worse on lying flat; asthma will usually be worse at certain times of the year (e.g. due to pollen allergy, cold climate), in certain places (e.g. in dusty environments, or when the pets are around), during intense cardiovascular exercise (e.g. running), or in the early hours of the morning. Psychogenic hyperventilation will be worse at times of anxiety and stress. • Smoking? Never forget to ask about smoking and to quantify this in terms of ‘pack years’ smoked (1 pack = 20 cigarettes; 20 cigarettes a day for a year = 1 pack year). • Pets? The patient may be allergic to pets, especially new ones. • Occupational history? Ask about jobs—there are still lots of people who have been exposed to asbestos, silica dust, and coal particulates in past jobs and who are at risk of pneumoconioses. • Medications? Certain drugs can cause hypersensitivity pneumonitis (previously called extrinsic allergic alveolitis, a type of interstitial lung disease), e.g. nitrofurantoin, amiodarone, methotrexate, bleomycin. • Past medical history? Autoimmune conditions such as rheumatoid arthritis and systemic lupus erythematosus can cause interstitial lung disease and pleural effusions. • Cough? A cough points strongly towards a respiratory pathology. The nature of the cough is important: Is it productive? What colour is the sputum? Is there any blood? When does the cough occur? What does the cough sound like? A persistent, productive cough over the last few days suggests pneumonia; a persistent, productive cough on most days of the past 3 months and spanning years suggests chronic bronchitis; a dry cough present mainly during the episodes of shortness of breath or at night suggests asthma, but may also be a feature of left ventricular failure; bloodstained sputum may suggest a PE, lung cancer, or a cavitating pneumonia.
Rectal bleeding
Authors: Farne Hugo , Norris-Cervetto Edward , Warbrick-Smith James
Published: November 2020

As with all acute patients, always start by assessing ABCDE: airways, breathing, circulation, disability, and exposure. In a patient with acute gastrointestinal (GI) haemorrhage (whether upper or lower), assessing their circulation (i.e. haemodynamic status) is a priority. If there are clinical features to suggest haemodynamic instability—such as hypotension, tachycardia, cool peripheries, tachypnoea, or decreased consciousness—then the immediate priority is to resuscitate the patient before proceeding to a thorough history and examination. The differential diagnosis for rectal bleeding is shown in Figure 21.1. There are a couple of points to note about this differential diagnosis. GI haemorrhage may present as overt or occult bleeding. This table, and the indications of prevalence within it, refers to overt rectal bleeding as occult rectal bleeding will not be noticed by the patient. The second point to note is that upper GI sources of haemorrhage may occasionally present with rectal bleeding alone. Although it is more likely that such upper GI sources will also present with haematemesis, you should note that large volumes of blood in the GI tract can act as a cathartic (stimulant of peristalsis) and the resultant rapid transit through the intestine leads to the passage of red blood per rectum. • How much blood has been passed? This question is directly relevant to your initial haemodynamic status survey. Ask the patient to quantify approximately how much blood they have passed—familiar measures such as a teaspoon, eggcup, or wine glass may be easier for the patient than asking them to provide an estimate in millilitres. Note, however, that it is very easy to overestimate volumes of blood loss if, for example, blood has mixed with water in the toilet bowl. You should additionally enquire about symptoms of hypovolaemia—any light-headedness, collapse, chest pain or breathlessness? • What is the duration and frequency of the symptoms? • What did the blood look like? Generally speaking, the fresher the blood, the more distal the bleed. Substantial bleeding from lesions proximal in the GI tract may present with melaena (jet black, tarry stool caused by bacterial oxidation of haem) or may present as frank blood (haematochezia) if transit times are sufficiently rapid.
The Lives of Prehistoric Monuments in Iron Age, Roman, and Medieval Europe: An Introduction
Authors: Díaz-Guardamino Marta , Sanjuán Leonardo García
Published: November 2020

On 19 June 2014, while the final lines of this book were still being written, Felipe VI was proclaimed King of Spain, giving continuity into the twenty-first century to the Bourbon dynasty, which almost uninterruptedly has occupied the Spanish throne since AD 1714. As a 9-year-old child, on 1 November 1977, Felipe had been installed as Prince of Asturias and heir to the crown of Spain in a ceremony held at the site of Covadonga (Cangas de Onís, Asturias). Covadonga holds a very special position as a symbol of the Kingdom of Spain and is prominent in Spanish nationalist ideology and historiography. After the Arab invasion of Iberia in AD 711 and the subsequent collapse of the Visigoth Kingdom of Toledo, a battle was fought in Covadonga, in which the Christian communities of northern Spain defeated the Arab forces that had taken control of most of Iberia. Emerging as leader from this battle, King Pelayo founded the Christian Kingdom of Asturias. Far less prominent in standard historical accounts is the fact that both Pelayo and his son and successor Favila (AD 737–9) were subsequently buried in two chapels, each of which was built over, or next to, the remains of prehistoric megalithic monuments (i.e. Santa Cruz and Abamia). Both of these sites are very close to Covadonga, itself a place of sacred significance, probably since prehistoric times. As Blas Cortina explains in his contribution to this volume, Pelayo and Favila had themselves buried in chapels associated with the Neolithic monuments of Santa Cruz and Abamia because these were places vested with ‘ancestral power’. Through this association they sought to acquire symbolic capital to legitimate their position within the context of the political instability that followed the collapse of the Kingdom of Toledo and the threat of the Arab invasion. These ancestral monuments were chosen to provide such legitimacy, and when Felipe de Borbón y Grecia was invested as Prince of Asturias in 1977, he too was drawing on the same symbolic roots to nurture his eventual legitimacy as King Felipe VI.
Enduring Past: Megalithic Tombs of Brittany and the Roman Occupation in Western France
Authors: Vejby Mara
Published: November 2020

The extended lives of prehistoric monuments, whether or not they were interacted with once their initial phase of use had ended and how they were treated, can reveal valuable details about a culture. To interact with a place means that the action or inﬂuence is reciprocal. The individual, or group of individuals, is somehow affected by the physical contact they’ve had with the site, and the place in turn has been altered. Interactions are more than just reuse of a space. In fact, missing pieces of monuments’ biographies, evidence of subsequent use and treatment, are details that may tell us how a people dealt with their own past as well as that of others. The focus of this study is a region in which the biographies of a group of monuments appear to be intimately tied to clashing cultures during the Roman occupation: Morbihan, Brittany. Brittany is the westernmost province of France, roughly 30 kilometres north-west of the mouth of the Loire river, and extending over 200 kilometres westward into the Celtic Sea. The south-easternmost department of this province is Morbihan, which makes up over 6,800 square kilometres and centres on the Gulf of Morbihan, a few kilometres south of Vannes (Darioritum), the Roman-period civitas-capital of the Veneti. Darioritum was not only a port for commercial ships, but was also on the major road network connecting the Coriosolitae (Corseul), Osismes (Carhaix-Plouguer) and Namnetes (Nantes) civitates (Galliou and Jones 1991, 77, 81, 84). Evidence found in a thorough survey of Iron Age and Roman materials at megalithic tombs in Atlantic Europe revealed that Brittany is by far the region with the highest concentration of direct Roman period interactions, despite both the distribution of megalithic tombs across the peninsula and subsequent habitation patterns during the Iron Age and Roman periods (Scarre 2011, 29–33; Vejby 2012) . It also revealed that this activity is a major shift from the comparatively low number of megalithic tombs at which Iron Age materials have been found.