bluuebunny/crossref_metadata_2025 huggingface dataset:
The synthesis of conducting polymers based on heterocyclic compounds
Authors: Walton David J . , Davis Fred J.
Published: November 2020

Polymers are best known for their effectiveness as electrical insulators, indeed electrical wiring throughout the world is now sheathed in plastic. However, it was recognized early on that polymers with an appropriate structure ought to be able to conduct electricity. Unfortunately, the same features that might allow this phenomenon also introduce intractability and processing difficulties. As a consequence, it was not until the mid-1970s that the potential of these materials was explored and better-defined materials started to be made. There are now numerous polymers with substantial electrical conductivities and the topic of electrically conducting polymers still continues to excite with many hundreds of new publications printed each year. The backbone structures of some of conjugated polymers are given in Table 6.1. In this chapter we shall deal with electrochemical and chemical syntheses of some relatively simple examples. For electrical conductivity, it is necessary to transfer charge along a conjugated chain, between chains, and also along grain boundaries or between particles. The most energetically difficult process will control the rate of charge transport and this will vary with nature of the polymer, its physical form, and other parameters, but in all cases conjugation along the chain is necessary although it is not sufficient for carbonaceous polymers to simply possess a conjugated chain. To promote conductivity π-overlap along the entire polymer chain length is required to give a half-filled band of delocalized π -electrons. In real systems, distortions of the bonds disrupt the conjugation, and the materials are generally semiconductors. The higher metallic conduction can be achieved by a process known as doping in which electrons are added or more generally removed from the conjugated system (although this is not same as the doping process found in semiconductor technology) The simplest conjugated polymer chain is a polyacetylene chain. Such materials can be prepared by coordination polymerization, or using a sophisticated route involving the degradation of a soluble precursor polymer.
Matrix Group Actions Transforming Patterns
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

Thus far Pattern theory has been combinatore constructing complex patterns by connecting simpler ones via graphs. Patterns typically occurring in nature may be extremely complex and exhibit invariances. For example, spatial patterns may live in a space where the choice of coordinate system is irrelevant; temporal patterns may exist independently of where time is counted from, and so on. For this matrix groups as transformations are introduced, these transformations often forming groups which act on the generators.
Jump Diffusion Inference in Complex Scenes
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

This chapter explores random sampling algorithms introduced in for generating conditional expectations in hypothesis spaces in which there is a mixture of discrete, disconnected subsets. Random samples are generated via the direct simulation of a Markov process whose state moves through the hypothesis space with the ergodic property that the transition distribution of the Markov process converges to the posterior distribution. This allows for the empirical generation of conditional expectations under the posterior. To accommodate the connected and disconnected nature of the state spaces, the Markov process is forced to satisfy jump–diffusion dynamics. Through the connected parts of the parameter space (Lie manifolds) the algorithm searches continuously, with sample paths corresponding to solutions of standard diffusion equations. Across the disconnected parts of parameter space the jump process determines the dynamics. The infinitesimal properties of these jump–diffusion processes are selected so that various sample statistics converge to their expectation under the posterior.
Computational Methods
Authors: Gautschi Walter
Published: November 2020

The fundamental problem is to compute the first n recursion coefficients αk (dλ), Βk(dλ), k = 0, 1, . . . , n − 1 (cf. §1.3.1), where n ≥ 1 is a (typically large) integer and dλ a positive measure given either implicitly via moment information or explicitly. In the former case, an important aspect is the sensitivity of the problem with respect to small perturbations in the data (the first 2n moments or modified moments); this is the question of conditioning. In principle, there is a simple algorithm, essentially due to Chebyshev, that produces the desired recursion coefficients from given moment information. The effectiveness of this algorithm, however, depends critically on the conditioning of the underlying problem. If the problem is ill-conditioned, as it often is, recourse has to be made either to symbolic computation or to the explicit form of the measure. A procedure applicable in the latter case is discretization of the measure and subsequent approximation of the desired recursion coefficients by those relative to a discrete measure. Other problems calling for numerical methods are the evaluation of Cauchy integrals of orthogonal polynomials and the problem of passing from the recursion coefficients of a measure to those of a modified measure—the original measure multiplied by a rational function. Finally, Sobolev orthogonal polynomials present their own problems of calculating recursion coefficients and zeros. Orthogonal polynomials as well as their recursion coefficients are expressible in determinantal form in terms of the moments of the underlying measure. Indeed, much of the classical theory of orthogonal polynomials is moment-oriented. This is true, in particular, of a classical algorithm due to Chebyshev, which generates the recursion coefficients directly from the moments, bypassing determinants. The use of moments, unfortunately, is numerically problematic inasmuch as they give rise to severe ill-conditioning. In many cases, particularly for measures with bounded support, it is possible, however, to work with the so-called “modified moments,” which lead to better conditioned problems and a more stable analog of the Chebyshev algorithm.
Diffraction
Authors: Blow David
Published: November 2020

Diffraction refers to the effects observed when light is scattered into directions other than the original direction of the light, without change of wavelength. An X-ray photon may interact with an electron and set the electron oscillating with the X-ray frequency. The oscillating electron may radiate an X-ray photon of the same wavelength, in a random direction, when it returns to its unexcited state. Other processes may also occur, akin to fluorescence, which emit X-rays of longer wavelengths, but these processes do not give diffraction effects. Just as we see a red card because red light is scattered off the card into our eyes, objects are observed with X-rays because an illuminating X-ray beam is scattered into the X-ray detector. Our eye can analyse details of the card because its lens forms an image on the retina. Since no X-ray lens is available, the scattered X-ray beam cannot be converted directly into an image. Indirect computational procedures have to be used instead. X-rays are penetrating radiation, and can be scattered from electrons throughout the whole scattering object, while light only shows the external shape of an opaque object like a red card. This allows X-rays to provide a truly three-dimensional image. When X-rays pass near an atom, only a tiny fraction of them is scattered: most of the X-rays pass further into the object, and usually most of them come straight out the other side of the whole object. In forming an image, these ‘straight through’ X-rays tell us nothing about the structure, and they are usually captured by a beam stop and ignored. This chapter begins by explaining that the diffraction of light or X-rays can provide a precise physical realization of Fourier’s method of analysing a regularly repeating function. This method may be used to study regularly repeating distributions of scattering material. Beginning in one dimension, examples will be used to bring out some fundamental features of diffraction analysis. Graphic examples of two-dimensional diffraction provide further demonstrations. Although the analysis in three dimensions depends on exactly the same principles, diffraction by a three-dimensional crystal raises additional complications.
Density-modification procedures: improving a calculated map before interpretation
Authors: Blow David
Published: November 2020

Procedures to determine the phases of the structure factors, by isomorphous replacement, by anomalous scattering, or by molecular replacement, were described in the Chapters 7–9. Using one or more of these methods, phases are generated which allow an electron-density map to be calculated, at a resolution to which the phases are thought to be reliable. In many cases this electron density can be confidently interpreted in terms of atomic positions. But this is not always the case. Quite often, the procedures so far described offer a tantalizing puzzle map, with some features which I think I can interpret, but raising many questions. Before devoting effort to interpreting an unsatisfactory electron-density map, a number of procedures are available, which might make a striking improvement. Perhaps the most important strategy is to seek out more isomorphous and anomalous scattering derivatives. Before doing that, there are other possibilities which may improve an electron-density map without any more experimental data. These methods are known collectively as density modification. The first group of methods exploits features of the electron density which result from the packing of molecules into a crystal. Macromolecular crystals composed of rigid molecules have voids between the molecules filled with disordered solvent, often including the precipitants used in the crystallization process. These solvent regions present featureless density between the structured density of the macromolecules. A high-quality electron-density map will show these featureless regions clearly. In a map of poorer quality, the voids between molecules may be clearly defined, but far from featureless. This provides a method to improve the map. Although some solvent molecules are immobilized on the surface of the macromolecule, those further from the surface are in a disordered liquid-like state which presents a uniform density. Except in very small proteins, the majority of solvent is disordered. If such uniform solvent regions can be recognized, they allow surfaces to be defined which separate solvent regions from protein regions. Two procedures are described below. It has become almost a matter of routine to use one or both of these methods.
Dielectric constant
Authors: Newnham Robert E.
Published: November 2020

The dielectric constant K is a measure of a material’s ability to store electric charge. In scalar form the defining relations are as follows: . . . D = εE, . . . where D is the electric displacement measured in C/m2, ε is the electric permittivity in F/m, and E is electric field in V/m. The dielectric constant K is the relative permittivity: . . . K = ε/ε0, . . . where ε0 = 8.85 × 10−12 F/m is the permittivity of free space. The electric displacement D is equal to the sum of the charges stored on the electrode plus those originating from the polarization, P [C/m2] . . . D = ε0 E + P. . . . In this chapter we discuss the tensor nature of the dielectric constant, how it is represented geometrically, and some typical structure–property relationships. Dielectric constants range over about four orders of magnitude in insulator materials. Because of their low density, gases have dielectric constants only slightly larger than one. At one atmosphere, the dielectric constant of air is 1.0006. Most common ceramics and polymers have dielectric constants in the range between 2 and 10. Polyethylene is 2.3 and silica glass is 3.8. These are low-density dielectrics with substantially covalent bonding. More ionic materials like NaCl and Al2O3 have slightly higher K values in the 6–10 range. High K materials like water (K ∽ 80) and BaTiO3 (K∽1000) have special polarization mechanisms involving rotating dipoles or ferroelectric phase transformations. A schematic view of the principal types of polarization mechanisms is illustrated in Fig. 9.1. The electronic component of polarization arising from field-induced changes in the electron cloud around each atom is found in all matter. The ionic contribution is also common and is associated with the relative motions of cations and anions in an electric field. Orientational polarizability arises from the rotation of molecular dipoles in the field. These motions are common in organic substances. Many materials also contain mobile charge carriers in the form of ions or electrons that can migrate under applied fields.
Crystal optics
Authors: Newnham Robert E.
Published: November 2020

Calcite (CaCO3) is a beautiful transparent mineral that readily cleaves into rhombohedra. Images viewed through a thin slice of a cleaved calcite crystal are split into two images, an effect known as double refraction, or birefringence. Birefringence is the most obvious manifestation of optical anisotropy in crystals. For any given wave normal, there are two light waves, transversely polarized in mutually perpendicular directions, traveling with different velocities, and consequently different refractive indices. Double refraction is caused by dielectric anisotropy. For transparent crystals like calcite, the magnetic susceptibility is small and the permeability μ ≌ μ0, the permeability of free space. In this class of materials the refractive index n = c/v = where c is the speed of light in vacuum, v the velocity of light in the crystal, and K is the dielectric constant measured at optical frequencies. Refractive indices of transparent materials lie between 1 and 3. Electromagnetic waves differ from acoustic waves in that there are, for a given wave normal, two waves rather than three. In the acoustic case there are, in general, two quasitransverse waves and a quasilongitudinal wave. Starting with Maxwell’s Equations and the material constitutive relations, the propagation of electromagnetic waves through transparent crystals are described in terms of the refractive indices, wave normals, and polarization directions.
Oxygen deficiency in the oceans
Authors: Hallam Tony
Published: November 2020

We are all very much aware that oxygen deprivation leads quickly to death, and this is true not just of our own species but of virtually the whole organic world. There are indeed very few exceptions, such as the anaerobic bacteria that derive their energy from reducing sulphates to sulphides, which flourish in the absence of free oxygen. (As these organisms do not leave a fossil record they provide no clues for the geological detective.) Today the atmosphere never lacks oxygen, except in artificially enclosed conditions, but oxygen deficiency can be lethal in certain marine environments and thus must be explored as a possible factor in causing mass extinctions. Mixing with atmospheric winds ensures that the surface waters of the ocean, down to the greatest depth attained by storm waves, always contain plenty of oxygen. Most of the oceans and marginal seas today contain oxygen throughout their depth, but in certain circumstances an oxygen deficiency can occur in the lower parts of the ocean. In parts of some tropical oceans, for instance, the oxygen content decreases with depth until near the ocean bottom, where under the influence of currents driven by cold water from around Antarctica, the oxygen content increases again. This gives rise to a zone in the ocean known as the oxygen minimum zone. The rapid deep ocean circulation is today driven ultimately by the presence of polar ice on Antarctica, which is the main cause of the strong sea-water temperature gradient from the tropics to the poles. For long periods in the Earth’s history substantial polar ice caps were lacking, and many geologists believe that during those periods latitudinal ocean currents were more sluggish. The deep ocean must then have been largely deficient in oxygen, if not completely lacking in oxygen (anoxic). (Sea water with a content of one or more millilitres of oxygen per litre of water is called oxic; 0.1 ml or less is anoxic; and for any intermediate value the water is dysoxic.) Certain parts of the sea bed where the overlying water is deficient in oxygen are enriched in organic matter derived principally from the plankton.
Case Study Of Static Simulation
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

Having discussed the basic concepts of atomistic simulations, we now turn to a case study that demonstrates the use of the static simulation techniques and, along the way, reveals some of the realistic aspects of the dislocation core structure and highlights the coupling between continuum and atomistic descriptions of dislocations. Section 3.1 explains how to use simple solutions of the continuum elasticity theory for setting up initial positions of atoms. The important issue of boundary conditions is then discussed in Section 3.2. Section 3.3 presents several practical methods for visualization of dislocations and other crystal defects in an atomistic configuration. This first case study sets the stage for a subsequent exploration of more complex aspects of dislocation behavior, which demands more advanced methods of atomistic simulations to be discussed in Chapters 4 through 7. In Section 1.2 we already considered the atomistic structure of dislocations in simple cubic crystals. In other crystals, the atomistic structure of dislocations is considerably more complicated but can be revealed through an atomistic simulation. This is the topic of this chapter. An atomistic structure is specified by the positions xi of all atoms. In a perfect crystal, xi ´s are completely determined by the crystal’s Bravais lattice, its atomic basis and its lattice constant (Section 1.1). Now assume a dislocation or some other defect is introduced, distorting the crystal structure and moving atoms to new positions x´i . A good way to describe the new structure is by specifying the displacement vector ui ≡x'i −xi for every atom i. The relationship between ui and xi can be obtained analytically if we approximate the crystal as a continuum linear elastic solid. This is certainly an approximation, but it works well as long as crystal distortions remain small. Let us define x as the position of a material point in the continuum before the dislocation is introduced and x´ as the position of the same material point after the dislocation is introduced. Here, x is a continuous variable and the displacement vector u(x)≡x´−x expressed as a function of x is the displacement field.
Free-Energy Calculations
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

Free energy is of central importance for understanding the properties of physical systems at finite temperatures. While in the zero temperature limit the system should evolve to a state of minimum energy (Section 2.3), this is not necessarily the case at a finite temperature. When an open system exchanges energy with the outside world (a thermostat) and maintains a constant temperature, its evolution proceeds towards minimizing its free energy. For example, a crystal turns into a liquid when the temperature exceeds its melting temperature precisely because the free energy of the liquid state becomes lower than that of the crystalline state. In the context of dislocation simulations, free energy is all important when one has to decide which of the possible core configurations the dislocation is likely to adopt at a given temperature.
Finding Transition Pathways
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

As was discussed in Chapter 2, stable and accurate numerical integration of the MD equations of motion demands a small time step. In MD simulations of solids, the integration step is usually of the order of one femtosecond (10−15 s). For this reason, the time horizon ofMDsimulations of solids rarely exceeds one nanosecond (10−9 s). On the other hand, dislocation behaviors of interest typically occur on time scales of milliseconds (10−3 s) or longer. Such behaviors remain out of reach for direct MD simulations. Time-scale limits of a similar nature also exist in MC simulations. For instance, the magnitude of the atomic displacements in the Metropolis algorithm has to be sufficiently small to ensure a reasonable acceptance ratio, which results in a slow exploration of the configurational space. This disparity of time scales can be traced to certain topographical features of the potential-energy function of the many-body system, typically consisting of deep energy basins separated by high energy barriers. The system spends most of its time wandering around within the energy basins (metastable states) only rarely interrupted by transitions from one basin to another. Whereas the long-term evolution of a solid results from transitions between the metastable states, direct MDand MC simulations spend most of the time faithfully tracing the unimportant fluctuations within the energy basins. In this sense, most of the computing cycles are wasted, leading to very low simulation efficiency. Because the transition rates decrease exponentially with the increasing barrier heights and decreasing temperature, this problem of time-scale disparity can be severe.
Quantum information processing
Authors: Barnett Stephen
Published: November 2020

We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.
Introduction To Solids And Their Interfaces
Authors: Nitzan Abraham
Published: November 2020

The study of dynamics of molecular processes in condensed phases necessarily involves properties of the condensed environment that surrounds the system under consideration. This chapter provides some essential background on the properties of solids while the next chapter does the same for liquids. No attempt is made to provide a comprehensive discussion of these subjects. Rather, this chapter only aims to provide enough background as needed in later chapters in order to take into consideration two essential attributes of the solid environment: Its interaction with the molecular system of interest and the relevant timescales associated with this interaction. This would entail the need to have some familiarity with the relevant degrees of freedom, the nature of their interaction with a guest molecule, the corresponding densities of states or modes, and the associated characteristic timescales. Focusing on the solid crystal environment we thus need to have some understanding of its electronic and nuclear dynamics. The geometry of a crystal is defined with respect to a given lattice by picturing the crystal as made of periodically repeating unit cells. The atomic structure within the cell is a property of the particular structure (e.g. each cell can contain one or more molecules, or several atoms arranged within the cell volume in some given way), however, the cells themselves are assigned to lattice points that determine the periodicity. This periodicity is characterized by three lattice vectors, ai, i = 1, 2, 3, that determine the primitive lattice cell—a parallelepiped defined by these three vectors.
Time Correlation Functions
Authors: Nitzan Abraham
Published: November 2020

In the previous chapter we have seen how spatial correlation functions express useful structural information about our system. This chapter focuses on time correlation functions that, as will be seen, convey important dynamical information. Time correlation functions will repeatedly appear in our future discussions of reduced descriptions of physical systems. A typical task is to derive dynamical equations for the time evolution of an interesting subsystem, in which only relevant information about the surrounding thermal environment (bath) is included. We will see that dynamic aspects of this relevant information usually enter via time correlation functions involving bath variables. Another type of reduction aims to derive equations for the evolution of macroscopic variables by averaging out microscopic information. This leads to kinetic equations that involve rates and transport coefficients, which are also expressed as time correlation functions of microscopic variables. Such functions are therefore instrumental in all discussions that relate macroscopic dynamics to microscopic equations of motion. It is important to keep in mind that dynamical properties are not exclusively relevant only to nonequilibrium system. One may naively think that dynamics is unimportant at equilibrium because in this state there is no evolution on the average. Indeed in such systems all times are equivalent, in analogy to the fact that in spatially homogeneous systems all positions are equivalent. On the other hand, just as in the previous chapter we analyzed equilibrium structures by examining correlations between particles located at different spatial points, also here we can gain dynamical information by looking at the correlations between events that occur at different temporal points. Time correlation functions are our main tools for conveying this information in stationary systems. These are systems at thermodynamic equilibrium or at steady state with steady fluxes present.
Categorical logic
Authors: Pitts Andrew M.
Published: November 2020

This chapter provides an introduction to the interaction between category theory and mathematical logic. Category theory describes properties of mathematical structures via their transformations, or ‘morphisms’. On the other hand, mathematical logic provides languages for formalizing properties of structures directly in terms of their constituent parts—elements of sets, functions between sets, relations on sets, and so on. It might seem that the kind of properties that can be described purely in terms of morphisms and their composition would be quite limited. However, beginning with the attempt of Lawvere [1964; 1966; 1969; 1970] to reformulate the foundations of mathematics using the language of category theory, the development of categorical logic over the last three decades has shown that this is far from true. Indeed it turns out that many logical constructs can be characterized in terms of relatively few categorical ones, principal among which is the concept of adjoint functor. In this chapter we will see such categorical characterizations for, amongst other things, the notions of variable, substitution, prepositional connectives and quantifiers, equality, and various type-theoretic constructs. We assume that the reader is familiar with some of the basic notions of category theory, such as functor, natural transformation, (co)limit, and adjunction: see Poigné’s [1992] chapter on Basic Category Theory in Vol. I of this handbook, or any of the several available introductions to category theory slanted towards computer science, such as [Barr and Wells, 1990] and [Pierce, 1991]. There are three recurrent themes in the material we present. Categorical semantics. Many systems of logic can only be modelled in a sufficiently complete way by going beyond the usual set-based structures of classical model theory. Categorical logic introduces the idea of a structure valued in a category C, with the classical model-theoretic notion of structure [Chang and Keisler, 1973] appearing as the special case when C is the category of sets and functions. For a particular logical concept, one seeks to identify what properties (or extra structure) are needed in an arbitrary category to interpret the concept in a way that respects given logical axioms and rules. A well-known example is the interpretation of simply typed lambda calculus in cartesian closed categories.
Introduction: Logic and Logic Programming Languages
Authors: O’Donnell Michael J.
Published: November 2020

Logic, according to Webster’s dictionary [Webster, 1987], is ‘a science that deals with the principles and criteria of validity of inference and demonstration: the science of the formal principles of reasoning.' Such 'principles and criteria’ are always described in terms of a language in which inference, demonstration, and reasoning may be expressed. One of the most useful accomplishments of logic for mathematics is the design of a particular formal language, the First Order Predicate Calculus (FOPC). FOPC is so successful at expressing the assertions arising in mathematical discourse that mathematicians and computer scientists often identify logic with classical logic expressed in FOPC. In order to explore a range of possible uses of logic in the design of programming languages, we discard the conventional identification of logic with FOPC, and formalize a general schema for a variety of logical systems, based on the dictionary meaning of the word. Then, we show how logic programming languages may be designed systematically for any sufficiently effective logic, and explain how to view Prolog, Datalog, λProlog, Equational Logic Programming, and similar programming languages, as instances of the general schema of logic programming. Other generalizations of logic programming have been proposed independently by Meseguer [Meseguer, 1989], Miller, Nadathur, Pfenning and Scedrov [Miller et al., 1991], Goguen and Burstall [Goguen and Burstall, 1992]. The purpose of this chapter is to introduce a set of basic concepts for understanding logic programming, not in terms of its historical development, but in a systematic way based on retrospective insights. In order to achieve a systematic treatment, we need to review a number of elementary definitions from logic and theoretical computer science and adapt them to the needs of logic programming. The result is a slightly modified logical notation, which should be recognizable to those who know the traditional notation. Conventional logical notation is also extended to new and analogous concepts, designed to make the similarities and differences between logical relations and computational relations as transparent as possible. Computational notation is revised radically to make it look similar to logical notation.
Meta-Programming in Logic Programming
Authors: Hill P. M. , Gallagher J.
Published: November 2020

A meta-program, regardless of the nature of the programming language, is a program whose data denotes another (object) program. The importance of meta-programming can be gauged from its large number of applications. These include compilers, interpreters, program analysers, and program transformers. Furthermore, if the object program is a logic or functional program formalizing some knowledge, then the meta-program may be regarded as a meta-reasoner for reasoning about this knowledge. In this chapter, the meta-program is assumed to be a logic program. The object program does not have to be a logic program although much of the work in this chapter assumes this. We have identified three major topics for consideration. These are the theoretical foundations of meta-programming, the suitability of the alternative meta-programming techniques for different applications, and methods for improving the efficiency of meta-programs. As with logic programs generally, meta-programs have declarative and procedural semantics. The theoretical study of meta-programming shows that both aspects of the semantics depend crucially on the manner in which object programs are represented as data in a meta-program. The second theme of the paper is the problem of designing and choosing appropriate ways of specifying important meta-programming problems, including dynamic metaprogramming and problems involving self-application. The third theme concerns efficient implementation of meta-programs. Meta-programming systems require representations with facilities that minimize the overhead of interpreting the object program. In addition, efficiency can be gained by transforming the meta-program, specializing it for the particular object program it is reasoning about. This chapter, which concentrates on these aspects of meta-programming, is not intended to be a survey of the field. A more complete survey of meta-programming for logic programming can be found in [Barklund, 1995]. Many issues in meta-programming have their roots in problems in logic which have been studied for several decades. This chapter emphasizes meta-programming solutions. It is not intended to give a full treatment of the underlying logical problems, though we try to indicate some connections to wider topics in meta-logic. The meta-programs in this chapter are logic programs based on first order logic.
Transformation of Logic Programs
Authors: Pettorossi Alberto , Proietti Maurizio
Published: November 2020

Program transformation is a methodology for deriving correct and efficient programs from specifications. In this chapter, we will look at the so called ’rules + strategies’ approach, and we will report on the main techniques which have been introduced in the literature for that approach, in the case of logic programs. We will also present some examples of program transformation, and we hope that through those examples the reader may acquire some familiarity with the techniques we will describe. The program transformation approach to the development of programs has been first advocated in the case of functional languages by Burstall and Darlington [1977]. In that seminal paper the authors give a comprehensive account of some basic transformation techniques which they had already presented in [Darlington, 1972; Burstall and Darlington, 1975]. Similar techniques were also developed in the case of logic languages by Clark and Sickel [1977], and Hogger [1981], who investigated the use of predicate logic as a language for both program specification and program derivation. In the transformation approach the task of writing a correct and efficient program is realized in two phases. The first phase consists in writing an initial, maybe inefficient, program whose correctness can easily be shown, and the second phase, possibly divided into various subphases, consists in transforming the initial program with the objective of deriving a new program which is more efficient. The separation of the correctness concern from the efficiency concern is one of the major advantages of the transformation methodology. Indeed, using this methodology one may avoid some difficulties often encountered in other approaches. One such difficulty, which may occur when following the stepwise refinement approach, is the design of the invariant assertions, which may be quite intricate, especially when developing very efficient programs. The experience gained during the past two decades or so shows that the methodology of program transformation is very valuable and attractive, in particular for the task of programming ‘in the small’, that is, for writing single modules of large software systems.
Diversity
Authors: Gray John S. , Elliott Michael
Published: November 2020

In the previous chapter we covered ways of describing samples of benthos, but specifically did not include diversity. We can talk of primary community variables, such as abundance (A), species richness (S) and biomass (B), and derived variables from these such as true diversity indices, evenness indices, and ratios indicating the relationship between species richness and abundance (A/S, the abundance ratio or the average abundance per species) and between biomass and abundance (B/A, the biomass ratio or the mean biomass per individual). Diversity is not just simply about the number of species found in a sample or area, but also uses data on the abundances of individuals among the species and the way those abundances are distributed among the species within the assemblage. There are many ways of describing diversity. Here we give a summary of the most important ones and reference sources of recent literature on the subject (see also the data analysis summary in Chapter 11). In the following section we consider simple indices (univariate) as measures of diversity; multivariate methods of analysing patterns will be covered in Chapter 7 on the effects of disturbance. The simplest way to measure diversity is the number of species found in a sample, called the species richness (S or SR). Yet diversity is not just about numbers of species; it is also concerned with the distribution of numbers of individuals per species. For example, if one assemblage has 50 individuals of each of 2 species A and B whereas another assemblage has 99 individuals of species A and 1 individual of species B, then both have the same species richness but the first assemblage is the more diverse. Thus a measure of diversity (an index) must take into account not only the number of species, but also the number of individuals per species. To distinguish this from species richness, the combination of individuals per species and number of species is called heterogeneity diversity. In fact there are a large number of diversity indices, and we do not propose to consider them all here (Magurran 2004 gives an excellent and detailed account and others are mentioned in the summary in Chapter 11).
Linear Algebra and the Dirac Notation
Authors: Kaye Phillip , Laflamme Raymond , Mosca Michele
Published: November 2020

We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course. The linear algebra notation used in quantum computing will likely be familiar to the student of physics, but may be alien to a student of mathematics or computer science. It is the Dirac notation, which was invented by Paul Dirac and which is used often in quantum mechanics. In mathematics and physics textbooks, vectors are often distinguished from scalars by writing an arrow over the identifying symbol: e.g a⃗. Sometimes boldface is used for this purpose: e.g. a. In the Dirac notation, the symbol identifying a vector is written inside a ‘ket’, and looks like |a⟩. We denote the dual vector for a (defined later) with a ‘bra’, written as ⟨a|. Then inner products will be written as ‘bra-kets’ (e.g. ⟨a|b⟩). We now carefully review the definitions of the main algebraic objects of interest, using the Dirac notation. The vector spaces we consider will be over the complex numbers, and are finite-dimensional, which significantly simplifies the mathematics we need. Such vector spaces are members of a class of vector spaces called Hilbert spaces. Nothing substantial is gained at this point by defining rigorously what a Hilbert space is, but virtually all the quantum computing literature refers to a finite-dimensional complex vector space by the name ‘Hilbert space’, and so we will follow this convention. We will use H to denote such a space. Since H is finite-dimensional, we can choose a basis and alternatively represent vectors (kets) in this basis as finite column vectors, and represent operators with finite matrices. As you see in Section 3, the Hilbert spaces of interest for quantum computing will typically have dimension 2n, for some positive integer n. This is because, as with classical information, we will construct larger state spaces by concatenating a string of smaller systems, usually of size two.
Superdense Coding and Quantum Teleportation
Authors: Kaye Phillip , Laflamme Raymond , Mosca Michele
Published: November 2020

We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
Entanglement
Authors: Weiner J. S. , Stringer Chris
Published: November 2020

To Professor Teilhard de Chardin the idea that either Dawson or Woodward was in any way wittingly implicated in this business is completely unthinkable. He holds both of these men in the greatest respect, and indeed is inclined to doubt whether a real hoax occurred at all. It seems to him not impossible that the pit at Barkham Manor was used as a rubbish dump where, over a course of years, all sorts of objects including bones from some discarded collection could have been deposited. The heavily iron-bearing water of the gravel would soon stain the bones dark brown (for Professor Teilhard says that fresh bone left in the water of the Weald does stain easily). To be sure, the queer accumulation must have come from some collector’s hoard! But this suggestion of a rubbish dump leaves, of course, too much unexplained and far too many coincidences. It would be an amazing accident that would bring together an, unusual cranium, the jaw, the remarkable canine, a bone implement of unique character, a number of flints of spurious workmanship (one of which is stained with chromate), and bones partly changed to gypsum and radio-active fossil teeth of a sort never found in England! That all this curious medley, this ‘accidental’ assemblage, should be uncovered in a particular sequence—as Sir Arthur Keith said to us, cas if to confute me personally!’—is straining our acceptance of coincidence too much. Miss Kenward, who lived at Barkham Manor for many years, is positive that the pit was not a general rubbish dump and that the gravel was being dug from an unbroken surface. Lady Smith Woodward, too, rules out the suggestion. There is nothing to commend this rubbish dump theory, for we have seen that hardly anything of the whole collection of material can with certainty be said to have come from gravel originally, although this does not rule out the possibility that at least the cranium, even stained as it is, may not have been genuinely found in the pit and that after treatment it was redeposited in the gravel pit.
The Old World: Southern Africa and Australasia
Authors: Mitchell Peter
Published: November 2020

So far we have seen how Indigenous societies in North and South America exploited the opportunities created by the horse’s reintroduction in the aftermath of Columbus’ voyage of 1492. But the Americas were not the only part of the world to which Europeans brought the horse. In southern Africa other members of the genus Equus, the plains and mountain zebras, were long established, but before European settlement the only animal ridden there—and then very little—was the ox. Australia, on the other hand, though rich in marsupials, had no purely terrestrial placental mammals except people and dogs. Finding a vacant ecological niche, horses and other animals introduced by Europeans quickly established themselves in the wild. Much the same holds for New Zealand, which had no mammals at all (save bats) until Polynesians settled it less than four hundred years before the first European visitor, Abel Tasman, in 1642. Southern Africa, Australia, and New Zealand therefore all gave new, and different, opportunities to horses. How their Indigenous human populations interacted with the new arrival also varied. In southern Africa horses encountered some societies that had domestic livestock of their own, others who combined livestock with cereal cultivation, and yet others (those of greatest interest here) who were hunters and gatherers. In Australia, only the last of these variations was present, while in New Zealand, although most Māori did grow crops, dogs were the only domestic animals. The first Europeans to visit southern Africa were the Portuguese. Rounding the Cape of Good Hope in 1488 they completed the circumnavigation of the continent’s southern tip ten years later to reach India. Portugal did not, however, establish settlements in what eventually became South Africa, preferring to sail round it to reach Mozambique. For over a century its disinterest was shared by the other Europeans who occasionally used Cape Town’s Table Bay or other spots along the coast to take on fresh water or trade for livestock from Indigenous Khoe herders.