This chapter contains Gaussian optics and employs a matrix formalism to describe optical image formation through light rays. In optics, a ray is an idealized model of light. However, in a subsequent chapter, we will also see a matrix formalism can also be used to describe, for example, a Gaussian laser beam under diffraction through the wave optics approach. The advantage of the matrix formalism is that any ray can be tracked during its propagation though the optical system by successive matrix multiplications, which can be easily programmed on a computer. This is a powerful technique and is widely used in the design of optical element. In this chapter, some of the important concepts in resolution, depth of focus, and depth of field are also considered based on the ray approach.

Chapter 13 begins with a definition of story and a brief overview of past theory and research.Then story structure, master-plots, and themes are discussed, using examples from well-known literature as well as from actual discourse.Different forms and uses of stories in conversation are discussed, including retold stories and stories that express or celebrate group identity.

Three important properties associated with a classification of any group of organisms are diagnosability, monophyly and resolution. In this chapter we explore the interrelationships between these three properties in the context of cryptic taxa, here defined as a clade with no obvious diagnostic morphological support. We present the view that the number of nodes on a phylogenetic tree of all flowering plants that have morphological diagnostic support is less than five percent; as such, cryptic nodes are much more common than non-cryptic nodes. Because of this, we suggest that the phrase ‘cryptic nodes’ is a preferable description as opposed to cryptic taxa because taxa in the sense of traditional classifications are generally diagnostic. By reference to a global taxonomic study of the genus Ipomoea, we discuss the role of diagnosability at various scales including major infrageneric clade, genus and species. We demonstrate that the level of diagnosability for Ipomoea is relatively low, therefore making cryptic nodes the rule and not the exception. We provide several examples of such cryptic nodes, detail how we discovered them and place them in a wider conceptual framework of diagnosability in angiosperms.

Theories about plot structure and the extent of their value. ‘The Seven Basic Plots’ (Christopher Booker). Five-act structure (Gustav Freytag). Joseph Campbell’s hero’s journey. Tsvetan Todorov’s five stages of action. The inevitability of plot. Kenn Adams’s story spine. Kurt Vonnegut’s story shapes. ‘Seeding’ conditions in order to make later events believable. The use of more than one timeframe. The risks inherent in confounding reader expectation.

‘You have a broad trajectory for your story when you start writing because you know the beginning and have a sense of an ending, but this trajectory will not be a straight line – the most direct journey from A to Z, where everything goes right, is the least interesting and probably not worth writing about.’

This chapter presents a general overview of sensor characterization from a system perspective, without any reference to a specific implementation. The systems are defined on the basis of input and output signal description and the overall architecture is discussed, showing how the information is transduced, limited, and corrupted by errors. One of the main points of this chapter is the characterization of the error model, and how this one could be used to evaluate the uncertainty of the measure, along with its relationship with resolution, precision and accuracy of the overall system. Finally, the quantization process, which is at the base of any digital sensor systems, is illustrated, interpreted, and included in the error model.

The application of gravity gradient measurements to exploration has been growing over the past 20 years. The ability of tensor gradiometry instruments to greatly improve signal/noise when deployed on mobile platforms has transformed the usefulness of this technology. Airborne and marine Full Tensor Gradiometry (FTG) surveys have become an increasingly common part of the exploration and production toolkit. The ability of the modern instruments to provide high-resolution, spatial accuracy and very good signal/noise data has made this technology a more common part of integrated exploration and production management. The technology has a distinct cost advantage over seismic data acquisition and as such can deliver a competitive solution for imaging problems in some circumstances. There are now numerous published examples of effective use of FTG in the oil industry. The development of better instruments such as integration of direct contemporaneous measurement of conventional gravity is encouraging more interest in the technology. The potential for extending the use of FTG to reservoir monitoring and carbon dioxide sequestration assurance is likely to increase the popularity of the technology in future.

Thomas Adès has mused on symphonic form in terms of logic and resolution – as ‘something which closes a circle’. Nevertheless, his interest in the symphonies of Jean Sibelius is sparked by their resistance to this trend; the one-movement Seventh Symphony, in particular, is a work he hears as ‘painfully inconclusive’. This contradiction plays out in Adès’s own one-movement symphony, Tevot (2007). In both works, audible developments are underpinned by a carefully managed network of tempos. Recurring sonorities not only delineate this structure but also prompt perceptual shifts, underlining forms that are at once stable and volatile, recurrent and changing, static and dynamic, closed and open. In this chapter, the Seventh Symphony offers a potent lens through which Tevot can be viewed, shedding light not only upon Adès’s navigation of symphonic resolution, but also upon the way in which he – like Sibelius – engages with symphonic traditions at large.

The multilateral proposed changes require significant infrastructural changes to the existing tax framework. How should such changes be implemented? Some changes are required at both the domestic law level and in the public international law arena of double taxation treaties. Other changes can be made in one or other of these fields of law (domestic or international). What other matters need to be addressed? There are many questions in the area of implementation, such as dispute resolution and dispute prevention, calculation and collection of tax, use of multilateral instruments, and the prevention of double taxation.

The multilateral proposed changes require significant infrastructural changes to the existing tax framework. How should such changes be implemented? Some changes are required at both the domestic law level and in the public international law arena of double taxation treaties. Other changes can be made in one or other of these fields of law (domestic or international). What other matters need to be addressed? There are many questions in the area of implementation, such as dispute resolution and dispute prevention, calculation and collection of tax, use of multilateral instruments, and the prevention of double taxation.

We here establish basic inversion framework in a Bayesian context, with introduction of measures of data fit and model suitability. We introduce Bayes’ theorem and identify the conditional probability with posterior probability distribution for model parameters through a composite misfit combining the match between observations and simulations and assumptions about the nature of acceptable models. We discuss Monte Carlo techniques and the assessment of model resolution, leading into the formulation of the non-linear inversion process in terms of optimisation of a measure of misfit.

This chapter presents an overview of the book’s main arguments as well as summaries of its chapters. It begins with an accounting of recent historiographical trends, primarily in the West but also in Japan, concerning the Meiji Restoration and the creation of the Japanese nation-state. It follows with a brief discussion of the development of the fields of global and world history in the West and Japan. It then details the thematic threads - economic trends, internal conflicts that raged throughout the 1860s, and post-Restoration reconciliation/resolution - that run through the volume, highlighting the ways in which the book shows the immediate and contextual intersections of each with the nineteenth-century world. In its concluding pages, the chapter presents how the book’s three sections - global connections, internal conflicts, and domestic resolutions - are formulated, pointing out ways in which the chapters connect across the span of the volume.

Against the backdrop of the 2007–2009 financial crisis, this chapter discusses the growing importance of macroprudential supervision. In contrast to microprudential supervision, which focuses on the soundness of individual institutions, macroprudential supervision focuses on the stability of the financial system as a whole and on monitoring and assessing so-called systemic risk. This is the risk of a breakdown of an entire financial system rather than the failure of individual parts. The chapter sets out the key features of the conceptual framework for macroprudential supervision. Next, macroprudential instruments are discussed. Finally, the chapter touches on the issue of crisis management and resolution, discussing the main instruments that can be considered in crisis situations.