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In order to identify the essential items of the mode-coupling-theory scenarios, this chapter describes asymptotic expansions of the correlation functions for small frequencies and small separations of the coupling constants from their critical values. For generic glass transitions the leading-order asymptotic contributions are specified by two scaling laws. The slowing down of the dynamics is governed by two time scales, which exhibit power-law dependencies on the separation coordinates. Stretching is caused by the interplay of a critical power-law relaxation and a von-Schweidler-power-law decay. Logarithmic relaxation is the leading-order behaviour near higher-order singularities. The leading-order asymptotic corrections determine the range of validity of the leading-order formulas. Strong-coupling effects are shown to cause Cole–Cole relaxation processes for the critical decay near generic transitions and sublinear power-law variations of the mean-squared displacements near higher-order ones.

This chapter describes basic biological mechanisms in a way that can be represented by simple dynamical models. It begins with a discussion of the basic modeling formalisms that will be utilized to model biomolecular feedback systems. The focus in this chapter (as well as the next) is on deterministic models using ordinary differential equations. Here, the chapter proceeds to study a number of core processes within the cell, providing different model-based descriptions of the dynamics that will be used in later chapters to analyze and design biomolecular systems. In this chapter, emphasis is placed on dynamics with time scales measured in seconds to hours and mean behavior averaged across a large number of molecules.

In this chapter, the general concepts are introduced, which are used to describe simple-liquid dynamics. The hydrodynamic-limit expressions are derived for the correlation functions, which are formed with the small-wave-number fluctuations of the conserved densities. Langevin's theory for the velocity correlations, Maxwell's model for visco-elastic effects, and Mountain's formulas for the central peak of the density-fluctuation spectra are deduced from the assumption of a separation of the time scale for the correlation decay of currents and stresses from that specifying the reduced dynamics of the decay-causing fluctuating forces. The chapter explains that the onset of glassy dynamics is related to an increasing violation of the time-scale-separation property. Ideal glass states manifest themselves by the simultaneous occurrence of arrested parts of the correlations for density fluctuations and for fluctuating forces.

Kenneth Pomeranz, whose book The Great Divergence was one of the key starting points for global history, has developed a methodological approach to the concept of ‘divergence’. Historical divergences raise many questions: those of perspective, issues of ‘origin’, points where differences become divergences and those of multiple time scales.

One approach to understanding the psychological processes involved in perceptual organization, and the one presented in this chapter, is to study the evolution of perceptual organization in two different time scales: microgenetically (the unfolding of perceptual organization during the act of perception in adult observers) and ontogenetically (the developmental course of perceptual organization). The chapter begins with a brief review of major findings that have emerged from microgenetic research and developmental research on perceptual organization. Next, two series of studies are described that seek to reveal the processes involved in perceptual grouping and individuation in hierarchical organization and grouping of shape by perceptual closure by exploring their microgenesis and ontogenetic development. The findings of these studies are consistent with a view of perceptual organization as a multiplicity of processes that vary in time course, attentional demands, and developmental trajectory. In closing, implications for linking microgenesis and ontogenesis are discussed.

This chapter discusses a new and controversial development in perinatal epidemiology. The chapter begins with an overview of some traditional concepts in perinatology, namely, the calculation of birth weight and gestational age-specific perinatal mortality rates and the use of dual, overlapping time scales for estimating the duration of gestational and chronologic age. This is followed by a review of the conundrums extant in contemporary perinatology and a proposal for an alternative formulation (called the fetuses-at-risk approach) for the calculation of rates in perinatal epidemiology. The focus under this alternate approach is on incidence measures, with gestational age treated as survival time. Latent period considerations for perinatal phenomena that have intrauterine origins are also an integral part of this formulation. Finally, there is reframing of the traditional and fetuses-at-risk models as serving prediction (noncausal) and causal functions, respectively.

This chapter focuses on the so-called ecology cycle and Sweden's strategies for temporally rational ecological governance. It discusses the criteria for temporally rational ecological governance and relevance of land use planning and restrictions for ecological governance. This chapter proposes management by objectives (MBO) as a flexible way of moving towards commonly formulated and shared views of a future state of affairs. It also argues that temporally rational ecological governance is not just about how to arrange political institutions to take account of different life cycles and time scales important to the balance of ecosystems, it is also about ‘just in time’ political accountability.

This chapter provides an introduction to fossils and a geologic time frame, which provides a context for interpreting marine mammal fossils and possible causes for their origin and diversification. The evolution of marine mammal communities through space and time are considered, as well as what may have led marine mammals back to the sea. The use of stable isotope technology is explored for ecologic studies that range from reconstructing paleotemperatures and climate change to documenting diet and foraging ecology among both living and fossil marine mammals.

This chapter expands the discussion of how time and scale interact with risk when managing infrastructures for reliability. The whole cycle of infrastructure operations ranges from normal to disrupted, restored, failed, recovered, and new normal. Risks vary by the stage of the cycle, and each stage is managed for reliability differently. Thus, a disruption in one infrastructure of an ICIS requires not only zooming down to determine root causes but also zooming up to determine its impact on the entire infrastructure as a system and zooming across to determine how these impacts affect infrastructures interconnected with it. Two examples-the 2010 San Bruno gas explosion and the major nexus of infrastructure on an island in the Delta-illustrate how risk analysis is to be undertaken in the ICIS setting.

This chapter stresses the difficulty of perceiving the immense time scale of evolution and relating it to the cyclic time scale of the natural changes observed within one generation. It discusses the three geneses of life; the hierarchy of evolutionary mechanisms; the metaphor of the central cupola of the Basilica of San Marco in Venice; transformation of species through time and the lifespan of a species; current perceptible evolution; and current unfortunate evolution.

The interview with the eminent Dutch astronomer Willem de Sitter took place in Leiden in 1933, at a time when the expanding universe was accepted by many astronomers. De Sitter looked back to the development of cosmology since 1917 and expressed his satisfaction with the expanding solutions which explain the observed redshifts. He argued that the cosmological constant is responsible for the expansion and discussed the serious problem of the much too low time-scale. He also reflected on cosmology as a science and his own view of what a theory of the universe should look like. As an astronomer he was critical of theories that are mathematical in nature and not closely related to observations. Among the theories he clearly disliked he mentioned E. A. Milne’s new cosmology.

This chapter explores the host of mechanisms involving biological and physical processes in the context of the evolution of ocean chemistry on geologic time scales. Large fluctuations in the salinity of the ocean are unlikely to have occurred, although periods following the deposition of evaporite “giants” may have been anomalously low in salinity. The Ca concentration and alkalinity of the ocean are regulated by the sensitive response of the ocean’s calcium carbonate compensation depth to variations in the oceanic C_aCO₃ saturation state. Potential metal toxicity is prevented by the production of specific metal-binding ligands by the marine biota. Overall, the system is resilient, but human activity may be perturbing important state variables of the ocean to an extent that will be detrimental to marine life.

This chapter examines the question of slowness in music by focusing on the Halberstadt John Cage Organ Project (2001) and 9 Beet Stretch (2002). It considers a number of projects that involve extremely extended time scales, such as Danny Hillis's installation called the Clock of the Long Now and Jem Finer's composition Longplayer. Evoking the mathematical sublime from Immanuel Kant to Jean-François Lyotard, the chapter asks what happens in these very long works when the musical now virtually breaks and each single instant takes up many months. It also shows how slowness can be reconceived in terms of a Kittlerian time axis manipulation and how pieces based on time axis manipulation can alter the parameter of tone in terms of a second-order spatiality that then may become a liminal aural space for listeners to explore.

This chapter sets the context for the book. We note the purpose of economics should be to describe concepts and models that can be made consistent with sound scientific understanding of the other aspects of life. At a minimum economic behaviour is embedded within the organic system we call the society: it affects extraction, production, utilization, exchange, consumption and disposal of physical entities and services. We consider the main questions about how to contextualize economics. It can be argued that the economy is a mechanism to organize a subset of decisions in a larger highly distributed society. The social organization obeys no simple model of control; its dynamics is often evolutionary at many scales of time, space and material content; and with these it is subject to both historical contingency and great complexity.

This chapter examines various opinions on rhythm and meter. To begin with a relatively neutral assessment, one may turn first to the thought of Alfred Lorenz. Lorenz assimilates both meter and rhythm to form and refers the difference between regularity and irregularity—or rational and irrational—to a difference of time scale. In equating form and rhythm, Lorenz designates meter as rationale Rhythmik, one means of rhythmic formation among many. Moritz Hauptmann also identifies the metrical with the rational but insists upon a strict separation between meter and rhythm in which rhythm itself is viewed as irrational. Meanwhile, Friedrich Neumann proposes a much starker separation of meter and rhythm. Neumann characterizes meter as “quantitative/outer time”—time viewed in relation to space. Rhythm, on the other hand, is “qualitative/inner time”—time viewed from the standpoint of being and becoming, past and future, and memory and anticipation. The chapter also looks at Thrasybulos Georgiades' argument that it is precisely meter, newly conceived as a relatively autonomous “concept,” that is the hallmark of High Classical style.

This chapter analyses the musical compositions of George Frideric Handel during the 1740s. The decade marked the emergence of a creative period that saw oratorio-type masterworks follow each other, bearing a comparison to his best periods. All works produced by Handel during the 1740s had the same technical parameters: they employed the various forms of recitative, aria, and chorus, in different proportions according to the requirements of each libretto, and were intended to be performed in ‘still life’. As his programmes from 1743 onwards consisted exclusively of such works, it is not surprising that they came to be considered together in common parlance as ‘oratorios’, for they indeed constituted similar elements. The chapter describes how Handel's ‘mature’ oratorios were conceived on the time scale inherited from Italian opera: an evening's entertainment at the theatre consisted of a work in three acts lasting something over three hours in performance, including intervals.

Of the estimated one to four billion species that have existed on the Earth since life first appeared here (Simpson 1952), less than 50 million are still alive today (May 1990). All the others became extinct, typically within about ten million years (My) of their first appearance. It is clearly a question of some interest what the causes are of this high turnover, and much research has been devoted to the topic (see, for example, Raup (1991a) and Glen (1994) and references therein). Most of this work has focussed on the causes of extinction of individual species, or on the causes of identifiable mass extinction events, such as the end-Cretaceous event. However, a recent body of work has examined instead the statistical features of the history of extinction, using mathematical models of extinction processes and comparing their predictions with global properties of the fossil record. In this book we will study these models, describing their mathematical basis, the extinction mechanisms that they incorporate, and their predictions. Before we start looking at the models however, we need to learn something about the trends in fossil and other data which they attempt to model. This is the topic of this introductory chapter. Those well versed in the large-scale patterns seen in the Phanerozoic fossil record may wish to skip or merely browse this chapter, passing on to chapter 2, where the discussion of the models begins. There are two primary colleges of thought about the causes of extinction. The traditional view, still held by most palaeontologists as well as many in other disciplines, is that extinction is the result of external stresses imposed on the ecosystem by the environment (Benton 1991; Hoffmann and Parsons 1991; Parsons 1993). There are indeed excellent arguments in favor of this viewpoint, since we have good evidence for particular exogenous causes for a number of major extinction events in the Earth's history, such as marine regression (sealevel drop) for the late-Permian event (Jablonski 1985; Hallam 1989), and bolide impact for the end-Cretaceous (Alvarez et al. 1980; Alvarez 1983, 1987).