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This chapter discusses theoretical autocovariance, autocorrelation functions of autoregressive models of orders 1 and 2, and autocorrelation function-derived timescale. The autocorrelation function of a scalar time series is a prime tool for estimating the characteristic timescale separating successive independent realizations in the time series. Any process other than completely random noise has some serial correlations. Even variables as volatile and nondeterministic as measures of stock market performance, when valuated close enough, are unlikely to vary appreciably. Thus, a time series of the index at 1-second intervals likely contains significant redundancy; it can be almost as representative and contain almost as much information if degraded to valuation intervals of T > 1 second. Identifying an acceptable characteristic timescale T separating successive independent realization in the time series that balances the need to retain maximum information while minimizing storage and transmission burdens is a key role of the autocorrelation function.

The introduction describes the village today, the storyteller and the archives. It asks how changing the timescale shifts conventional narratives of Christianity in China, and it considers the impact of focusing on a single village rather than a nation. It argues that, rather than following a process of acculturation, over the centuries, religious practice has moved closer to global norms, through global links and a desire for authenticity. Finally, it discusses community memory and writing a history in English.

This chapter addresses the questions posed in Chapter 4. Using the general principle introduced in Chapter 5 as a guide, it reappraises different anatomical structures within the skull. Once analyzed under the perspective of IIT, the paradoxes posed by cerebellum, the basal ganglia, and by other large neuronal aggregates that seem irrelevant for consciousness, are less disconcerting; their architecture is not suited for integrating information, whereas the thalamocortical system seems to contain a core of high Φ‎. The chapter ends by suggesting that the time scale at which conscious experience flows (hundreds of milliseconds) may be related to the time it takes for the brain to integrate information.

This chapter applies dynamic field theory to word learning. The use of one-dimensional neural fields to represent labels and the combination of these with a feature dimension are introduced. These label-feature fields keep a record of prior feature-label associations via the memory trace mechanism. Using a robotic instantiation, the chapter show how individual features of objects, represented in multiple feature-label fields, can be bound via a shared label dimension. The result is a dynamic field model that can 1) learn robust novel label-object mappings after only a few presentations of the label and/or the object, 2) demonstrate emergent categories, 3) fill in missing information, and 4) distinguish between two different objects that share a value on one feature dimension but not others. An expanded version of this model includes two feature-label and two feature-space fields, which enable the model to overcome referential ambiguity by binding names to objects across a shared spatial dimension. This model can capture multiple word-learning behaviors, thus pointing to a critical innovation of this work—the integration of timescales.

The mathematical theory of dynamical systems can potentially address any complexity arising from the unique and stochastic nature of individual life histories, the interactions between individuals, the spatial heterogeneity and temporal variability of their environments, and the complexity of natural communities. Identification of individual states determining an organism’s response to its environment and the corresponding theory of structured populations provides general applicability for the theory of ecology. Deaths and births are stochastic events, but the expected behaviour of individuals still can be specified under well-defined conditions. Complex dynamics of interaction networks can be simplified by time-scale separations, because various environmental and population processes often have different temporal scales. The practical challenges for applied ecology call for fitting models to the plethora of empirical data supplied by automated data-collection technologies. The chapter closes, therefore, with a short introduction to maximum likelihood parameter estimation techniques and the related concept of model selection.

Over the past decade there has been rapidly growing interest in the potential effects of ocean acidification and perturbations of the carbonate system on marine organisms. While early studies focused on a handful of phytoplankton and calcifying invertebrates, an increasing number of investigators have begun to examine the sensitivity to ocean acidification of various planktonic and benthic organisms across the marine food web. Several excellent review articles have recently summarized the rapidly expanding literature on this topic (Fabry et al. 2008; Doney et al. 2009 ; Joint et al. 2011). The focus of this chapter is on the potential ecosystem-level effects of ocean acidification. Starting with a brief review of the basic physical, chemical, and biological processes which structure pelagic marine ecosystems, the chapter explores how organismal responses to perturbations of the carbonate system could scale up in both time and space to affect ecosystem functions and biogeochemical processes. As with many chapters in this volume, and indeed much of the ocean acidification literature at present, our review raises more questions than it answers. It is hoped that these questions will prove useful for articulating and addressing key areas of future research. Complexity in marine pelagic food webs results from the interactions of multiple trophic levels across a range of temporal and spatial scales. The traditional view of marine food webs (Steele 1974) involved a relatively short trophic system in which large phytoplankton (e.g. net plankton such as diatoms) were grazed by a variety of mesozooplankton (e.g. copepods), which were in turn consumed by second-level predators, including many economically important fish and invertebrate species. This ‘classic’ marine food web is typical of high-productivity regions such as coastal upwelling regimes (Lassiter et al. 2006). A characteristic feature of these systems is a strong decoupling between primary production and grazing, which results from the different metabolic rates of consumers and producers and, in many cases, ontogenetic and seasonal delays in the emergence of feeding predators. The uncoupling between phytoplankton and their consumers leads to significant export of organic material out of the euphotic zone, the so-called biological carbon pump (discussed further below).

Although the changes in the chemistry of seawater driven by the uptake of CO2 by the oceans have been known for decades, research addressing the effects of elevated CO2 on marine organisms and ecosystems has only started recently (see Chapter 1). The first results of deliberate experiments on organisms were published in the mid 1980s (Agegian 1985) and those on communities in 2000 (Langdon et al. 2000; Leclercq et al. 2000 ). In contrast, studies focusing on the response of terrestrial plant communities began much earlier, with the first results of free-air CO2 enrichment experiments (FACE) being published in the late 1960s (see Allen 1992 ). Not surprisingly, knowledge about the effects of elevated CO2 on the marine realm lags behind that concerning the terrestrial realm. Yet ocean acidification might have significant biological, ecological, biogeochemical, and societal implications and decision-makers need to know the extent and severity of these implications in order to decide whether they should be considered, or not, when designing future policies. The goals of this chapter are to summarize key information provided in the preceding chapters by highlighting what is known and what is unknown, identify and discuss the ecosystems that are most at risk, as well as discuss prospects and recommendation for future research. The chemical, biological, ecological, biogeochemical, and societal implications of ocean acidification have been comprehensively reviewed in the previous chapters with one minor exception. Early work has shown that ocean acidification significantly affects the propagation of sound in seawater and suggested possible consequences for marine organisms sensitive to sound (Hester et al . 2008). However, sub sequent studies have shown that the changes in the upper-ocean sound absorption coefficient at future pH levels will have no or a small impact on ocean acoustic noise (Joseph and Chiu 2010; Udovydchenkov et al . 2010). The goal of this section is to condense the current knowledge about the consequences of ocean acidification in 15 key statements. Each statement is given levels of evidence and, when possible, a level of confidence as recommended by the Intergovernmental Panel on Climate Change (IPCC) for use in its 5th Assessment Report (Mastrandrea et al. 2010).