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This chapter is mainly concerned with the connectivity threshold T on n random points (i.e., the smallest r at which G(n,r) is connected). The results for this threshold are similar to those for the threshold M at which G(n,r) has no isolated points. For uniformly distributed points, these two thresholds are equal with high probability, and more generally the asymptotics for T are similar to those for M discussed in Chapters 7 and 8. Extensions to k-connectivity are considered, and a central limit theorem for the number of components of G(n,r) in the thermodynamic limit is presented.

A national railway system can be analyzed as a collection of regional sub-systems joined by an inter-regional trunk network. A major weakness of the British railway system, as developed in Victorian Britain, was that it failed to generate coherent regional sub-systems. This was because most regions were served both by an established company and a competitive invader. Each company operated its own network and the established company sought to inhibit the interchange of traffic between them. Thus, although competition at the regional level produced a relatively high density of lines, duplication was rife and network connectivity was poor.

This chapter explores the spatial dynamics of invading species, paying particular attention to the patterns formed as they spread, i.e., the rate of increase of the area invaded and the rate at which their boundaries move. The development of models for population expansion — comprising a range of structures and assumptions both simple and complex — is reviewed. Rare long distance dispersal events are shown to dictate the rate of spread, the pattern in population margins, and the distribution of genotypes. Movement through heterogeneous landscapes is shown to be further affected by the connectivity and distribution of suitable patches.

The study of Cyprus's prehistoric and early historic past has been dominated by a tendency to see the island's social, economic, cultural, and even artistic development as the result of migrations, invasions, colonization, diffusion, or other external factors, whether Near Eastern or Aegean (or both) in origin. Such an approach distorts the long‐term history of Cyprus and precludes attempts to consider how insularity and local enterprise impacted on the islanders' identity and the emergence of a complex, hierarchical society. This introductory chapter sets the island of Cyprus in its Mediterranean island context, and provides initial comments on the volume's central themes: insularity, connectivity, and social identity. It summarizes the contents of each chapter and provides brief discussions of previous works that treat island archaeology and history, island identity, and ‘islandscapes’ throughout the Mediterranean world.

Advances in imaging technologies provide today an abundance of qualitatively diverse brain data sets with the purpose to guide the placement of subdural electrodes as a pre-requisite for epilepsy surgery. Current efforts focus on the development of integrative computational frameworks that allow quantitative assessment of relationships in anatomical and functional domains between complementing modalities. It is believed that such an approach is not simply additive but possesses an amplifying effect, as the information entailed in one modality is used to both enhance and re-interpret information derived from complementing modalities. By taking advantage of these advanced data integration schemes, quantitative results are subsequently combined into data structures that provide a consistent framework for the application of advanced data mining techniques. Such multimodality database structures hold promise of providing new insights into the formation, identification and maturation of epileptic foci and might eventually lead to new approaches in epilepsy surgery that are likely to improve clinical management of patients suffering from intractable epilepsy.

This chapter describes methods which allow the investigation of long-range dynamic interactions between brain areas based on MEG recordings. The aim is not a complete review of available methods but rather an introduction to concepts, methods, and approaches that currently play a role in the rapidly evolving field of functional connectivity analysis with MEG.

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some standard definitions in graph theory and probability theory. Specific terminology is introduced for two limiting regimes in the choice of r=r(n) (namely the thermodynamic limit where the mean vertex degree is made to approach a finite constant) and the connectivity regime (where it grows logarithmically with n). Some elementary probabilistic results are given on large deviations for the binomial and Poisson distribution, and on Poisson point processes.

Heavy metal scenes can be found throughout the Middle East as in almost any other region of the world. Although still marginal in terms of numbers and public attention, the metal scene in the region, particularly in urban centers in Turkey, Lebanon, and Israel, has developed its own infrastructure consisting of bands, magazines, independent labels, distributors, festivals, and bars. This chapter, based on two case studies from Turkey, explores the impact of newly emerging “metal spaces” on already existing social and public spaces. It considers aspects of both local embeddedness and of translocal connectivity to illustrate how youthful “metal heads” negotiate boundaries in everyday life. The first case study focuses on the emergence of Turkey’s very first rock bar, whereas the second case sheds light on cultural globalization and the translocal connectivity among metal heads of different ethnic, religious, and national backgrounds.

This chapter studies random, steady state food webs of varying size and complexity (up to 2,000 species and 1.3 million connections) which were generated with and without ecologically realistic constraints. This chapter analyses trends in network metrics, such as ascendancy, developmental capacity, and throughput as functions of size and complexity while holding constant the total annual gross primary production. It shows that total system biomass declined as the number of nodes representing biodiversity increased, or as the connectivity of the network increased. Total consumer biomass was not affected by the number of nodes or connections, and was not correlated with primary producer biomass. Therefore, loss of total biomass was more associated with decreased NPP and a decrease in the efficiency of primary production than a loss of consumer biomass. The ratio of tertiary consumer to detritivore biomass, an indicator of the direction of energy flow, was positively correlated to taxonomic diversity, but negatively correlated with the number of connections. The ratio of ascendancy to capacity was negatively correlated with network size, and complexity was within the range of those of real aquatic ecosystems of similar size. The trends indicate that more energy is dissipated as the density of network connections increases.

This chapter delves into how young Americans emotionally experience their sexual relationships and activity patterns. Men and women report very different levels of emotional connectivity over sex, both on surveys and in person. We explore here the emotions to sex, and note how different sexual traits — like the frequency of intercourse and partner cycling — differentially affect young women’s emotional health. Women and men often want different things from their relationships, and often get different things. Some types of sexual relationship tend to make people more contented and secure, and some do not. It is sexual security that the data point to as most valuable and valued by women. Toward that end, many young women spend considerable time “managing their hearts,” making effort to like the sorts of relationships they’re in, even when what they describe is destructive, one-sided, or clearly unfulfilling. Among women, virgins and those in stable relationships fare best emotionally.

Evidence from neuroimaging studies shows that increased recruitment of prefrontal cortex and greater functional connectivity between prefrontal and other brain regions, including the medial temporal lobes, are often associated with better memory performance in older adults. These alterations in memory-related brain activity may be compensatory, but may also indicate less efficient use of these regions. A major unresolved issue is the relation between these functional age differences and structural brain changes with age, particularly in the white matter tracts that support communication between brain areas. The use of network approaches for image analysis has considerable potential to inform us about how brain areas work together to mediate memory function and how these networks change as we get older.

Population density methods have a rich history in theoretical and computational neuroscience. In earlier years, these methods were used in large part to study the statistics of spike trains. Starting in the 1990s population density function (PDF) methods have been used as an analytical and computational tool to study neural network dynamics. In this chapter, we discuss the motivation and theory underlying PDF methods and a few selected examples of computational and analytical applications in neural network modelling.

Conceptual approaches used to understand conservation in fragmented landscapes are summarized in this chapter by Andrew F. Bennett and Denis A. Saunders. Destruction and fragmentation of habitats are major factors in the global decline of species, the modification of native plant and animal communities and the alteration of ecosystem processes. Habitat destruction, habitat fragmentation (or subdivision) and new forms of land use are closely intertwined in an overall process of landscape change. Landscape change is not random: disproportionate change typically occurs in flatter areas, at lower elevations and on more‐productive soils. Altered physical processes (e.g. wind and water flows) and the impacts of human land‐use have a profound influence on fragments and their biota, particularly at fragment edges. Different species have different ecological attributes (such as scale of movement, life‐history stages, what constitutes habitat) which influence how a species perceives a landscape and its ability to survive in modified landscapes. Differences in the vulnerability of species to landscape change alter the structure of communities and modify interactions between species (e.g. pollination, parasitism). Changes within fragments, and between fragments and their surroundings, involve time‐lags before the full consequences of landscape change are experienced. Conservation in fragmented landscapes can be enhanced by: (i) protecting and increasing the amount of habitat: (ii) improving habitat quality; (iii) increasing connectivity; (iv) managing disturbance processes in the wider landscape; (v) planning for the long term; and (vi) learning from conservation actions undertaken.

Microbes, including bacteria, archaea, viruses, fungi, protozoans and microalgae, are the most abundant and arguably the most important members of coral reef communities. They occur in the water column and sediment, and in association with other reef organisms. This chapter describes the abundance, diversity, function and productivity of microbes, with an emphasis on free-living types. They are key to recycling and retention of organic matter via the ‘microbial loop’, and are an important food source for larger reef organisms. The metazoan zooplankton are also described, including larvae of most reef invertebrates and fish. They are described in terms of their duration in the plankton, settlement behaviour (e.g. of coral larvae), daily migration patterns, and as a food source for larger organisms. Their importance for inter-reef connectivity is discussed.

This concluding chapter looks at the implications for Central Asia of new rail links between China and Europe, which foreshadow the region's return after half a millennium to being the central hub of Eurasia. A quarter century after independence, the hard infrastructure of roads, airports, border crossing points, and so forth, has been steadily improved. The hard infrastructure would be of limited value without substantial improvement in soft infrastructure, which has changed more slowly in Central Asia. However, there is evidence that this is starting to happen. Governments are beginning to undertake measures with the specific goal of trade facilitation. Indeed, the China–Europe Landbridge could signal a new opportunity for Central Asia. Connectivity will be improved, especially if there are multiple routes, which may be stimulated by Iran's reintegration into the global economy and Turkey's rail tunnel under the Bosporus.