This chapter extends the ideas of complex data by looking into cybersecurity through network and graph data.

Chapter 9, using the new capacity scaling law presented in the previous chapter, explores three relevant network optimization problems: i) the small cell base station deployment/activation problem, ii) the network-wide user equipment admission/scheduling problem, and iii) the spatial spectrum reuse problem. These problems are formally presented, and exemplary solutions are provided, with the corresponding discussion on the intuition behind the proposed solutions.

Chapter 3 summarizes the modelling, derivations and main findings of probably one of the most important works on small cell theoretical performance analysis, which concluded that the fears of an inter-cell interference overload in small cell networks were not well-grounded, and that the network capacity – or in more technical words, the area spectral efficiency – linearly grows with the number of deployed small cells. This research was the cornerstone of much of the research that followed on small cells performance analysis.

Chapter 1 introduces the capacity challenge faced by modern wireless communication systems and presents ultra-dense wireless networks as an appealing solution to address it. Moreover, it provides background on the small cell concept – the fundamental building block of an ultra-dense wireless network – describing its main characteristics, benefits and drawbacks. This chapter also presents the structure of the book and the fundamental concepts required for its systematic understanding.

Chapter 6 brings attention to another important feature of ultra-dense networks, i.e. the surplus of the number of small cell base stations with respect to the amount of user equipment. Building on this fact and looking ahead at next generation small cell base stations, the ability to go into idle mode, transmit no signalling meanwhile, and thus mitigate inter-cell interference is presented in this chapter, as a key tool to enhance ultra-dense network performance and combat the previously presented caveats. Special attention is paid to the upgraded modelling and analysis of the idle mode capability at the small cell base stations.

Chapter 5 studies in detail – and also from a theoretical perspective – yet another and more important caveat towards a satisfactory network performance in the ultra-dense regime, i.e. that of the impact of the antenna height difference between the user equipment and the small cell base stations. Similarly as in the previous chapter, such antenna-related modelling upgrades, the new derivations in a three-dimensional space and the new obtained results are carefully presented and discussed in this book chapter for the better understanding of the readers. Moreover, several small cell deployment and configuration guidelines are provided to improve the network performance.

Chapter 7 investigates the impact of ultra-dense networks on multi-user diversity. A denser network reduces the number of user equipment per small cell in a significant manner, and thus can significantly reduce – and potentially neglect – the gains of channel-dependent scheduling techniques. These performance gain degradations are theoretically analyzed in this chapter, and the performance of a proportional fair scheduler is compared to that of a round robin one.

Chapter 8, standing on the shoulders of all previous chapters, presents a new capacity scaling law for ultra-dense networks. Interestingly, the signal and the inter-cell interference powers become bounded in the ultra-dense regime. The former is due to the antenna height difference between the user equipment and the small cell base stations, and the latter is due to the finite user equipment density as well as the idle mode capability at the small cell base stations. This leads to a constant signal-to-interference-plus-noise ratio at the user equipment, and thus to an asymptotic capacity behaviour in such a regime. From this new capacity scaling law, it can be concluded that, for a given user equipment density, the network densification should not be abused indefinitely, and instead, it should be stopped at a certain level. Network densification beyond such a point is a waste of both invested money and energy consumption.

Chapter 4 analyzes in detail – from a theoretical perspective – the first practical caveat towards such linear growth of capacity in the ultra-dense regime, i.e. that of the impact of the transition of a large number of interfering links from non-line-of-sight to line-of-sight. Importantly, this chapter shows that the theoretical tools used until then to analyze traditional sparse or dense small cell networks, such as that presented in the previous chapter, do not directly apply to ultra-dense ones, and neither do their conclusions. In this chapter, we detail the path loss modelling upgrades necessary for a more realistic and accurate modelling of ultra-dense networks, present the subsequent and new theoretical derivations, and analyze the obtained results for the better understanding of the readers.

This chapter outlines the three aims of the book: to resolve the stability paradox; to reconcile an idiolect-centred perspective on language change with corpus-linguistic methodology; and to carry out four case studies of colloquialization and densification. Some limitations in scope are also addressed, and the structure of the remainder of the book is outlined.

Participle clauses as postmodifiers in noun phrases (e.g. the window broken by the thief) have been discussed as a potential indication of densification, as they are shorter than their most obvious alternative, that is, finite relative clauses. A careful examination reveals that only a subset of tokens of participle and relative clauses can be considered equivalent and exchangeable, and to reflect this finding both variationist and text-linguistic analyses are carried out. There is some evidence of densification in newspaper language and, to some extent, scientific texts; history texts, in contrast, develop in the opposite direction, underscoring the importance of considering subgenres of academic writing. Among the newspapers considered, the Poor Man’s Guardian, which was aimed at working-class readers, shows no tendencies towards densification; this may be due to journalists’ perceptions about the paper’s readership. The issue of whether variationist or text-linguistic approaches are more suitable is discussed. Non-restrictive participle clauses are shown not to indicate densification; instead, they function as a characterizing or backgrounding device in narrative texts.

In the final chapter, the three aims of the book are returned to and discussed from a holistic perspective. The book ends with a few concluding remarks.

In this chapter, the idiolect-centred approach to language change is reconciled with historical corpus linguistics as a methodology. The issue of what corpus-based studies can and cannot tell us is discussed in terms of the granularity of the analyses. The two types of change in focus in the case studies, colloquialization and densification, are introduced. The two main ways of operationalizing frequency in syntactic studies, namely variationist and text-linguistic approaches, are contrasted. Finally, the two corpora on which the case studies are based, CONCE and CNNE, are introduced; CNNE and its relationship to the newspaper market in nineteenth-century England is discussed in some detail, as CNNE is a new corpus and as the newspaper trade underwent far-reaching changes during the period covered by the corpus. The importance of considering a wide variety of genres owing to the increasing linguistic genre differences that characterize Late Modern English is emphasized.

The increase in nouns as premodifiers in noun phrases (e.g. the stone church) is a well-known aspect of densification in Late Modern English. The corpus analysis shows that both common and proper nouns become more frequent as premodifiers. While newspapers represent the most advanced usage, the general increase in the frequency of this feature and the fact that women use it more than men in letters indicate that there may be two separate developments underway: a general increase in premodifying nouns in the communal language as a change from below and a separate trend towards additional usage as part of the densification of informational writing. Semantic analyses show that most semantic relationships between common nouns as premodifiers and their heads were already present by 1800, though some tendencies towards more opaque combinations could be found in genres where a high frequency of the feature was noted; as regards proper nouns as premodifiers, the increase in frequency was coupled with a trend towards more animate referents. Overall, the results provide clear evidence of densification in, above all, newspaper language.