The aim in Chapter 7 is to take into account the role of the means of information transmission on the nature of the states that can be perceived. Our point of departure is the recognition that the information we obtain is acquired by observers who monitor fragments of the same environment that decohered the system, einselecting preferred pointer states in the process. Moreover, we only intercept a fraction of the environment. The only information about the system that can be transmitted by its fraction must have been reproduced in many copies in that environment. This process of amplification limits what can be found out to the states einselected by decoherence. Quantum Darwinism provides a simple and natural explanation of this restriction, and, hence, of the objective existence—the essence of classicality—for the einselected states. This chapter introduces and develops information-theoretic tools and concepts (including, e.g., redundancy) that allow one to explore and characterize correlations and information flows between systems, environments, and observers, and illustrates them on an exactly solvable yet non-trivial model.

This chapter covers digital information sources in some depth. It provides intuition on the information content of a digital source and introduces the notion of redundancy. As a simple but important example, discrete memoryless sources are described. The concept of entropy is defined as a measure of the information content of a digital information source. The properties of entropy are studied, and the source-coding theorem for a discrete memoryless source is given. In the second part of the chapter, practical data compression algorithms are studied. Specifically, Huffman coding, which is an optimal data-compression algorithm when the source statistics are known, and Lempel–Ziv (LZ) and Lempel–Ziv–Welch (LZW) coding schemes, which are universal compression algorithms (not requiring the source statistics), are detailed.

In Chapter 13 we will discuss how to produce compression schemes that do not require a priori knowledge of the generative distribution. It turns out that designing a compression algorithm able to adapt to an unknown distribution is essentially equivalent to the problem of estimating an unknown distribution, which is a major topic of statistical learning. The plan for this chapter is as follows: (1) We will start by discussing the earliest example of a universal compression algorithm (of Fitingof). It does not talk about probability distributions at all. However, it turns out to be asymptotically optimal simultaneously for all iid distributions and with small modifications for all finite-order Markov chains. (2) The next class of universal compressors is based on assuming that the true distribution belongs to a given class. These methods proceed by choosing a good model distribution serving as the minimax approximation to each distribution in the class. The compression algorithm for a single distribution is then designed as in previous chapters. (3) Finally, an entirely different idea are algorithms of Lempel–Ziv type. These automatically adapt to the distribution of the source, without any prior assumptions required.

Concision is about more than writing like Hemingway or following Strunk & White’s edict to eliminate unnecessary words. Instead, concision relies on writers recognizing the myriad redundancies in English, a reflection of its evolution from the collision of Latin, French, and Old English in the decades following the Norman Conquest. Moreover, redundancies also litter English in the form of redundant modifiers, throat-clearing, and metadiscourse. By recognizing these words and phrases, writers can quickly pare sentences to their essentials, without fretting over the havoc deletions can wreak on the meaning of their sentences.

Text comprehension and picture comprehension can be synthesized into a common conceptual framework which differentiates between external and internal descriptive and depictive representations. Combining this framework with the human cognitive architecture including sensory registers, working memory, and long-term memory leads to an integrated model of text and picture comprehension. The model consists of a descriptive branch and a depictive branch of processing. It includes multiple sensory modalities. Due to a flexible combination of sensory modalities and representational formats, the model covers listening comprehension, reading comprehension, visual picture comprehension, and sound comprehension. The model considers text comprehension and picture comprehension to be different routes for constructing mental models and propositional representations with the help of prior knowledge. It allows us to explain the effects of coherence, text modality, split attention, text–picture contiguity, redundancy, sequencing, and the effects of different types of visualization.

This chapter completes our critical exploration of Popper’s key work, the Logic of Scientific Discovery and how it applies to corpus linguistics. In this chapter we address the question of how easily linguistics may be viewed as a science, in Popper’s terms. We also consider important critiques of Popper’s work and use those to both clarify and, where necessary, adapt the framework.

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

The SVCs have a cluster of grammatical traits not derivable exclusively from UG, some of which have been misrepresented/misunderstood in the UG literature. The first functional void of UG is proposed which limits the lexicalization of a semantic relation R to only those cases where R connects first-order entities. All the characteristic properties of SVCs result from this functional void collaborating with the proposed Serial Verb Parameter (SVP) in the theory of the UG–iconicity interface. It also explains a wide range of related cross-linguistic facts, from phrasal SVCs to compounds, the parametric variations between Chinese and Gbe languages in (dis)allowing ditransitive V1, why the resultative SVC acts in a particular set of ways different from other types and the subtle disparities between head-initial and head-final SVCs, as well as the full range of variations among Kwa languages in object- and verb-fronting. The relation between the linearization pattern of UG and the iconicity-induced word order of SVCs is shown to pattern with the “high” and “low” neural pathways underlying fear, with implications on the nature of redundancy in biologically based systems and suggestive of an evolutionary connection between these two linearization mechanisms in language.

Synthesising different collapse mechanisms for indeterminate beams and frames is considered via the prospect of their salient bending moments (without solving for their exact values) as candidate positions for the formation of plastic hinges. The method of Instantaneous Centre is introduced for calculating the relative motion of sub-structures within frames, including those with pitched roofs under distributed loading.

Maxwell's Rule conveys a statement of rigidity for a given truss framework. When the number of bars or supports is reduced, the truss will inevitably lose rigidity and collapse as a mechanism. This consequence can also be captured by Maxwell's Rule in a modified statement, which leads to a discussion about its interplay with states of self-stress, illustrated using the simplest pin-jointed arch.

We suggest (Proposition 5) that a community is functionally assembled when there is at least one species representing each functional type that is adapted to the habitat. We suggest (Proposition 6) that a community is fully assembled when each functional type has the maximum number of species that can coexist. Much biological diversity lies in the lower tail of the log-normal distribution, yet ecologists frequently trim this tail of rare species to construct models. The rising tide of species extinctions requires us to revisit this procedure, and to consider how to include conservation of rare species in models for community assembly. This requires us to recognize that there are two types of “rare” species in ecological data sets: those that are merely rare in samples and those that are designated as globally rare and at risk of extinction. Most communities arise from pre-existing communities, so when filters change there is often inertia in community response, and this inertia is related to traits. The principles laid out in this book provide a guide not only to theoretical understanding but for the challenges of ecological restoration.

We give a short introduction to some classical information-theoretic quantities: joint entropy, conditional entropy and mutual information. We then interpret their exponentials ecologically, as meaningful measures of subcommunities of a larger metacommunity. These subcommunity and metacommunity measures have excellent logical properties, as we establish. We also show how all these quantities can be presented in terms of relative entropy and the value measures of the previous chapter.