This chapter is a state/signal counterpart to Chapter 8. We recall that a s/s system is bounded if and only if it has at least one bounded i/s/o representation. In the semi-bounded setting, we turn this property into a definition and say that a s/s system is semi-bounded if it has at least one semi-bounded i/s/o representation. Most of the results presented in Chapter 7 for bounded s/s systems remain valid in one form or another for semi-bounded s/s systems, but there is one major exception: in the case of a bounded s/s system, the direction of time does not play an important role, i.e., most of the results that are true in the forward time direction are also true in the backward time direction. This is no longer true in the semi-bounded case. The even larger class of well-posed s/s systems is discussed in Chapter 15, and many of the results in the present chapter remain valid even in the well-posed setting.

In this chapter, we study well-posed s/s systems. By definition, a s/s system is well-posed if it has at least one well-posed i/s/o representation (and then usually infinitely many wellposed i/s/o representations). The results presented here are analogous to the corresponding well-posed i/s/o results in Chapter 14, and most of the proofs consist of showing how to reduce a particular well-posed s/s result to the corresponding well-posed i/s/o result. In the well-posed i/s/o setting, we can interpret a well-posed i/s/o system as a realization of a continuous linear causal shift-invariant exponentially bounded operator. In the well-posed s/s setting, we can instead interpret a well-posed s/s system as a realization of a well-posed future, past, or two-sided behavior. Each one of these behaviors determine, the other two uniquely. Two well-posed s/s systems are externally equivalent if and only if they have the same well-posed behaviors. At the end of this chapter, we define the notion of a passive state/signal system and show that passive state/signal systems are well-posed. A passive state/signal system is characterized by the fact that it is regular, and its generating subspace is a maximally nonnegative subspace of the Kreĭn node space.

Chapter 7 uses three case studies to describe existing practice and processes for using and sharing data for linkage research in three jurisdictions: Western Australia, Scotland and Manitoba. Each case study looks at the decision makers; the relevant law, policy and guidelines regulating the decision-making process; and the ethical review process. The chapter assesses the practice and process in each case study against metrics of good decision making. These metrics are efficiency, transparency, accountability and community participation. The chapter concludes that there are significant similarities between the jurisdictions but that there are many areas in which decision making can be improved in all jurisdictions.

In Chapter 5, we defined various dynamic time domain notions for i/s/o systems, such as reachable and unobservable subspaces, controllability and observability, strong and unobservable invariance, external equivalence, intertwinements, compressions, dilations, restrictions, extensions, and projections. Here, we present frequency domain counterparts of these definitions. One of the four components of a frequency domain trajectory is a constant representing an “initial state,” and the other three components are analytic functions defined on some open subset Ω of the complex plane, representing a “frequency domain state,” a “frequency domain input,” and a “frequency domain output.” By the frequency domain i/s/o system induced by an i/s/o node Σ, we mean the node Σ itself together with the set of all frequency domain trajectories. Some of our frequency domain definitions can be applied to arbitrary i/s/o nodes, but most of the time we assume that Σ is resolvable and that the set Ω on which the trajectories are defined is contained in the resolvent set of Σ.

Chapter 6 considers the legal basis on which linked data is used and disclosed for research in the three jurisdictions under consideration. The bodies of law relevant to research using individual-level data without consent are examined. The chapter describes how these bodies of law regulate the use of data and balance the relevant private and public interests in play. The chapter critiques these bodies of law in terms of clarity and consistency, including consistency with the human rights norms and ethical principles discussed in previous chapters.

Chapter two considers the interwoven interests of individual participants, collectives interests and the wider public interests in research using linked data. The chapter discusses the research participants interests including dignity, autonomy and privacy and the traditional approaches to protecting them — consent and anonymisation — and concludes that these do not operate to effectively to protect individual interests in this context. Research using linked data can also have impacts, both beneficial and harmful on others, including socio-demographic groups, disease groups and the wider community and these should be explicitly recognised and evaluated by decision makers. The current legal and ethical regulation of data linkage research are critiqued for being too individualistic and alternative approaches are discussed.

Chapter 8 concludes the book by proposing ways to improve decision-making in relation to sharing linked data for research. It considers improvements in a number of areas: the decision-making framework of interests, values, and rights; the decision-making criteria and conditions; the decision makers who are best placed to make each decision; and the decision-making process. The chapter sets out the interests, values and rights that should frame decisions in this sphere, not all of which are currently represented in decision-making frameworks. It provides a list of decision-making criteria and considerations that should be taken into consideration by the relevant decision makers. The chapter distinguishes between ethical decisions, which should be made by ethics committees and governance decisions, which should be made data custodians. Finally, the chapter makes recommendations for a decision-making process that will be efficient, transparent, accountable and collaborative. This process is designed to lead to better decisions and to ensure that both the decision-making process and the decisions themselves develop and sustain the social licence needed to support the important enterprise of research using linked data.

In this chapter, we study internally well-posed systems. An internally well-posed i/s/o system is a resolvable i/s/o system whose main operator is the generator of a C0 semigroup, and an internally well-posed s/s system is a s/s system that has at least one internally wellposed i/s/o representation. Most of the results that we present for these classes of i/s/o and s/s systems are based on the results on resolvable i/s/o and s/s systems presented in Chapters 11 and 12. Internally well-posed systems are uniquely solvable, but they need not have the continuation property, and in the time-domain study of these systems the notions of a classical trajectory is more important than the notion of a generalized or mild trajectory. Many of the basic transformations and interconnections of i/s/o and s/s systems discussed in earlier chapters have the property that they preserve internal well-posedness.

In this chapter, we continue the study of the resolvent set and the i/s/o resolvent matrix of an i/s/o node Σ begun in Chapter 5. In particular, we show that if Σ is resolvable, i.e., if Σ has a nonempty resolvent set ρ(Σ), then the main operator A of Σ is also resolvable and ρ(Σ) = ρ(A). Moreover, the i/s/o resolvent matrix is analytic and satisfies the i/s/o resolvent identity in ρ(Σ). Even more interesting is the converse claim: every i/s/o pseudoresolvent is a restriction of the i/s/o resolvent matrix of a unique i/s/o node Σ, where we by an i/s/o pseudo-resolvent mean a locally bounded block matrix operator-valued function that satisfies the i/s/o resolvent identity in some open subset Ω of C. In particular, every i/s/o pseudo-resolvent is analytic. Our class of regular resolvable i/s/o nodes is known from before in the literature with more complicated definitions and different names (e.g., in Staffans, 2005; systems that belong to this class are called “operator nodes”). At the end of this chapter, we continue the study of the connection between the characteristic bundles of a s/s system Σ and the i/s/o resolvent matrices of i/s/o representations of Σ and show that these characteristic bundles are analytic in ρ(Σ).

Chapter five describes the ethical framework regulating research using linked data and examines the applicable international ethics guidelines. A hypothetical research project is used to compare how these guidelines address the ethical assessment of research using linked data and in particular to compare how they address a waiver of consent and the extent to which they consider collective interests. The chapter goes on to discuss how the core ethical values of research merit and integrity, justice, beneficence, and respect can be reinterpreted to encompass the ethical concerns raised by research using linked data.