It is fair to say that international law has always considered its fundamental purpose to be the maintenance of international peace. Although ethical preoccupations stimulated its development and inform its growth, international law has historically been regarded by the international community primarily as a means to ensure the establishment and preservation of world peace and security. This chapter is concerned with the procedures available within the international order for the peaceful resolution of disputes and conflicts, except for judicial procedures covered elsewhere.

In this chapter we review probability and statistics. We define the ideas of probability, the probability density function, and the cumulative density function. We introduce Bayes’ theorem that relates prior, marginal, posterior, and conditional probability densities, which allows us to define the maximum a posterior and the maximum likelihood estimators. We discuss central moments of distributions. We review multivariate probability distributions including the correlated multivariate complex circularly symmetric Gaussian distributions. We also review a set of useful distributions, including Rayleigh, exponential, χ2, and Rician. Finally, we discuss random processes.

The rise of individual criminal responsibility directly under international law marks the coming together of elements of traditional international law with more modern approaches to human rights law and humanitarian law, and involves consideration of domestic as well as international enforcement mechanisms. Although the rights of individuals in international law have evolved significantly in the post-1945 era, the placing of obligations directly upon persons as opposed to states has a distinct, if narrow, pedigree. Those committing piracy or slave trading have long been regarded as guilty of crimes against international society bearing direct responsibility, for which they may be punished by international tribunals or by any state at all. Jurisdiction to hear the offence is not confined to, for example, the state on whose territory the act took place, or the national state of the offender or the victim. This universal jurisdiction over piracy constitutes a long-established principle of the world community. All states may both arrest and punish pirates, provided of course that they have been apprehended on the high seas or within the territory of the state concerned. The punishment of the offenders takes place whatever their nationality and wherever they happened to carry out their criminal activities.

The reader will probably be familiar with the notion of a real or complex vector space. In Galois theory we need to consider vector spaces over an arbitrary field 𝐾: we replace the field of scalars ℝ or ℂ by an arbitrary field 𝐾

The seas have historically performed two important functions: first, as a medium of communication; and, secondly, as a vast reservoir of resources, both living and non-living. Both of these functions have stimulated the development of legal rules. The fundamental principle governing the law of the sea is that ‘the land dominates the sea’ so that the land territorial situation constitutes the starting point for the determination of the maritime rights of a coastal state.

International law since the middle of the last century has been developing in many directions, as the complexities of life in the modern era have multiplied. For, as already emphasised, law reflects the conditions and cultural traditions of the society within which it operates. The community evolves a certain specific set of values – social, economic and political – and this stamps its mark on the legal framework which orders life in that environment. Similarly, international law is a product of its environment. It has developed in accordance with the prevailing notions of international relations and to survive it must be in harmony with the realities of the age.

It is generally accepted today that judicial review is the principal machinery through which courts exercise their constitutional function of controlling the executive. For many scholars it is the centrepiece of administrative law. But judicial review has not always occupied its present paramount position in administrative law. Since time immemorial, wrongful and illegal action by public officials could be challenged by means of an action for damages. In the famous eighteenth-century ‘General Warrant cases’, warrants issued by the Home Secretary to search premises, seize property and arrest those engaged in the publication of The North Briton, a paper published by John Wilkes, a well-known radical deemed dangerous by the authorities, were successfully challenged. Wilkes and his printers and publishers sued successfully for trespass to goods, trespass to land and false imprisonment; the warrants did not, as they should have done, specifically name the premises to be searched, the owners or the property to be seized. The judgments in which the officials were held liable still stand as landmarks in the vindication of civil liberties; they are routinely cited by modern courts which, as we shall see, are still hearing similar cases.

This chapter focuses on some major contract-type techniques of great importance in the changing landscape of law and administration. Their scale and diversity underwrite the zeal of the ‘contractual revolution’ in governance and with it the pervasive sense of experimentation. Once again practical problems of legal protection and of vindicating core values of transparency, accountability and participation (TAP) in the face of complex and policy-laden forms of contractual technique loom large. The design and workings of administrative procedure is typically a key piece in the jigsaw.

In this chapter, we consider how to map bits to a sequence of voltages or signal levels at complex baseband. We introduce the idea of a constellation, which defines a lattice of allowed baseband signaling voltages. We provide a discussion of modulation-specific capacities. We introduce the idea of pulse shaping that we use to reduce the spectral spread of our signals. We discuss channel estimation and compensation. We evaluate the raw bit error rate of BPSK and symbol error rates of QPSK modulations. We discuss demodulation and consider both hard decisions and soft decisions, which involves estimating likelihoods of possible symbols.