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Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.
Among the foundational projects in the study of childhood and culture is the “Six Cultures” survey from the late 1960s. Observational data were collected to map children’s daily activity in six village/small town settings around the world. Only in the single US middle-class community of “Orchard Town” were children not routinely engaged in chores (Whiting and Whiting 1975: 84). Nowhere are the gerontocracy and neontocracy perspectives further apart than on the issue of work.2 Indeed, “the dissociation of childhood from the performance of valued work is considered a yardstick of modernity” (Nieuwenhuys 1996: 237). While we hamstring our children to keep them from working, fearing their loss of innocence and studiousness, the norm elsewhere is to open the pathway to adulthood.
When international organizations were first established in the nineteenth century, they were largely seen as self-contained entities, performing functions for their member states but not much else. What was relevant was the set-up of each and every individual organization; nothing more, nothing less. The idea of such organizations entering into arrangements with other organizations, or even with third states, was for a long time considered anathema.
The growth and development of the United Nations as the major universal organisation has been accompanied by a no less dramatic increase in the number and range of organisations with membership drawn from the states of a particular region. Such regional organisations frequently become involved in the resolution of disputes.1 Sometimes this is because dispute settlement has been defined as a goal of the organisation. Article 4(e) of the Constitutive Act of the African Union, for example, lays down as one of its aims the peaceful resolution of conflicts between member states, and similar provisions can be found in the constitutions of other organisations. But even organisations whose primary concern is with matters of no present relevance may find themselves involved in some form of settlement activity. For bringing states together in an institutional setting provides the parties to a dispute with an opportunity to settle their differences and regional neighbours with the chance to add their encouragement, assistance and pressure as an incentive.
The present chapter, and the two that follow, will largely address the position of international organizations vis-à-vis the outside world, discussing three broad issues. First, this chapter will be devoted to whether organizations can conclude treaties, and on what basis. The next chapter will discuss with whom they enter into relations, and the subsequent chapter will analyse what will (or may) happen if something goes wrong in relations between an international organization and some other actor.
In Chapter 2 we saw that a computer performs computation by processing instructions. A computer instruction set must include a variety of features to achieve flexible programmability, including varied arithmetic and logic operations, conditional computation, and application-defined data structures. As a result, the execution of each instruction requires a number of steps: instruction fetch and decode, arithmetic or logic computation, read or write memory, and determination of the next instruction. The instruction set definition is a contract between software and hardware, the fundamental software–hardware interface, that enables software to be portable. After portability, the next critical attribute is performance, so computer hardware is designed to execute instructions as fast as possible.
An oft-heard complaint about the UN is that it does not deliver what it promises. The organization carries the promise of universal peace and security, but sometimes fails to show up in crisis situations, or shows up too late, or does too little. One of the standard replies on the part of the organization is that it lacks the funds, and could do a lot more if only its member states would pay their contributions, and would pay them on time and in good order. And that, in turn, signifies that, however esoteric the topic may seem, the financing of international organizations is of the utmost practical relevance. As Singer put it in the early 1960s: ‘Until the policy decisions of the various organs are translated into budget items, there is no visiting mission to encourage Togoland’s movement toward eventual self-government, no ceasefire observer in the Middle East, no rehabilitation commission in South Korea, and no Public Administration advisor in Santiago.’1
Memory is a critical part of computing systems. In the organization of computers and the programming model, memory was first separated logically from the computing (CPU) part, and then later physically. This separation of CPU and memory in a structure known as the von Neumann architecture was covered in Chapter 2 and is illustrated in Figure 5.1.
The eclectic character of the method is at once apparent. The Conciliation Commission in the ‘Timor Sea Conciliation’ explained that conciliation ‘seeks to combine the function of a mediator with the more active and objective role of a commission of inquiry’.2 If mediation is essentially an extension of negotiation, conciliation puts third-party intervention on a formal legal footing and institutionalises it in a way comparable, but not identical, to inquiry or arbitration. For the fact-finding exercise that is the essence of inquiry may or may not be an important element in conciliation, while the search for terms ‘susceptible of being accepted’ by the parties, but not binding on them, provides a sharp contrast with arbitration and a reminder of the link between conciliation and mediation.
When the parties to an international dispute are unable to resolve it by negotiation, the intervention of a third party is a possible means of breaking the impasse and producing an acceptable solution. Such intervention can take a number of different forms. The third party may simply encourage the disputing states to resume negotiations, or do nothing more than provide them with an additional channel of communication. In these situations, the intermediary is said to be contributing ‘good offices’. On the other hand, the assignment may be to investigate the dispute and to present the parties with a set of formal proposals for its solution. As we shall see in Chapter 5, this form of intervention is called ‘conciliation’. Between good offices and conciliation lies the form of third-party activity known as ‘mediation’.1
While international organizations are generally created for longer periods of time, indeed usually even without any definite time period in mind,1 not all of them manage to survive indefinitely. Some simply disappear without being succeeded to in any way; prime examples are the Warsaw Pact and Comecon, both of which were dismantled after the fall of communism and the dissolution of the Soviet Union. On 26 June 1991, a ministerial meeting of Comecon members decided to dissolve the organization; the Warsaw Pact was disbanded at a meeting of its Political Consultative Committee in Prague on 1 July 1991.2
The constituent documents of international organizations are strange creatures, often said to occupy a special place in international law. On the one hand, they are treaties,1 concluded between duly authorized representatives of states, and as such no different from other treaties.2 Thus, one would expect, they are simply subject to the general law of treaties.