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This article identifies a potential authorial signature in the opening lines of Lucan’s Bellum Ciuile. The adjacent letters LVCAN appear in a central position of emphasis in the poem’s first two lines and constitute the core of a signature that can be extended in multiple directions to form longer intexts such as LVCANI SVM (‘I am Lucan’s’), LV(canus) AN(naeus) M(arcus), LVCANI MVSIS (‘with the Muses of Lucan’) and LVCANI M. VIS CERA DEXTRA (‘the power of M. Lucanus with his right hand on the wax’, or ‘the power of M. Lucanus on the wax on the right-hand side’). The article proposes that this multiform signature is accompanied by signposts to help identify it and that it engages with models of such wordplay in Aratus, Lucretius, Virgil and Ovid.
This chapter considers the law of treaties in the light primarily of the key Vienna Convention on the Law of Treaties, 1969, much of which is considered as part of customary law. The chapter discusses the role and nature of international treaties in the light of their binding nature upon states parties (pacta sunt servanda). The making of treaties, from the formalities and methods of consent from signature to ratification, is covered before the chapter turns to reservations. The nature of reservations and their effect upon third parties is addressed is addressed as is the process of amendment of treaties. Consideration of treaty interpretation then follows with the various methodologies examined from the textual, intention and object, and purpose of the treaty points of view, with a careful look at case law. The particular position of human rights treaties in this process is noted. The chapter then turns to the invalidity, termination and suspension of treaties, including a discussion of the concepts of peremptory norms (jus cogens), material breach, supervening impossibility of performance and fundamental change of circumstances (rebus sic stantibus).
In this work, by considering coherent systems comprising independent components with discrete lifetimes, we introduce the notion of discrete-time signature and then discuss some of its properties. With the use of the introduced signature, a stochastic ordering result is also established. We then introduce transformation formulas for the discrete-time signature to facilitate the comparison of systems of different sizes. Some examples are also presented to illustrate all the results developed here.
We determine the list of automorphism groups for smooth plane septic curves over an algebraically closed field $K$ of characteristic $0$, as well as their signatures. For each group, we also provide a geometrically complete family over$K$, which consists of a generic defining polynomial equation describing each locus up to $K$-projective equivalence. Notably, we present two distinct examples of what we refer to as final strata of smooth plane curves.
Motivated by insurance applications, we propose a new approach for the validation of real-world economic scenarios. This approach is based on the statistical test developed by Chevyrev and Oberhauser ((2022) Journal of Machine Learning Research, 23(176), 1–42.) and relies on the notions of signature and maximum mean distance. This test allows to check whether two samples of stochastic processes paths come from the same distribution. Our contribution is to apply this test to a variety of stochastic processes exhibiting different pathwise properties (Hölder regularity, autocorrelation, and regime switches) and which are relevant for the modelling of stock prices and stock volatility as well as of inflation in view of actuarial applications.
Before the 20th century, most rules of international law were in the form of customary international law. Since then, the increased complexity of international relations and rapid international development have led to a substantial growth in the number and diversity of treaties. Article 38(1)(a) of the Statute of the International Court of Justice (‘ICJ Statute’) recognises treaties as a (material) source of international law by referring to ‘international conventions, whether general or particular, establishing rules expressly recognized by the contesting states’. Treaties now regulate trade, communications, environmental protection, military cooperation and defence, and human rights, to name but a few of the myriad topics. International environmental law, for example, is almost entirely governed by treaties, and international trade, investment and communications ‘are unimaginable without treaties’. The main rules in the law of treaties are contained in the 1969 Vienna Convention on the Law of Treaties (‘VCLT’), which governs treaty relations between states and is the focus of this chapter.
This new edition of a textbook first published in 2000 provides a comprehensive account of the law of treaties from the viewpoint of two experienced practitioners. It draws on the combined experience of Anthony Aust, the original author, and Jeremy Hill, until recently Legal Counsellor in the Foreign, Commonwealth and Development Office, London. The book provides a wealth of examples of the problems experienced with treaties on a daily basis. The authors explore numerous precedents from treaties and other related documents, such as non-legally binding instruments. Using clear and accessible language, the authors cover the full extent of treaty law, with both practitioners and students in mind. Modern Treaty Law and Practice is essential reading for officials in governments and international organisations, lawyers practising in international law, and teachers and students of law, political science, international relations and diplomacy who have an interest in treaties.
This chapter examines how a state becomes a party to a treaty, including signature, initialling and ratification, where applicable. Whether a state can participate in a multilateral treaty depends on the terms of the treaty. The practice of the Council of Europe is examined. Signature may express consent to be bound but often signature will be subject to ratification. Ratification is the international act whereby a state establishes on the international plane its consent to be bound. It is to be distinguished from the domestic process which enables a state to ratify. Advice is given on the form and content of an instrument of ratification. A state may also consent to be bound by acceptance, approval or accession. Accession is primarily the means by which a state may become a party if it is unable to sign the treaty. The chapter also examines rights and obligations prior to entry into force, the possibility of withdrawing consent to be bound, and the ways in which treaties might be developed.
In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.
We discuss several versions of the Family Signature Theorem: in rational cohomology using ideas of Meyer, in $KO[\tfrac {1}{2}]$-theory using ideas of Sullivan, and finally in symmetric $L$-theory using ideas of Ranicki. Employing recent developments in Grothendieck–Witt theory, we give a quite complete analysis of the resulting invariants. As an application we prove that the signature is multiplicative modulo 4 for fibrations of oriented Poincaré complexes, generalizing a result of Hambleton, Korzeniewski and Ranicki, and discuss the multiplicativity of the de Rham invariant.
In this chapter, we will discuss the (infinite-dimensional) geometric framework for rough paths and their signature. Rough path theory originated in the 1990s with the work of T. Lyons. It seeks to establish a theory of integrals and differential equations driven by rough signals. For example, one is interested in controlled ordinary differential equations driven by a rough signal. Here, a rough signal is a Hölder continuous path of potentially low Hölder regularity. Numerical methods for equations with more regularity suggest that iterated integrals of the rough signal against itself are needed to construct solutions. However due to Youngs theorem, these iterated integrals do not exist. To compensate this problem, the notion of a rough path was developed. After a qucik introduction to the theory of rough paths, we shall see that rough paths of various flavours can be understood as certain continuous paths taking values in infinite-dimensional Lie groups. The main focus of the chapter is to present an introduction to this geometric side of the theory.
The chapter considers the range of features that enable investigators to describe a killing as ‘sexual’, such as clothes removed, objects inserted into the body and presence of seminal fluids on the body. Some killing done in association with sexual behaviour is not motivated by lust. For example, it might represent an attempt to avoid capture following a sexual assault or the accidental result of choking. Some killers reach orgasm from simply cutting a victim, while others (e.g. David Berkowitz) are sexually aroused by shooting a courting couple. The chapter describes a number of common features of a ‘composite killer’, such as cruelty to animals and voyeurism. Various ruses might be used in order to get a victim in the situation where he or she can be killed, such as offering a lift or seeking help. However, the most common method appears to be to engage the services of a sex worker.
We know a lot about Jack the Ripper’s crimes, but have no idea as to who he was. His crimes had a sexual character, and his dislike of women could be because he caught venereal disease from one. He targeted, amongst other regions, the women’s sex organs. We don’t know the identity of the Zodiac Killer, who targeted courting couples. It is likely that he felt envy towards them. Although Albert DeSalvo was widely believed to be the ‘Boston Strangler’, not everyone is in agreement about this and he was not found guilty of these crimes. However, his toxic upbringing and his characteristics of offending fit the pattern of other known serial killers. He showed evidence of dissociation. DNA evidence points to his involvement in at least one of the murders. A perspective of motivation might cast some light on these cases.
Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components.
Katie Mitchell has been directing opera since 1996, when she debuted on the operatic stage with Mozart and Da Ponte’s Don Giovanni at the Welsh National Opera. Since then, she has directed more than twenty-nine operas in major opera houses around the world. Mitchell here speaks of her directorial approach when working with the genre, addressing various aspects of interest for those who want a better grasp of the dynamics of opera-making in the twenty-first century. Ranging from the director’s imprint, or signature on the work they put on the stage, to the relationships forged with people running opera institutions, Mitchell reflects on her experiences when staging opera productions. She sheds light on some fundamental differences between theatre-making and opera production, including the issue of text – the libretto, the dramatic text, and the musical score – and the very basic fact that in opera a director is working with singers, that is, with musicians whose attitude and behaviour on stage is necessarily different from that of actors in the theatre. Running throughout the conversation is Mitchell’s commitment to ensure that young and contemporary audiences do not see opera as a museum artefact but as a living performative experience that resonates with the aesthetics and political imperatives of our contemporary world. She speaks of the uncompromising political imperatives that remain central to her work ethic, even if this means deserting a project before it starts, and reflects on her long-term working relations with opera institutions that are open to new and alternative approaches to opera-making strategies. Mitchell underlines her respect for the specific rules of an art form that, because of its collaborative nature, must allow more space for theatre-makers to venture within its complex performative paths if it wants to secure a place in the future. Mario Frendo is Senior Lecturer of Theatre and Performance and Head of the Department of Theatre Studies at the School of Performing Arts, University of Malta, where he is the director of CaP, a research group focusing on the links between culture and performance.
This chapter studies Anna May Wong’s active construction of her international star/celebrity status through “greetings” to the world. My goal is to understand how she mobilized such “greetings” to retool the film and media apparatus into an empowering relation-building vehicle. I argue that her relation-building stems from multi-registered audience address in her “greetings,” which elicit divergent responses depending on the viewers’ lingua-cultural knowledge and sociopolitical consciousness. I dwell on two categories of “greetings”: scriptural “greetings” as illustrated in her signature in gifted photos, in Piccadilly (dir. E. A. Dupont 1929) and in a lithographic visual map showing the European cities she performed in from 1933 to 1934; and performative “greetings” as seen in her reiterative dialect performances in Hollywood on Parade A-3 (June 5, 1932) and the “China Mary” episode of an ABC Western TV show, The Life and Legend of Wyatt Earp (aired on March 15, 1960). Methodologically, I depart from simply tracing Wong’s empirical reception to develop strategies of taking cues from Wong’s “greetings” so as to reactivate and parse out her ability to speak to audiences of disparate stances across history. This alternative lineage of performer-spectator dynamic deconstructs the race-gender ideology underpinning mainstream film and media, and harbingers a more self-reflexive interstitial identitarian position.
In this chapter, I begin by covering the legal definitional differences between treaty signature and treaty ratification. I discuss the two-step legal nature of signing and ratifying international treaty law and present an argument of when and why signature is important. I posit that states confronting domestic legislative barriers to ratification place an importance on the act of signature, as it is easier for these states to sign than it is to ratify. I examine the case of the United States and the historic hurdles confronted ratifying human rights law. Then, I statistically test the effect of signing human rights treaties on human rights behavior on the ICCPR and CEDAW treaties. I find that for states confronting domestic legislative barriers to ratification, signature is a significant indicator of improved human rights. This finding does not hold for states without such barriers.
In this chapter, I introduce the central claim of the manuscript – that the different types of treaty commitment need to be analyzed and considered as distinct when generating expectations of human rights behavior. The legal paths that states take concerning commitment to human rights treaties are consequential for how they engage with the law and human rights behavior. The chapter devotes attention to fine descriptive data analytics demonstrating a variety of differences across the four commitment actions.
International treaties are the primary means for codifying global human rights standards. However, nation-states are able to make their own choices in how to legally commit to human rights treaties. A state commits to a treaty through four commitment acts: signature, ratification, accession, and succession. These acts signify diverging legal paths with distinct contexts and mechanisms for rights change reflecting legalization, negotiation, sovereignty, and domestic constraints. How a state moves through these actions determines how, when, and to what extent it will comply with the human rights treaties it commits to. Using legal, archival, and quantitative analysis this important book shows that disentangling legal paths to commitment reveals distinct and significant compliance outcomes. Legal context matters for human rights and has important implications for the conceptualization of treaty commitment, the consideration of non-binding commitment, and an optimistic outlook for the impact of human rights treaties.
Providing optimal strategies for maintaining technical systems in good working condition is an important goal in reliability engineering. The main aim of this paper is to propose some optimal maintenance policies for coherent systems based on some partial information about the status of components in the system. For this purpose, in the first part of the paper, we propose two criteria under which we compute the probability of the number of failed components in a coherent system with independent and identically distributed components. The first proposed criterion utilizes partial information about the status of the components with a single inspection of the system, and the second one uses partial information about the status of component failure under double monitoring of the system. In the computation of both criteria, we use the notion of the signature vector associated with the system. Some stochastic comparisons between two coherent systems have been made based on the proposed concepts. Then, by imposing some cost functions, we introduce new approaches to the optimal corrective and preventive maintenance of coherent systems. To illustrate the results, some examples are examined numerically and graphically.