Generalised golden ratios over integer alphabets

It is a well known result that for β ∈ (1,1+√52) and x ∈ (0,1β−1) there exists uncountably many (ǫi)∞i=1 ∈ {0,1}N such that x = P∞i=1ǫiβ−i. When β ∈ (1+√52,2] there exists x ∈ (0,1β−1) for which there exists a unique (ǫi)∞i=1 ∈ {0,1}N such that x=P∞i=1ǫiβ−i. In this paper we consider the more general case when our sequences are elements of {0, . . . , m}N. We show that an analogue of the golden ratio exists and give an explicit formula for it.

The Golden Age returns: Virgil's fourth Eclogue in the political panegyric of the Italian courts

E. H. Gombrich and others have analysed the uses made of language and imagery from Virgil's famous fourth Eclogue in panegyrical writing by partisans of the Medici dynasty in Florence. This study examines the appropriation of the theme of the returning Golden Age and related motifs from the fourth Eclogue in other Italian courts during the same period, by supporters of the Visconti and Sforza of Milan, the Gonzaga of Mantua, Leonello d'Este and his successors in Ferrara, and the Bentivoglio of Bologna, among others. The deployment of this Virgilian material in political panegyric is seen to be a central element in the self-definition and self-promotion of dynastic rulers throughout the peninsula.

The foundations of the rule of law

Formal conceptions of the rule of law are popular among contemporary legal philosophers. Nonetheless, the coherence of accounts of the rule of law committed to these conceptions is sometimes fractured by elements harkening back to substantive conceptions of the rule of law. I suggest that this may be because at its origins the ideal of the rule of law was substantive through and through. I also argue that those origins are older than is generally supposed. Most authors tend to trace the ideas of the rule of law and natural law back to classical Greece, but I show that they are already recognisable and intertwined as far back as Homer. Because the founding moment of the tradition of western intellectual reflection on the rule of law placed concerns about substantive justice at the centre of the rule of law ideal, it may be hard for this ideal to entirely shrug off its substantive content. It may be undesirable, too, given the rhetorical power of appeals to the rule of law. The rule of law means something quite radical in Homer; this meaning may provide a source of normative inspiration for contemporary reflections about the rule of law.

Towards expressive rule induction on IP network event streams

In order to gain insights into events and issues that may cause errors and outages in parts of IP networks, intelligent methods that capture and express causal relationships online (in real-time) are needed. Whereas generalised rule induction has been explored for non-streaming data applications, its application and adaptation on streaming data is mostly undeveloped or based on periodic and ad-hoc training with batch algorithms. Some association rule mining approaches for streaming data do exist, however, they can only express binary causal relationships. This paper presents the ongoing work on Online Generalised Rule Induction (OGRI) in order to create expressive and adaptive rule sets real-time that can be applied to a broad range of applications, including network telemetry data streams.

Pension scheme redesign and wealth redistribution between the members and sponsor: the USS rule change in October 2011

The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs.

The rise of the Golden Dawn in Greece

This report focuses on the rise of the Golden Dawn in the context of economic, social and political crisis, as well as the fascist character of the party.