Unifying scheme for generating discrete integrable systems including inhomogeneous and hybrid models

A unifying scheme based on an ancestor model is proposed for generating a wide range of integrable discrete and continuum as well as inhomogeneous and hybrid models. They include in particular discrete versions of sine-Gordon, Landau-Lifshitz, nonlinear Schr\"odinger (NLS), derivative NLS equations, Liouville model, (non-)relativistic Toda chain, Ablowitz-Ladik model etc. Our scheme introduces the possibility of building a novel class of integrable hybrid systems including multi-component models like massive Thirring, discrete self trapping, two-mode derivative NLS by combining different descendant models. We also construct inhomogeneous systems like Gaudin model including new ones like variable mass sine-Gordon, variable coefficient NLS, Ablowitz-Ladik, Toda chains etc. keeping their flows isospectral, as opposed to the standard approach. All our models are generated from the same ancestor Lax operator (or its q -> 1 limit) and satisfy the classical Yang-Baxter equation sharing the same r-matrix. This reveals an inherent universality in these diverse systems, which become explicit at their action-angle level.Comment: Latex, 20 pages, 2 figures, v3, final version to be published in J. Math Phy

Three Optimisations for Sharing

In order to improve precision and efficiency sharing analysis should track both freeness and linearity. The abstract unification algorithms for these combined domains are suboptimal, hence there is scope for improving precision. This paper proposes three optimisations for tracing sharing in combination with freeness and linearity. A novel connection between equations and sharing abstractions is used to establish correctness of these optimisations even in the presence of rational trees. A method for pruning intermediate sharing abstractions to improve efficiency is also proposed. The optimisations are lightweight and therefore some, if not all, of these optimisations will be of interest to the implementor.Comment: To appear in Theiry and Practice of Logic Programmin

Sharing of Unlicensed Spectrum by Strategic Operators

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of spectrum which anyone can use for free without having to obtain a license. Major standards bodies are currently considering a proposal to retool and deploy Long Term Evolution (LTE) technologies in unlicensed bands below 6 GHz. This paper studies the fundamental questions of whether and how the unlicensed spectrum can be shared by intrinsically strategic operators without suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme which allows dynamic spectrum borrowing and lending between operators is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results to the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.Comment: To appear in the IEEE Journal on Selected Areas in Communications, Special Issue on Game Theory for Network

Communitarian perspectives on social enterprise

Concepts of social enterprise have been debated repeatedly, and continue to cause confusion. In this paper, a meta-theoretical framework is developed through discussion of individualist and communitarian philosophy. Philosophers from both traditions build social theories that emphasise either consensus (a unitarist outlook) or diversity (a pluralist outlook). The various discourses in corporate governance reflect these assumptions and create four distinct approaches that impact on the relationship between capital and labour. In rejecting the traditional discourse of private enterprise, social enterprises have adopted other approaches to tackle social exclusion, each derived from different underlying beliefs about the purpose of enterprise and the nature of governance. The theoretical framework offers a way to understand the diversity found within the sector, including the newly constituted Community Interest Company (CIC).</p

Why the idea of framework propositions cannot contribute to an understanding of delusions

One of the tasks that recent philosophy of psychiatry has taken upon itself is to extend the range of understanding to some of those aspects of psychopathology that Jaspers deemed beyond its limits. Given the fundamental difficulties of offering a literal interpretation of the contents of primary delusions, a number of alternative strategies have been put forward including regarding them as abnormal versions of framework propositions described by Wittgenstein in On Certainty. But although framework propositions share some of the apparent epistemic features of primary delusions, their role in partially constituting the sense of inquiry rules out their role in helping to understand delusions

Declaration on Religious Freedom: Three Developmental Aspects

This article considers key aspects of the Vatican II declaration on religious freedom Dignitatis Humanae and John Courtney Murray’s role in its formulation. This will be done with concern for the broader theological context as exemplified in Thomas Aquinas. After a brief outline of the difficulties Murray faced and their resolution, the discussion moves in four stages: a summary of the key ideas in the document on the relationship between truth and freedom from which the following three ideas receive a focus; the person (dignity and conscience); rights and their evolving context; historical consciousness and its role as a mode and locus of theological reflection. Here, a suggestion is offered about the interrelationship of speculative and practical reason in doctrinal development