We study active set methods for optimization problems in Block Angular Form (BAF). We begin by reviewing some standard basis factorizations, including Saunders' orthogonal factorization and updates for the simplex method that do not impose any restriction on the pivot sequence and maintain the basis factorization structured in BAF throughout the algorithm. We then suggest orthogonal factorization and updating procedures that allow coarse grain parallelization, pivot updates local to the affected blocks, and independent block reinversion. A simple parallel environment appropriate (...) to the description and complexity analysis of test procedures is defined in Section 5. The factorization and updating procedures are presented in Sections 6 and 7. Our update procedure outperforms conventional Updating procedures even in a purely sequential environment. (shrink)

The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of grid graphs.

The unique discourse of Confucian ritual practice encompasses a powerful and sophisticated way of talking about individual fulfillment within the context of more substantive or universal conceptions of the good life. To make this case, I will consider both the text of the "Analects" and the influential readings of the "Analects" offered by Fingarette in "Confucius: The Secular as Sacred" and by Hall and Ames in "Thinking through Confucius". Though the two interpretive works are helpful in articulating the classical Confucian (...) contribution to the problem of balancing conformity and individuality, I will argue that an alternative reading is required to appreciate fully how values thought to embody and express the fullest humanity might be inculcated in ethical agents without undoing their individuality. Such an alternative is developed here. (shrink)

SummaryThe Admonition Controversy, largely between Thomas Cartwright and John Whitgift has proven fecund ground for intellectual historians analysing the religious dimension to early-modern political ideas. This paper argues that the religious dimension of Cartwright's mixed constitutionalism needs better explanation, rather than just noting that his ecclesiastical mixed constitutionalism mirrors his political mixed constitutionalism. This paper tracks Cartwright's progressive, dialogical unfolding of his mixed constitutionalism in response to Whitgift's attempt to derive episcopacy from the fact of English monarchy, effectively discrediting the (...) Admonition to Parliament. Furthermore, the essay outlines how the Cartwright–Whitgift debate led Cartwright to emphasise a parliamentarist mixed constitution when most of his contemporaries, especially the more famous mixed constitutionalist, Thomas Smith, portrayed the English parliament leaning noticeably towards the monarch. This analysis accepts that religious polemic was a major driving force in the normalisation of parliamentarism, yet seeks to show exactly how this worked out in one of the most important church–state disputes in Elizabethan England. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the identification of the continuity condition (...) necessary for the revelation of linear utility. (shrink)

The incompleteness of the task of integrating the influences made upon Jonathan Edwards by Calvinism and the moral sense leaves open a great many questions central to identifying his ethical position with any detail. This should worry ethicists, theologians, and church historians alike. For the puzzle of what Edwards meant by virtue is at the heart not only of his ethics but of a great many strands of his thought. It must be pieced together from diverse sources; and there are (...) multiple meanings to be sifted through. But it is nevertheless possible to bring the concepts made available by the diverse moral traditions upon which Edwards drew into a generally coherent counterpoise. Such a counterpoise is not merely of antiquarian interest. Lacking a precise account of Edwards's ethical position, it is awkward to talk about applying it to the problems of the twenty-first, or any, century. (shrink)

Clearchus of Soloi, a junior colleague of Aristotle's, devoted a work in at least two books to the topic of eros. Like most of what survives from his once substantial corpus, the remains of this work display wide learning, especially in history and literature, and a moralizing orientation. The work did not circulate widely; all that survives is a handful of passages in Athenaeus (frs. 21-35 Wehrli), most very brief. That is far too little to permit any reconstruction of its (...) overall structure or scope. But some of its interests and themes can be recovered. Clearchus discussed love, especially between the sexes, with more sympathy and subtlety than previous scholarship has recognized. His work on eros also appears to have been largely in tune with trends in early Hellenistic poetry. (shrink)

In Book IX of the Nicomachean Ethics, Aristotle discusses the motivating psychology of the benefactor. He finds that self-love is the crucial element of consciousness that accounts for the benefactor’s desire to participate constructively in the community of being. His analysis invites comparison with Aquinas’s treatment of the theological virtue of caritas. Similarities are found, but Aquinas’s approach leads to a discussion of divine beatitude where we find a somewhat surprising analogy between Aristotle’s human and Aquinas’s divine benefactor. For Aquinas (...) finds that divine beatitude is also a self-love flowing outward to the divine creative project. (shrink)

This paper presents a concept for using robots as part of a design strategy that encourages a ‘bottom-up’ approach to environmental control. Robot friendly environments within the building enclosure are proposed and an analogy is made to natural ‘ecosystems’. Detail design issues are discussed, including the relationships that might occur between robots, building users and maintenance engineers. The concept is speculative in that it presents some of the implications of a mode of actuation that is radically different from the usual.

Drawing on Protestant scholasticism, Puritan "precisionism," and virtue ethics, "Virtue Reformed" offers a comprehensive rereading of the ethical position of ...