Decorous lower bounds for minimum linear arrangement

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this paper, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances

Hegel’s absolute: A monistic interpretation

It is the intention of this thesis to propose a monistic interpretation of Hegel's theological system, and to analyse the mechanics of this structure with particular emphasis on Hegel's use of dialectic and the manner in which the historical, phenomenal world subsists within the monistic framework proposed, Thus, it is a thesis which concentrates largely on interpretation rather than evaluation, and the majority of its critical analysis will focus on alternative understanding's of Hegel’s theology rather than the theology itself. Owing to limitations imposed on the length of the thesis, I have reluctantly had to omit many important aspects of Hegel's theology, most notably the Trinity, creation, and the Fall. I have instead selected issues which I feel most cover the workings of the system, and how these workings effect an immanent deity. Broadly speaking, the thesis moves from an exposition of the triadic structure, to the role and status of the phenomenal world, and it concludes by discussing how Hegel views God’s being vis-a-vis time and history. I have also included a section on Hegel's ontological argument as a means of cementing his theology as a plausible proposition. The majority of primary text material is taken from Hegel's Logic and Lectures on the Philosophy of Religion. In terms of his development, I have therefore tried to confine the exposition to his latter period when in Berlin (c.1824-31), and the translation of the Logic is of the third editon of 1830

Off-leash dog parks: Not just for dogs

This project examines dog owners’ and non dog owners’ use of an off-leash urban dog park to learn how such public space is used and by whom. As cities densify, the challenges of defining public and private space and of ensuring space for all users will intensify. Given these limitations, why should public land be devoted to dogs and their owners? This ethnographically based project contributes to answering that question by observing and analyzing the role off-leash dog parks play in facilitating social interactions between dogs, dog owners, and others. While the role of urban parks in facilitating such interactions has been widely researched and positively reported upon, the social role and usage of off-leash dog parks has been less studied. Off-leash dog parks, as a particular type of setting, provide a distinctive venue in which dog owners, dogs, and other visitors may shape varied yet satisfying interactions