The restructuring and future of the British Rail system

The paper focuses mainly on reviewing and analysing the restructuring of Britain’s railways, including the re-cently published proposals for its future. The objective is to investigate the current market structure, the market behaviour and the overall performance of the British rail system over time. In order to learn what other people think about the problems of the industry and their solutions, interviews with key people associated with the in-dustry and several submissions of some key interest parties to the 2004 railway structure review are used in this paper. The results are that all major characteristics of the rail reform in Britain are seen as workable and empiri-cal data reveal that they have worked comparatively successfully, before Hatfield. Because of bad implementa-tion some of the features, and in particular the private infrastructure manager, have not worked well. Most of the problems have arisen because of indecision over refranchising and the disruption following Hatfield. Further-more the policy of the Government after Hatfield created an extremely risk averse culture within the industry, at a time when Railtrack had not enough insights about the state of the rail network. Although empirically unjustified, safety improvement became the main issue, costs escalated and reliability and productivity experienced a huge fall. The current White Paper “The Future of Rail” is seen as partially misleading and not at all detailed. At present it is only clear that the proposals will result in further increase of political interference. Much will depend on the precise implementation of the proposed measures and therefore the future of British rail remains unclear

An O(1)-Approximation for Minimum Spanning Tree Interdiction

Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is minimum spanning tree (MST) interdiction. Here, an undirected multigraph with nonnegative edge weights and positive interdiction costs on its edges is given, together with a positive budget B. The goal is to find a subset of edges R, whose total interdiction cost does not exceed B, such that removing R leads to a graph where the weight of an MST is as large as possible. Frederickson and Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction, where m is the number of edges. Since then, no further progress has been made regarding approximations, and the question whether MST interdiction admits an O(1)-approximation remained open. We answer this question in the affirmative, by presenting a 14-approximation that overcomes two main hurdles that hindered further progress so far. Moreover, based on a well-known 2-approximation for the metric traveling salesman problem (TSP), we show that our O(1)-approximation for MST interdiction implies an O(1)-approximation for a natural interdiction version of metric TSP

What is a Merciful Heart? Affective-Motivational Aspects of the Second Love Command

In this paper, I argue that Christ’s second love command implies not only that people’s volitions and actions be Christ-like, but also that their affective-motivational dispositions be Christ-like. More specifically, I argue that the command implies that people have aretaic obligations to strive to cultivate a merciful heart with the kind of affective depth described by St. Isaac of Syria in his 71st ascetical homily—i.e., one that is disposed to becoming inflamed, such that it is gripped by “strong and vehement mercy.

Matroidal Degree-Bounded Minimum Spanning Trees

We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical degree-constrained MST problem, where for every vertex v, a simple upper bound on the degree is imposed. Iterative rounding/relaxation algorithms became the tool of choice for degree-bounded network design problems. A cornerstone for this development was the work of Singh and Lau, who showed for the degree-bounded MST problem how to find a spanning tree violating each degree bound by at most one unit and with cost at most the cost of an optimal solution that respects the degree bounds. However, current iterative rounding approaches face several limits when dealing with more general degree constraints. In particular, when several constraints are imposed on the edges adjacent to a vertex v, as for example when a partition of the edges adjacent to v is given and only a fixed number of elements can be chosen out of each set of the partition, current approaches might violate each of the constraints by a constant, instead of violating all constraints together by at most a constant number of edges. Furthermore, it is also not clear how previous iterative rounding approaches can be used for degree constraints where some edges are in a super-constant number of constraints. We extend iterative rounding/relaxation approaches both on a conceptual level as well as aspects involving their analysis to address these limitations. This leads to an efficient algorithm for the degree-constrained MST problem where for every vertex v, the edges adjacent to v have to be independent in a given matroid. The algorithm returns a spanning tree T of cost at most OPT, such that for every vertex v, it suffices to remove at most 8 edges from T to satisfy the matroidal degree constraint at v

Results from the ICARUS T600 module - A measurement of the muon decay spectrum

We have studied the muon decay energy spectrum from a sample of stopping muon events acquired during the test run of the ICARUS T600 prototype. This detector allows the spatial reconstruction of the events with fine granularity, hence the precise measurement of the muon range and dE/dx with high sampling rate. This information is used to compute the correction factors needed for the calorimetric reconstruction. The Michel rho parameter is then measured by comparison of the experimental and Monte Carlo simulated muon decay spectra, obtaining rho = 0.72 +/- 0.06 (stat) +/- 0.08 (syst).Comment: 3 pages. Proceedings for the International Europhysics Conference on High Energy Physics EPS (July 17th-23rd 2003) in Aachen, German