A correction on Shiloach's algorithm for minimum linear arrangement of trees

More than 30 years ago, Shiloach published an algorithm to solve the minimum linear arrangement problem for undirected trees. Here we fix a small error in the original version of the algorithm and discuss its effect on subsequent literature. We also improve some aspects of the notation.Comment: A new introductory paragraph has been added; error solutions and notation improvements are discussed with more dept

The contribution of experts in care proceedings : evaluation of independent social work reports on care proceedings

Several concerns surround the use of independent social work (ISW) assessments in care proceedings. Some result from the exclusion of this work from a review of legal aid for expert assessments in this field, a cap on ISW fees, and fears about a resulting reduction in the availability of ISWs. At the same time, submissions to the Family Justice Review (FJR) claimed that ISWs cause delay, simply duplicate existing local authority assessments, add nothing new and undermine confidence in social work assessments. It was also said that ISW reports result from parents utilising human rights claims to gain a second opinion of a local authority assessment – and to which courts too readily accede. ... But while strong views have been expressed about the use of independent social work assessments, there is little hard evidence. This evaluation, commissioned following submissions to the FJR, begins to address that lack. It is based on 65 cases concerning 121 children and 82 reports for courts in England and Wales. The sample was drawn from the records of three independent agencies providing ISWs

Apollo Applications Program /AAP/ payload integration. General design plan. Technical study and analysis report

Design plan, experiments, and payload integration for Apollo applications progra

The sum of edge lengths in random linear arrangements

Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In spatial networks, the cost of a link depends on the edge length, i.e. the distance between the nodes that define the edge. Hypothesizing that there is pressure to reduce the length of the edges of a network requires a null model, e.g., a random layout of the vertices of the network. Here we investigate the properties of the distribution of the sum of edge lengths in random linear arrangement of vertices, that has many applications in different fields. A random linear arrangement consists of an ordering of the elements of the nodes of a network being all possible orderings equally likely. The distance between two vertices is one plus the number of intermediate vertices in the ordering. Compact formulae for the 1st and 2nd moments about zero as well as the variance of the sum of edge lengths are obtained for arbitrary graphs and trees. We also analyze the evolution of that variance in Erdos-Renyi graphs and its scaling in uniformly random trees. Various developments and applications for future research are suggested

Mediations of the Bible in Late Medieval England.

PhDDirect access to the Bible was the exception rather than the rule in medieval Europe. Limitations imposed by cost, sacrality and degrees of literacy determined people's ability to own or consult the Bible. The multitude of events and objects, which offered mediated access to the Bible, stand at the core of the dissertation. From liturgy and sermons to church murals and ornate Gospel Books, a mediated biblical world-view was presented to medieval audiences. A close analysis of these media reveals that, although relying on the Bible as a source of authority, its language and narrative were altered in an attempt to make it palatable and effective to medieval audiences. Analyses of specific test cases, such as Palm Sunday processions and Advent sermons, reveal a constant clerical effort of displaying the Bible and its narratives in visual, vernacular and performative ways. The Bible can never be divorced from its physical form and shape. Through an extensive survey of biblical manuscripts, their layout and additions, an inner-biblical hierarchy unfolds, in which the book of Psalms took precedence. This reflects not only the reception of the Psalms, but also the place of these manuscripts at the junction between preaching and liturgy. Attitudes towards biblical manuscripts, and especially gospel books, supply additional evidence for use and provenance of Bibles. An examination of veneration of the Bible in civic and ecclesiastical rituals, from the Ordinary of the Mass to oaths in courts of law, leads to a reevaluation of Bibles and gospel books. The dissertation leads to a new understanding of the Bible within the late medieval sacrede conomy. It shows how ritual behaviour, content and appearancew ere intertwined to present a complex notion of the Bible, which has endured until modernity

The contribution of experts in care proceedings : evaluation of independent social work reports on care proceedings

Several concerns surround the use of independent social work (ISW) assessments in care proceedings. Some result from the exclusion of this work from a review of legal aid for expert assessments in this field, a cap on ISW fees, and fears about a resulting reduction in the availability of ISWs. At the same time, submissions to the Family Justice Review (FJR) claimed that ISWs cause delay, simply duplicate existing local authority assessments, add nothing new and undermine confidence in social work assessments. It was also said that ISW reports result from parents utilising human rights claims to gain a second opinion of a local authority assessment ? and to which courts too readily accede. ... But while strong views have been expressed about the use of independent social work assessments, there is little hard evidence. This evaluation, commissioned following submissions to the FJR, begins to address that lack. It is based on 65 cases concerning 121 children and 82 reports for courts in England and Wales. The sample was drawn from the records of three independent agencies providing ISWs