A duality between small-face problems in arrangements of lines and Heilbronn-type problems

AbstractArrangements of lines in the plane and algorithms for computing extreme features of arrangements are a major topic in computational geometry. Theoretical bounds on the size of these features are also of great interest. Heilbronn's triangle problem is one of the famous problems in discrete geometry. In this paper we show a duality between extreme (small) face problems in line arrangements (bounded in the unit square) and Heilbronn-type problems. We obtain lower and upper combinatorial bounds (some are tight) for some of these problems

Knowledge and Civil Society

This open access book focuses on the role of civil society in the creation, dissemination, and interpretation of knowledge in geographical contexts. It offers original, interdisciplinary and counterintuitive perspectives on civil society. The book includes reflections on civil and uncivil society, the role of civil society as a change agent, and on civil society perspectives of undone science. Conceptual approaches go beyond the tripartite division of public, private and civic sectors to propose new frameworks of civic networks and philanthropic fields, which take an inclusive view of the connectivity of civic agency across sectors. This includes relational analyses of epistemic power in civic knowledge networks as well as of regional giving and philanthropy. The original empirical case studies examine traditional forms of civic engagement, such as the German landwomen’s associations, as well as novel types of organizations, such as giving circles and time banks in their geographical context. The book also offers insider reflections on doing civil society, such as the cases of the Umbrella Movement in Hong Kong, epistemic activism in the United States, and the #FeesMustFall movement in South Africa

Knowledge and Civil Society

This open access book focuses on the role of civil society in the creation, dissemination, and interpretation of knowledge in geographical contexts. It offers original, interdisciplinary and counterintuitive perspectives on civil society. The book includes reflections on civil and uncivil society, the role of civil society as a change agent, and on civil society perspectives of undone science. Conceptual approaches go beyond the tripartite division of public, private and civic sectors to propose new frameworks of civic networks and philanthropic fields, which take an inclusive view of the connectivity of civic agency across sectors. This includes relational analyses of epistemic power in civic knowledge networks as well as of regional giving and philanthropy. The original empirical case studies examine traditional forms of civic engagement, such as the German landwomen’s associations, as well as novel types of organizations, such as giving circles and time banks in their geographical context. The book also offers insider reflections on doing civil society, such as the cases of the Umbrella Movement in Hong Kong, epistemic activism in the United States, and the #FeesMustFall movement in South Africa

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Characterisation of Spherical Splits

We investigate the properties of collections of linear bipartitions of points embedded into $\R^3$, which we call collections of affine splits. Our main concern is characterising the collections generated when the points are embedded into $S^2$; that is, when the collection of splits is spherical. We find that maximal systems of splits occur for points embedded in general position or general position in $S^2$ for affine and spherical splits, respectively. Furthermore, we explore the connection of such systems with oriented matroids and show that a maximal collection of spherical splits map to the topes of a uniform, acyclic oriented matroid of rank 4, which is a uniform matroid polytope. Additionally, we introduce the graphs associated with collections of splits and show that maximal collections of spherical splits induce maximal planar graphs and, hence, the simplicial 3-polytopes. Finally, we introduce some methodologies for generating either the hyperplanes corresponding to a split system on an arbitrary embedding of points through a linear programming approach or generating the polytope given an abstract system of splits by utilising the properties of matroid polytopes. Establishing a solid theory for understanding spherical split systems provides a basis for not only combinatorial–geometric investigations, but also the development of bioinformatic tools for investigating non-tree-like evolutionary histories in a three-dimensional manner

Education policy: process, themes and impact

Education policy is high on the agenda of governments across the world as global pressures focus increasing attention on the outcomes of education policy and on the implications for economic prosperity and social citizenship. However, there is often an underdeveloped understanding of how education policy is formed, what drives it and how it impacts on schools and colleges. Education Policy: Process, Themes and Impact makes these connections and links them to the wider challenges of educational leadership in a contemporary context

Nuremberg’s Noble Servant. Werner von Parsberg (d. 1455) between Town and Nobility in Late Medieval Germany

The nobleman Werner von Parsberg served the imperial town of Nuremberg between 1430 and his death in 1455 as a mounted retainer and (from 1442) as the town’s imperial chief magistrate. In 1450 he carried Nuremberg’s standard in battle during the Second South German Towns’ War. This long record of close engagement with Nuremberg contrasts with the tradition of reading ‘town’ and ‘nobility’ in Germany as mutually exclusive and inherently antagonistic. In Parsberg’s time this was a position advocated by Nuremberg’s opponents amongst the territorial princes and rural nobility, and from the Enlightenment onwards a more rigid version of this dichotomy was projected back onto the late Middle Ages. This perceived opposition between ‘town’ and ‘nobility’ denied the possibility of meaningful cooperation between townspeople and rural nobles: all such relationships have consequently been described as the result of economic and political weakness on the part of the nobles concerned. Recent research, however, suggests that a re-examination of these relationships is necessary, and the case of Werner von Parsberg offers a model for such a reassessment. This article shows that Parsberg’s service for Nuremberg was not a symptom of weakness, but part of an assertive strategy to advance the independence from princely authority of his family’s lordship in the Upper Palatinate. Through this appreciation of the factors supporting town–noble cooperation in the late Middle Ages we are better able to understand the formation and development of the dialectic of town and nobility as a way of understanding German society

American Square Dance Vol. 33, No. 8 (Aug. 1978)

Monthly square dance magazine that began publication in 1945

International Project Management Association Research Conference 2017

Conference papers from the International Project Management Association Research Conference (IPMA), held on 2-4 November 2017 in Incheon, Republic of Korea, hosted by IPMA-Korea. This year's theme was: Projects, management and success: do we need a new understanding