26,307 research outputs found
The Dispersive Art Gallery Problem
No full textWe introduce a new variant of the art gallery problem that comes from safety
issues. In this variant we are not interested in guard sets of smallest
cardinality, but in guard sets with largest possible distances between these
guards. To the best of our knowledge, this variant has not been considered
before. We call it the Dispersive Art Gallery Problem. In particular, in the
dispersive art gallery problem we are given a polygon and a real
number , and want to decide whether has a guard set such
that every pair of guards in this set is at least a distance of apart.
In this paper, we study the vertex guard variant of this problem for the
class of polyominoes. We consider rectangular visibility and distances as
geodesics in the -metric. Our results are as follows. We give a (simple)
thin polyomino such that every guard set has minimum pairwise distances of at
most . On the positive side, we describe an algorithm that computes guard
sets for simple polyominoes that match this upper bound, i.e., the algorithm
constructs worst-case optimal solutions. We also study the computational
complexity of computing guard sets that maximize the smallest distance between
all pairs of guards within the guard sets. We prove that deciding whether there
exists a guard set realizing a minimum pairwise distance for all pairs of
guards of at least in a given polyomino is NP-complete. We were also able
to find an optimal dynamic programming approach that computes a guard set that
maximizes the minimum pairwise distance between guards in tree-shaped
polyominoes, i.e., computes optimal solutions. Because the shapes constructed
in the NP-hardness reduction are thin as well (but have holes), this result
completes the case for thin polyominoes.Comment: 21 pages, 17 figures, full version of an extended abstract that
appeared in the proceedings of the 33rd International Symposium on Algorithms
and Computation (ISAAC 2022); revised versio
Towards a Christian Philosophy
No full textAuthor did not sign the LAC Non-Exclusive License form.The relationship between philosophy and Christianity has, of course, a long history, as do the discussions of that relationship. My own position is not dissimilar to that of many of the early Church Fathers, though of course that position must be elaborated differently for various historical and personal reasons, and hopefully enriched by attention to the history of Western philosophy. As with all such relations, one's understanding of this relation has a lot to do with one's understanding of the terms involved. To promote the possibility of "Christian philosophy" is also to comment on that "and" which might be understood to relate two otherwise distinct and irreconcilable terms. In the end I claim this "and" must be understood as that "love" which defines philosophy as the "love of wisdom" (and finally, the wisdom of love), and does so in terms which (almost) merge-with the surprising assistance of such thinkers as Martin Heidegger, Jacques Derrida, and Paul Ricoeur-with those of the Church Fathers cited. On the one hand, I intend nothing but the historical, orthodox, and catholic understanding of Christianity, especially with regard to the central figure of Jesus the Christ, the Trinitarian God whom He embodies, represents, and reveals, and the Scriptures given as The Bible. On the other hand, I present the specifically philosophical pertinence of this unique Person as such emerges from the texts of the "philosophers" considered, and in a manner which I claim does not force the issue by reading into their texts what is not there. Attending to a (Christian) philosophical reflection on (Christian) philosophy also offers elaborations of inherited doctrines, both Christian and philosophical, including a way to read and think unique to the outcome. Such is the adventure of this current work
Approximate Shortest Distances Among Smooth Obstacles in 3D
No full textWe consider the classic all-pairs-shortest-paths (APSP) problem in a three-dimensional environment where paths have to avoid a set of smooth obstacles whose surfaces are represented by discrete point sets with n sample points in total. We show that if the point sets represent epsilon-samples of the underlying surfaces, (1 ± O(sqrt{epsilon}))-approximations of the distances between all pairs of sample points can be computed in O(n^{5/2} log^2 n) time
Bey Der vergnügten Ehelichen Verbindung, Des Hoch-Edlen und Hoch-Gelahrten Herrn, Hrn. Georg Albrecht Scheffern, Hoch-Gräfl. Stolberg-Wernigerödischen Regierungs-Secretarii, Mit der Hoch-Edlen, Hoch-Ehr-Sitt und Tugend-gezierten Frauen, Frauen Cathar. Elisabethen Susannen Sinninn, Geb. Rundinn, Welche den 21. Martii 1737. ... vollzogen wurde, Solte seine gehorsamste Pflicht mit diesen geringen Zeilen ablegen / Christian Ludowig Somburg, Lycei VVernigerod. Alumnus
No full textHochzeitsgedicht auf Georg Albrecht Scheffer, Regierungssekretär, und Katharina Elisabeth Susanne Sinn, geb. Runde, 21. März 1737Autopsie nach Exemplar der ULB Sachsen-AnhaltVorlageform des Erscheinungsvermerks: Wernjgerode, Gedruckt mit Struckischen Schriften
The Christian Right and US Foreign Policy in the Twenty-first Century
No full textThe thesis discusses the role of the Christian Right in the US foreign policy decision making process. The research revealed that the Christian Right has long been fascinated with some international issues in general and US foreign policy in particular. The Christian Right’s interest in international issues increased markedly during years of the George W. Bush presidency. It successfully widened its activities from domestic social conservative issues to foreign policy issues by participating in, articulating and lobbying for its religious version of American foreign policy. In assessing the role of the Christian Right in US foreign policy making, this dissertation examines three aspects of US foreign policy, namely Israel, international religious freedom and global humanitarianism. Based on these aspects, the Christian Right is seen as skilled in framing and defining issues. The Christian Right seems effective in selecting and prioritizing international issues that have a reasonable chance of being selected by foreign policy decision makers, especially in Congress. Moreover, the Christian Right has shown its maturity in seeking engagement and cooperation with other organizations, secular and religious, in order to advance its international goals. Finally, in pursuing and conveying its international agenda, the Christian Right has adopted a more moderate and less overtly religious approach. Instead of using its traditional religious rhetoric, the Christian Right has successfully projected its foreign policy preferences into the conventional realist discourse of American foreign policy that is largely based on the objective of national interest and national security. Nevertheless, this study does not, in any way, conclude that the Christian Right was able to influence or determine the direction of US foreign policy and its outcomes; however, it does suggest that the Christian Right did contribute and have an impact on the formulation of some US foreign policy. As such, the research contends that the role of the Christian Right is similar to other interest group lobbies and that its perceived influence on US foreign policy should not be exaggerated. Finally, the research suggests that the emergence of the Christian Right as an actor in asserting its global agenda through US foreign policy can possibly provide an example of how religious beliefs and values can become a potential source of “soft power”. Together with the “climate of opinion” of the American public during the Bush administration, the “soft power” at domestic level could serve as a valuable new explanatory variable in understanding how the US foreign policy was formulated in the early 21st century
Sabbath, Psalms and Eucharist: Christopher Southgate considers Christian perspectives on the climate emergency
No full textThis is the author accepted manuscript. The final version is available from Green Christian via the URL in this record In this brief article I want to explore what resources Christian thought might offer the
climate emergency, and those challenged by the slowness with which the generation
with the power (my own) are addressing the huge challenges that are ever more
evidently unfolding on our planet
Dare We Call it a Christian Business Division?
No full textThe author in this article explores the question: What, if anything, distinguishes a Christian business program from a secular program? The author answers the question by suggesting some areas he believes should be distinctive. His purpose is to open up a dialogue that has not occurred at the program level, not to claim all that could be said about this topic. Most discussion has focused on the macro picture of Christian colleges or the micro picture of how one’s faith might impact how one teaches a certain discipline. The article looks at themes or emphases in business programs that aspire to describe themselves as Christian
Journal of African Christian Biography: v. 6, no. 4
No full textA publication of the Dictionary of African Christian Biography with U.S. offices located at the Center for Global Christianity and Mission at Boston University. This issue focuses on: Tributes to Andrew Walls and Benedict Ssettuuma (Uganda); Samuel T. O. Akande (Nigeria).
This issue of the Journal of African Christian Biography honors the memory of "Prof." Andrew Finlay Walls and Fr. Benedict Ssettuuma, Jr. It also celebrates the contribution of Dr. Michael Adeleke Ogunewu to the work of the DACB both as an author and a mentor-teacher. One of his biographies, that of Samuel T. O. Akande, is included. The issue also includes a serialized chapter from African Christian Biography by Roger Levine and a new section, "Teaching with the DACB," featuring the reflections of a North American student on what the DACB has taught her
Approximating the Integral Fréchet Distance
No full textWe present a pseudo-polynomial time (1 + epsilon)-approximation algorithm for computing the integral and average Fréchet distance between two given polygonal curves T_1 and T_2. The running time is in O(zeta^{4}n^4/epsilon^2) where n is the complexity of T_1 and T_2 and zeta is the maximal ratio of the lengths of any pair of segments from T_1 and T_2.
Furthermore, we give relations between weighted shortest paths inside a single parameter cell C and the monotone free space axis of C. As a result we present a simple construction of weighted shortest paths inside a parameter cell. Additionally, such a shortest path provides an optimal solution for the partial Fréchet similarity of segments for all leash lengths. These two aspects are related to each other and are of independent interest
Packing Disks into Disks with Optimal Worst-Case Density
No full textWe provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a disk is 0.5. This implies that any set of (not necessarily equal) disks of total area delta 0 there are sets of disks of area 1/2+epsilon that cannot be packed. The proof uses a careful manual analysis, complemented by a minor automatic part that is based on interval arithmetic. Beyond the basic mathematical importance, our result is also useful as a blackbox lemma for the analysis of recursive packing algorithms
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