Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition

Let $\mathcal{D}$ be a set of $n$ pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set $P$ containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of $P$. Our data structure can be built in $O(n \log n)$ time and has linear size. Given $P$, we can find its onion decomposition in $O(n \log k)$ time, where $k$ is the number of layers. We also provide a matching lower bound. Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onionComment: 10 pages, 5 figures; a preliminary version appeared at WADS 201

Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent

We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms run in deterministic linear time on a pointer machine. Our work builds on and extends previous results by Krznaric and Levcopolous and Buchin and Mulzer. Our main tool for the second algorithm is the well-separated pair decomposition(WSPD), a structure that has been used previously to find Euclidean minimum spanning trees in higher dimensions (Eppstein). We show that knowing the WSPD (and a quadtree) suffices to compute a planar Euclidean minimum spanning tree (EMST) in linear time. With the EMST at hand, we can find the Delaunay triangulation in linear time. As a corollary, we obtain deterministic versions of many previous algorithms related to Delaunay triangulations, such as splitting planar Delaunay triangulations, preprocessing imprecise points for faster Delaunay computation, and transdichotomous Delaunay triangulations.Comment: 37 pages, 13 figures, full version of a paper that appeared in SODA 201

Wie sind Unternehmen zu bewerten, wenn ihr Verschuldungsgrad nicht in Markt-, sondern in Buchwerten gemessen wird?

Die DCF-Verfahren setzen sich bei der Unternehmensbewertung immer stärker durch. Besonders häufig wird mit dem WACC-Konzept gearbeitet. Bei dieser Bewertungsmethode wird unterstellt, dass die Manager des zu bewertenden Unternehmens eine Fremdkapitalquote exogen vorgeben (Zielkapitalstruktur). Beim traditionellen WACC-Ansatz ist es notwendig, die Zielkapitalstrukturen in Marktwerten zu messen. Jedoch erscheint es - so Essler/Kruschwitz/Löffler - sehr viel realistischer, davon auszugehen, dass Manager Zielkapitalstrukturen verfolgen, die sie in Buchwerten messen. Im nachfolgenden Beitrag stellen die Autoren eine Bewertungsgleichung vor, die diesem Aspekt Rechnung trägt

Preprocessing Imprecise Points for Delaunay Triangulation: Simplified and Extended

Suppose we want to compute the Delaunay triangulation of a set P whose points are restricted to a collection R of input regions known in advance. Building on recent work by Löffler and Snoeyink, we show how to leverage our knowledge of R for faster Delaunay computation. Our approach needs no fancy machinery and optimally handles a wide variety of inputs, e.g., overlapping disks of different sizes and fat regions. Keywords: Delaunay triangulation - Data imprecision - Quadtree

Effects of a Short Strategy Training on Metacognitive Monitoring across the Life-span

The present study was conducted to explore the potential positive influence of a short strategy training on metacognitive monitoring competencies covering a life-span approach. Participants of four age groups (3rd-grade children, adolescents, younger and older adults) concluded a paired-associate learning task. Additionally, they gave delayed Judgments-of-Learning (JOLs), that is, they rated their certainty that they would later be able to recall specific details correctly, and Confidence Judgements (CJs), that is, they rated their certainty that the provided answers in the recall test were correct. Half of the participants underwent a short strategy training in order to enhance their recollection of contextual details thus providing a diagnostic basis for forming metacognitive judgements.Results revealed significant gains in memory performance after completing the strategy training. Moreover, a positive effect of the strategy training on JOLs and CJs differentiation and accuracy could be detected. Effects were most pronounced for children and older adults. Participants who had completed the strategy training also reported a decrease of familiarity-based metacognitive judgments and were able to identify memories for which no reliable cues existed more easily than participants in the control condition. Accordingly, improvements in monitoring performance seemed to be due to a shift in underlying cues. In sum, this study integrates traditional aims from the relatively separately existing lines of metacognitive research in the developmental and cognitive literature and adds to understanding and improving monitoring judgments in a life-time sample

Stimulated Raman adiabatic passage in optomechanics

Stimulated Raman adiabatic passage (STIRAP) describes adiabatic population transfer between two states coherently coupled via a mediating state that remains unoccupied. This renders STIRAP robust against loss in the mediating state, leading to profound applications in atomic- and molecular-beam research, trapped-ion physics, superconducting circuits, other solid-state systems, optics, in entanglement generation and qubit operations. STIRAP in optomechanics has been considered for optical frequency conversion where a mechanical mode provides the mediating state. Given the advances of optomechanical devices with exceptionally high mechanical-quality factors, STIRAP between mechanical modes has the prospect of generating macroscopic quantum superposition and of supporting quantum information protocols. An optical cavity mode can mediate the coupling between mechanical modes, without detrimental effects of optical losses. We demonstrate STIRAP between two mechanical modes of a phononic membrane-in-the-middle system with an efficiency of 86% and immune against photon loss through the mediating optical cavity.Comment: 10 page

Convex Hull of Points Lying on Lines in o(n log n) Time after Preprocessing

Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we study the following problem: given a set L of n lines in the plane, we wish to preprocess L such that later, upon receiving a set P of n points, each of which lies on a distinct line of L, we can construct the convex hull of P efficiently. We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n alpha(n) log* n) expected time. If we further assume that the points are "oblivious" with respect to the data structure, the running time improves to O(n alpha(n)). The analysis applies almost verbatim when L is a set of line-segments, and yields similar asymptotic bounds. We present several extensions, including a trade-off between space and query time and an output-sensitive algorithm. We also study the "dual problem" where we show how to efficiently compute the (<= k)-level of n lines in the plane, each of which lies on a distinct point (given in advance). We complement our results by Omega(n log n) lower bounds under the algebraic computation tree model for several related problems, including sorting a set of points (according to, say, their x-order), each of which lies on a given line known in advance. Therefore, the convex hull problem under our setting is easier than sorting, contrary to the "standard" convex hull and sorting problems, in which the two problems require Theta(n log n) steps in the worst case (under the algebraic computation tree model).Comment: 26 pages, 5 figures, 1 appendix; a preliminary version appeared at SoCG 201