103,092 research outputs found
An die Zukunft erinnern: Hintergrund, Werdegang und Funktion der Erzählung um den Propheten Micha ben Jimla in 1 Kön 22,1-38
No full textKern G. An die Zukunft erinnern: Hintergrund, Werdegang und Funktion der Erzählung um den Propheten Micha ben Jimla in 1 Kön 22,1-38. Bielefeld; 2017
On the Complexity of the k-Level in Arrangements of Pseudoplanes
No full textA classical open problem in combinatorial geometry is to obtain tight asymptotic bounds on the maximum number of k-level vertices in an arrangement of n hyperplanes in R^d (vertices with exactly k of the hyperplanes passing below them). This is essentially a dual version of the k-set problem, which, in a primal setting, seeks bounds for the maximum number of k-sets determined by n points in R^d, where a k-set is a subset of size k that can be separated from its complement by a hyperplane. The k-set problem is still wide open even in the plane. In three dimensions, the best known upper and lower bounds are, respectively, O(nk^{3/2}) [M. Sharir et al., 2001] and nk * 2^{Omega(sqrt{log k})} [G. Tóth, 2000].
In its dual version, the problem can be generalized by replacing hyperplanes by other families of surfaces (or curves in the planes). Reasonably sharp bounds have been obtained for curves in the plane [M. Sharir and J. Zahl, 2017; H. Tamaki and T. Tokuyama, 2003], but the known upper bounds are rather weak for more general surfaces, already in three dimensions, except for the case of triangles [P. K. Agarwal et al., 1998]. The best known general bound, due to Chan [T. M. Chan, 2012] is O(n^{2.997}), for families of surfaces that satisfy certain (fairly weak) properties.
In this paper we consider the case of pseudoplanes in R^3 (defined in detail in the introduction), and establish the upper bound O(nk^{5/3}) for the number of k-level vertices in an arrangement of n pseudoplanes. The bound is obtained by establishing suitable (and nontrivial) extensions of dual versions of classical tools that have been used in studying the primal k-set problem, such as the Lovász Lemma and the Crossing Lemma
How to Find a Point in the Convex Hull Privately
No full textWe study the question of how to compute a point in the convex hull of an input set S of n points in ℝ^d in a differentially private manner. This question, which is trivial without privacy requirements, turns out to be quite deep when imposing differential privacy. In particular, it is known that the input points must reside on a fixed finite subset G ⊆ ℝ^d, and furthermore, the size of S must grow with the size of G. Previous works [Amos Beimel et al., 2010; Amos Beimel et al., 2019; Amos Beimel et al., 2013; Mark Bun et al., 2018; Mark Bun et al., 2015; Haim Kaplan et al., 2019] focused on understanding how n needs to grow with |G|, and showed that n=O(d^2.5 ⋅ 8^(log^*|G|)) suffices (so n does not have to grow significantly with |G|). However, the available constructions exhibit running time at least |G|^d², where typically |G|=X^d for some (large) discretization parameter X, so the running time is in fact Ω(X^d³).
In this paper we give a differentially private algorithm that runs in O(n^d) time, assuming that n=Ω(d⁴ log X). To get this result we study and exploit some structural properties of the Tukey levels (the regions D_{≥ k} consisting of points whose Tukey depth is at least k, for k=0,1,…). In particular, we derive lower bounds on their volumes for point sets S in general position, and develop a rather subtle mechanism for handling point sets S in degenerate position (where the deep Tukey regions have zero volume). A naive approach to the construction of the Tukey regions requires n^O(d²) time. To reduce the cost to O(n^d), we use an approximation scheme for estimating the volumes of the Tukey regions (within their affine spans in case of degeneracy), and for sampling a point from such a region, a scheme that is based on the volume estimation framework of Lovász and Vempala [László Lovász and Santosh S. Vempala, 2006] and of Cousins and Vempala [Ben Cousins and Santosh S. Vempala, 2018]. Making this framework differentially private raises a set of technical challenges that we address
Bibliographie Hilarion G. Petzold 1958 – 2009 mit Anhang als Einführung
No full textDieses Archiv enthält die Gesamtbibliographie der Werke des Autors nebst einiger Texte „Über H. G. Petzold“ im Schlussteil der Bibliographie sowie einen Anhang mit einer Einführung in die Architektur des Werkes in seinem wissenslogischen Aufbau als Ausarbeitung seines „Tree of Science Modells“ (2007).This archive contains the complete bibliography of the author and some texts about H. G. Petzold, moreover an epilogue with an introduction to the architecture of the works in its epistemological structure and composition and as an elaborations of Petzold’s „Tree of Science Modell (2007).https://www.fpi-publikation.de/polyloge/01-2009-petzold-h-g-gesamtbibliographie-h-g-petzold-1958-2009-updating-november2009/peerReviewedpublishedVersio
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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3346: Samuel G. Freedman, author, 2013
No full textPhotograph of author Samuel G. Freedman, at NT Daily Slash meeting in the Mayborn School of Journalism at UNT
The Right to Strike under the United States Constitution: Theory, Practice, and Possible Implications for Canada
No full textAnswering critics of the Canadian Supreme Court's judgment in B.C. Health, the author argues that the Court laid the foundation for a principled and durable doctrine protecting constitutional labour rights, one that goes directly to the heart of the matter — the inequality of workers’ power in the employment relation. In the author’s view, two paths could lead from B.C. Health to the recognition of Charter protec- tion for a right to strike: one that treats the right as an accessory to col- lective bargaining, and one that upholds the right directly on the basis of the Charter values of equality and participation. The author supports the latter approach, contending that constitutional rights should be defined in relation to fundamental values, in a way that is not contingent on time-bound or fact-sensitive assessments about the role of strikes within a particular collective bargaining regime. Although a Charter right to strike may involve the courts in difficult choices about when to defer to legislative policy decisions, and courts may lack the institutional capac- ity to deal effectively with labour law issues, the author points out that judges can look to ILO standards for expert guidance. Noting that the U.S. experience in this area might be of considerable use to Canadians, the author concludes by providing an overview of American case law concerning a constitutional right to strike.Peer reviewe
On Reverse Shortest Paths in Geometric Proximity Graphs
No full textLet S be a set of n geometric objects of constant complexity (e.g., points, line segments, disks, ellipses) in ℝ², and let ϱ: S× S → ℝ_{≥ 0} be a distance function on S. For a parameter r ≥ 0, we define the proximity graph G(r) = (S,E) where E = {(e₁,e₂) ∈ S×S ∣ e₁≠e₂, ϱ(e₁,e₂) ≤ r}. Given S, s,t ∈ S, and an integer k ≥ 1, the reverse-shortest-path (RSP) problem asks for computing the smallest value r^* ≥ 0 such that G(r^*) contains a path from s to t of length at most k.
In this paper we present a general randomized technique that solves the RSP problem efficiently for a large family of geometric objects and distance functions. Using standard, and sometimes more involved, semi-algebraic range-searching techniques, we first give an efficient algorithm for the decision problem, namely, given a value r ≥ 0, determine whether G(r) contains a path from s to t of length at most k. Next, we adapt our decision algorithm and combine it with a random-sampling method to compute r^*, by efficiently performing a binary search over an implicit set of O(n²) candidate values that contains r^*.
We illustrate the versatility of our general technique by applying it to a variety of geometric proximity graphs. For example, we obtain (i) an O^*(n^{4/3}) expected-time randomized algorithm (where O^*(⋅) hides polylog(n) factors) for the case where S is a set of pairwise-disjoint line segments in ℝ² and ϱ(e₁,e₂) = min_{x ∈ e₁, y ∈ e₂} ‖x-y‖ (where ‖⋅‖ is the Euclidean distance), and (ii) an O^*(n+m^{4/3}) expected-time randomized algorithm for the case where S is a set of m points lying on an x-monotone polygonal chain T with n vertices, and ϱ(p,q), for p,q ∈ S, is the smallest value h such that the points p' := p+(0,h) and q' := q+(0,h) are visible to each other, i.e., all points on the segment p'q' lie above or on the polygonal chain T
G-Rank: Unsupervised Continuous Learn-to-Rank for Edge Devices in a P2P Network
No full textRanking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and Web3 protocols deliberately eschew centralized databases and computational architectures when designing services and features. As such, robust search-and-rank algorithms designed for such domains must be engineered specifically for decentralized networks, and must be lightweight enough to operate on consumer-grade personal devices such as a smartphone or laptop computer. We introduce G-Rank, an unsupervised ranking algorithm designed exclusively for decentralized networks. We demonstrate that accurate, relevant ranking results can be achieved in fully decentralized networks without any centralized data aggregation, feature engineering, or model training. Furthermore, we show that such results are obtainable with minimal data preprocessing and computational overhead, and can still return highly relevant results even when a user’s device is disconnected from the network. G-Rank is highly modular in design, is not limited to categorical data, and can be implemented in a variety of domains with minimal modification. The results herein show that unsupervised ranking models designed for decentralized p2p networks are not only viable, but worthy of further research.https://github.com/awrgold/G-RankComputer Scienc
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