Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Validity and worth in the science curriculum: learning school science outside the laboratory

It is widely acknowledged that there are problems with school science in many developed countries of the world. Such problems manifest themselves in a progressive decline in pupil enthusiasm for school science across the secondary age range and the fact that fewer students are choosing to study the physical sciences at higher levels and as careers. Responses to these developments have included proposals to reform the curriculum, pedagogy and the nature of pupil discussion in science lessons. We support such changes but argue from a consideration of the aims of science education that secondary school science is too rooted in the science laboratory; substantially greater use needs to be made of out-of-school sites for the teaching of science. Such usage should result in a school science education that is more valid and more motivating and is better at fulfilling defensible aims of school science education. Our contention is that laboratory-based school science teaching needs to be complemented by out-of-school science learning that draws on the actual world (e.g. through fieldtrips), the presented world (e.g. in science centres, botanic gardens, zoos and science museums) and the virtual worlds that are increasingly available through information and communications technologies (ICT)

“Knowledge Is Power”: A Mixed-Methods Study Exploring Adult Audience Preferences for Engagement and Learning Formats Over 3 Years of a Health Science Festival

© 2015, © 2015 SAGE Publications. Science festivals enable scientists to engage with publics, but format design reflecting different engagement models is contested. This study gathered mixed-methods data over 3 years (2011-2013) from on-site surveys (N = 661) of a health science festival, exploring audience preferences for dissemination or dialogue formats (lectures, discussions, community expo, lab experiments, and day out). Irrespective of time, age–group, or gender, lectures were significantly ranked the main attraction (76.8%), most highly attended (89.1%), and most useful format (83.8%). Thematic analysis revealed five themes exploring nonformal learning motivations for audiences, highlighting that knowledge/understanding acquisition is perceived as empowering greater health literacy

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Hardness of Approximate Nearest Neighbor Search

We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for every $\delta>0$ there exists a constant $\epsilon>0$ such that computing a $(1+\epsilon)$-approximation to the Bichromatic Closest Pair requires $n^{2-\delta}$ time. In particular, this implies a near-linear query time for Approximate Nearest Neighbor search with polynomial preprocessing time. Our reduction uses the Distributed PCP framework of [ARW'17], but obtains improved efficiency using Algebraic Geometry (AG) codes. Efficient PCPs from AG codes have been constructed in other settings before [BKKMS'16, BCGRS'17], but our construction is the first to yield new hardness results

Double-slit interference pattern from single-slit screen and its gravitational analogues

The double slit experiment (DSE) is known as an important cornerstone in the foundations of physical theories such as Quantum Mechanics and Special Relativity. A large number of different variants of it were designed and performed over the years. We perform and discuss here a new verion with the somewhat unexpected results of obtaining interference pattern from single-slit screen. This outcome, which shows that the routes of the photons through the array were changed, leads one to discuss it, using the equivalence principle, in terms of geodesics mechanics. We show using either the Brill's version of the canonical formulation of general relativity or the linearized version of it that one may find corresponding and analogous situations in the framework of general relativity.Comment: 51 pages, 12 Figures five of them contain two subfigures and thus the number of figures is 17, 1 Table. Some minor changes introduced, especially, in the reference

Geometric Triangular Chiral Hexagon Crystal-Like Complexes Organization in Pathological Tissues Biological Collision Order

The present study describes and documents self-assembly of geometric triangular chiral hexagon crystal like complex organizations (GTCHC) in human pathological tissues.The authors have found this architectural geometric expression at macroscopic and microscopic levels mainly in cancer processes. This study is based essentially on macroscopic and histopathologic analyses of 3000 surgical specimens: 2600 inflammatory lesions and 400 malignant tumours. Geometric complexes identified photographically at macroscopic level were located in the gross surgical specimen, and these areas were carefully dissected. Samples were taken to carry out histologic analysis. Based on the hypothesis of a collision genesis mechanism and because it is difficult to carry out an appropriate methodological observation in biological systems, the authors designed a model base on other dynamic systems to obtain indirect information in which a strong white flash wave light discharge, generated by an electronic device, hits over the lines of electrical conductance structured in helicoidal pattern. In their experimental model, the authors were able to reproduce and to predict polarity, chirality, helicoid geometry, triangular and hexagonal clusters through electromagnetic sequential collisions. They determined that similar events among constituents of extracelular matrix which drive and produce piezoelectric activity are responsible for the genesis of GTCHC complexes in pathological tissues. This research suggests that molecular crystals represented by triangular chiral hexagons derived from a collision-attraction event against collagen type I fibrils emerge at microscopic and macroscopic scales presenting a lateral assembly of each side of hypertrophy helicoid fibers, that represent energy flow in cooperative hierarchically chiral electromagnetic interaction in pathological tissues and arises as a geometry of the equilibrium in perturbed biological systems. Further interdisciplinary studies must be carried out to reproduce, manipulate and amplify their activity and probably use them as a base to develop new therapeutic strategies in cancer

Simple robust parameter estimation for the Birnbaum-Saunders distribution

© 2015, Wang et al. We study the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution. It is well known that the maximum likelihood estimator (MLE) is efficient when the underlying model is true but at the same time it is quite sensitive to data contamination that is often encountered in practice. In this paper, we propose several estimators which have simple closed forms and are also robust to data contamination. We study the breakdown points and asymptotic properties of the proposed estimators. These estimators are then applied to both simulated and real datasets. Numerical results show that the proposed estimators are attractive alternative to the MLE in that they are quite robust to data contamination and also highly efficient when the underlying model is true

Information storing by biomagnetites

Since the discovery of the presence of biogenic magnetites in living organisms, there have been speculations on the role that these biomagnetites play in cellular processes. It seems that the formation of biomagnetite crystals is a universal phenomenon and not an exception in living cells. Many experimental facts show that features of organic and inorganic processes could be indistinguishable at nanoscale levels. Living cells are quantum "devices" rather than simple electronic devices utilizing only the charge of conduction electrons. In our opinion, due to their unusual biophysical properties, special biomagnetites must have a biological function in living cells in general and in the brain in particular. In this paper we advance a hypothesis that while biomagnetites are developed jointly with organic molecules and cellular electromagnetic fields in cells, they can record information about the Earth's magnetic vector potential of the entire flight in migratory birds.Comment: 17 pages, 3 figure