Minimum Convex Partitions and Maximum Empty Polytopes

Let $S$ be a set of $n$ points in $\mathbb{R}^d$. A Steiner convex partition is a tiling of ${\rm conv}(S)$ with empty convex bodies. For every integer $d$, we show that $S$ admits a Steiner convex partition with at most $\lceil (n-1)/d\rceil$ tiles. This bound is the best possible for points in general position in the plane, and it is best possible apart from constant factors in every fixed dimension $d\geq 3$. We also give the first constant-factor approximation algorithm for computing a minimum Steiner convex partition of a planar point set in general position. Establishing a tight lower bound for the maximum volume of a tile in a Steiner convex partition of any $n$ points in the unit cube is equivalent to a famous problem of Danzer and Rogers. It is conjectured that the volume of the largest tile is $\omega(1/n)$. Here we give a $(1-\varepsilon)$-approximation algorithm for computing the maximum volume of an empty convex body amidst $n$ given points in the $d$-dimensional unit box $[0,1]^d$.Comment: 16 pages, 4 figures; revised write-up with some running times improve

A well-separated pairs decomposition algorithm for k-d trees implemented on multi-core architectures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Variations of k-d trees represent a fundamental data structure used in Computational Geometry with numerous applications in science. For example particle track tting in the software of the LHC experiments, and in simulations of N-body systems in the study of dynamics of interacting galaxies, particle beam physics, and molecular dynamics in biochemistry. The many-body tree methods devised by Barnes and Hutt in the 1980s and the Fast Multipole Method introduced in 1987 by Greengard and Rokhlin use variants of k-d trees to reduce the computation time upper bounds to O(n log n) and even O(n) from O(n2). We present an algorithm that uses the principle of well-separated pairs decomposition to always produce compressed trees in O(n log n) work. We present and evaluate parallel implementations for the algorithm that can take advantage of multi-core architectures.The Science and Technology Facilities Council, UK

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

Peningkatan Kompentensi Guru IPA Biologi Sekolah Menengah Pertama melalui Pelatihan dan Pembekalan Materi di Laboratorium Kabupaten Pesisir Selatan

Tujuan pengabdian pada masayarakat ini untuk meningkatkan pemahaman guru Biologi tentang materi dan konsep IPA, dan meningkatkan kreatifitas serta menemukan cara-cara pendekatan pembelajaran yang kreatif dan inovatif sehingga materi mudah dimengerti oleh siswa, membantu guru mendiskusikan topik-topik yang kurang dipahami siswa sehingga guru bisa secara bersama-sama merencanakan pembelajaran yang lebih baik. Pendekatan yang dilakukan dengan memberikan pelatihan/penyuluhan berupa penguatan materi terutama di laboratorium, memberikan stimulasi kepada guru bagaimana mengembangkan ide dan pendekatan-pendekatan kreatif yang dapat membantu siswa memahami konsep yang diajarkan guru, membantu guru yang akan mengikuti ujian kompetensi guru agar lebih siap dan dan lebih memahami materi yang mungkin diujikan sebagai persiapan sertifikasi. Kegiatan PPM yang sudah dilakukan yaitu persiapan dengan mengadakan pertemuan dengan pihak Diknas Kabupaten Pesisir Selatan untuk memantapkan proses pelaksanaan dengan mendatangkan guru-guru IPA SMP sebanyak 20 Orang yang berasal dari berbagai kecamatan yang ada di Kabupaten Pesisir Selatan. Hasil analisis angket kompetensi guru-guru IPA didapat informasi pada aspek perencanaan memperoleh 68,74% dengan criteria cukup, hal yang sama terjadi pada evaluasi dengan nilai 65,65%. Sementara itu pada aspek pelaksanaan memperoleh 85,93% dengan criteria Baik sekali

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far

Risk measures for direct real estate investments with non-normal or unknown return distributions

The volatility of returns is probably the most widely used risk measure for real estate. This is rather surprising since a number of studies have cast doubts on the view that volatility can capture the manifold risks attached to properties and corresponds to the risk attitude of investors. A central issue in this discussion is the statistical properties of real estate returns—in contrast to neoclassical capital market theory they are mostly non-normal and often unknown, which render many statistical measures useless. Based on a literature review and an analysis of data from Germany we provide evidence that volatility alone is inappropriate for measuring the risk of direct real estate. We use a unique data sample by IPD, which includes the total returns of 939 properties across different usage types (56% office, 20% retail, 8% others and 16% residential properties) from 1996 to 2009, the German IPD Index, and the German Property Index. The analysis of the distributional characteristics shows that German real estate returns in this period were not normally distributed and that a logistic distribution would have been a better fit. This is in line with most of the current literature on this subject and leads to the question which indicators are more appropriate to measure real estate risks. We suggest that a combination of quantitative and qualitative risk measures more adequately captures real estate risks and conforms better with investor attitudes to risk. Furthermore, we present criteria for the purpose of risk classification

Modes of Foreign Entry under Asymmetric Information about Potential Technology Spillovers

This paper studies the effect of technology spillovers on the entry decision of a multinational enterprise into a foreign market. Two alternative entry modes for a foreign direct investment are considered: Greenfield investment versus acquisition. We find that with quantity competition a spillover makes acquisitions less attractive, while with price competition acquisitions become more attractive. Asymmetric information about potential spillovers always reduces the number of acquisitions independently of whether the host country or the entrant has private information. Interestingly, we find that asymmetric information always hurts the entrant, while it sometimes is in favor of the host country

Advanced Sectioned Images of a Cadaver Head with Voxel Size of 0.04 mm

BACKGROUND: The sectioned images of a cadaver head made from the Visible Korean project have been used for research and educational purposes. However, the image resolution is insufficient to observe detailed structures suitable for experts. In this study, advanced sectioned images with higher resolution were produced for the identification of more detailed structures. METHODS: The head of a donated female cadaver was scanned for 3 Tesla magnetic resonance images and diffusion tensor images (DTIs). After the head was frozen, the head was sectioned serially at 0.04-mm intervals and photographed repeatedly using a digital camera. RESULTS: On the resulting 4,000 sectioned images (intervals and pixel size, 0.04 mm(3); color depth, 48 bits color; a file size, 288 Mbytes), minute brain structures, which can be observed not on previous sectioned images but on microscopic slides, were observed. The voxel size of this study (0.04 mm(3)) was very minute compared to our previous study (0.1 mm(3); resolution, 4,368 x 2,912) and Visible Human Project of the USA (0.33 mm(3); resolution, 2,048 x 2,048). Furthermore, the sectioned images were combined with tractography of the DTIs to elucidate the white matter with high resolution and the actual color of the tissue. CONCLUSION: The sectioned images will be used for diverse research, including the applications for the cross sectional anatomy and three-dimensional models for virtual experiments

Research Notes : India : A narrow leaf type soybean variety -PK-308

PK-308\u27 has been developed at this station from a cross of T-31 x Hardee following the pedigree method of breeding. It has been released by the Central Varietal Release Committee, Government of India, in 1984, for general cultivation in the northern plains of India. This is the first narrow-leaf type cultivar released in this country