Approximate Nearest-Neighbor Search for Line Segments

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider nearest-neighbor queries against a set of line segments in $\mathbb{R}^d$, for constant dimension $d$. Given a set $S$ of $n$ disjoint line segments in $\mathbb{R}^d$ and an error parameter $\varepsilon > 0$, the objective is to build a data structure such that for any query point $q$, it is possible to return a line segment whose Euclidean distance from $q$ is at most $(1+\varepsilon)$ times the distance from $q$ to its nearest line segment. We present a data structure for this problem with storage $O((n^2/\varepsilon^{d}) \log (\Delta/\varepsilon))$ and query time $O(\log (\max(n,\Delta)/\varepsilon))$, where $\Delta$ is the spread of the set of segments $S$. Our approach is based on a covering of space by anisotropic elements, which align themselves according to the orientations of nearby segments.Comment: 20 pages (including appendix), 5 figure

Smooth Distance Approximation

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously. In many real-world applications of geometric data structures, it is assumed that query results are continuous, free of jump discontinuities. This is at odds with many modern data structures in computational geometry, which employ approximations to achieve efficiency, but these approximations often suffer from discontinuities. In this paper, we present a general method for transforming an approximate but discontinuous data structure into one that produces a smooth approximation, while matching the asymptotic space efficiencies of the original. We achieve this by adapting an approach called the partition-of-unity method, which smoothly blends multiple local approximations into a single smooth global approximation. We illustrate the use of this technique in a specific application of approximating the distance to the boundary of a convex polytope in ?^d from any point in its interior. We begin by developing a novel data structure that efficiently computes an absolute ?-approximation to this query in time O(log (1/?)) using O(1/?^{d/2}) storage space. Then, we proceed to apply the proposed partition-of-unity blending to guarantee the smoothness of the approximate distance field, establishing optimal asymptotic bounds on the norms of its gradient and Hessian

Economical Delone Sets for Approximating Convex Bodies

Convex bodies are ubiquitous in computational geometry and optimization theory. The high combinatorial complexity of multidimensional convex polytopes has motivated the development of algorithms and data structures for approximate representations. This paper demonstrates an intriguing connection between convex approximation and the classical concept of Delone sets from the theory of metric spaces. It shows that with the help of a classical structure from convexity theory, called a Macbeath region, it is possible to construct an epsilon-approximation of any convex body as the union of O(1/epsilon^{(d-1)/2}) ellipsoids, where the center points of these ellipsoids form a Delone set in the Hilbert metric associated with the convex body. Furthermore, a hierarchy of such approximations yields a data structure that answers epsilon-approximate polytope membership queries in O(log (1/epsilon)) time. This matches the best asymptotic results for this problem, by a data structure that both is simpler and arguably more elegant

Smooth Distance Approximation

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously. In many real-world applications of geometric data structures, it is assumed that query results are continuous, free of jump discontinuities. This is at odds with many modern data structures in computational geometry, which employ approximations to achieve efficiency, but these approximations often suffer from discontinuities. In this paper, we present a general method for transforming an approximate but discontinuous data structure into one that produces a smooth approximation, while matching the asymptotic space efficiencies of the original. We achieve this by adapting an approach called the partition-of-unity method, which smoothly blends multiple local approximations into a single smooth global approximation. We illustrate the use of this technique in a specific application of approximating the distance to the boundary of a convex polytope in $\mathbb{R}^d$ from any point in its interior. We begin by developing a novel data structure that efficiently computes an absolute $\varepsilon$-approximation to this query in time $O(\log (1/\varepsilon))$ using $O(1/\varepsilon^{d/2})$ storage space. Then, we proceed to apply the proposed partition-of-unity blending to guarantee the smoothness of the approximate distance field, establishing optimal asymptotic bounds on the norms of its gradient and Hessian.Comment: To appear in the European Symposium on Algorithms (ESA) 202

The Potential Use of Intrauterine Insemination as a Basic Option for Infertility: A Review for Technology-Limited Medical Settings

Objective. There is an asymmetric allocation of technology and other resources for infertility services. Intrauterine insemination (IUI) is a process of placing washed spermatozoa transcervically into the uterine cavity for treatment of infertility. This is a review of literature for the potential use of IUI as a basic infertility treatment in technology-limited settings. Study design. Review of articles on treatment of infertility using IUI. Results. Aspects regarding the use of IUI are reviewed, including ovarian stimulation, semen parameters associated with good outcomes, methods of sperm preparation, timing of IUI, and number of inseminations. Implications of the finding in light of the needs of low-technology medical settings are summarized. Conclusion. The reviewed evidence suggests that IUI is less expensive, less invasive, and comparably effective for selected patients as a first-line treatment for couples with unexplained or male factor infertility. Those couples may be offered three to six IUI cycles in technology-limited settings

Composition, repellent and fumigant toxicity of Mentha longifolia essential oil on Tetranychus urticae and three predatory mites of the family phytoseiidae (Acari: Tetranychidae: Phytoseiidae)

The chemical composition of essential oil extracted from leaves of the medicinal plant Mentha longifolia (L.) Huds growing in Egypt, were determined through Gas Chromatography/Mass Spectrometry ( GC/MS). The analyses revealed that the major component of M. longifolia was Monterpene ketone (piperitone oxide). Mentha longifolia was potent for the pest Tetranychus urticae Koch with a significant increase in repellency. In addition, it exhibited strong oviposition deterrence to the pest based on a 99.4% reduction of the total number of eggs on leaf discs treated with the oil. The LC50 values of M. longifolia against eggs, nymphs and females of T. urticae by fumigant application, were 2.95, 3.47, 3.74 μL / L, while the LC90 values were 8.99, 9.41, 11.01 μL/ L, respectively. The toxicity of M. longifolia oil by fumigant application to females and eggs of 3 predatory phytoseiid mites was tested. Neoseiulus californicus (McGregor) is extremely insusceptible to M. longifolia oil than the pest T. urticae and both phytoseiid mites, Neoseiuls barkeri (Hughes) and Typhlodromips swirskii (Athias Henriot) under laboratory conditions. When both stages of tested predatory mites, exposed to fumigant of LC50 and LC90 μL/L values reported on T. urticae, female’s mortality of N. californicus was lesser than that reported on N. barkeri and T. swirskii. These show that the fumigant toxicity of M. longifolia oil has the highest lethal activity to the pest T. urticae and the least to the predatory mite N. californicus. Results indicated that the mode of delivery of the essential oil was largely a result of action in the vapor phase via respiratory system. Data was suggested that M. longifolia oil have the potential agent to be used in the maintainable management of T. urticae combined with N. californicus

Effects of methimepip and JNJ-5207852 in Wistar rats exposed to an open-field with and without object and in Balb/c mice exposed to a radial-arm maze

The role of the histamine H3 receptor (H3R) in anxiety is controversial, due to limitations in drug selectivity and limited validity of behavioral tests used in previous studies. In the present report, we describe two experiments. In the first one, Wistar rats were treated with an H3R agonist (methimepip), and exposed to an open-field. In the second one, Balb/c mice were treated with H3R agonist (methimepip) or antagonist (JNJ-5207852), and exposed to an open space 3D maze which is a modified version of the radial-arm maze. C57BL/6J saline treated mice were included for comparisons. When exposed to an empty open field, Wistar rats spent more time in the outer area and made very low number of brief crossings in the central area. However, when an object occupied the central area, rats crossed frequently into and spent a long time in the central area. Administration of a range of different doses of methimepip (selective H3R agonist) reduced the entries into the central area with a novel object, indicating enhanced avoidance response. In the 3D maze, both Balb/c and C57BL/6J saline-treated mice crossed frequently onto the bridges that radiate from the central platform but only C57BL/6J mice crossed onto the arms which extend the bridges. This suggests that Balb/c mice are more anxious than C57BL/6J mice. Neither methimepip nor JNJ-5207852 (selective H3R antagonist/inverse agonist) induced entry into the arms of the maze, indicative of lack of anxiolytic effects

Diatom Assemblage in the Lake of Gaberoun, Southern Libya

The lake of Gaberoun in the southern district of Libya was studied to assess the diatom community composition in the littoral zone. Planktic and attached diatoms were listed and information on the constituent species made known (images are shown). Some criteria of the water characteristics are also given such as the pH, which is an average of 8.3, electrical conductivity which accounted for 1.4 µSim/cm1- and total dissolved salts (TDS) of 189.0mg/L1-

A rare case of giant dermoid cyst with ipsilateral paratubal cystadenoma during pregnancy

Dermoid cysts are considered the most common ovarian cysts in adolescents and pregnant women. In rare cases, they can attain a huge size. Paratubal cysts are also common in adolescents. They are usually simple cysts present in the broad ligament. In this case, we report a giant dermoid cyst with ipsilateral paratubal serous cystadenoma discovered during pregnancy of a 20-year-old primigravida. Both cysts were managed conservatively, and then removed successfully at the time of cesarean section by cystectomy