Approximating Nearest Neighbor Distances

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we consider the most natural metric with this property, which we call the nearest neighbor metric. Given a point set P and a path $\gamma$, our metric charges each point of $\gamma$ with its distance to P. The total charge along $\gamma$ determines its nearest neighbor length, which is formally defined as the integral of the distance to the input points along the curve. We describe a $(3+\varepsilon)$-approximation algorithm and a $(1+\varepsilon)$-approximation algorithm to compute the nearest neighbor metric. Both approximation algorithms work in near-linear time. The former uses shortest paths on a sparse graph using only the input points. The latter uses a sparse sample of the ambient space, to find good approximate geodesic paths.Comment: corrected author nam

Physical properties of alfalfa hay : Specific weight of chopped hay fragments : Porosity of alfalfa hay masses

Digitized 2007 AES.Includes bibliographical references (page 11)

Bulk density of chopped alfalfa hay

Digitized 2007 AES.Includes bibliographical references (page 28)

Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of \epsilon and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself

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

Improved diagnostic accuracy in differentiating malignant and benign lesions using single-voxel proton MRS of the breast at 3 T MRI

AIM: To investigate the diagnostic accuracy of single-voxel proton magnetic resonance spectroscopy (SV (1)H MRS) by quantifying total choline-containing compounds (tCho) in differentiating malignant from benign lesions, and subsequently, to analyse the relationship of tCho levels in malignant breast lesions with their histopathological subtypes. MATERIALS AND METHODS: A prospective study of SV 1H MRS was performed following dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) in 61 women using a 3 T MR system. All lesions (n = 57) were analysed for characteristics of morphology, contrast-enhancement kinetics, and tCho peak heights at SV (1)H MRS that were two-times above baseline. Subsequently, the tCho in selected lesions (n = 32) was quantified by calculating the area under the curve, and a tCho concentration equal to or greater than the cut-off value was considered to represent malignancy. The relationship between tCho in invasive ductal carcinomas (IDCs) and their Bloom & Richardson grading of malignancy was assessed. RESULTS: Fifty-two patients (57 lesions; 42 malignant and 15 benign) were analysed. The sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV), of predicting malignancy were 100, 73.3, 91.3, and 100%, respectively, using DCE-MRI and 95.2, 93.3, 97.6, and 87.5%, respectively, using SV (1)H MRS. The tCho cut-off for receiver operating characteristic (ROC) curve was 0.33 mmol/l. The relationship between tCho levels in malignant breast lesions with their histopathological subtypes was not statistically significant (p = 0.3). CONCLUSION: Good correlation between tCho peaks and malignancy, enables SV (1)H MRS to be used as a clinically applicable, simple, yet non-invasive tool for improved specificity and diagnostic accuracy in detecting breast cancer

Antioxidative Properties and Phenolic Profile of the Core, Pulp and Peel of Commercialized Kiwifruit by LC-ESI-QTOF-MS/MS

The kiwifruit is cultivated globally due to its diversity of phytochemicals, especially phenolic compounds, which have antioxidant, anti-inflammatory and anti-cancer medical effects. However, only the pulp of the kiwifruit is consumed, while the peels and cores—which are also rich in phytochemicals—are usually wasted. Meanwhile, detailed information on the comparison among the three parts is still limited. In this study, the antioxidant potentials in the core, pulp, and peel of the three most commercialized kiwifruit cultivars (Australian-grown Hayward kiwifruit, New Zealand-grown Zesy002 kiwifruit, and New Zealand-grown organic Hayward kiwifruit) were selected. Their antioxidant capacities were tested, and their phenolic profiles were identified and characterized by liquid chromatography-electrospray ionization quadrupole time-of-flight mass spectrometry (LC-ESI-QTOF-MS/MS). The antioxidant results showed that the peel of New Zealand-grown organic Hayward kiwifruit contained the highest total phenolic content (9.65 mg gallic acid equivalent (GAE) mg/g) and total antioxidant capacity (4.43 mg ascorbic acid equivalent (AAE) mg/g), respectively. In addition, the antioxidant capacity of the peel is generally higher than that of the pulp and cores in all species, especially ABTS (2,2-Azino-bis-3ethylbenzothiazoline-6-sulfonic acid (ABTS) radical scavenging ability), ranging from 13.25 mg AAE/g to 18.31 mg AAE/g. The LC-ESI-QTOF-MS/MS tentatively identified the phenolic compounds present in the three kiwifruit species, including 118 unique compounds in kiwifruit peel, 12 unique compounds in the kiwifruit cores, and three unique compounds in kiwifruit pulp. The comprehensive characterization of the phenolics in the kiwifruits’ parts indicates the importance of their waste part as a promising source of phenolics with antioxidant properties. Therefore, this study can guide the industry with meaningful information on kiwifruit waste, and can provide it with the utilization of food and pharmacological aspects