Matching Points with Things

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their number is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete

Spanning Properties of Theta-Theta Graphs

We study the spanning properties of Theta-Theta graphs. Similar in spirit with the Yao-Yao graphs, Theta-Theta graphs partition the space around each vertex into a set of k cones, for some fixed integer k > 1, and select at most one edge per cone. The difference is in the way edges are selected. Yao-Yao graphs select an edge of minimum length, whereas Theta-Theta graphs select an edge of minimum orthogonal projection onto the cone bisector. It has been established that the Yao-Yao graphs with parameter k = 6k' have spanning ratio 11.67, for k' >= 6. In this paper we establish a first spanning ratio of $7.82$ for Theta-Theta graphs, for the same values of $k$. We also extend the class of Theta-Theta spanners with parameter 6k', and establish a spanning ratio of $16.76$ for k' >= 5. We surmise that these stronger results are mainly due to a tighter analysis in this paper, rather than Theta-Theta being superior to Yao-Yao as a spanner. We also show that the spanning ratio of Theta-Theta graphs decreases to 4.64 as k' increases to 8. These are the first results on the spanning properties of Theta-Theta graphs.Comment: 20 pages, 6 figures, 3 table

Multidimensional Scaling of Varietal Data in Sedimentary Provenance Analysis

Varietal studies of sedimentary provenance use the properties of individual minerals or mineral groups. These are recorded as lists of numerical tables that can be difficult to interpret. Multidimensional Scaling (MDS) is a popular multivariate ordination technique for analyzing other types of provenance data based on, for example, detrital geochronology or petrography. Applying MDS to varietal data would allow them to be treated on an equal footing with those other provenance proxies. MDS requires a method to quantify the dissimilarity between two samples. This paper introduces three ways to do so. The first method (“treatment-by-row”) turns lists of (compositional) data tables into lists of vectors, using principal component analysis. These lists of vectors can then be treated as “distributional” data and subjected to MDS analysis using dissimilarity measures such as the Kolmogorov-Smirnov statistic. The second method (“treatment-by-column”) turns lists of compositional data tables into multiple lists of vectors, each representing a single component of the varietal data. These multiple distributional data sets are subsequently subjected to Procrustes analysis or 3-way MDS. The third method uses the Wasserstein-2 distance to jointly compare the rows and columns of varietal data. This arguably makes the best use of the data but acts more like a “black box” than the other two methods. Applying the three methods to a detrital titanite data set from Colombia yields similar results. After converting varietal data to dissimilarity matrices, they can be combined with other types of provenance data, again using Procrustes analysis or 3-way MDS

Trapping cold atoms near carbon nanotubes: thermal spin flips and Casimir-Polder potential

We investigate the possibility to trap ultracold atoms near the outside of a metallic carbon nanotube (CN) which we imagine to use as a miniaturized current-carrying wire. We calculate atomic spin flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism and we compute the minimum distance to the carbon nanotube at which an atom can be trapped.Comment: 8 pages, 3 figure

Voronoi diagrams of lines in 3 space under polyhedral convex distance functions

The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n 2 (n) logn), where is a slowly growing inverse of the Ackermann function. There are arrangements of n lines where this complexity can be as large as (n

\pi N scattering in relativistic baryon chiral perturbation theory revisited

We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to {\cal O}(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, \sqrt{s}\lesssim1.14 GeV. New values are provided for the {\cal O}(q^2) and {\cal O}(q^3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.Comment: 26 pages, 5 figures, 5 table

Racism and the Pinkerton syndrome in Singapore: effects of race on hiring decisions

The aim of the study was to examine racism and the Pinkerton syndrome in Singapore. Specifically, the study examined the effects of race on hiring decisions in a simulated hiring decision task. Participants were 171 (61% males) Singaporean Chinese undergraduates from a private university in Singapore. They were randomly assigned into one of nine groups and asked to review a resume of a job applicant. The study used a 3 (Academic qualifications: strong, moderate, or weak) × 3 (Race: White, Chinese, or Malay) between-subjects design with perceived warmth, competence, applicant suitability and recommended salary as the dependent variables. The results showed that while Chinese participants discriminated against Malay applicants (racism), they discriminated in favor of White applicants (the Pinkerton syndrome). The results provided a potential explanation to the economic disparities between Malays and the other races, and first experimental evidence for racism and the Pinkerton syndrome in Singapore

Clinical Use of Cinacalcet in MEN1 Hyperparathyroidism

Background. Management of multiple-endocrine neoplasia type 1- (MEN1-) associated hyperparathyroidism is associated with high recurrence rates and high surgical morbidity due to multiple neck explorations. Cinacalcet, a calcimimetic agent licensed for the treatment of secondary hyperparathyroidism and parathyroid carcinoma, may provide a medical alternative for the management of these complex patients. Methods. A prospective audit was performed of eight patients; three males and five females, aged 20–38 at diagnosis. Two patients commenced cinacalcet as primary treatment and six had previous surgery. Six patients had complications of hyperparathyroidism: renal calculi, renal dysfunction, and reduced bone mineral density. All were commenced on cinacalcet 30 mg bd for MEN1 associated hyperparathyroidism; doses were subsequently reduced to 30 mg od in four patients. Results. Significant reductions were observed in serum calcium and PTH measurements. Serum calcium reduced by a median of 0.35 mmol/L (P = .012 Wilcoxon Signed Rank). Serum PTH levels decreased by a median of 5.05 pmol/L (P = .012). There was no change in urine calcium. Duration ranged from 10–35 months with maintenance of control. Cinacalcet was well tolerated by six patients; one experienced nausea and one experienced diarrhoea. Conclusion. Cinacalcet is an effective and well-tolerated medical treatment for the management of complex primary hyperparathyroidism

Dynamics of light propagation in spatiotemporal dielectric structures

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the refractive index are studied by using a two-component, highly symmetric version of Maxwell's equations. The use of any slow varying amplitude approximation is avoided. Transfer matrices of sharp nonstationary interfaces are calculated explicitly, together with the amplitudes of all secondary waves produced in the scattering. Time-varying multilayer structures and spatiotemporal lenses in various configurations are investigated analytically and numerically in a unified approach. Several new effects are reported, such as pulse compression, broadening and spectral manipulation of pulses by a spatiotemporal lens, and the closure of the forbidden frequency gaps with the subsequent opening of wavenumber bandgaps in a generalized Bragg reflector

Balancing Minimum Spanning and Shortest Path Trees

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the two trees and epsilon > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1+epsilon times the shortest-path distance, and yet the total weight of the tree is at most 1+2/epsilon times the weight of a minimum spanning tree. This is the best tradeoff possible. The paper also describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993