A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs

We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our algorithm runs in expected time $O(2^{O(d)}(n\log n + m))$, where $n$ is the input size, $m$ is the output point set size, and $d$ is the ambient dimension. The constants only depend on the desired element quality bounds. To gain this new efficiency, the algorithm approximately maintains the Voronoi diagram of the current set of points by storing a superset of the Delaunay neighbors of each point. By retaining quality of the Voronoi diagram and avoiding the storage of the full Voronoi diagram, a simple exponential dependence on $d$ is obtained in the running time. Thus, if one only wants the approximate neighbors structure of a refined Delaunay mesh conforming to a set of input points, the algorithm will return a size $2^{O(d)}m$ graph in $2^{O(d)}(n\log n + m)$ expected time. If $m$ is superlinear in $n$, then we can produce a hierarchically well-spaced superset of size $2^{O(d)}n$ in $2^{O(d)}n\log n$ expected time.Comment: Full versio

Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.Comment: 5 pages, 6 figures, typos corrected, references adde

The Parkinson\u27s experience of group physical activity: Understanding social support, social comparison, physical self-perceptions, and posttraumatic growth

Group physical activity programs for clinical populations can provide opportunities for adaptive social interactions, improving perceptions of competence, and may facilitate posttraumatic growth (positive psychological changes resulting from traumatic life experiences). Therefore, the purpose of this study was to examine how people with Parkinson\u27s experience social interactions and physical challenges in a group physical activity program, and to investigate what role they think those experiences play in posttraumatic growth. The study employed interpretative phenomenological analysis methodology (Smith, Flowers & Larkin, 2009). N= 20 participants ( n = 12 women; age = 56-79 years) in a boxing-based group exercise program for people with Parkinson\u27s were interviewed. The findings included four collective narratives characterized by (1) finding a safe space in the program; (2) perceiving improvement in symptoms through self-regulation despite loss of control; (3) anxiety relief through shared humor with others who have Parkinson\u27s; and (4) focusing on helping others in lower level classes. The findings of this research may have important implications for how to structure adaptive group physical activity programs for those with Parkinson\u27s disease

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

Social Comparisons, Social Support, and Self-Perceptions in Group Exercise for People With Parkinson's Disease

People with Parkinson's disease (PD) may experience declining function and limited interaction with others with PD. Group exercise provides opportunities for physical accomplishment and social support, as well as potential social challenges. We used interpretative phenomenological analysis to examine experiences of social comparison, social support, and self-perceptions of 20 people with PD in group exercise. Participants experienced (a) reticence evolving to inspiration, (b) anxiety relief through camaraderie and breaking taboos, and (c) maintaining athletic identity through participating and helping others. Practical implications include facilitating a safe space and support to alleviate anxiety and sustain participation

Imaging of the Stellar Population of IC10 with Laser Guide Star Adaptive Optics and the Hubble Space Telescope

We present adaptive optics (AO) images of the central starburst region of the dwarf irregular galaxy IC10. The Keck 2 telescope laser guide star was used to achieve near diffraction-limited performance at H and K' (Strehls of 18% and 32%, respectively). The images are centered on the putative Wolf-Rayet (W-R) object [MAC92]24. We combine our AO images with F814W data from HST. By comparing the K' vs. [F814W]-K' color-magnitude diagram (CMD) with theoretical isochrones, we find that the stellar population is best represented by at least two bursts of star formation, one ~ 10 Myr ago and one much older (150-500 Myr). Young, blue stars are concentrated in the vicinity of [MAC92]24. This population represents an OB association with a half-light radius of about 3 pc. We resolve the W-R object [MAC92]24 into at least six blue stars. Four of these components have near-IR colors and luminosities that make them robust WN star candidates. By matching the location of C-stars in the CMD with those in the SMC we derive a distance modulus for IC10 of about 24.5 mag. and a foreground reddening of E(B-V) = 0.95. We find a more precise distance by locating the tip of the giant branch in the F814W, H, and K' luminosity functions. We find a weighted mean distance modulus of 24.48 +/- 0.08. The systematic error in this measurement, due to a possible difference in the properties of the RGB populations in IC10 and the SMC, is +/- 0.16 mag.Comment: 13 pages, 13 figures, ApJ in pres

Density of states in d-wave superconductors disordered by extended impurities

The low-energy quasiparticle states of a disordered d-wave superconductor are investigated theoretically. A class of such states, formed via tunneling between the Andreev bound states that are localized around extended impurities (and result from scattering between pair-potential lobes that differ in sign) is identified. Its (divergent) contribution to the total density of states is determined by taking advantage of connections with certain one-dimensional random tight-binding models. The states under discussion should be distinguished from those associated with nodes in the pair potential.Comment: 5 pages, 1 figur

Exaggerated Sexual Swellings and the Probability of Conception in Wild Sanje Mangabeys (Cercocebus sanjei)

© 2017, The Author(s). Females of several catarrhine primate species exhibit exaggerated sexual swellings that change in size and coloration during the menstrual cycle and, in some species, gestation. Although their function remains under debate, studies indicate that swellings may contain information males could use to discern ovulation and the probability that a cycle will be conceptive. Here we combine visual ratings of swellings with hormonal data for a group of Sanje mangabeys (18 adult, 3 adolescent females) to determine if their swellings provide reliable information on female fertility. In all cases where ovulation was detected (N=7), it occurred during maximum tumescence, and in 83.3% during the first two days of the “shiny phase,” a period during maximum tumescence when the swelling was brightest. There were no significant differences in maximum tumescence and shiny phase duration among cycles of different probability of conception, although there was a trend toward conceptive cycles exhibiting shorter shiny phases than nonconceptive ones. Only 25% (N=4) of postconceptive swellings developed the shiny phase, and adolescents displayed the longest maximum tumescence and shiny phases. The conspicuous nature of the shiny phase and the frequent overlap between its onset and ovulation suggest that its presence serves as a general signal of ovulation and that the cycle has a high probability of being conceptive. It also suggests that swellings in some Sanje mangabeys are more accurate signals of fertility than in other primates