Creation and characterization of vortex clusters in atomic Bose-Einstein condensates

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed, or induce clusters of like-signed vortices in 2D Bose-Einstein condensates. We propose new statistical measures of clustering based on Ripley's K-function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.Comment: 15 pages, 9 figure

Environmental limits to the distribution of Scaevola plumieri along the South African coast

Scaevola plumieri is an important pioneer on many tropical and subtropical sand dunes, forming a large perennial subterranean plant with only the tips of the branches emerging above accreting sand. In South Africa it is the dominant pioneer on sandy beaches along the east coast, less abundant on the south coast and absent from the southwest and west coasts. Transpiration rates (E) of S. plumieri are predictably related to atmospheric vapour pressure deficit under a wide range of conditions and can therefore be predicted from measurement of ambient temperature and relative humidity. Scaling measurements of E at the leaf level to the canopy level has been demonstrated previously. Using a geographic information system, digital maps of regional climatic variables were used to calculate digital maps of potential transpiration from mean monthly temperature and relative humidity values, effectively scaling canopy level transpiration rates to a regional level. Monthly potential transpiration was subtracted from the monthly median rainfall to produce a map of mean monthly water balance. Seasonal growth was correlated with seasonal water balance. Localities along the coast with water deficits in summer corresponded with the recorded absence of S. plumieri, which grows and reproduces most actively in the summer months. This suggests that reduced water availability during the summer growth period limits the distribution of S. plumieri along the southwest coast, where water deficits develop in summer. Temperature is also important in limiting the distribution of S. plumieri on the southwest coast of South Africa through its effects on the growth and phenology of the plant

Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Pollination biology of Bergeranthus multiceps (Aizoaceae) with preliminary observations of repeated flower opening and closure

Little is known about pollination of the Aizoaceae (Mesembryanthemaceae). There are sparse reports of generalist pollination in the family by a variety of insects (predominantly bees). Furthermore, most species are self-incompatible in cultivation. In this study, observations were made on two populations of Bergeranthus multiceps (Salm-Dyck) Schwantes growing in the Eastern Cape province of South Africa. Insects visiting the flowers were collected and examined for pollen. While 79 individual insects (in 24 genera representing 14 families and four orders) were collected visiting the flowers, the majority (43 individuals) were female Allodapula variegata bees (Apidae, subfamily Xylocopinae, tribe Allodapini)collecting pollen. All other bee visitors were also female, suggesting pollen collection as the primary activity at the flowers. The protandrous flowers were found to be self-incompatible, pointing to the importance of bee-mediated xenogamy in this species. The flowers of B. multiceps are bright yellow in the human visual spectrum. In addition, the petals of this species reflect ultraviolet light. In contrast, the yellow anthers absorb UV. Flower opening and closing is common in the Aizoaceae. Interestingly, in B. multiceps flowers open at about 15:30 and remain open for approximately three hours before closing again in the late afternoon. These afternoon flower opening events were found to be closely correlated to ambient temperatures above 23°C, relative humidity lower than 50% and vapour pressure deficit below 1.05 kPa measured from as early as 09:00 on the days when flowers opened

Quantification of the photosynthetic performance of phosphorus-deficient Sorghum by means of chlorophyll-a fluorescence kinetics

Chlorophyll fluorescence induction curves have been used as a sensitive tool for screening the photosynthetic performance of plants. Experimental treatments involving nitrate supply and chilling stress have been shown to affect fluorescence induction curves and other measures of photosynthesis. We have investigated the photosynthetic performance of Sorghum bicolor supplied with Long Ashton growth solution containing standard (20 μmol mol^(–1)) or low (5 μmol mol^(–1)) phosphorus. The JIP-test based on the chlorophyll fluorescence induction curve was used as a non-destructive method to measure the relative proportions of energy dissipated by different processes (termed energy fluxes) in the light reactions. The various energy fluxes or derived parameters were compared to find the measures that were most sensitive to the experimental conditions. Plant response to treatments was first evident in selected chlorophyll fluorescence parameters, particularly performance index (PI_ABS_); plants with increased PI_ABS_ manifested higher electron transport activity and dissipated less energy as heat, possibly as a result of their better phosphorus status, leading to more functional reaction centres. Observed changes in fluorescence were correlated to changes in gas exchange and biomass. Standard phosphorus treatments significantly increased biomass, leaf area, photosynthetic and respiratory rates, carboxylation efficiencies and levels of ribulose biphosphate regeneration rates, relative to plants with low supplies of nutrients

Comparing models for predicting species' potential distributions : a case study using correlative and mechanistic predictive modelling techniques

Models used to predict species’ potential distributions have been described as either correlative or mechanistic. We attempted to determine whether correlative models could perform as well as mechanistic models for predicting species potential distributions, using a case study. We compared potential distribution predictions made for a coastal dune plant (Scaevola plumieri) along the coast of South Africa, using a mechanistic model based on summer water balance (SWB), and two correlative models (a profile and a group discrimination technique). The profile technique was based on principal components analysis (PCA) and the group-discrimination technique was based on multiple logistic regression (LR). Kappa (κ) statistics were used to objectively assess model performance and model agreement. Model performance was calculated by measuring the levels of agreement (using κ) between a set of testing localities (distribution records not used for model building) and each of the model predictions. Using published interpretive guidelines for the kappa statistic, model performance was “excellent” for the SWB model (κ=0.852), perfect for the LR model (κ=1.000), and “very good” for the PCA model (κ=0.721). Model agreement was calculated by measuring the level of agreement between the mechanistic model and the two correlative models. There was “good” model agreement between the SWB and PCA models (κ=0.679) and “very good” agreement between the SWB and LR models (κ=0.786). The results suggest that correlative models can perform as well as or better than simple mechanistic models. The predictions generated from these three modelling designs are likely to generate different insights into the potential distribution and biology of the target organism and may be appropriate in different situations. The choice of model is likely to be influenced by the aims of the study, the biology of the target organism, the level of knowledge the target organism’s biology, and data quality

How good are your fits? Unbinned multivariate goodness-of-fit tests in high energy physics

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned methods for determining the goodness of fit of the p.d.f. to the data. The application and performance of each method is discussed in the context of a real-life high energy physics analysis (a Dalitz-plot analysis). Several of the methods presented in this paper can also be used for the non-parametric determination of whether two samples originate from the same parent p.d.f. This can be used, e.g., to determine the quality of a detector Monte Carlo simulation without the need for a parametric expression of the efficiency.Comment: 32 pages, 12 figure

Frequency Dependent Rheology of Vesicular Rhyolite

Frequency dependent rheology of magmas may result from the presence of inclusions (bubbles, crystals) in the melt and/or from viscoelastic behavior of the melt itself. With the addition of deformable inclusions to a melt possessing viscoelastic properties one might expect changes in the relaxation spectrum of the shear stresses of the material (e.g., broadening of the relaxation spectrum) resulting from the viscously deformable geometry of the second phase. We have begun to investigate the effect of bubbles on the frequency dependent rheology of rhyolite melt. The present study deals with the rheology of bubble-free and vesicular rhyolite melts containing spherical voids of 10 and 30 vol %. We used a sinusoidal torsion deformation device. Vesicular rhyolite melts were generated by the melting (at 1 bar) of an Armenian obsidian (Dry Fountain, Erevan, Armenia) and Little Glass Mountain obsidian (California). The real and imaginary parts of shear viscosity and shear modulus have been determined in a frequency range of 0.005–10 Hz and temperature range of 600°–900°C. The relaxed shear viscosities of samples obtained at low frequencies and high temperatures compare well with data previously obtained by parallel plate viscometry. The relaxed shear viscosity of vesicular rhyolites decreases progressively with increasing bubble content. The relaxation spectrum for rhyolite melt without bubbles has an asymmetric form and fits an extended exponent relaxation. The presence of deformable bubbles results in an imaginary component of the shear modulus that becomes more symmetrical and extends into the low-frequency/high-temperature range. The internal friction Q −1 is unaffected in the high-frequency/low-temperature range by the presence of bubbles and depends on the bubble content in the high-temperature/low-frequency range. The present work, in combination with the previous study of Stein and Spera (1992), illustrates that magma viscosity can either increase or decrease with bubble content, depending upon the rate of style of strain during magmatic flow