Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

Coboson formalism for Cooper pairs used to derive Richardson's equations

We propose a many-body formalism for Cooper pairs which has similarities to the one we recently developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences that $N$ Cooper pairs differ from $N$ single pairs through electron exchange only: no direct coupling exists due to the very peculiar form of the BCS potential. As a first application, we here use this formalism to derive Richardson's equations for the exact eigenstates of $N$ Cooper pairs. This gives hints on why the $N(N-1)$ dependence of the $N$-pair ground state energy we recently obtained by solving Richardson's equations analytically in the low density limit, stays valid up to the dense regime, no higher order dependence exists even under large overlap, a surprising result hard to accept at first. We also briefly question the BCS wave function ansatz compared to Richardson's exact form, in the light of our understanding of coboson many-body effects

Metal Surface Energy: Persistent Cancellation of Short-Range Correlation Effects beyond the Random-Phase Approximation

The role that non-local short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and non-uniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a non-local exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation and support the conclusion that the error introduced by the local-density approximation is small.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Range expansion of the hadeda ibis Bostrychia hagedash in southern Africa

The southern African range of the habeda ibis Bostrychia hagedash has expanded from 530 900 km 2 in 1910 to 1 323 300 km2 in 1985. Major range expansions have occurred in the fynbos biome of the south-western Cape, the Karoo, the grasslands of the eastern Cape, the Orange Free State and the Transvaal highveld. Smaller expansions are documented for Lesotho, eastern Zimbabwe, central Mozambique and westwards along the Zambezi, Okavango, Limpopo and Orange rivers. The reasons for this expansion were investigated. Important factors include reduction in human persecution following the introduction of legislation in the period 1934 to 1941 and an increase of alien trees in formerly treeless areas. The increases in artificial impoundments and areas under irrigation are thought to have played a smaller role

Instability of the rhodium magnetic moment as origin of the metamagnetic phase transition in alpha-FeRh

Based on ab initio total energy calculations we show that two magnetic states of rhodium atoms together with competing ferromagnetic and antiferromagnetic exchange interactions are responsible for a temperature induced metamagnetic phase transition, which experimentally is observed for stoichiometric alpha-FeRh. A first-principle spin-based model allows to reproduce this first-order metamagnetic transition by means of Monte Carlo simulations. Further inclusion of spacial variation of exchange parameters leads to a realistic description of the experimental magneto-volume effects in alpha-FeRh.Comment: 10 pages, 13 figures, accepted for publication in Phys. Rev.

Heterogeneous space-division multiplexing and joint wavelength switching demonstration

We demonstrate a six spatial-mode, wavelength-routing network interoperable with few-mode, coupled-multi-core, and single-mode fiber spans using a custom 57-port wavelength-selective switch configured for joint-switching of spatial-superchannels

Allelopathic effects of invasive Eucalyptus camaldulensis on germination and early growth of four native species in the Western Cape, South Africa

Eucalyptus camaldulensis Dehnh. (red river gum; Myrtaceae) is an invasive tree in riparian habitats of the Western Cape, South Africa, where it replaces indigenous vegetation and affects ecosystem functioning. These invasions lead to changes in river geomorphology and reduction in stream flow. The mechanisms that drive these effects are poorly understood. The potential for allelopathic effects of aqueous extracts of E. camaldulensis tissues and of soil and litter collected beneath E. camaldulensis trees on the germination and seedling growth of four selected native plant species was investigated in a greenhouse experiment. Soils collected beneath E. camaldulensis trees were used in three treatments: untreated soils, sterilised soils and sterilised soils overlaid with a eucalypt litter layer. In addition, soils collected from underneath native species were used in two treatments: untreated soils and soils overlaid with a eucalypt litter layer. All soil treatments were watered with three E. camaldulensis leaf, bark and root aqueous treatments. Compounds present in the aqueous extracts and fresh samples were identified using gas chromatography. Soil and aqueous treatments showed varying effects on germination and seedling growth of the four native species. Germination and seedling growth of Olea europaea subsp. africana and Dimorphotheca pluvialis were significantly reduced by E. camaldulensis root and bark aqueous extracts as well as by the soils treatments. The addition of eucalypt litter to native and sterilised soils reduced shoot and root growth of all four native species. Compounds such as -phellandrene, eucalyptol, p-menth-1-en-8-ol and a-pinene, which have the potential to inhibit germination and plant growth, were identified in E. camaldulensis aqueous extracts and fresh samples. Although the methods applied in this study had limitations (e.g. lack of control treatment to litter addition), the results provide an additional motivation to prioritise removal of invasive E. camaldulensis stands from riparian ecosystems. Restoration initiatives should target native species that are not negatively affected by allelopathy

Performance of seedlings of the invasive alien tree Schinus molle L. under indigenous and alien host trees in semi-arid savanna

We assessed the importance of host trees in influencing invasion patterns of the alien tree Schinus molle L. (Anacardiaceae) in semi-arid savanna in South Africa. Recruitment of S. molle is dependent on trees in its invaded habitat, particularly Acacia tortilis Hayne. Another leguminous tree, the invasive alien mesquite (Prosopis sp.), has become common in the area recently, but S. molle rarely recruits under canopies of this species. Understanding of the association between these species is needed to predict invasion dynamics in the region. We conducted experiments to test whether: (i) seedling survival of S. molle is better beneath A. tortilis than beneath mesquite canopies; (ii) growth rates of S. molle seedlings are higher beneath A. tortilis than beneath mesquite. Results showed that growth and survival of S. molle did not differ significantly beneath the native A. tortilis and the alien Prosopis species. This suggests that microsites provided by canopies of mesquite are as good for S. molle establishment as those provided by the native acacia. Other factors, such as the failure of propagules to arrive beneath mesquite trees, must be sought to explain the lack of recruitment beneath mesquite.Centre of Excellence for Invasion Biolog