Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

Distribution of 25 semi-volatile organic compounds of two urban lakes in Wuhan, China

In this study, the levels of 25 semi-volatile organic compounds (SVOCs) were measured in samples of water, suspended particulate matter (SPM) and sediment from two urban lakes in Wuhan, China. The total concentrations of 25 SVOCs varied from 529.4 to 2168.9 ng/L, 120.7 to 22543.7 ng/g dry weight and 1577.3 to 61579.6 ng/g dry wt. in water, SPM and sediment, respectively. The concentration of SVOCs in SPM was 9-10 times higher than that in water, and the concentration of SVOCs in sediment 1.5-2 times higher than that in SPM. The level of total SVOC25 in the samples from Moshuihu Lake was higher than that in Yuehu Lake. Among the 25 SVOCs, phthalate compounds were on the highest level in all observed samples ranging between 441.9-1831.2 ng/L, 116.3-17566.8 ng/g, dry wt. and 6432.8-48177.6 ng/g dry wt. in water, SPM and sediment, respectively. Bis(2-ethylhexyl)phthalate, the predominant component of the analyzed pollutants, was in the range from 246.7 to 537.5 ng/l, 51.2 to 15540.0 ng/g dry wt. and 468.2 to 45010.3 ng/g dry wt. in water, SPM and sediment, respectively. The content of PAHs, dinitrotoluene and isophoton in sediment was higher than that in water and SPM at most of the locations. The possible sources of the pollutants and their inter-relation with human activities were discussed.

Gastropods on submersed macrophytes in Yangtze lakes: Community characteristics and empirical modelling

Epiphytic gastropods in Yangtze lakes have suffered from large-scale declines of submersed macrophytes during past decades. To better understand what controls gastropod community, monthly investigations were carried out in four Yangtze lakes during December, 2001-March, 2003. Composed of 23 species belonging to Pulmonata and Prosobranchia, the community is characterized by the constitution of small individuals. The average density and biomass were 417 +/- 160 ind/m(2) and 18.05 +/- 7.43 g/m(2), with maxima a-round August. Submersed macrophyte biomass is shown to be the key factor affecting species number, density, and biomass of gastropods. Accordingly, a series of annual and seasonal models yielding high predictive powers were generated. Preference analyses demonstrated that pulmonates and prosobranchs with different respiratory organs prefer different macrophyte functional groups.

Empirical modelling of submersed macrophytes in Yangtze lakes

Submersed macrophytes in Yangtze lakes have experienced large-scale declines due to the increasing human activities during past decades. To seek the key factor that affects their growth, monthly investigations of submersed macrophytes were conducted in 20 regions of four Yangtze lakes during December, 2001-March, 2003. Analyses based on annual values show that the ratio of Secchi depth to mean depth is the key factor (50% of macrophyte biomass variability among these lakes is statistically explained). Further analyses also demonstrate that the months from March to June are not only the actively growing season for most macrophytes, but the key time the factor acts. Five key-time models yielding higher predictive power (r(2) reaches 0.75,0.76,0.77,0.69 and 0.81) are generated. A comparison between key-time models and traditional synchronic ones indicates that key-time models have higher predictive power. Analyses of transparency thresholds during macrophyte growing season and the limitations of the models are presented. The models and other results may benefit the work concerning submersed macrophyte recovery in Yangtze lakes. (c) 2005 Elsevier B.V. All rights reserved.

Classification using log Gaussian Cox processes

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.

Quantum Mechanical Study on Tunnelling and Ballistic Transport of Nanometer Si MOSFETs

Using self-consistent calculations of million-atom Schrodinger-Poisson equations, we investigate the I-V characteristics of tunnelling and ballistic transport of nanometer metal oxide semiconductor field effect transistors (MOSFET) based on a full 3-D quantum mechanical simulation under nonequilibtium condition. Atomistic empirical pseudopotentials are used to describe the device Hamiltonian and the underlying bulk band structure. We find that the ballistic transport dominates the I-V characteristics, whereas the effects of tunnelling cannot be neglected with the maximal value up to 0.8mA/mu m when the channel length of MOSFET scales down to 25 nm. The effects of tunnelling transport lower the threshold voltage V-t. The ballistic current based on fully 3-D quantum mechanical simulation is relatively large and has small on-off ratio compared with results derived from the calculation methods of Luo et al.

Sixfold symmetry of excitonic transition energies in c-plane for wurtzite GaN

The optical properties of the strained wurtzite GaN are investigated theoretically within the nearest neighbor tight-binding method. The piezoelectric effect is also taken into account. The empirical rule has been used in the strained band-structure calculation. The results show that the excitonic transition energies are anisotropic in the c-plane in a high electronic concentration system and have a 60 degrees periodicity, which is in agreement with experiment. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3001937]

Multiple valley couplings in nanometer Si metal-oxide-semiconductor field-effect transistors

We investigate the couplings between different energy band valleys in a metal-oxide-semiconductor field-effect transistor (MOSFET) device using self-consistent calculations of million-atom Schrodinger-Poisson equations. Atomistic empirical pseudopotentials are used to describe the device Hamiltonian and the underlying bulk band structure. The MOSFET device is under nonequilibrium condition with a source-drain bias up to 2 V and a gate potential close to the threshold potential. We find that all the intervalley couplings are small, with the coupling constants less than 3 meV. As a result, the system eigenstates derived from different bulk valleys can be calculated separately. This will significantly reduce the simulation time because the diagonalization of the Hamiltonian matrix scales as the third power of the total number of basis functions. (C) 2008 American Institute of Physics.

A fully three-dimensional atomistic quantum mechanical study on random dopant-induced effects in 25-nm MOSFETs

A fully 3-D atomistic quantum mechanical simulation is presented to study the random dopant-induced effects in nanometer metal-oxide-semiconductor field-effect transistors. The empirical pseudopotential is used to represent the single particle Hamiltonian, and the linear combination of bulk band method is used to solve the million atom Schrodinger equation. The gate threshold fluctuation and lowering due to the discrete dopant configurations are studied. It is found that quantum mechanical effects increase the threshold fluctuation while decreasing the threshold lowering. The increase of threshold fluctuation is in agreement with the researchers' early study based on an approximated density gradient approach. However, the decrease in threshold lowering is in contrast with the density gradient calculations.

Integratable and High Speed Complex-Coupled MQW-DFB Lasers Fabricated on Semi-Insulating Substrates

A novel integratable and high speed InGaAsP multi-quantum well (MQW) complex-coupled distributed feedback (DFB) laser is successfully fabricated on a semi-insulating substrate. The fabricated ridge DFB laser exhibits a threshold current of 26 mA, a slope efficiency of 0.14 W.A(-1) and a side mode suppression ratio of 40 dB together with a 3 dB bandwidth of more than 8 GHz. The device is suitable for 10 Gbit/s optical fiber communication.