Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Geometric perspectives on MDO and MDO architectures

Two main perspectives have been developed within the Multidisciplinary Design Optimization (MDO) literature for classifying and comparing MDO architectures: a numerical point of view and a formulation/data flow point of view. Although significant work has been done here, these perspectives have not provided much in the way of a priori information or predictive power about architecture performance. In this report, we outline a new perspective, called the geometric perspective, which we believe will be able to provide such predictive power. Using tools from differential geometry, we take several prominent architectures and describe mathematically how each constructs the space through which it moves. We then consider how the architecture moves through the space which it has constructed. Taken together, these investigations show how each architecture relates to the original feasible design manifold, how the architectures relate to each other, and how each architecture deals with the design coupling inherent to the original system. This in turn lays the groundwork for further theoretical comparisons between and analyses of MDO architectures and their behaviour using tools and techniques derived from differential geometry. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Temporal and Spatial Distributions of Rotifers in Xiangxi Bay of the Three Gorges Reservoir, China

From July 2003 to June 2005, investigations of rotifer temporal and spatial distributions were carried out in a bay of the Three Gorges Reservoir, Xiangxi Bay, which is the downstream segment of the Xiangxi River and the nearest bay to the Three Gorges Reservoir dam in Hubei Province, China. Thirteen sampling sites were selected. The results revealed a high species diversity, with 76 species, and 14 dominant species; i.e., Polyarthra vulgaris, Keratella cochlearis, Keratella valga, Synchaeta tremula, Synchaeta stylata, Trichocerca lophoessa, Trichocerca pusilla, Brachionus angularis, Brachionus calyciflorus, Brachionus forficula forficula, Ascomorpha ovalis, Conochilus unicornis, Ploesoma truncatum and Anuraeopsis fissa. After the first year of the reservoir impoundment, the rotifer community was dominated by ten species; one year later it was dominated by eight species. The community in 2003/2004 was dissimilar to that in 2004/2005, which resulted from the succession of the dominant species. The rotifer community exhibited a patchy distribution, with significant heterogeneity observed along the longitudinal axis. All rotifer communities could be divided into three groups, corresponding to the riverine, the transition and the lacustrine zone, respectively.

VERTICAL DISTRIBUTIONS OF SIZE-FRACTIONATED IRON IN THREE TYPICAL BAYS OF LAKE DIANCHI (CHINA)

In order to elucidate the vertical distributions of iron in three typical bays (Haigeng bay, Macun bay and Haidong bay) of Lake Dianchi (China), the investigation was conducted on March, 2003. Results showed that the vertical distributions were influenced by monsoon, cyanobacterial bloom and water depth as well as sediment resuspension, which indicated that their translocations and transformations were decided by geographical and physical as well as chemical and biological characteristics.

Tissue distributions and seasonal dynamics of the hepatotoxic microcystins-LR and -RR in two freshwater shrimps, Palaemon modestus and Macrobrachium nipponensis, from a large shallow, eutrophic lake of the subtropical China

So far no information is available on microcystin (MC) contents in shrimps, prawns or crayfish from natural freshwaters. Tissue distributions and seasonal dynamics of the hepatotoxic MC-LR and -RR in two freshwater shrimps, Palaemon modestus and Macrobrachium nipponensis were studied monthly (during June-November, 2003) in a Chinese lake containing toxic cyanobacterial blooms. The shrimps P. modestus and M. nipponensis accumulated high MCs not only in the hepatopancreas (mean 4.29 and 0.53 mu g g(-1) DW, respectively) but also in the gonad (mean 1.17 and 0.48 mu g g-1 DW, respectively), and the crayfish Procambarus clarkii accumulated as much as 0.93 mu g g(-1) DW in the gonad. This indicates that gonads of these invertebrates are the second important target organ of MCs. P. modestus apparently accumulated more MCs in their organs than M. nipponensis, which might be a reflection of their difference in trophic niche. Eggs of the shrimps accumulated 8.4% (M. nipponensis, 0.27 mu g g(-1) DW) and 29.0% (P. modestus, 2.34 mu g g(-1) DW) of total toxin burden, indicating that MCs had been transferred into offspring from their adults. Among the shrimp muscle samples analyzed, 31% were above the provisional WHO TDI level, suggesting the risk of consuming shrimps in Lake Chaohu. (c) 2005 Elsevier Ltd. All rights reserved.

Tissue distributions and seasonal dynamics of the hepatotoxic microcystins-LR and -RR in a freshwater snail (Bellamya aeruginosa) from a large shallow, eutrophic lake of the subtropical China

Tissue distributions and seasonal dynamics of the hepatotoxic microcystins-LR and -RR in a freshwater snail (Bellamya aeruginosa) were studied monthly in a large shallow, eutrophic lake of the subtropical China during June-November, 2003. Microcystins (MCs) were quantitatively determined by High-Performance Liquid Chromatography (HPLC) with a qualitative analysis by a Finnigan LC-MS system. On the average of the study period, hepatopancreas was the highest in MC contents (mean 4.14 and range 1.06-7.42 mug g(-1) DW), followed by digestive tracts (mean 1.69 and range 0.8-4.54 mug g(-1) DW) and gonad (mean 0.715 and range 0-2.62 mug g(-1) DW), whereas foot was the least (mean 0.01 and range 0-0.06 mug g(-1) DW). There was a positive correlation in MC contents between digestive tracts and hepatopancreas. A constantly higher MC content in hepatopancreas than in digestive tracts indicates a substantial bioaccumulation of MCs in the hepatopancreas of the snail. The average ratio of MC-LR/MC-RR showed a steady increase from digestive tracts (0.44) to hepatopancreas (0.63) and to gonad (0.96), suggesting that MC-LR was more resistant to degradation in the snail. Since most MCs were present in the hepatopancreas, digestive tracts and gonad with only a very small amount in the edible foot, the risk to human health may not be significant if these toxic parts are removed prior to snail consumption. However, the possible transference of toxins along food chains should not be a negligible concern. (C) 2004 Elsevier Ltd. All rights reserved.

A derivation of the source-channel error exponent using nonidentical product distributions

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight. © 2014 IEEE.

Suckers (Fish, Catostomidae) from the Eocene of China account for the family's current disjunct distributions

Unequivocal Eocene suckers from China are for the first time reported here. This discovery demonstrates that catostomids of the Eocene Epoch (some 55-35 Ma ago) are scattered widely on mainland Asia as well as western North America. The present day disjunct distribution pattern of catostomids, with 68 extant species widespread in North America and the northern part of Middle America and only two in the restricted areas of Asia, is the result of their post-Eocene decline in Asia due to the competitive pressure from cyprinids, their Late Cenozoic radiation in North America, and the vicariant and dispersal events triggered by the changed biogeographic landscape. All of these prove to be a historical product of the geological, biological, and climatic changes throughout the Cenozoic.

Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously. and can also cause sudden change of the Berry phase for some weak magnetic field cases. (c) 2008 Elsevier B.V. All rights reserved.

Size distributions of quantum islands on stepped substrates

The size distributions of self-assembled quantum islands on stepped substrates are studied using kinetic Monte Carlo simulations. It is found that the energy barrier E-SW between the step and the terrace region is the key factor in affecting the size distribution of islands. With small E-SW (<= 0.1 eV), lines of uniform islands can be obtained at relative low surface coverage. As the surface coverage is increased, wirelike islands can be obtained. Scaling behavior is obeyed for the size distributions of the wirelike islands. When the size distributions are separated into their width and length components, however, scaling is only observed in the length distribution of the wirelike islands. With larger E-SW, the size distribution of islands shows a clear bimodal size distribution and anomalous growth temperature dependent island size evolutions are observed. The simulation results reproduce qualitatively the phenomena observed in the cases of InAs islands grown on stepped GaAs substrates. (c) 2009 American Institute of Physics. [doi:10.1063/1.3248367]

The strain distributions and carrier's confining potentials of self-organized InAs/GaAs quantum dot

On the basis of the finite element approach, we systematically investigated the strain field distribution of conical-shaped InAs/GaAs self-organized quantum dot using the two-dimensional axis-symmetric model. The normal strain, the hydrostatic strain and the biaxial strain components along the center axis path of the quantum dots are analyzed. The dependence of these strain components on volume, height-over-base ratio and cap layer (covered by cap layer or uncovered quantum dot) is investigated for the quantum grown on the (001) substrate. The dependence of the carriers' confining potentials on the three circumstances discussed above is also calculated in the framework of eight-band k (.) p theory. The numerical results are in good agreement with the experimental data of published literature.

Finite element analysis of stress and strain distributions in InAs/GaAs quantum dots

In this paper, we perform systematic calculations of the stress and strain distributions in InAs/GaAs truncated pyramidal quantum dots (QDs) with different wetting layer (WL) thickness, using the finite element method (FEM). The stresses and strains are concentrated at the boundaries of the WL and QDs, are reduced gradually from the boundaries to the interior, and tend to a uniform state for the positions away from the boundaries. The maximal strain energy density occurs at the vicinity of the interface between the WL and the substrate. The stresses, strains and released strain energy are reduced gradually with increasing WL thickness. The above results show that a critical WL thickness may exist, and the stress and strain distributions can make the growth of QDs a growth of strained three-dimensional island when the WL thickness is above the critical value, and FEM can be applied to investigate such nanosystems, QDs, and the relevant results are supported by the experiments.

Ultrafast geometric manipulation of electron spin and detection of the geometric phase via Faraday rotation spectroscopy

Time-resolved Faraday rotation spectroscopy is currently exploited as a powerful technique to probe spin dynamics in semiconductors. We propose here an all-optical approach to geometrically manipulate electron spin and to detect the geometric phase by this type of extremely sensitive experiment. The global nature of the geometric phase can make the quantum manipulation more stable, which may find interesting applications in quantum devices.