Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. © 2013 Springer-Verlag Berlin Heidelberg.

Photosynthetic physiology and growth as a function of colony size in the cyanobacterium Nostoc sphaeroides

Algal size can affect the rate of metabolism and of growth. Different sized colonies of Nostoc sphaeroides were used with the aim of determining the effects of colony size on photosynthetic physiology and growth. Small colonies showed higher maximum photosynthetic rates per unit chlorophyll, higher light saturation point, and higher photosynthetic efficiency (a) than large colonies. Furthermore, small colonies had a higher affinity for DIC and higher DIC-saturated photosynthetic rates. In addition, small colonies showed higher photosynthetic rates from 5-45degreesC than large colonies. There was a greater decrease in Fv/Fm after exposure to high irradiance and less recovery in darkness for large colonies than for small colonies. Relative growth rate decreased with increasing colony size. Small colonies had less chl a and mass per unit surface area. The results indicate that small colonies can harvest light and acquire DIC more efficiently and have higher maximum photosynthetic rates and growth rates than large colonies.

Optimization of growth and fatty acid composition of a unicellular marine picoplankton, Nannochloropsis sp., with enriched carbon sources

A unicellular marine picoplankton, Nannochloropsis sp., was grown under CO2-enriched photoautotrophic or/and acetate-added mixotrophic conditions. Photoautotrophic conditions with enriched CO2 of 2800 mul CO2 l(-1) and aeration gave the highest biomass yield (634 mg dry wt l(-1)), the highest total lipid content (9% of dry wt), total fatty acids (64 mg g(-1) dry wt), polyunsaturated fatty acids (35% total fatty acids) and eicosapentaenoic acid (EPA, 20:5omega3) (16 mg g(-1) dry wt or 25% of total fatty acids). Mixotrophic cultures gave a greater protein content but less carbohydrates. Adding sodium acetate (2 mM) decreased the amounts of the total fatty acids and EPA. Elevation of CO2 in photoautotrophic culture thus enhances growth and raises the production of EPA in Nannochloropsis sp.

Optimization of control parameters for petroleum waste composting

Composting is being widely employed in the treatment of petroleum waste. The purpose of this study was to find the optimum control parameters for petroleum waste in-vessel composting. Various physical and chemical parameters were monitored to evaluate their influence on the microbial communities present in composting. The CO2 evolution and the number of microorganisms were measured as the activity of composting. The results demonstrated that the optimum temperature, pH and moisture content were 56.5 - 59.5 degreesC, 7.0 - 8.5 and 55 % - 60%, respectively. Under the optimum conditions, the removal efficiency of petroleum hydrocarbon reached 83.29% after 30 days composting.

Studies of polysaccharides from three edible species of Nostoc (cyanobacteria) with different colony morphologies: Structural characterization and effect on the complement system of polysaccharides from Nostoc commune

The cyanobacterium Nostoc commune Vaucher produces quite complex extracellular polysaccharides. The cyanobacterium is nitrogen fixing, and on growing the cyanobacterium in media with and without nitrogen, different types of extracellular polysaccharides were obtained. These were also different from the polysaccharides present in N. commune collected in the field. High pH anion exchange chromatography (HPAEC) of weak acid hydrolysates of the culture-grown material demonstrated that, in this case, HPAEC was useful for comparison of the different polymers. The main differences between the polymers from the field group and the culture-grown samples were the presence of substantial amounts of arabinose, 2-O-methylglucose, and glucuronic acid in the latter. Methylation studies also revealed a difference in the branching points on the glucose units between the field and cultured samples, being 1,4,6 for the first and 1,3,6 for the latter. The field acidic fraction gave, on weak acid hydrolysis and separation on BioGel P2 and HPAEC, 12 oligosaccharide fractions that were isolated and studied by different mass spectroscopy techniques. The structures of the oligosaccharides were determined, and two different series that can originate from two repeating pentamers were identified: GlcAl-4/6GlcM1-4Ga11-4Glc1-4Xyl and GlcAl-4/6Glc1-4Ga11-4Glc1-4Xyl. The difference between these oligosaccharides lies in the methyl substituent on carbon 2 of the glucose unit next to the nonreducing glucuronic acid unit. The polysaccharides from field material were shown to have a strong effect on the complement system.

Studies on polysaccharides from three edible species of Nostoc (Cyanobacteria) with different colony morphologies: Comparison of monosaccharide compositions and viscosities of polysaccharides from field colonies and suspension cultures

Hot water-soluble polysaccharides woe extracted from field colonies and suspension cultures of Nostoc commune Vaucher, Nostoc flagelliforme Berkeley et Curtis, and Nostoc sphaeroides Kutzing. Excreted extracellular polymeric substances (EPS) were isolated from the media in which the suspension cultures were grown. The main monosaccharides of the field colony polysaccharides from the three species were glucose, xylose, and galactose, with an approximate ratio of 2:1:1. Mannose was also present, but the levels varied among the species, and arabinose appeared only in N. flagelliforme. The compositions of the cellular polysaccharides and EPS from suspension cultures were more complicated than those of the field samples and varied among the different species. The polysaccharides from the cultures of N. flagelliforme had a relatively simple composition consisting of mannose, galactose, glucose, and glucuronic acid, but no xylose, as was found in the field colony polysaccharides. The polysaccharides from cultures of N. sphaeroides contained glucose (the major component), rhamnose, fucose, xylose, mannose, and galactose. These same sugars were present in the polysaccharides from cultures of N. commune, with xylose as the major component. Combined nitrogen in the media had no qualitative influence on the compositions of the cellular polysaccharides but affected those of the EPS of N. commune and N. flagelliforme. The EPS of N. sphaeroides had a very low fetal carbohydrate content and thus was not considered to be polysaccharide in nature. The field colony polysaccharides could be separated by anion exchange chromatography into neutral and acidic fractions having similar sugar compositions. Preliminary linkage analysis showed that 1) xylose, glucose, and galactose were 1-->4 linked, 2) mannose, galactose, and xylose occurred as terminal residues, and 3) branch points occurred in glucose as 1-->3,4 and 1-->3,6 linkages and in xylose as a 1-->3,4 linkage. The polymer preparations from field colonies had higher kinematic viscosities than those from corresponding suspension cultures. The high viscosities of the polymers suggested that they might DE suitable for industrial uses.

Design and optimization of photonic crystal coupling layer for bi-color quantum well infrared photodetectors

Finite difference time domain (FDTD) method is used for the simulation and analysis of electromagnetic field in the top coupling layer of GaAs/AlGaAs quantum well infrared photodetector (QWIP). Simulation results demonstrated the coupling efficiencies and distributions of electromagnetic (EM) field in a variety of 2D photonic crystal coupling layer structures. A photonic crystal structure for bi-color-QWIP is demonstrated with high coupling efficiency for two wavelengths.

Optimization of metamorphic InGaAs quantum wells on GaAs grown by molecular beam epitaxy

We investigate the molecular beam epitaxy growth of metamorphic InxGa(1-x)As materials (x up to 0.5) on GaAs substrates systematically. Optimization of structure design and growth parameters is aimed at obtaining smooth surface and high optical quality. The optimized structures have an average surface roughness of 0.9-1.8 nm. It is also proven by PL measurements that the optical properties of high indium content (55%) InGaAs quantum wells are improved apparently by defect reduction technique and by introducing Sb as a surfactant. These provide us new ways for growing device quality metamorphic structures on GaAs substrates with long-wavelength emissions.

Fabrication and optical optimization of spot-size converters with strong cladding layers

A silicon-on-insulator (SOI) optical fiber-to-waveguide spot-size converter (SSC) overlaid with specially treated silica is investigated for integrated optical circuits. Unlike the conventional process of simply depositing the hot silica on silicon waveguides, two successive layers of silicon dioxide were grown on etched SSC structures by PECVD (plasma-enhanced chemical vapor deposition). The two layers have 0.8% index contrast and supply stronger cladding for an incident light beam. Additionally, this process is able to reduce the effective refractive index of the input mode to less than 1.47 (extremely close to that of the fiber), substantially weakening the unwanted back reflection. Exploiting this technology, it was demonstrated that the SSC showed a theoretical low mode mismatch loss of 1.23 dB for a TE-like mode and has an experimental coupling efficiency of 66%.

Overall optimization of high-speed semiconductor laser modules

Based on the high frequency techniques such as frequency response measurement, equivalent circuit modeling and packaging parasitics compensation, a comprehensive optimization method for packaging high-speed semiconductor laser module is presented in this paper. The experiments show that the small-signal magnitude frequency response of the TO packaged laser module is superior to that of laser diode in frequencies, and the in-band flatness and the phase-frequency linearity are also improved significantly.

Optimization of GaInNAs(Sb)/GaAs quantum wells at 1.3-1.55 mu m grown by molecular beam epitaxy

The InGaNAs(Sb)/(GaNAs)/GaAs quantum wells (QWs) emitting at 1.3-1.55 mu m have been grown by molecular beam epitaxy (MBE). The parameters of the radio frequency (RF) such as RF power and flow rate are optimized to reduce the damages from the ions or energetic species. The growth temperature is carefully controlled to prevent the phase segregation and strain relaxation. The effects of Sb on the wavelength and quality are investigated. The GaNAs barrier is used to extend the wavelength and reduce the strain. A 1.5865 mu m InGaNAs(Sb)/GaNAs SQW edge emitting laser lasing at room temperature at continuous wave operation mode is demonstrated. (c) 2006 Elsevier B.V. All rights reserved.

Grating optimization and experiment on high-power distributed feedback lasers

Coupling coefficient is an important parameter for distributed feedback lasers. Modified coupled-wave equations are used to calculate the effect of grating shape on coupling coefficient of the second-order gratings. Corresponding devices demonstrate that the maximum kink-free power per facet reaches 50 mW and the sidemode suppression ratio is 36 dB.

Structure optimization of field-plate AlGaN/GaN HEMTs

AlGaN/GaN high electron mobility transistors (HEMTs) on 6H-SiC with varying field-plate length and gate-drain spacing were fabricated and analyzed. The classical small signal FET model and the well-known ColdFET method were used to extract the small signal parameters of the devices. Though the devices with field plates exhibited lower better f(T) characteristic, they did demonstrate better f(max), MSG and power density performances than the conventional devices without field plate. Besides, no independence of DC characteristic on field-plate length was observed. With the increase of the field-plate length and the gate-drain spacing, the characteristic of f(T) and f(max), degraded due to the large parasitic effects. Loadpull method was used to measure the microwave power performance of the devices. Under the condition of continuous wave at 5.4 GHz, an output power density of 4.69 W/mm was obtained for device with field-plate length of 0.5 mu m and gate-drain length of 2 mu m. (c) 2006 Elsevier Ltd. All rights reserved.

Optimization of mechanically induced long-period fibre grating transmission spectrum

A new double-layer grating template is designed to reduce the out-of-band loss as much as 1.8dB when the loss of LP03 reaches 10.2 dB. Meanwhile, we propose a method to remove the sidelobes in the transmission spectra by the adjustment of the thickness of pressure plates. The plate-thickness-induced shift of resonant wavelength and the attenuation of loss peak intensity when removing sidelobes can be modified by the fibre distance and contact point on the pressure plates.

Geometry parameter optimization of large cross-sectional S-shaped bent rib waveguides for silicon based optical switches

地址: Chinese Acad Sci, Inst Semicond, State Key Lab Integrated Optoelect, Beijing 100083, Peoples R China