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.

Photodegradation dynamics of pure microcystin variants with illumination of fixed wavelength UV-lights

Photolysis of microcystins by UV irradiation and the effects of different environmental factors on efficiency of UV degradation were studied. The results indicated that the rates of the photolytical degradation reactions of microcystin-LR and RR-follow pseudo-first-order kinetic process. The results also showed that the concentrations of two microcystin variants decreased significantly by UV-C Irradiation; the wavelength and intensitiy of UV irradiation are two very important factors affecting the rate of degradation; temperature and pH value could also affect the half life of degradation rates. When irradiated by weaker UV-Iight, isomerization could be detected in the course of photolytical degradation. The concentrations of two isomers transformed from microcystin-LR reached its maximum at the third minute and decreased with the time afterwards. To simulate photolysis of microcystins in the field water body, microcystins with low concentration were used. It was found that UV-C illumination was capable of decomposing over 95% of microcystins within 40 min. In the presence of humic substances the photodecomposition slowed down to a certain extent. These results are valuable in using UV irradiation for elimination microcystins from raw water.

Effect of implantation of nitrogen into SIMOX buried oxide on its fixed positive charge density

In order to obtain greater radiation hardness for SIMOX (separation by implanted oxygen) materials, nitrogen was implanted into SIMOX BOX (buried oxide). However, it has been found by the C-V technique employed in this work that there is an obvious increase of the fixed positive charge density in the nitrogen-implanted BOX with a 150 out thickness and 4 x 10(15) cm(-2) nitrogen implantation dose, compared with that unimplanted with nitrogen. On the other hand, for the BOX layers with a 375 nm thickness and implanted with 2 x 10(15) and 3 x 10(15) cm(-2) nitrogen doses respectively, the increase of the fixed positive charge density induced by implanted nitrogen has not been observed. The post-implantation annealing conditions are identical for all the nitrogen-implanted samples. The increase in fixed positive charge density in the nitrogen-implanted 150 nm BOX is ascribed to the accumulation of implanted nitrogen near the BOX/Si interface due to the post-implantation annealing process according to SIMS results. In addition, it has also been found that the fixed positive charge density in initial BOX is very small. This means SIMOX BOX has a much lower oxide charge density than thermal SiO2 which contains a lot of oxide charges in most cases.

Transport phenomena in radial flow MOCVD reactor with three concentric vertical inlets

Transport phenomena in radial flow metalorganic chemical vapor deposition (MOCVD) reactor with three concentric vertical inlets are studied by two-dimensional numerical modeling. By varying the parameters such as gas pressure, flow rates combination of multi-inlets, geometric shapes and sizes of reactor and flow distributor, temperatures of susceptor and ceiling, and susceptor rotation, the corresponding velocity, temperature, and concentration fields inside the reactor are obtained; the onset and change of flow recirculation cells under influences of those parameters are determined. It is found that recirculation cells, originated from flow separation near the bend of reactor inlets, are affected mainly by the reactor height and shape, the operating pressure, the flow rates combination of multi-inlets, and the mean temperature between susceptor and ceiling. By increasing the flow rate of mid-inlet and the mean temperature, decreasing the pressure, maintaining the reactor height below certain criteria, and trimming the bends of reactor wall and flow distributor to streamlined shape, the recirculation cells can be minimized so that smooth and rectilinear flow prevails in the susceptor region, which corresponds to smooth and rectilinear isotherms and larger reactant concentration near the susceptor. For the optimized reactor shape, the reactor size can be enlarged to diameter D = 40 cm and height H = 2 cm without flow recirculation. The susceptor rotation over a few hundred rpm around the reactor central axis will induce the recirculation cell near the exit and deflect the streamlines near the susceptor, which is not the case for vertical reactors. (c) 2006 Elsevier B.V. All rights reserved.

Influences of reactor pressure of GaN buffer layers on morphological evolution of GaN grown by MOCVD

The morphological evolution of GaN thin films grown on sapphire by metalorganic chemical vapor deposition was demonstrated to depend strongly on the growth pressure of GaN nucleation layer (NL). For the commonly used two-step growth process, a change in deposition pressure of NL greatly influences the growth mode and morphological evolution of the following GaN epitaxy. By means of atomic force microscopy and scanning electron microscope, it is shown that the initial density and the spacing of nucleation sites on the NL and subsequently the growth mode of FIT GaN epilayer may be directly controlled by tailoring the initial low temperature NL growth pressure. A mode is proposed to explain the TD reduction for NL grown at relatively high reactor pressure. (C) 2003 Elsevier B.V. All rights reserved.

Effects of reactor pressure on GaN nucleation layers and subsequent GaN epilayers grown on sapphire substrate

The influence of reactor pressure on GaN nucleation layer (NL) and the quality of subsequent GaN on sapphire is studied. The layers were grown by low-pressure metalorganic chemical vapor deposition (MOCVD) on c-plane sapphire substrates and investigated by in situ laser reflectometry, atomic force microscope, scanning electron microscope, X-ray diffraction and photoluminescence. With the increase of reactor pressure prior to high-temperature GaN growth, the size of GaN nuclei formed after annealing decreases, the spacing between nucleation sites increases and the coalescence of GaN nuclei is deferred. The optical and crystalline qualities of GaN epilayer were improved when NLs were deposited at high pressure. The elongated lateral overgrowth of GaN islands is responsible for the quality improvement. (C) 2003 Elsevier Science B.V. All rights reserved.

Origin of the vertical-anticorrelation arrays of InAs/InAlAs nanowires with a fixed layer-ordering orientation

InAs/In0.52Al0.48As nanowire multilayer arrays were grown on (001) InP substrate by molecular-beam epitaxy. The structural property of the arrays was investigated by transmission electron microscopy. The results clearly showed the formation of InAs nanowires, evolution of InAs/InAlAs interface, and composition and thickness modulations in the InAlAs spacer layer. A fixed spatial ordering of InAs/InAlAs nanowires was revealed for all the samples. Regardless of the change in InAlAs spacer thickness of different samples, (i) the nanowires of one InAs layer are positioned above the nanowire spacing in the previous InAs layer and (ii) the layer-ordering orientation angle of nanowires is fixed. The results were explained from the viewpoint of the growth kinetics. The effect of InAlAs spacers is suggested to play an important role on the spatial ordering of the nanowire arrays. (C) 2002 American Institute of Physics.

Operational Optimization of GaN Thin Film Growth Employing Numerical Simulation in a Showerhead MOCVD Reactor

A detailed reaction-tran sport model was studied in a showerhead reactor for metal organic chemical vapor deposition of GaN film by using computational fluid dynamics simulation. It was found that flat flow lines without swirl are crucial to improve the uniformity of the film growth, and thin temperature gradient above the suscptor can increase the film deposition rate. By above-mentioned research, we can employ higher h (the distance from the susceptor to the inlet), P (operational pressure) and the rate of susceptor rotation to improve the film growth.