Consistency of sparse PCA in High Dimension, Low Sample Size contexts

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension, Low Sample Size (HDLSS)). We consider the previously studied single spike covariance model and assume in addition that the maximal eigenvector is sparse. We extend the existing HDLSS asymptotic consistency and strong inconsistency results of conventional PCA in an entirely new direction. We find a large set of sparsity assumptions under which sparse PCA is still consistent even when conventional PCA is strongly inconsistent. The consistency of sparse PCA is characterized along with rates of convergence. Furthermore, we clearly identify the mathematical boundaries of the sparse PCA consistency, by showing strong inconsistency for an oracle version of sparse PCA beyond the consistent region, as well as its inconsistency on the boundaries of the consistent region. Simulation studies are performed to validate the asymptotic results in finite samples

Preparation of atomically clean and flat Si(100) surfaces by low-energy ion sputtering and low-temperature annealing

Si(100) surfaces were prepared by wet-chemical etching followed by 0.3-1.5keV Ar ion sputtering, either at elevated or room temperature. After a brief anneal under ultrahigh vacuum conditions, the resulting surfaces were examined by scanning tunneling microscopy. We find that wet-chemical etching alone cannot produce a clean and flat Si(100) surface. However, subsequent 300eV Ar ion sputtering at room temperature followed by a 973K anneal yields atomically clean and flat Si(100) surfaces suitable for nanoscale device fabrication.Comment: 13 pages, 3 figures, to be published in Applied Surface Scienc

Hole spin polarization in GaAlAs:Mn structures

A self-consistent calculation of the electronic properties of GaAlAs:Mn magnetic semiconductor quantum well structures is performed including the Hartree term and the sp-d exchange interaction with the Mn magnetic moments. The spin polarization density is obtained for several structure configurations. Available experimental results are compared with theory.Comment: 4 page

The role of antiphase boundaries during ion sputtering and solid phase epitaxy of Si(001)

The Si(001) surface morphology during ion sputtering at elevated temperatures and solid phase epitaxy following ion sputtering at room temperature has been investigated using scanning tunneling microscopy. Two types of antiphase boundaries form on Si(001) surfaces during ion sputtering and solid phase epitaxy. One type of antiphase boundary, the AP2 antiphase boundary, contributes to the surface roughening. AP2 antiphase boundaries are stable up to 973K, and ion sputtering and solid phase epitaxy performed at 973K result in atomically flat Si(001) surfaces.Comment: 16 pages, 4 figures, to be published in Surface Scienc

Evolution and instabilities of disks harboring super massive black holes

The bar formation is still an open problem in modern astrophysics. In this paper we present numerical simulation performed with the aim of analyzing the growth of the bar instability inside stellar-gaseous disks, where the star formation is triggered, and a central black hole is present. The aim of this paper is to point out the impact of such a central massive black hole on the growth of the bar. We use N-body-SPH simulations of the same isolated disk-to-halo mass systems harboring black holes with different initial masses and different energy feedback on the surrounding gas. We compare the results of these simulations with the one of the same disk without black hole in its center. We make the same comparison (disk with and without black hole) for a stellar disk in a fully cosmological scenario. A stellar bar, lasting 10 Gyrs, is present in all our simulations. The central black hole mass has in general a mild effect on the ellipticity of the bar but it is never able to destroy it. The black holes grow in different way according their initial mass and their feedback efficiency, the final values of the velocity dispersions and of the black hole masses are near to the phenomenological constraints.Comment: 10 pages, 8 figures, accepted for pubblication in "Astrophysics and Space Science

Simulation of reference crop evapotransiration in a plastic solar green house using a simplified energy balance approach

Proceedings of International conference on Agricultural and Biological Sciences (ABS 2015) held in Beijing, China on July 25-27, 2015With larger planting areas being used in greenhouses, evaluating crop evapotranspiration in a greenhouse has garnered greater attention. Currently, calculating the reference crop evapotranspiration for a greenhouse crop through using the Penman-Monteith formula recommended by FAO is difficult because the wind speed in a greenhouse is approximate zero. In order to calculate reference crop evapotranspiration in a greenhouse by the Penman-Monteith modified formula, a simplified model for calculating reference crop evapotranspiration in a greenhouse was proposed based on the energy balance equation, which was the correlative function between reference crop evapotranspiration and radiation and temperature. The model's parameters were obtained through meteorological data taken from the inside of a greenhouse in 2011. Then, the model was validated by using meteorological data within the greenhouse in 2012, and the fitted value of the model agreed with the calculated value of the formulas with a determination coefficient (R2) of 0.9554. This model is an easy means of calculating the reference crop evapotranspiration in a greenhouse because less meteorological factors are needed. Furthermore, the model provides a theoretical basis for crop irrigation in greenhouses

The instability of Alexander-McTague crystals and its implication for nucleation

We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that satisfies the Alexander-McTague condition is not stable. We investigate the implication of this result for nucleation near the pseudo- spinodal in near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review

Ferromagnetism and Canted Spin Phase in AlAs/GaMnAs Single Quantum Wells: Monte Carlo Simulation

The magnetic order resulting from a confinement-adapted Ruderman-Kittel-Kasuya-Yosida indirect exchange between magnetic moments in the metallic phase of a AlAs/Ga(1-x)Mn(x)As quantum well is studied by Monte Carlo simulation. This coupling mechanism involves magnetic moments and carriers (holes), both coming from the same Mn(2+) ions. It leads to a paramagnetic, a ferromagnetic, or a canted spin phase, depending on the carrier concentration, and on the magnetic layer width. It is shown that high transition temperatures may be obtained.Comment: 7 figure

Stress Dependence of Exciton Relaxation Processes in Cu2O

A comprehensive study of the exciton relaxation processes in Cu2O has led to some surprises. We find that the ortho-para conversion rate becomes slower at high stress, and that the Auger nonradiative recombination rate increases with stress, with apparently no Auger recombination at zero stress. These results have important consequences for the pursuit of Bose-Einstein condensation of excitons in a harmonic potential.Comment: 10 figures, 1 tabl

Study on the Cracking Mechanism of YQ450NQR1 High-Strength Weathering Steel

YQ450NQR1 high-strength weathering steel is prone to cracking. The cracking patterns and morphology were detected by metallographic and scanning electron microscopies. The decarburized layer around the cracks is indicative of their origination in the continuous casting bloom. Then, the controlling factors were established by analyzing the carbon content of molten steel, residual elements in the alloy, purity and performance of the mold powder, and secondary cooling water flow of the mold. Results show that the process optimization reduced the cracking reject ratio from 3.5 to 0.78%.Высокопрочная сталь YQ450NQR1, стойкая к атмосферной коррозии, проявляет склонность к образованию трещин. Исследованы характер трещинообразования и морфология с помощью металлографической и сканирующей электронной микроскопии. Образование обезуглероженного слоя вокруг трещин свидетельствует об их зарождении в непрерывной литой заготовке. Установлены регулирующие факторы путем анализа содержания углерода в расплавленной стали, остаточных элементов в сплаве, чистоты и эффективности пресс-порошка, расхода воды вторичного охлаждения формы. Показано, что оптимазация процесса снизила уровень отбраковки материала, содержащего трещины, с 3,50 до 0,78%