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.

Micro-mould method for self-assembling three-dimensional opal photonic crystals

By vertical sedimentation, silica micro-spheres were grown in different shapes of concave micro-zones which were etched on a (100) p-silicon substrate. The following were found: this method can effectively raise the quality of films by avoiding cracks; the geometry of the micro-zones affects the sediment of the film; regular hexagons and triangles best facilitate the growth of photonic crystals. This method is practical for its ability to fabricate self-assembly photonic crystals in previously designed small areas.

Wettability designing by ZnO periodical surface textures

A facile and effective aqueous chemical synthesis approach towards well control of periodical ZnO textures in large-scale areas is reported, by which considerable adjusting of surface wettability can be realized. With the assistance of polystyrene spheres monolayer template and morphology control agent, we succeeded in preparing a series of ordered ZnO microbowls with different sag height. It was found that the contact angle could be well adjusted by changing geometry of microbowl. Such novel, ordered arrays are expected to exploit the great potentiality in waterproof or self-cleaning micro/nanodevices, and even microfluidic devices. (C) 2010 Elsevier Inc. All rights reserved.

Photo-induced reactions in the ion-molecule complex Mg+-OCNC2H5

Ion - molecule complexes of magnesium cation with ethyl isocyanate were produced in a laser- ablation supersonic expansion nozzle source. Photo- induced reactions in the 1: 1 complexes have been studied in the spectral range of 230 - 410 nm. Photodissociation mass spectrometry revealed the persistent product Mg+ from nonreactive quenching throughout the entire wavelength range. As for the reactive channels, the photoproducts, Mg+OCN and C2H5+, were produced only in the blue absorption band of the complex with low yields. The action spectrum of Mg+(OCNC2H5) consists of two pronounced peaks on the red and blue sides of the Mg+ 3(2)P <-- 3(2)S atomic transition. The ground state geometry of Mg+ - OCNC2H5 was fully optimized at B3LYP/6- 31 - G** level by using GAUSSIAN 98 package. The calculated absorption spectrum of the complex using the optimized structure of its ground state agrees well with the observed action spectrum. Photofragment branching fractions of the products are almost independent of the photolysis photon energy for the 3P(x,y,z) excitations. The very low branching ratio of reactive products to nonreactive fragment suggests that evaporation is the main relaxation pathway in the photo- induced reactions of Mg+ (OCNC2H5). (C) 2003 American Institute of Physics.

16-and 18-electron Cp*Rh complexes with 1,2-dicarba-closo-dodecabofane(12)-1,2-dichalcogenolato ligands, as studied by multinuclear magnetic resonance

The reaction of [Cp*RhCl2](2) 1 with dilithium 1,2-dicarba-closo-dodecaborane(12)-1,2-dithiolate (a) and -diselenolate (b) afforded the 16-electron rhodium(III) half-sandwich complexes Cp*Rh[E2C2(B10H10)] [E=S (3a), Se (3b)]. The 18-electron trimethylphosphane rhodium(III) half-sandwiches Cp*Rh(PMe3)[E2C2(B10H10)] 4a-c were prepared from the reaction of Cp*RhCl2(PMe3) 2 with the same dichalcogenolates, including the ditelluride (c). The complexes 4a,b could also be obtained from the reaction of 3a,b with trimethylphosphane. The molecular geometry of 4b was determined by X-ray structural analysis. The 16-electron complexes 3 an monomeric in solution as shown by multinuclear magnetic resonance (H-1-, B-11-, C-13-, P-31- Se-77-, Rh-103-, Te-125-NMR). also in comparison with the data for the trimethylphosphane analogues 4a-c and for 6a in which the rhodium bears the eta(5)-1,3-C5H3 Bu-t(2) ligand. The Rh-103 nuclear shielding is reduced by 831 ppm (3a) and 1114 ppm (3b) with respect to the 18-electron complexes 4a,b. Similarly, the Se-77 nuclear shielding in 3b is reduced by 676.4 ppm with respect to that in 4b. (C) 1999 Elsevier Science S.A. All rights reserved.

Temperature phase tilt in unstable baroclinic waves

A general property on the phase relation in linear baroclinic instability is proved analytically: in a potential vorticity homogenization regime, the complex geometry of the quasigeostrophic equations determines that the phase lines of temperature and pressure disturbances tilt with height in opposite directions.

喜马拉雅西构造结区岩石圈演化三维有限元动力学数值模拟

The past three decades have seen numerous attempts to numerically model stress and strain patterns in the lithosphere of the Earth on both global and regional scales. This efforts have been indispensable in identifying the features we need to include in our endeavour to develop better models of our planet’s lithosphere and they have also raised our awareness for the many unresolved issue in the deep geodynamical issues that need to be addressed in the future. Nonetheless, in most models, the lithosphere is treated as a single layer with depth-averaged properties, and as the same distribution in the stress and strain fields, and as deforming under plane strain. All these above make a great hander for its reality and degree of recognition. As the beginning in this paper, some principal numerical models and results on the evolution of Tibetan plateau are reviewed and analyzed. Then, the geological and geophysical expedition on the Western Himalayan Syntaxis is briefly reviewed. Furthermore, we analysis the feature in deep geophysical field studies in this area and adjacent regions. Because, for most continents, stress models driven by plate boundary forces have successfully reproduced the main characteristics of the stress and strain field, we present a set of three-dimensional models of lithosphere system for a simplified geometry of the Western Himalayan Syntaxis area and its adjacent regions, where we try to match the first-order characteristics of the stress and strain fields of lithosphere since 10 Ma, and deformation and geodynamical evolution process in former 2Ma. Of course, the kinematic boundary conditions of the stress models driven by plate boundary forces were applied. The rheology plays a significant role in the lithospheric tectonics, which lead to different rheological parameters were used in different works although the have the same constitutive equations in models. So, in this paper we do not aim to produce all characteristics of the Western Himalayan Syntaxis areas’ stress and strain fields by the choices of various parameters, but rather the dynamic response between various rheological parameters and stress and strain fields. We have chosen to concentrate on the importance of rheology and lateral strength variations for lithospheric stress and strain patterns and use our findings to build a model of the Western Himalayan Syntaxis areas. In doing so, we want to go beyond purely elastic models or purely viscoelastic models. Compared the results of the crust viscosity in the Western Himalayan Syntaxis areas, we believed that, when various viscoelastic models are adopted, the selection of the coefficient of viscosity in the Western Syntaxis area has important influence on the its uplifts and evolutions. A wider uplift ranges and gently elevation was observed at the same time when a lower viscosity was used in our models, and vice versa. Data of stress magnitudes are not available, but it is clear that the stress levels must be at or below the failure threshold of rock under compression. Under these criteria, the calculation results show that the viscosity in the Western Syntaxis area should be smaller than 1023Pa.s When elastic model is adopted in relatively rigid Tarim basin, obvious changes are induced to the stress and strain fields of the whole Western Syntaxis area. We found that rigid block of lithosphere reduced stress levels within its interior and that, at the edges of such regions, stress orientation can change. Furthermore there is no evidence that such rigid regions act as stress barriers in that they shield areas in opposite sides of the structure from the influence of one another. In our models, the upper crustal material of the Western Syntaxis area does not turns to move westward. Whereas, because of the stress and strain fields have been decoupling at the interior of the lithosphere, we can get the results that the deep material must not move westward.

中强地震震源的破裂过程

With the large developments of the seismic sources theory, computing technologies and survey instruments, we can model and rebuild the rupture process of earthquakes more realistically. On which earthquake sources' properties and tectonic activities law are realized more clearly. The researches in this domain have been done in this paper as follows. Based on the generalized ray method, expressions for displacement on the surface of a half-space due to an arbitrary oriented shear and tensile dislocation are also obtained. Kinematically, fault-normal motion is equivalent to tensile faulting. There is some evidence that such motion occurs in many earthquakes. The expressions for static displacements on the surface of a layered half-space due to static point moment tensor source are given in terms of the generalized reflection and transmission coefficient matrix method. The validity and precision of the new method is illustrated by comparing the consistency of our results with the analytical solution given by Okada's code employing same point source and homogenous half-space model. The computed vertical ground displacement using the moment tensor solution of the Lanchang_Gengma earthquake displays considerable difference with that of a double couple component .The effect of a soft layer at the top of the homogenous half-space on a shallow normal-faulting earthquake is also analyzed. Our results show that more seismic information would be obtained utilizing seismic moment tensor source and layered half-space model. The rupture process of 1999 Chi-Chi, Taiwan, earthquake investigated by using co-seismic surface displacement GPS observations and far field P-wave records. In according to the tectonic analysis and distributions of aftershock, we introduce a three-segment bending fault planes into our model. Both elastic half-space models and layered-earth models to invert the distribution of co-seismic slip along the Chi-Chi earthquake rupture. The results indicate that the shear slip model can not fit horizontal and vertical co-seismic displacements together, unless we add the fault-normal motion (tensile component) in inversions. And then, the Chi Chi earthquake rupture process was obtained by inversion using the seismograms and GPS observations. Fault normal motions determined by inversion, concentrate on the shallow northern bending fault from Fengyuan to Shuangji where the surface earthquake ruptures reveal more complexity and the developed flexural slip folding structures than the other portions of the rupture zone For understanding the perturbation of surface displacements caused by near-surface complex structures, We have taken a numeric test to synthesize and inverse the surface displacements for a pop-up structure that is composed of a main thrust and a back thrust. Our result indicates that the pop-up structure, the typical shallow complex rupture that occurred in the northern bending fault zone form Fengyuan to Shuangji, can be modeled better by a thrust fault added negative tensile component than by a simple thrust fault. We interpret the negative tensile distributions, that concentrate on the shallow northern bending fault from Fengyuan to Shuangji, as a the synthetic effect including the complexities of property and geometry of rupture. The earthquake rupture process also reveal the more spatial and temporal complexities form Fenyuan to SHuangji. According to the three-components teleseismic records, the S-wave velocity structure beneath the 59 teleseismic stations of Taiwan obtained by using the transform function method and the SA techniques. The integrated results, the 3D crustal structure of Taiwan reveal that the thickest part of crustal local in the western Central Range. This conclusion is consistent with the result form the Bouguer gravity anomaly. The orogenic evolution of Taiwan is young period, and the developing foot of Central Range dose not in static balancing. The crustal of Taiwan stays in the course of dynamic equilibrium. The rupture process of 2003)2,24,Jiashi, Xinjiang earthquake was estimated by the finite fault model using far field broadband P wave records of CDSN and IRIS. The results indicate that the earthquake focal is north dip trust fault including some left-lateral strike slip. The focal mechanism of this earthquake is different form that of earthquakes occurred in 1997 and 1998, but similar to that of 1996, Artux, Xinjiang earthquake. We interpreted that the earthquake caused trust fault due to the Tarim basin pushing northward and orogeny of Tianshan mountain. In the end, give a brief of future research subject: Building the Real Time Distribute System for rupture process of Large Earthquakes Based on Internet.

Error Detection and Recovery for Robot Motion Planning with Uncertainty

Robots must plan and execute tasks in the presence of uncertainty. Uncertainty arises from sensing errors, control errors, and uncertainty in the geometry of the environment. The last, which is called model error, has received little previous attention. We present a framework for computing motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.

Shape from Contour

The problem of using image contours to infer the shapes and orientations of surfaces is treated as a problem of statistical estimation. The basis for solving this problem lies in an understanding of the geometry of contour formation, coupled with simple statistical models of the contour generating process. This approach is first applied to the special case of surfaces known to be planar. The distortion of contour shape imposed by projection is treated as a signal to be estimated, and variations of non-projective origin are treated as noise. The resulting method is then extended to the estimation of curved surfaces, and applied successfully to natural images. Next, the geometric treatment is further extended by relating countour curvature to surface curvature, using cast shadows as a model for contour generation. This geometric relation, combined with a statistical model, provides a measure of goodness-of-fit between a surface and an image contour. The goodness-of-fit measure is applied to the problem of establishing registration between an image and a surface model. Finally, the statistical estimation strategy is experimentally compared to human perception of orientation: human observers' judgements of tilt correspond closely to the estimates produced by the planar strategy.

On Motion Planning with Uncertainty

Robots must successfully plan and execute tasks in the presence of uncertainty. Uncertainty arises from errors in modeling, sensing, and control. Planning in the presence of uncertainty constitutes one facet of the general motion planning problem in robotics. This problem is concerned with the automatic synthesis of motion strategies from high level task specification and geometric models of environments. In order to develop successful motion strategies, it is necessary to understand the effect of uncertainty on the geometry of object interactions. Object interactions, both static and dynamic, may be represented in geometrical terms. This thesis investigates geometrical tools for modeling and overcoming uncertainty. The thesis describes an algorithm for computing backprojections o desired task configurations. Task goals and motion states are specified in terms of a moving object's configuration space. Backprojections specify regions in configuration space from which particular motions are guaranteed to accomplish a desired task. The backprojection algorithm considers surfaces in configuration space that facilitate sliding towards the goal, while avoiding surfaces on which motions may prematurely halt. In executing a motion for a backprojection region, a plan executor must be able to recognize that a desired task has been accomplished. Since sensors are subject to uncertainty, recognition of task success is not always possible. The thesis considers the structure of backprojection regions and of task goals that ensures goal recognizability. The thesis also develops a representation of friction in configuration space, in terms of a friction cone analogous to the real space friction cone. The friction cone provides the backprojection algorithm with a geometrical tool for determining points at which motions may halt.

Synteza oraz właściwości fizykochemiczne bis-interkalatorów naftalimidowych

Wydział Chemii

Edukacyjne implikacje technologii cyfrowych

W ciągu minionych trzech dekad świat radykalnie się zmienił. Jesteśmy świadkami transformacji od społeczeństwa przemysłowego do społeczeństwa informacyjnego. Jeśli chcielibyśmy określić tą zmianę jednym słowem byłoby nim: cyfryzacja. Początkiem było wynalezienie cyfrowego komputera, a później wszystkie stare analogowe formy medialne (tekst, dźwięk, obraz, film) reprezentowane poprzez ciągłe (analogowe) sygnały zostały zastąpione przez nowe postaci cyfrowe. Pojęcie cyfrowy oznacza, że dowolne informacje mogą być reprezentowana w formie ciągów liczb zapisanych w dwójkowym systemie liczbowym (jako ciąg znaków: 0 i 1). W artykule pokazujemy funkcjonalne ograniczenia mediów analogowych oraz rozważamy korzyści wynikające z cyfrowych reprezentacji różnych form informacji wskazując równocześnie zmiany jakie implikuje to dla procesu uczenia się i edukacji.

Visible Volume: a Robust Measure for Protein Structure Characterization

We propose a new characterization of protein structure based on the natural tetrahedral geometry of the β carbon and a new geometric measure of structural similarity, called visible volume. In our model, the side-chains are replaced by an ideal tetrahedron, the orientation of which is fixed with respect to the backbone and corresponds to the preferred rotamer directions. Visible volume is a measure of the non-occluded empty space surrounding each residue position after the side-chains have been removed. It is a robust, parameter-free, locally-computed quantity that accounts for many of the spatial constraints that are of relevance to the corresponding position in the native structure. When computing visible volume, we ignore the nature of both the residue observed at each site and the ones surrounding it. We focus instead on the space that, together, these residues could occupy. By doing so, we are able to quantify a new kind of invariance beyond the apparent variations in protein families, namely, the conservation of the physical space available at structurally equivalent positions for side-chain packing. Corresponding positions in native structures are likely to be of interest in protein structure prediction, protein design, and homology modeling. Visible volume is related to the degree of exposure of a residue position and to the actual rotamers in native proteins. In this article, we discuss the properties of this new measure, namely, its robustness with respect to both crystallographic uncertainties and naturally occurring variations in atomic coordinates, and the remarkable fact that it is essentially independent of the choice of the parameters used in calculating it. We also show how visible volume can be used to align protein structures, to identify structurally equivalent positions that are conserved in a family of proteins, and to single out positions in a protein that are likely to be of biological interest. These properties qualify visible volume as a powerful tool in a variety of applications, from the detailed analysis of protein structure to homology modeling, protein structural alignment, and the definition of better scoring functions for threading purposes.

Nanosize effect in germanium nanowire growth with binary metal alloys

This article describes feasible and improved ways towards enhanced nanowire growth kinetics by reducing the equilibrium solute concentration in the liquid collector phase in a vapor-liquid-solid (VLS) like growth model. Use of bi-metallic alloy seeds (AuxAg1-x) influences the germanium supersaturation for a faster nucleation and growth kinetics. Nanowire growth with ternary eutectic alloys shows Gibbs-Thompson effect with diameter dependent growth rate. In-situ transmission electron microscopy (TEM) annealing experiments directly confirms the role of equilibrium concentration in nanowire growth kinetics and was used to correlate the equilibrium content of metastable alloys with the growth kinetics of Ge nanowires. The shape and geometry of the heterogeneous interfaces between the liquid eutectic and solid Ge nanowires were found to vary as a function of nanowire diameter and eutectic alloy composition.