Optimization Algorithms on Matrix Manifolds

This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.

Study on small-strain behaviours of methane hydrate sandy sediments using discrete element method

Methane hydrate bearing soil has attracted increasing interest as a potential energy resource where methane gas can be extracted from dissociating hydrate-bearing sediments. Seismic testing techniques have been applied extensively and in various ways, to detect the presence of hydrates, due to the fact that hydrates increase the stiffness of hydrate-bearing sediments. With the recognition of the limitations of laboratory and field tests, wave propagation modelling using Discrete Element Method (DEM) was conducted in this study in order to provide some particle-scale insights on the hydrate-bearing sandy sediment models with pore-filling and cementation hydrate distributions. The relationship between shear wave velocity and hydrate saturation was established by both DEM simulations and analytical solutions. Obvious differences were observed in the dependence of wave velocity on hydrate saturation for these two cases. From the shear wave velocity measurement and particle-scale analysis, it was found that the small-strain mechanical properties of hydrate-bearing sandy sediments are governed by both the hydrate distribution patterns and hydrate saturation. © 2013 AIP Publishing LLC.

Determination of the rheological parameters of self-compacting concrete matrix using slump flow test

The classification of a concrete mixture as self-compacting (SCC) is performed by a series of empirical characterization tests that have been designed to assess not only the flowability of the mixture but also its segregation resistance and filling ability. The objective of the present work is to correlate the rheological parameters of SCC matrix, yield stress and plastic viscosity, to slump flow measurements. The focus of the slump flow test investigation was centered on the fully yielded flow regime and an empirical model relating the yield stress to material and flow parameters is proposed. Our experimental data revealed that the time for a spread of 500 mm which is used in engineering practice as reference for measurement parameters, is an arbitrary choice. Our findings indicate that the non-dimensional final spread is linearly related to the non-dimensional yield-stress. Finally, there are strong indications that the non-dimensional viscosity of the mixture is associated with the non-dimensional final spread as well as the stopping time of the slump flow; this experimental data set suggests an exponential decay of the final spread and stopping time with viscosity. © Appl. Rheol.

Dynamics of filopodium-like protrusion and endothelial cellular motility on onedimensional extracellular matrix fibrils

Endothelial filopodia play key roles in guiding the tubular sprouting during angiogenesis. However, their dynamic morphological characteristics, with the associated implications in cell motility, have been subjected to limited investigations. In this work, the interaction between endothelial cells and extracellular matrix fibrils was recapitulated in vitro, where a specific focus was paid to derive the key morphological parameters to define the dynamics of filopodium-like protrusion during cell motility. Based on one-dimensional gelatin fibrils patterned by near-field electrospinning (NFES), we study the response of endothelial cells (EA.hy926) under normal culture or ROCK inhibition. It is shown that the behaviour of temporal protrusion length versus cell motility can be divided into distinct modes. Persistent migration was found to be one of the modes which permitted cell displacement for over 300 μm at a speed of approximately 1 μm min-1. ROCK inhibition resulted in abnormally long protrusions and diminished the persistent migration, but dramatically increased the speeds of protrusion extension and retraction. Finally, we also report the breakage of protrusion during cell motility, and examine its phenotypic behaviours. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Determination of 266 pesticide residues in apple juice by matrix solid-phase dispersion and gas chromatography-mass selective detection

A macro matrix solid-phase dispersion (MSPD) method was developed to extract 266 pesticides from apple juice samples prior to gas chromatography-mass selective detection (GC-MSD) determination. A 10 g samples was mixed with 20 g diatomaceous earth. The mixture was transferred into a glass column. Pesticide residues were leached with a 160 mL hexane-dichloromethane (1:1) at 5 mL/min. Two hundred and sixty-six pesticides were divided into three groups and detected by GC-MSD under selective ion monitoring. The proposed method takes advantage of both liquid-liquid extraction and conventional MSPD methods. Application was illustrated by the analysis of 236 apple juice samples produced in Shaanxi province China mainland this year. (C) 2004 Elsevier B.V. All rights reserved.

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.

Cementing mechanism of algal crusts from desert area

34-, 17-, 4-, 1.5-year old natural algal crusts were collected from Shapotou Scientific Station of the Chinese Academy of Sciences, 40-day old field and greenhouse artificial algal crusts were in situ developed in the same sandy soil and the same place (37degrees27'N, 104degrees57'E). Their different cohesions both against wind force and pressure were measured respectively by a sandy wind-tunnel experiment and a penetrometer. On the basis of these algal crusts, the cementing mechanism was revealed from many subjects and different levels. The results showed that in the indoor artificial crusts with the weakest cohesion bunchy algal filaments were distributed in the surface of the crusts, produced few extracellular polymers (EPS), the binding capacity of the crusts just accomplished by mechanical bundle of algal filaments. For field crusts, most filaments grew toward the deeper layers of algal crusts, secreted much more EPS, and when organic matter content was more than 2.4 times of chlorophyll a, overmuch organic matter (primarily is EPS) began to gather onto the surface of the crusts and formed an organic layer in the relatively lower micro-area, and this made the crust cohesion increase 2.5 times. When the organic layer adsorbed and intercepted amounts of dusts, soil particles and sand grains scattered down from wind, it changed gradually into an inorganic layer in which inorganic matter dominated, and this made the crusts cohesion further enhanced 2-6 times. For crust-building species Microcoleus vaginatus, 88.5% of EPS were the acidic components, 78% were the acidic proteglycan of 380 kD. The uronic acid content accounted for 8% of proteglycan, and their free carboxyls were important sites of binding with metal cations from surrounding matrix.

Broadband Emitting Superluminescent Diodes With InAs Quantum Dots in AlGaAs Matrix

Superluminescent diodes were fabricated by using InAs-AlGaAs self-assembled quantum dots (QDs) as the active region. The ultrawide emitting spectrum of 142 nm was achieved. The short migration length of indium adatoms on AlGaAs surface increases the size dispersion of InAs QDs, resulting in the broadening of optical gain spectrum.

Coherence loss and recovery of an electron spin coupled inhomogeneously to a one-dimensional interacting spin bath: An adaptive time-dependent density-matrix renormalization group study

Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, are studied using the adaptive time-dependent density-matrix renormalization group method. It is found that the interplay of the coupling inhomogeneity and the transverse intrabath interactions results in two qualitatively different coherence evolutions, namely, a coherence-preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron-spin flip at time tau exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at root 2 tau for the decoherence evolution, respectively. With the diagonal intrabath interaction included, the specific feature of the periodic regime is kept, while the root 2 tau-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of tau is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.