Deterministic Column-Based Matrix Decomposition

In this paper, we propose a deterministic column-based matrix decomposition method. Conventional column-based matrix decomposition (CX) computes the columns by randomly sampling columns of the data matrix. Instead, the newly proposed method (termed as CX_D) selects columns in a deterministic manner, which well approximates singular value decomposition. The experimental results well demonstrate the power and the advantages of the proposed method upon three real-world data sets.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Topological constraints on scroll and spiral waves in excitable media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

Article: Overview of Analytical Methodologies for Sea Water Analysis: Part I-Metals

A comprehensive, critical and up-to-date review of analytical methods developed during the last decade for metals present in sea water is presented. Separate sections are devoted to singular and multimetal determinations. Furthermore, a critical comparison of relative merits or demerits of a particular procedure is made in terms of sensitivity, selectivity and precision. Various aspects of analysis of sea water samples for metals are summarized, and the future trends are discussed.

Physical and spectral characterization of the human cyclin A gene and its interactions with anthracycline anticancer drugs

Over expression of cyclin A in human tumors has been linked to cancer by various experimental lines of evidence. However, physical and spectral characterization of the human cyclin A gene and its interactions with anticancer drugs have not been reported. Our gene sequence analysis, singular value decomposition method and melting studies in the presence of antitumor agents, daunomycin, doxorubicin and Hoechst 33258 showed that cyclin A gene had both AT-rich and GC-rich domains. For a ligand with unknown DNA binding specificity, this gene sequence can be used to differentiate its DNA binding preference.

pH-dependent conformational changes of ferricytochrome c induced by electrode surface microstructure

pH-dependent processes of bovine heart ferricytochrome c have been investigated by electronic absorption and circular dichroism (CD) spectra at functionalized single-wall carbon 'nanotubes (SWNTs) modified glass carbon electrode (SWNTs/ GCE) using a long optical path thin layer cell. These methods enabled the pH-dependent conformational changes arising from the heme structure change to be monitored. The spectra obtained at functionalized SWNTs/GCE reflect electrode surface microstructure-dependent changes for pH-induced protein conformation, pK(a) of alkaline transition and structural microenvironment of the ferricytochrome c heme. pH-dependent conformational distribution curves of ferricytochrome c obtained by analysis of in situ CD spectra using singular value decomposition least square (SVDLS) method show that the functionalized SWNTs can retain native conformational stability of ferricytochrome c during alkaline transition.

In situ circular dichroic electrochemical study of bilirubin and bovine serum albumin complex

The electrooxidation of bilirubin (BR) and bovine serum albumin (BSA) complexes was studied by in situ circular dichroism (CD) spectroelectrochemistry. The result showed that the mechanism of the whole electrooxidation process of this complex corresponded to electrochemical processes (EE mechanism) in aqueous solution. Some parameters of the process were obtained by double logarithm method, differential method and nonlinear regression method. In visible region, CD spectra of the two enantiomeric components of the complex and their fraction distribution against applied potentials were obtained by singular value decomposition least-square (SVDLS) method. Meanwhile, the distribution of the five components of secondary structure was also obtained by the same method in far-UV region. The peak potential gotten from EE mechanism corresponds to a turning point for the component transition, beyond which the whole reaction reaches a new equilibrium. Under applied positive potentials, the enantiomeric equilibrium between M and P form is broken and M form transfers to its enantiomer of P, while the fraction of alpha-helix increases and that improves the transition to P form.

Conformational transition of DNA induced by cationic lipid vesicle in acidic solution: spectroscopy investigation

The conformational transition of DNA induced by the interaction between DNA and a cationic lipid vesicle, didodecyidimethylammonium bromide (DDAB), had been investigated by circular dichroism (CD) and UV spectroscopy methods. We used singular value decomposition least squares method (SVDLS) to analyze the experimental CD spectra. Although pH value influenced the conformation of DNA in solution, the results showed that upon binding to double helical DNA, positively charged liposomes induced a conformational transition of DNA molecules from the native B-form to more compact conformations. At the same time, no obvious conformational changes occurred at single-strand DNA (ssDNA). While the cationic lipid vesicles and double-strand DNA (dsDNA) were mixed at a high molar ratio of DDAB vesicles to dsDNA, the conformation of dsDNA transformed from the B-form to the C-form resulting in an increase in duplex stability (DeltaT(m) = 8 +/- 0.4 degreesC). An increasing in T-m was also observed while the cationic lipid vesicles interacted with ssDNA.

Structural electrochemical study of hemoglobin by in situ circular dichroism thin layer spectroelectrochemistry

Secondary and tertiary or quaternary structural changes in hemoglobin (HB) during an electroreduction process were studied by in situ circular dichroism (CD) spectroelectrochemistry with a long optical path thin-layer cell. By means of singular value decomposition least-squares analysis, CD spectra in the far-UV region give two similar a components with different CD intensity, indicating slight denaturation in the secondary structures due to the electric field effect. CD spectra in the Soret band show a R --> T transition of two quaternary structural components induced by electroreduction of the heme, which changes the redox states of the center ion from Fe3+ to Fe2+ and the coordination number from 6 to 5. The double logarithmic analysis shows that electroreduction of hemoglobin follows a chemical reaction with R --> T transition. Some parameters in the electrochemical process were obtained: formal potential, E-0t = -0.167 V; electrochemical kinetic overpotential, DeltaE(0) = -0.32 V; standard electrochemical reaction rate constant, k(0) = 1.79 x 10(-5) cm s(-1); product of electron transfer coefficient and electron number, alphan=0.14; and the equilibrium constant of R --> T transition, K-c = 9.0.

Conformational transition of DNA in electroreduction studied by in situ UV and CD thin layer spectroelectrochemistry

Electrochemically induced three conformational transitions of calf thymus DNA from B-10.4 to Z(10.2)-DNA and from B-10.2 to B-10.4 and to C-DNA in 10 mM phosphate buffer solution (pH 7.21) at glassy carbon electrode are found and studied by in situ circular dichroism (CD) thin layer spectroelectrochemistry with singular value decomposition least square (SVDLS) analysis. It indicates that the so-called B-10.2 form and the C-form of DNA may be composed of B-10.4 and left-A DNA and of B-10.4 and right-A DNA, respectively. The irreversible electrochemical reduction of adenine and cytosine groups in the DNA molecule is studied by UV-Vis spectroelectrochemistry. Some electrochemical parameters alphan = 0.17, E-0' = -0.70 V (vs. Ag/AgCl), and the standard heterogeneous electron transfer rate constant, k(0) = 1.8 x 10(-5) cm s(-1) are obtained by double logarithmic analysis and non-linear regression. (C) 2000 Elsevier Science B.V. All rights reserved.

Circular dichroism spectro electrochemical and voltammetric studies of vitamin B-2

Electroreduction of vitamin B-2 (VB2) was studied by in situ circular dichroism (CD) spectroelectrochemistry (SEC) with a long optical path length thin layer cell (LOPLTLC). The results showed that the electroreduction of VB2 in phosphate buffer solution (PBS) (PH 6.8) was a two-electron electrochemical process with weak adsorption of the reactant at the glassy carbon (GC) electrode surface. The CD spectra change of VB2 in the reduction process was explained with the theory of electronic states. We also treated the CD spectra with a singular value decomposition least square (SVDLS) method, and have found not only the number of components and their spectra, but also the fraction distribution of each component in the electroreduction process of VB2.

The electrochemically induced conformational transition of disulfides in bovine serum albumin studied by thin layer circular dichroism spectroelectrochemistry

The conformational transition of disulfides in bovine serum albumin (BSA) induced by electrochemical redox reaction of disulfides were monitored by in-situ circular dichroism (CD) spectroelectrochemistry, with a long optical path thin layer cell and analyzed by a singular value decomposition least square (SVDLS) method. Electrochemical reduction of disulfides drives the left-handed conformation of disulfides changed into the right-handed. At open circuit, eight of the 17 disulfides were of left-handed conformation. Four of the 17 disulfides took part in the electrochemical reduction with an EC mechanism. Only one-fourth of the reduced disulfides returned to left-handed conformation in the re-oxidation process. Some parameters of the electrochemical reduction process, i.e. the number of electrons transferred and electron transfer coefficient, n=8, alphan=0.15, apparent formal potential, E-1(0') = -0.65(+/-0.01) V, standard heterogeneous electron transfer rate constant, k(1)(0) = (2.84 +/- 0.14)x 10(-5) cm s(-1) and chemical reaction equilibrium constant, K-c=(5.13 +/- 0.12) x 10(-2), were also obtained by double logarithmic analysis based on the near-UV absorption spectra with applied potentials. (C) 2001 Elsevier Science B.V. All rights reserved.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.