Manopt, a matlab toolbox for optimization on manifolds

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design effcient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier. © 2014 Nicolas Boumal.

A 16-term error model based on linear equations of voltage and current variables

Formulation of a 16-term error model, based on the four-port ABCD-matrix and voltage and current variables, is outlined. Matrices A, B, C, and D are each 2 x 2 submatrices of the complete 4 x 4 error matrix. The corresponding equations are linear in terms of the error parameters, which simplifies the calibration process. The parallelism with the network analyzer calibration procedures and the requirement of five two-port calibration measurements are stressed. Principles for robust choice of equations are presented. While the formulation is suitable for any network analyzer measurement, it is expected to be a useful alternative for the nonlinear y-parameter approach used in intrinsic semiconductor electrical and noise parameter measurements and parasitics' deembedding.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.

Optimization and comparison of single- and dual-pump fiber-optical parametric amplifiers with dispersion fluctuations

Solutions for fiber-optical parametric amplifiers (FOPAs) with dispersion fluctuations are derived using matrix operators. On the basis of the propagation matrix product and the hybrid genetic algorithm, we have optimized and compared single- and dual-pump FOPAs with zero-dispersion-wavelength variations. The simulations prove that the design of FOPAs involves multimodal function optimization problems. The numerical results show that dual-pump FOPAs are highly sensitive to dispersion fluctuations whereas dispersion variations have less impact on the gain of single-pump FOPAs. To increase signal gain and reduce ripple, dual-pump FOPAs, instead of single-pump FOPAs, have to be carefully optimized with a suitable multisegment fiber structure rather than a one-segment fiber structure. The different combinations of multisegment fibers can provide highly different gain properties. The increase in gain is at the cost of the ripple.

Design optimization of the APF DTL in the SSC-linac

A linear accelerator as a new injector for the SSC (Separated Sector Cyclotron) of the HIRFL (Heavy ton Research Facility Lanzhou) is being designed. The DTL (Drift-Tube-Linac) has been designed to accelerate U-238(34+) from 0.140 MeV/u to 0.97 MeV/u. To the first accelerating tank which accelerates U-238(34+) to 0.54 MeV/u, the approach of Alternating-Phase-Focusing (APF) is applied. The phase array is obtained by coupling optimization software Dakota and beam optics code LINREV. With the hybrid of Multi-objective Genetic Algorithm (MOGA) and a pattern search method, an optimum array of asynchronous phases is determined. The final growth, both transversely and longitudinally, can meet the design requirements. In this paper, the deign optimization of the APF DTL is presented.

Mercury(II) ion sensing with PVC-matrix based membrane sensors

Thiosemicarbazone derivatives have been used as ion carriers for the preparation of PVC-matrix based mercury(II)-selective membrane sensors. The electrodes give near-Nernstian responses in the linear concentration range of 1.0×10-1-5.0×10-6 M with detection limits of the order of 10-6 M. The stable potentiometric signals are obtained within a short time period of 20-25s. The effect of different plasticizers has been studied and dioctylsebacate (DOS) found to give a better response in comparison to other plasticizers. Selectivity coefficient values (log KPotHg,M) have been evaluated using fixed interference method. Better selectivity for mercury(II) ions is observed over many of the monovalent (Na+, K+ and NH4+) and divalent ions (Mg2+, Ca2+, Zn2+, Pb2+, Ni2+, Co2+, etc.). The sensors have also been used as indicator electrodes in potentiometric titration of mercury(II) ions with EDTA and its determination in synthetic water samples.

Characterization of linear epitope of the beta(2)-microglobulin via combination of MALDI-TOF-MS with immunoaffinity

Matrix-assisted laser desorption ionization time-of-flight mass spectrometry(MALDI-TOF-MS), in combination with immunoaffinity provided a powerful tool for determining epitope (antigenic determinant) in protein. The linear epitope of the beta(2)-microglobulin was characterized in the paper. The method as follows: at first beta(2)-microglobulin was digested by a proteolytic enzyme to produce an appropriate set of peptide fragments, then peptide fragments containing the linear epitope were selected and separated from the pool of peptide fragments by immunoprecipitation with the monoclonal antibody. The agarose beads were collected carefully after the reaction. Unbound peptides would be washed away, while the peptides containing the epitope would remain bound to the immobilized antibody after. the beads were washed several times with appropriate buffer. At last the masses of the bound peptides were identified directly by MALDI-TOF MS. Using Endoproteinase Glu-C Endoproteinase Lys-C and Trypsin in the experiment, the linear epitope of beta(2)-microglobulin was located within peptide fragment 59-69, that is, DWSFYLLYYTE.

Determination of p-toluene sulfonic acid in phenol matrix by capillary zone electrophoresis with ultraviolet detection

The p-toluene sulfonic acid (MA) in phenol matrix was separated and determined by capillary electrophoresis with ultraviolet detector. the effect of the concentration and pH of the buffer on separation was investigated. Cinnamic acid has been chosen as the internal standard from four compounds, the calibration curves of PTSA in 50 mg/L phenol matrix were obtained with and without the internal standard. The linear range was from 1.25 to 12.5 mg/L and the correlation coefficient was 0.9999 for both curves. The limit of detection of PISA was 0.75 mg/L at 3 times of SIN. Finally, the concentration of PTSA in four synthesized samples was determined with method of standard additions, and the effect of matrix was discussed. The values of MA in these samples were 1.01, 0.94, 1.56 and 0.00 mg/L respectively.

Simultaneous spectrophotometric determination of trace iron (III) and aluminum (III) with hybrid linear analysis

Hybrid linear analysis (HLA) was applied to resolution of overlapping spectra of Fe3+-salicylfluorone and Al3+-salicylfluorone complexes and simultaneous spectrophotometric determination of Fe3+ and Al3+. The absorbance matrix of 7 standard mixtures at 41 measuring points ranged from the wavelength of 550 nm to 630 nm was used for calibration. To avoid the effect of interaction between the two components on the determination, the column vector of K matrix obtained from the standard mixtures with least squares was used as the pure spectrum of component. The recoveries of the two elements for the analysis of the synthetic samples were 93.3% similar to 107.5% in the range of the concentration ratio of Fe3+:Al3+ = 10:1 to 1:8. Comparing with the partial least squares (PIS) model, the HLA method was simple, accuracy and precise.

Factor analysis used to peak position optimization and spectral interference correction in inductively coupled plasma atomic emission spectrometry

Target transformation factor analysis was used to correct spectral interference in inductively coupled plasma atomic emission spectrometry (ICP-BES) for the determination of rare earth impurities in high purity thulium oxide. Data matrix was constructed with pure and mixture vectors and background vector. A method based on an error evaluation function was proposed to optimize the peak position, so the influence of the peak position shift in spectral scans on the determination was eliminated or reduced. Satisfactory results were obtained using factor analysis and the proposed peak position optimization method.

Self-gelatinizable graft copolymer of poly(vinyl alcohol) with 4-vinylpyridine as an immobilization matrix for the construction of a tyrosinase-based amperometric biosensor

A tyrosinase-based amperometric biosensor using a self-gelatinizable graft copolymer of poly(vinyl alcohol) with 4-vinylpyridine (PVA-g-PVP) as an immobilization matrix was constructed. The 4-vinylpyridine component of PVA-g-PVP enhances the adherence to a glassy carbon electrode surface. The content of 4-vinylpyridine in this immobilization matrix plays a key role in retaining the activity of tyrosinase. A simple, milder method was adopted by simply syringing the copolymer-tyrosinase aqueous solution on to the electrode surface and allowing water to evaporate at 4 degrees C in a refrigerator. Several parameters, including copolymer composition; pH, applied potential and enzyme membrane composition, ware optimized. The enzyme membrane composition can be varied to obtain higher sensitivity or a wider linear detection range. The biosensor was used for the determination of phenol, p-cresol and catechol. The biosensor exhibited excellent reproducibility, stability and sensitive response and can be used in flow injection analysis. The biosensor showed an extended linear range in hydrophilic organic solvents and it can be used in monitoring organic reaction processes. The analytical performance demonstrated this immobilization matrix is suitable for the immobilization of tyrosinase.

Blends of linear low-density polyethylene and a diblock copolymer of hydrogenated polybutadiene and methyl methacrylate

Blends of linear low-density polyethylene (LLDPE) and a diblock copolymer of hydrogenated polybutadiene and methyl methacrylate [P(HB-b-MMA)] were studied by transimission electron microscope (TEM), differential scanning calorimetry (DSC), and wide angle X-ray diffraction (WAXD). At 10 wt% block copolymer content, block copolymer chains exist as spherical micelles and cylindrical micelles in LLDPE matrix. At 50 wt% block copolymer content, block copolymer chains mainly form cylindrical micelles. The core and corona of micelles consist of PMMA and PHB blocks, respectively. DSC results show that the total enthalpy of crystallization of the blends varies linearly with LLDPE weight percent, indicating no interactions in the crystalline phase. In the blends, no distortion of the unit cell is observed in WAXD tests.

Seasonal and spatial distribution of matrix-bound phosphine and its relationship with the environment in the Changjiang River Estuary, China

Sediment is commonly considered as a source of phosphine, which is a highly toxic and reactive atmospheric trace gas. This study aims to investigate the seasonal and spatial distribution of matrix-bound phosphine (MBP) and its relationship with the environment in the Changjiang River Estuary. A total of 43 surface sediments were collected in four seasons of 2006, and concentrations of MBP and relative environmental factors were analyzed. MBP ranged from 1.93 to 94.86 ng kg(-1) dry weight (dw) with an average concentration of 17.14 ng kg(-1) dw. The concentrations of MBP in the tipper estuary were, higher than those in the lower estuary, which could be attributed to greater pollutant inputs in the upper estuary. The concentrations of MBP also varied with season, with November > August > May > February. Significant correlations existed between MBP and total phosphorus (TP), organic phosphorus (OP), inorganic phosphorus (W), organic carbon (OC), total nitrogen (TN), the grain size, and redox potential (Eh), suggesting that these sedimentary environmental characteristics played an important role in controlling the MBP levels in the sediments. Notably, there were positive linear relationships between the concentrations of soluble reactive phosphorus (SRP), TP, and chlorophyll a (Chl a) in bottom water and MBP in sediments. These relationships might be very complicated and need further exploration. This work is the first comprehensive study of the seasonal and spatial distribution of MBP in sediments and its relationships with environmental factors in a typical estuary, and will lead to deeper understanding of the phosphorus (P) biogeochemical cycle. (C) 2008 Elsevier Ltd. All rights reserved.

粘弹性介质中的地震波传播与波形反演研究

The real earth is far away from an ideal elastic ball. The movement of structures or fluid and scattering of thin-layer would inevitably affect seismic wave propagation, which is demonstrated mainly as energy nongeometrical attenuation. Today, most of theoretical researches and applications take the assumption that all media studied are fully elastic. Ignoring the viscoelastic property would, in some circumstances, lead to amplitude and phase distortion, which will indirectly affect extraction of traveltime and waveform we use in imaging and inversion. In order to investigate the response of seismic wave propagation and improve the imaging and inversion quality in complex media, we need not only consider into attenuation of the real media but also implement it by means of efficient numerical methods and imaging techniques. As for numerical modeling, most widely used methods, such as finite difference, finite element and pseudospectral algorithms, have difficulty in dealing with problem of simultaneously improving accuracy and efficiency in computation. To partially overcome this difficulty, this paper devises a matrix differentiator method and an optimal convolutional differentiator method based on staggered-grid Fourier pseudospectral differentiation, and a staggered-grid optimal Shannon singular kernel convolutional differentiator by function distribution theory, which then are used to study seismic wave propagation in viscoelastic media. Results through comparisons and accuracy analysis demonstrate that optimal convolutional differentiator methods can solve well the incompatibility between accuracy and efficiency, and are almost twice more accurate than the same-length finite difference. They can efficiently reduce dispersion and provide high-precision waveform data. On the basis of frequency-domain wavefield modeling, we discuss how to directly solve linear equations and point out that when compared to the time-domain methods, frequency-domain methods would be more convenient to handle the multi-source problem and be much easier to incorporate medium attenuation. We also prove the equivalence of the time- and frequency-domain methods by using numerical tests when assumptions with non-relaxation modulus and quality factor are made, and analyze the reason that causes waveform difference. In frequency-domain waveform inversion, experiments have been conducted with transmission, crosshole and reflection data. By using the relation between media scales and characteristic frequencies, we analyze the capacity of the frequency-domain sequential inversion method in anti-noising and dealing with non-uniqueness of nonlinear optimization. In crosshole experiments, we find the main sources of inversion error and figure out how incorrect quality factor would affect inverted results. When dealing with surface reflection data, several frequencies have been chosen with optimal frequency selection strategy, with which we use to carry out sequential and simultaneous inversions to verify how important low frequency data are to the inverted results and the functionality of simultaneous inversion in anti-noising. Finally, I come with some conclusions about the whole work I have done in this dissertation and discuss detailly the existing and would-be problems in it. I also point out the possible directions and theories we should go and deepen, which, to some extent, would provide a helpful reference to researchers who are interested in seismic wave propagation and imaging in complex media.

Using oxidized carbon nanotubes as matrix for analysis of small molecules by MALDI-TOF MS

Oxidized carbon nanotubes are tested as a matrix for analysis of small molecules by matrix assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS). Compared with nonoxidized carbon nanotubes, oxidized carbon nanotubes facilitate sample preparation because of their higher solubility in water. The matrix layer of oxidized carbon nanotubes is much more homogeneous and compact than that of nonoxidized carbon nanotubes. The efficiency of desorption/ionization for analytes and the reproducibility of peak intensities within and between sample spots are greatly enhanced on the surface of oxidized carbon nanotubes. The advantage of the oxidized carbon nanotubes in comparison with alpha-cyano-4-hydroxycinnamic acid (CCA) and carbon nanotubes is demonstrated by MALDI-TOF-MS analysis of an amino acid mixture. The matrix is successfully used for analysis of synthetic hydroxypropyl P-cyclodextrin, suggesting a great potential for monitoring reactions and for product quality control. Reliable quantitative analysis of jatrorrhizine and palmatine with a wide linear range (1-100 ng/mL) and good reproducibility of relative peak areas (RSD less than 10 %) is achieved using this matrix. Concentrations of jatrorrhizine (8.65 mg/mL) and palmatine (10.4 mg/mL) in an extract of Coptis chinensis Franch are determined simultaneously using the matrix and a standard addition method. (c) 2005 American Society for Mass Spectrometry.