Least-squares Procedure Research Articles

Oscillator Strengths and Lifetimes for the P XIII Spectrum

The P XIII spectrum has been analyzed by several authors using different light sources. The semi-empirical oscillator strengths (gf) and the lifetimes presented in this work for all known P XIII spectral lines and energy levels were carried out in a multi-configuration Hartree-Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure in order to improve the adjustment of theoretical to experimental energy levels. The method produces gf-values that are in agreement with intensity observations and lifetime values closer to the experimental ones.

Unsteady Compressible Flow Calculations with Least-Square Mesh-less Method

A dual-time implicit mesh-less method is presented for unsteady compressible flow calculations. Polynomial least-square (PLS) and Taylor series least-square (TLS) procedures are used to estimate the spatial derivatives at each node and their computational efficiencies are compared. Also, the effect of the neighbor stencil selection on the accuracy of the method is investigated. As a new approach, different neighboring stencils are used for the highly stretched point distribution inside the boundary layer region and the inviscid isotropic point distribution outside this area. The unsteady flows over stationary and moving objects at subsonic and transonic flow conditions are solved. Results indicate the computational efficiency of the method in comparison with the alternative approaches. The convergence histories of the flow solution show that the PLS method is computationally faster than TLS method. In addition, the eight point neighboring stencil inside the viscous region is more efficient than other choices.

3,5,7-Trimethoxyphenanthrene-1,4-dione: a new biologically relevant natural phenanthrenequinone derivative from Dioscorea prazeri and studies on its single X-ray crystallographic behavior, molecular docking and other physico-chemical properties

A naturally occurring new phenanthrenequinone derivative has been isolated from the yams of Dioscorea prazeri Prain and Burkil (Dioscoreaceae) and identified as 3,5,7-trimethoxyphenanthrene-1,4-dione (1) on the basis of its detailed spectral and single crystal X-ray analyses. The compound crystallizes in the triclinic space group P with the following unit-cell parameters: a = 7.7045(3), b = 8.5088(4), c = 16.3254(7) A, α = 98.908(2)°, β = 96.316(2)°, γ = 103.939(2)° and Z = 2. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0559 for 2832 observed reflections. Exhaustive theoretical studies on the molecular structure, vibrational spectra, HOMO, LUMO, MESP surfaces, reactivity descriptor and molecular docking of this plant-derived hitherto unknown natural molecule have also been performed. The equilibrium geometry of the title compound has been obtained and analyzed using the DFT-B3LYP/6-31+G(d,p) method. A comparison between the calculated vibrational spectral data with the experimental observations for the phenanthrenequinone molecule has been performed. The reactivity of this molecule is explained using various local as well as global molecular descriptors and reactivity surfaces have also been analyzed. The molecular docking study of the title molecule for predicting its possible anticancer property has also been investigated.

A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of a goodness-of-fit statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

Model-based real-time optimisation of a fed-batch cyanobacterial hydrogen production process using economic model predictive control strategy

Hydrogen produced by microorganisms has been considered as a potential solution for sustainable hydrogen production for the future. In the current study, an advanced real-time optimisation methodology is developed to maximise the productivity of a 21-day fed-batch cyanobacterial hydrogen production process, which to the best of our knowledge has not been addressed before. This methodology consists of an economic model predictive control formulation used to predict the future experimental performance and identify the future optimal control actions, and a finite-data window least-squares procedure to re-estimate model parameter values of the on-going process and ensure the high accuracy of the dynamic model. To explore the efficiency of the current optimisation methodology, effects of its essential factors including control position, prediction horizon length, estimation window length, model synchronising frequency, terminal region and terminal cost on hydrogen production have been analysed. Finally, by implementing the proposed optimisation strategy into the current computational fed-batch experiment, a significant increase of 28.7% on hydrogen productivity is achieved compared to the previous study.

A reciprocal identity method for large silencer analysis

Conventional techniques used in the boundary element method for evaluating muffler transmission loss have been limited by the cutoff frequency of the inlet and outlet ducts. Even though the boundary element method itself is a truly three-dimensional analysis tool, it has not been effectively used on large silencers due to the large inlet and outlet cross sections. In this paper, a numerical technique based on the reciprocal identity and the boundary element impedance matrix is proposed as a post-processing filter to extract the transmission loss of large silencers at all frequencies. Each reciprocal identity couples two different sound fields on the same silencer geometry. The first sound field has the analytical modal expansion in the inlet and outlet ducts, while the second sound field is the boundary element solution associated with a random boundary condition set. Depending on how many modes exist in the inlet and outlet ducts at a certain frequency, a minimum number of random boundary condition sets must be applied to the boundary element model. The boundary element impedance matrix provides more than enough such solution sets for the reciprocal identity coupling. The overdetermined system is then solved by a least-squares procedure. The proposed method is verified by comparing to the analytical solutions of a simple expansion chamber and a round bar silencer.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods.

Re-weighting estimation of the coefficients in the varying coefficient model with heteroscedastic errors

ABSTRACTThis article explores the estimation problem of the coefficients in the varying coefficient model with heteroscedastic errors. Specifically, we first present a method for estimating the variance function of the error term and the resulting estimator is proved to be consistent. Then, motivated by the generalized least-squares procedure for dealing with heteroscedasticity in the linear regression literature, we re-weight each squared residual term in the local linear smoother with the inverse of the corresponding estimated error variance to construct estimates of the coefficients. Simulation experiments and practical data analysis conducted demonstrate that the re-weighting approach can improve the accuracy of the coefficient estimates under a finite sample size, especially when the error heteroscedasticity is strong.

Extracting Infrared Spectra of Protein Secondary Structures Using a Library of Protein Spectra and the Ramachandran Plot.

Infrared (IR) spectra from 1200 to 1800 cm(-1) of the pure α-helix and β-sheet secondary structures have been extracted using a covariant least-squares procedure which relates a library of 40 infrared (IR) solution protein spectra from the work of Dong, Carpenter, and Caughey and amino acid fractions of the proteins based on assignments by STRIDE (secondary structure identification) of Eisenhaber and Argos. The excitonic splitting of the β-sheet structures is determined for this library of solution proteins. The method is extended to find a set of spectral basis functions that analyze IR spectra of protein samples for α-helix and β-sheet content. A rigorous error analysis including covariance, the correlations between the input library spectra, was used to justify the results and avoid less meaningful results. The utility of the results on α-helix and β-sheet regions is demonstrated by detecting protein changes due to cancer in imaging Fourier transform IR (FTIR) spectra of liver tissue slices. This work ends with a method to extract IR spectra of less prominent torsional angle distributions.

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years.

SYNTHESIS, SPECTROSCOPIC CHARACTERIZATION, X-RAY ANALYSIS OF DMSO SOLVATED 5'-CHLORO-1H,1"H-[3,3':3',3"-TERINDOL]-2'(1'H)-ONE

The title compound 5'-Chloro-1H,1H-[3,3':3',3-terindol]-2'(1'H)-one is synthesized via one-pot multicomponent reaction (MCR) at room temperature using commercially available sulfamic acid as inexpensive and environmentally benign organo-catalyst. It crystallizes in the monoclinic space group P2 1 /n with the unit-cell parameters: a = 15.3117(15), b = 10.9302(8), c = 16.591(2) A, a = 90.00 o β = 98.224(10) ° , γ = 90.00 ° and Z = 4. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0735 for 2539 observed reflections. Both the DMSO solvent molecules take part in the inter- and intramolecular interactions that are responsible for the formation of hydrogen bonded network. Two C-H∙∙∙π inter-molecular hydrogen bonds are also present in the crystal structure.

Least-squares fitting of Hartmann or Shack-Hartmann data with a circular array of sampling points.

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack-Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with three, four, five, six, or more sampling points are analyzed with more detail and better mathematical analysis than in previous publications.

Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values

A method is presented for analysing over-determined sets of clock frequency comparison data involving standards based on a number of different reference transitions. This least-squares adjustment procedure, which is based on the method used by CODATA to derive a self-consistent set of values for the fundamental physical constants, can be used to derive optimized values for the frequency ratios of all possible pairs of reference transitions. It is demonstrated to reproduce the frequency values recommended by the International Committee for Weights and Measures, when using the same input data used to derive those values. The effects of including more recently published data in the evaluation is discussed and the importance of accounting for correlations between the input data is emphasised.

X-RAY STUDIES OF 2-AMINO-4-ISOPROPYL-5-OXO-4,5-DIHYDROPYRANO[3,2-c]CHROMENE-3-CARBONITRILE

The title compound, 2-amino-4-isopropyl-5-oxo-4,5-dihydropyrano[3,2-c]chromene-3-carbonitrile (C 16 H 14 N 2 O 3 ) is synthesized via one-pot multi-component reaction (MCR) at room temperature using commercially available urea as inexpensive and environmentally benign organo catalyst and crystallizes in the triclinic space group P -1 with the unit-cell parameters: a= 7.8231(4), b= 8.0622(4), c= 12.3038(5) A, α = 99.443(4) o , β = 102.419(4) o , γ = 109.907(4) o and Z = 2. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0405 for 2118 observed reflections. The packing of molecules within the unit cell is stabilized by N-H…O and N-H…N type of intermolecular hydrogen interactions. In addition C-H…π and π-π interactions are also observed in the crystal structure.

Waveguide spectroscopy of bilayer structures

A least-squares procedure is proposed for the reconstruction of optical parameters of bilayer structures. The objective function is constructed using experimental and calculated data on the reflectance of a coupling prism. A structure consisting of two different silicon oxynitride films on a silicon substrate is studied. The effect of scattering on the solution of the inverse problem is analyzed.

An alternative empirical model for the relationship between the bond valence and the thermal expansion rate of chemical bonds.

The relationship between the bond valence s and the thermal expansion rate of chemical bonds (dr/dT) has been closely approximated by using the alternative three-parameter empirical model (dr/dT) = (u + vs)(-1/w), where u, v and w are the refinable parameters. Unlike the s-(dr/dT) model developed by Brown et al. [(1997), Acta Cryst. B53, 750-761], this alternative model can be optimized for particular s-(dr/dT) datasets in the least-squares refinement procedure. For routine calculations of the thermal expansion rates of chemical bonds, the alternative model with the parameters u = -63.9, v = 2581.0 and w = 0.647 can be recommended.

CRYSTAL STRUCTURE OF (2-METHYL-PHENOXY)-ACETOHYDRAZIDE

The title compound, (2-methyl-phenoxy)-acetohydrazide, was synthesized by refluxing compounds o -cresol, ethyl chloroacetate and anhydrous potassium carbonate in the presence of dry acetone. The compound crystallizes in the monoclinic crystal system with space group P2 1 /n having unit cell parameters: a = 11.5460(2), b = 6.86700(10), c = 12.7506(3)A, β = 110.022(2)o and Z = 4 . The crystal structure was solved by direct method using single crystal x-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R- value of 0.0377 for 1619 observed reflections. In the crystal structure, molecules are linked into infinite two-dimensional networks by the N–H···N and N–H···O, C−H…O and C−H…π type of hydrogen bonds.

X-RAY STUDIES OF METHYL 6-AMINO-5-CYANO-2-METHYL-4-(3-NITROPHENYL)-4H-PYRAN-3-CARBOXYLATE

The title compound, methyl 6-amino-5-cyano-2-methyl-4-(3-nitrophenyl)-4 H -pyran-3-carboxylate (C 15 H 13 N 3 O 5 ), was synthesized, in 92% yield, by one-pot multicomponent reaction of 3-nitrobenzaldehyde, malononitrile and methyl acetoacetate using 10 mol% urea as an organo-catalyst at room temperature.. It crystallizes in the triclinic space group P -1 with the unit-cell parameters: a= 8.1780(4), b= 8.3787(4), c= 11.8005(6) A, α = 75.703(4) o , β = 86.017(4) o , γ = 72.983(4) o and Z = 2. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0538 for 1896 observed reflections. The molecules within the unit cell are stabilized by C-H…O, N-H…O and N-H…N type of hydrogen bonding. In addition π-π interactions are also observed in the crystal structure

STRUCTURE OF 5'-CHLORO-5,5''-DIFLUORO-1H,1''H- (3,3':3',3''-TERINDOL)-2'(1'H)-ONE

The title compound 5'-chloro-5,5''-difluoro-1 H ,1'' H -[3,3':3',3''-terindol]-2'(1' H )-one synthesized via one-pot multicomponent reaction (MCR) at room temperature using commercially available sulfamic acid as inexpensive and environmentally benign organo-catalyst. It crystallizes in the monoclinic space group P 21 with the unit-cell parameters: a= 10.193(5), b= 9.012(5), c= 13.406(5) A, β = 102.767(5) o and Z = 2. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0390 for 1972 observed reflections. The molecules within the unit cell are stabilized by N-H..O and C-H..F type of hydrogen bonding. The sulphur atom of DMSO solvent molecule is found disordered over two set of sites S100 and S200 with occupancy ratio 0.70:0.30

Reduced-order subscales for POD models

In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-order model. The coefficients of this linear function are obtained by comparing the solution of the full-order model with the solution of the reduced-order model for the same initial conditions, which, for convenience, are evaluated in the snapshots used to train the original reduced-order-model. The difference between both solutions are the subscales, for which a model can be built using a least-squares procedure. The subscales are then introduced as a correction in the reduced-order model, resulting in an important improvement in accuracy. The enhanced reduced-order model is tested in several numerical examples. These practical cases show that the use of the subscales leads to more accurate solutions, successfully corrects errors introduced by hyper-reduction, and allows to solve complex flow problems using a reduced number of degrees of freedom.