Using the L1 norm to select basis set vectors for multivariate calibration and calibration updating

With projection based calibration approaches, such as partial least squares (PLS) and principal component regression (PCR), the calibration space is spanned by respective basis vectors (latent vectors). Up to rank k basis vectors are formed where k ≤ min(m,n) with m and n denoting the number of calibration samples and measured variables. The user needs to decide how many and which respective basis vectors (tuning parameters). To avoid the second issue, basis vectors are selected top‐down starting with the first and sequentially adding until model criteria are satisfied. Ridge regression (RR) avoids the issues by using the full set of basis vectors. Another approach is to select a subset from the total available. The presented work develops a process based on the L₁ vector norm to select basis vectors. Specifically, the L₁ norm is used to select singular value decomposition (SVD) basis set vectors for PCR (LPCR). Because PCR, PLS, RR, and others can be expressed as linear combination of the SVD basis vectors, the focus is on selection and comparison using the SVD basis set. Results based on respective tuning parameter selections and weights applied to the SVD basis vectors for LPCR, top‐down PCR, correlation PCR (CPCR), PLS, and RR are compared for calibration and calibration updating using spectroscopic data sets. The methods are found to predict equivalently. In particular, the L₁ norm produces similar results to those obtained by the well‐studied CPCR process. Thus, the new method provides a different theoretical framework than CPCR for selecting basis vectors. Copyright © 2016 John Wiley & Sons, Ltd.     

A Critical Evaluation and Modification of the Padé–Laplace Method for Deconvolution of Viscoelastic Spectra

This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known multi-exponential functions indicates that by increasing the level of Padé approximants, the condition number of a matrix whose entries are coefficients of a Taylor series in the Laplace space grows rapidly. When higher levels of Padé approximants need to be computed to achieve stable modes for separation of exponentials, the problem of generating matrices with large condition numbers becomes more pronounced. The analysis in this paper discusses the origin of ill-posedness of the PL method and it was shown that ill-posedness may be regularized by reconstructing the system of equations and using singular value decomposition (SVD) for computation of the Padé table. Moreover, it is shown that after regularization, the PL method can deconvolute the exponential decays even when the input parameter of the method is out of its optimal range.     

Characterization and determination of stability constants of copper(II)-l-histidine complexation system by using multivariate curve resolution method of visible spectra and two hard modeling methods in aqueous solutions

Multivariate curve resolution, alternating least-squares is applied to spectra data obtained in the study of Cu(II) complexation by l-histidine. The combination of several chemometric techniques based on factor analysis (FA), singular value decomposition (SVD), evolving factor analysis (EFA), and multivariate curve resolution with constrained alternating least-squares (ALS) is used to determine the number of species and their distribution diagram. This multivariate analysis data treatment simultaneously reveals the species Cu, CuL, CuLH, CuL₂, CuL₂H, and CuLOH, through the calculated concentration profiles and allows the assignment of numerically obtained pure individual spectra. Formation constants of these species were calculated by hard-modeling methods applied potentiometric and spectrophotometric measurements.     

CuO nanoparticles supported on three‐dimensional nitrogen‐doped graphene as a promising catalyst for thermal decomposition of ammonium perchlorate

In the present work, CuO nanoparticles grown on three‐dimensional nitrogen‐doped graphene‐based frameworks (CuO@3D‐(N)GFs) were synthesized using a two‐step method. After the synthesis of three‐dimensional nitrogen‐doped graphene, CuO nanoparticles were deposited on it, by adding cupric acetate followed by thermal treatment. Different analysis methods were used to characterize the products. The as‐prepared nanocomposite was used as a promising catalyst for thermal decomposition of ammonium perchlorate (AP) as one of the most common oxidizer in composite propellants. Differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA) techniques were used to investigate the thermal decomposition of ammonium perchlorate. According to the DSC/TGA, high temperature decomposition of AP decreased to 111 °C in the presence of 4% CuO@3D‐(N)GFs and the total heat release (ΔH) from decomposition of AP increased to 1893 J g^?1 which is much more than 590 J g^?1 for pure AP.     

Influences of product gases on the kinetics of thermal decomposition of synthetic malachite evaluated by controlled rate evolved gas analysis coupled with thermogravimetry

An instrument of controlled rate evolved gas analysis (CREGA) coupled with TG‐DTA was constructed for analyzing the influences of product gases on the kinetics and mechanism of the thermal decomposition of solids that produce more than one gaseous products at the same stage of reaction. The thermal decomposition of synthetic malachite, Cu₂(OH)₂CO₃, was subjected to the measurements of CREGA‐TG under controlled concentrations of H₂O and CO₂ in the reaction atmosphere with taking account of self‐generated H₂O and CO₂ during the course of reaction. By a series of CREGA‐TG measurements carried out under various atmospheric conditions, it was reconfirmed that the reaction is accelerated and decelerated by the effects of atmospheric H₂O and CO₂, respectively. From the kinetic analysis of the CREGA‐TG curves and results of high temperature X‐ray diffraction measurements under various reaction atmospheres, it was revealed that the anomalous effects of atmospheric H₂O on the reactivity and on the reaction rate of the thermal decomposition of synthetic malachite appear at the early stage of the reaction. Usefulness of the CREGA‐TG technique for measuring the kinetic rate data for the thermal decomposition of solids was demonstrated in the present study, by emphasizing the importance of quantitative control of self‐generated reaction atmosphere. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 346–354, 2005     

Thermal Decomposition Kinetics of Some Metal Complexes of 2,3-Hydroxyimino-4-phenyl-6-phenyazo-1-thia-4,5-diazacyclohexa-5-diene

The Ni(II), Cu(II) Co(II) and Zn(II) complexes of 2,3‐hydroxyimino‐4‐phenyl‐6‐phenyazo‐1‐thia‐4,5‐diaza‐ cyclohexa‐5‐diene (H₂L) were synthesized. Thermal behavior of these complexes was studied in dynamic nitrogen atmosphere by TA (thermogravimetric analysis), DTA (differential thermal analysis) and DTG (differential thermal gravimetry) techniques. The reaction order, the activation energies, the entropies, the enthalpies, the free energies, and the pre‐exponential factors of the thermal decomposition reactions were calculated from the thermogravimetric curves. The kinetic analysis of the thermogravimetric data was performed by using several methods such as MacCallum‐Tanner (MT), van Krevelen (vK), Madhusudanan‐Krishnan‐Ninan (MKN), Wanjun‐Yuwen‐Hen‐Cunxin (WYHC), Horowitz‐Metzger (HM) and Coats‐Redfern method (CR) based on the single heating rate. Most appropriate methods were determined for each decomposition step according to the least‐square linear regression. The Ni(II), Cu(II) Co(II) and Zn(II) complexes displayed one‐ or two‐stage decomposition pattern when heating in a dynamic nitrogen atmosphere and metal oxides remained as end products of the complexes. The characterization of the end products of the decomposition was performed by X‐ray diffraction.     

Theoretical investigation of the interactions between the π‐systems of molecular organic semiconductors and an analysis of the contributions of repulsion and electrostatics

A concept for the interactions between π‐systems is necessary to understand a number of phenomena in modern material sciences such as supramolecular properties and self‐assembly. In the present article, we investigate the intermolecular interaction energies between organic semiconductors with extended π‐systems using SAPT (symmetry‐adapted perturbation theory), LMO‐EDA (localized molecular orbital energy decomposition analysis), DFT‐D (density functional theory including dispersion corrections), and force‐field approaches. Both apolar organic molecules such as acenes and highly polarized π‐systems of merocyanines and squaraines were used to probe the influence of electrostatics on the shape of the potential energy surfaces (PES) governing the geometric structures of aggregates. Our results reveal that the shapes of the PESs result from variations in the short‐range, highly specific repulsion forces even for highly polar molecules. Using distributed quadrupoles, we show that it is nevertheless possible to mimic the intermolecular potentials with electrostatics. This is also possible with van‐der‐Waals potentials and a simple overlap‐based force‐field ansatz based on the overlap between p‐orbitals. © 2016 Wiley Periodicals, Inc.     

Hydrophobic distal pocket affects NO-heme geminate recombination dynamics in dehaloperoxidase and H64V myoglobin

The recombination dynamics of NO with dehaloperoxidase (DHP) from Amphitrite ornata following photolysis were measured by femtosecond time-resolved absorption spectroscopy. Singular value decomposition (SVD) analysis reveals two important basis spectra. The first SVD basis spectrum reports on the population of photolyzed NO molecules and has the appearance of the equilibrium difference spectrum between the deoxy and NO forms of DHP. The first basis time course has two kinetic components with time constants of tau(11) approximately 9 ps and tau(12) approximately 50 ps that correspond to geminate recombination. The fast geminate process tau(11) arises from a contact pair with the heme iron in a bound state with S = 3/2 spin. The slow geminate process tau(12) corresponds to the recombination from a more remote docking site >3 A from the heme iron with the greater barrier corresponding to a S = 5/2 spin state. The second SVD basis spectrum represents a time-dependent Soret band shift indicative of heme photophysical processes and protein relaxation with time constants of tau(21) approximately 3 ps and tau(22) approximately 17 ps, respectively. A comparison between the more rapid rate constant of the slow geminate phase in DHP-NO and horse heart myoglobin (HHMbNO) or sperm whale myoglobin (SWMbNO) suggests that protein interactions with photolyzed NO are weaker in DHP than in the wild-type MbNOs, consistent with the hydrophobic distal pocket of DHP. The slower protein relaxation rate tau(22) in DHP-NO relative to HHMbNO implies less effective trapping in the docking site of the distal pocket and is consistent with a greater yield for the fast geminate process. The trends observed for DHP-NO also hold for the H64V mutant of SWMb (H64V MbNO), consistent with a more hydrophobic distal pocket for that protein as well. We examine the influence of solution viscosity on NO recombination by varying the glycerol content in the range from 0% to 90% (v/v). The dominant effect of increasing viscosity is the increase of the rate of the slow geminate process, tau(12), coupled with a population decrease of the slow geminate component. Both phenomena are similar to the effect of viscosity on wild-type Mb due to slowing of protein relaxation resulting from an increased solution viscosity and protein surface dehydration.     

Complex numbers in chemometrics: examples from multivariate impedance measurements on lipid monolayers

Electrical impedance gives multivariate complex number data as results. Two examples of multivariate electrical impedance data measured on lipid monolayers in different solutions give rise to matrices (16x50 and 38x50) of complex numbers. Multivariate data analysis by principal component analysis (PCA) or singular value decomposition (SVD) can be used for complex data and the necessary equations are given. The scores and loadings obtained are vectors of complex numbers. It is shown that the complex number PCA and SVD are better at concentrating information in a few components than the na?ve juxtaposition method and that Argand diagrams can replace score and loading plots. Different concentrations of Magainin and Gramicidin A give different responses and also the role of the electrolyte medium can be studied. An interaction of Gramicidin A in the solution with the monolayer over time can be observed.     

A scalable optimization approach for fitting canonical tensor decompositions

Tensor decompositions are higher‐order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum of component rank‐one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience and web analysis. The task of computing CP, however, can be difficult. The typical approach is based on alternating least‐squares (ALS) optimization, but it is not accurate in the case of overfactoring. High accuracy can be obtained by using nonlinear least‐squares (NLS) methods; the disadvantage is that NLS methods are much slower than ALS. In this paper, we propose the use of gradient‐based optimization methods. We discuss the mathematical calculation of the derivatives and show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient‐based optimization methods are more accurate than ALS and faster than NLS in terms of total computation time. Copyright © 2011 John Wiley & Sons, Ltd.     

Confinement effects on the thermal stability of poly(ethylene oxide)/graphene nanocomposites: A reactive molecular dynamics simulation study

Nonisothermal and isothermal decomposition of poly(ethylene oxide) (PEO) loaded with different concentrations of pristine graphene (PG) and graphene oxide (GO) nanoplatelets were investigated using reactive molecular dynamics simulation. The onset of nonisothermal decomposition of the PG‐loaded PEO system was the highest among all systems, suggesting that introducing PG to the polymer improves its thermal stability (an effect that increases with an increase in the PG concentration). At low concentration, introducing GO to the polymer brings about a deterioration of the thermal stability of the polymer consistent with experimental findings. On average, the activation energy for the isothermal decomposition of PG‐loaded PEO system increases by 60% over that of the neat PEO system, while it decreases by 40% for the GO‐loaded PEO system. A time‐dependent analysis of the through‐thickness decomposition profile of the above systems reveals that the polymer confined between the PG sheets exhibit a higher thermal stability compared to the bulk polymer. However, an opposite effect is observed with the polymer confined between the GO sheets. The latter observation is attributed to accelerated polymer chain scission in confined regions due to the ejection of reactive hydroxyl radicals from the GO surface during the early stages of thermal decomposition. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1026–1035     

SVD Analysis in Fitting Property Surfaces

Previous calculated spectral properties of Li₃⁺associated with the [6,7] vibrational band origins were rendered as uncertain, due to the exclusion of cross-terms involving the breathe mode normal co-ordinate in the analytic expansion of the dipole moment surface. However, by applying a singular value decomposition (SVD) analysis the exclusion of these terms is shown to be appropriate with respect to their negligible effect on fit (via the square root of the sum of the square of the residuals) thereby validating previous prognosis.     

Solution of the inverse problem of light beating spectroscopy using singular value decomposition for analyzing the composition of polydisperse suspensions of nanoparticles

The inverse problem of light beating spectroscopy is numerically solved by the singular value decomposition (SVD) method. The developed algorithm allows for the positivity of the solution and a constant background signal. Examples of reconstructed model uni-, bi-, and multimodal distributions are presented. The influences of the noise of a recorded spectrum, the background signal, and the chosen frequency range for measuring the signal on the characteristics of the distribution reconstructed by the SVD method are studied by the example of numerically generated (and measured with allowance for the noise) spectra.     

Efficient newton–raphson/singular value decomposition-based optimization scheme with dynamically updated critical condition number for rapid convergence of weighted histogram analysis method equations

Selection of the successful optimization strategy is an essential part of solving numerous practical problems yet often is a nontrivial task, especially when a function to be optimized is multidimensional and involves statistical data. Here we propose a robust optimization scheme, referred to as NR/SVD-Cdyn, which is based on a combination of the Newton–Raphson (NR) method along with singular value decomposition (SVD), and demonstrate its performance by numerically solving a system of the weighted histogram analysis method equations. Our results show significant improvement over the direct iteration and conventional NR optimization methods. The proposed scheme is universal and could be used for solving various optimization problems in the field of computational chemistry such as parameter fitting for the methods of molecular mechanics and semiempirical quantum-mechanical methods. © 2019 Wiley Periodicals, Inc.     

Fast determination of the optimal rotational matrix for macromolecular superpositions

Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 × 3 or 4 × 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton‐Raphson quaternion‐based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high‐throughput analyses of molecular conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Low‐energy collision‐induced dissociation (low‐energy CID), collision‐induced dissociation (CID), and higher energy collision dissociation (HCD) mass spectrometry for structural elucidation of saccharides and clarification of their dissolution mechanism in DMAc/LiCl

The dissolution mechanism of oligosaccharides in N,N‐dimethylacetamide/lithium chloride (DMAc/LiCl), a solvent used for cellulose dissolution, and the capabilities of low‐energy collision‐induced dissociation (low‐energy CID), collision‐induced dissociation (CID), and higher energy collision dissociation (HCD) for structural analysis of carbohydrates were investigated. Comparing the spectra obtained using 3 techniques shows that, generally, when working with monolithiated sugars, CID spectra provide more structurally informative fragments, and glycosidic bond cleavage is the main pathway. However, when working with dilithiated sugars, HCD spectra can be more informative providing predominately cross‐ring cleavage fragments. This is because HCD is a nonresonant activation technique, and it allows a higher amount of energy to be deposited in a short time, giving access to more endothermic decomposition pathways as well as consecutive fragmentations. The difference in preferred dissociation pathways of monolithiated and dilithiated sugars indicates that the presence of the second lithium strongly influences the relative rate constants for cross‐ring cleavages vs glycosidic bond cleavages, and disfavors the latter. Regarding the dissolution mechanism of sugars in DMAc/LiCl, CID and HCD experiments on dilithiated and trilithiated sugars reveal that intensities of product ions containing 2 Li⁺ or 3 Li⁺, respectively, are higher than those bearing only 1 Li⁺. In addition, comparing the fragmentation spectra (both HCD and CID) of LiCl‐adducted lithiated sugar and NaCl‐adducted sodiated sugar shows that while, in the latter case, loss of NaCl is dominant, in the former case, loss of HCl occurs preferentially. The compiled evidence implies that there is a strong and direct interaction between lithium and the saccharide during the dissolution process in the DMAc/LiCl solvent system.     

Gas‐phase pyrolysis mechanisms of 3‐anilino‐1‐propanol: Density functional theory study

The gas‐phase pyrolytic decomposition mechanisms of 3‐anilino‐1‐propanol with the products of aniline, ethylene, and formaldehyde or N‐methyl aniline and aldehyde were studied by density functional theory. The geometries of the reactant, transition states, and intermediates were optimized at the B3LYP/6‐31G (d, p) level. Vibration analysis was carried out to confirm the transition state structures, and the intrinsic reaction coordinate method was performed to search the minimum energy path. Four possible reaction channels are shown, including two concerted reactions of direct pyrolytic decomposition and two indirect channels in which the reactant first becomes a ring‐like intermediate, followed by concerted pyrogenation. One of the concerted reactions in the direct pyrolytic decomposition has the lowest activation barrier among all the four channels, and so, it occurs more often than others. The results appear to be consistent with the experimental outcomes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Electronic Circular Dichroism Imaging (ECDi) Casts a New Light on the Origin of Solid-State Chiroptical Properties

Solid-state ECD (ss-ECD) spectra of a model microcrystalline solid, finasteride, dispersed into a KCl pellet were recorded by using the synchrotron radiation source at the Diamond B23 beamline. Scanning a surface of 36 mm² with a step of 0.5 mm, we measured a set of ECD imaging (ECDi) spectra very different from each other and from the ss-ECD recorded with a bench-top instrument (1 cm² area). This is due to the anisotropic part of the ECD (ACD), which averages to zero in solution or on a large number of randomly oriented crystallites, but can otherwise be extremely large. Two-way singular value decomposition (SVD) analysis, through experimental and simulated TDDFT spectra, disclosed that the measured and theoretical principal components are in line with each other. This finding demonstrates that the observed isotropic ss-ECD spectrum is governed by the anisotropy of locally oriented crystals. It also introduces a new quality for ss-ECD measurements and opens a new future for probing and mapping chiral materials in the solid state such as active pharmaceutical ingredients (APIs).     

A novel efficient way to estimate the chemical rank of high-way data arrays

A novel method, a subspace projection of pseudo high-way data array (SPPH), was developed for estimating the chemical rank of high-way data arrays. The proposed method determines the chemical rank through performing singular value decomposition (SVD) on the slice matrices of original high-way data array to produce a pseudo high-way data array and employing the idea of the difference of the original truncated data set and the pseudo one. Compared with traditional methods, it uses the information from eigenvectors combined with the projection residual to estimate the rank of the three-way data arrays instead of using the eigenvalue. In order to demonstrate the excellent performance of the new method, simulated and real three-way data arrays were carried out by the proposed method. The results showed that the proposed method could accurately and quickly determine the chemical rank to fit the trilinear model. Moreover, the newly proposed method was compared with the other four factor-determining methods, i.e. factor indicator function (IND), ADD-ONE-UP, core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approaches. It was found that the proposed method can deal with more complex situations with existence of severe collinearity and trace concentration than many other methods can and performs well in practical applications.