A Matrix Based Indexing HDMR method for multivariate data modelling

Modelling multivariate data of real life problems from engineering, chemistry, physics, mathematics or other related sciences, in which function values are known only at arbitrarily distributed points of the problem domain, is an important and complicated issue since there exist mathematical and computational complexities in the analytical structure construction process coming from the multivariance. The Plain High Dimensional Model Representation (HDMR) method expresses a multivariate problem in terms of less-variate problems. In this work, a Matrix Based Indexing HDMR method is developed to make the Plain HDMR philosophy employable for the multivariate data partitioning process. This new method will have the ability of dealing with less-variate data sets by partitioning the given data set into univariate, bivariate and trivariate data sets. Interpolating these partitioned data sets will construct an approximate analytical structure as the model of the given multivariate data modelling problem.     

Multivariate data modelling through Piecewise generalized HDMR method

This work aims to develop a new High Dimensional Model Representation (HDMR) based method which can construct an analytical structure for a given multivariate data modelling problem. Modelling multivariate data through a divide-and-conquer method stands for multivariate data partitioning process in which we deal with a number of less variate data sets instead of a single N dimensional problem. Generalized HDMR is one of these methods used to model a multivariate data set which has a number of scattered nodes with associated function values. However, Generalized HDMR includes a linear equation system with huge number of unknowns and equations to be solved. This equation sometimes has linearly dependent equations in it and this is an undesirable situation. This work offers a new method named Piecewise Generalized HDMR method which bypasses this disadvantage as well as reducing the mathematical complexity and CPU time needed to complete the algorithm of the previous method. Our new method splits the given problem domain into subdomains, applies the Generalized HDMR philosophy to each subdomain and superpositions the information coming from these subdomains. The algorithm of this new method and a number of numerical implementations are given in this paper.     

A novel piecewise multivariate function approximation method via universal matrix representation

Multivariance in science and engineering causes problematic situations even for continous and discrete cases. One way to overcome this situation is to decrease the multivariance level of the problem by using a divide—and—conquer based method. In this sense, Enhanced Multivariance Product Representation (EMPR) plays a part in the considered scenario and acts successfully. This method brings up a finite expansion to represent a multivariate function in terms of less-variate functions with the assistance of univariate support functions. This work aims to propose a new EMPR based algorithm which has two new features that improves the determination process of each expansion component through Fluctuation Free Integration method, which is an efficient method in evaluating multiple integrals through a universal matrix representation, and increases the approximation quality through inserting a piecewise structure into the standard EMPR algorithm. This new method is called Fluctuation Free Integration based piecewise EMPR. Some numerical implementations are also given to examine the performance of this proposed method.     

Trend analysis of time-series data: A novel method for untargeted metabolite discovery

A new strategy for biomarker discovery is presented that uses time-series metabolomics data. Data sets from samples analysed at different time points after an intervention are searched for compounds that show a meaningful trend following the intervention. Obviously, this requires new data-analytical tools to distinguish such compounds from those showing only random variation. Two univariate methods, autocorrelation and curve-fitting, are used either as stand-alone methods or in combination to discover unknown metabolites in data sets originating from target-compound analysis. Both techniques reduce the long list of detected compounds in the kinetic sample set to include only those having a pre-defined interesting time profile. Thus, new metabolites may be discovered within data structures that are usually only used for target-compound analysis.The new strategy is tested on a sample set obtained from a gut fermentation study of a polyphenol-rich diet. For this study, the initial list of over 9000 potentially interesting features was reduced to less than 150, thus significantly reducing the expensive and time-consuming manual examination.     

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.     

A novel method for monolayer deposition: water seepage method

A method has been developed to deposit monolayers of a supramolecular assembly of amphiphiles onto solid substrates. A stable monolayer in a solid state is allowed to form at the air-water interface. The subphase is then allowed to seep out at a controlled rate and the monolayer descends and ultimately is deposited on the solid substrate. The quality of the films thus formed is comparable to that of the film deposited by the Langmuir-Blodgett technique. The method is simple, cost-effective and adaptable for scaling up for industrial application or scaling down for specialized use.     

A new and consistent parameter for measuring the quality of multivariate analytical methods: Generalized analytical sensitivity

Generalized analytical sensitivity (γ) is proposed as a new figure of merit, which can be estimated from a multivariate calibration data set. It can be confidently applied to compare different calibration methodologies, and helps to solve literature inconsistencies on the relationship between classical sensitivity and prediction error. In contrast to the classical plain sensitivity, γ incorporates the noise properties in its definition, and its inverse is well correlated with root mean square errors of prediction in the presence of general noise structures. The proposal is supported by studying simulated and experimental first-order multivariate calibration systems with various models, namely multiple linear regression, principal component regression (PCR) and maximum likelihood PCR (MLPCR). The simulations included instrumental noise of different types: independently and identically distributed (iid), correlated (pink) and proportional noise, while the experimental data carried noise which is clearly non-iid.     

A matrix method for modelling liquid crystal textures

A simple method for modelling the textures of liquid-crystalline phases, recently proposed by Bedford et al., is here rewritten in matrix form. A formal similarity is found between their method and the continuum theory of liquid crystals. Disclination patterns are simulated by solving a modified matrix equation.     

PPM-Dom: A novel method for domain position prediction

Domains are the structural basis of the physiological functions of proteins, and the prediction of which is an advantageous process on the study of protein structure and function. This article proposes a new complete automatic prediction method, PPM-Dom (Domain Position Prediction Method), for predicting the particular positions of domains in a target protein via its atomic coordinate. The presented method integrates complex networks, community division, and fuzzy mean operator (FMO). The whole sequences are divided into potential domain regions by the complex network and community division, and FMO allows the final determination for the domain position. This method will suffice to predict regions that will form a domain structure and those that are unstructured based on completely new atomic coordinate information of the query sequence, and be able to separate different domains in the same query sequence from each other. On evaluating the performance using an independent testing dataset, PPM-Dom reached 91.41% for prediction accuracy, 96.12% for sensitivity and 92.86% for specificity. The tool bag of PPM-Dom is freely available at http://cic.scu.edu.cn/bioinformatics/PPMDom.zip.     

A novel method for enzyme design

Rational design of enzymes is a stringent test of our understanding of protein structure and function relationship, which also has numerous potential applications. We present a novel method for enzyme design that can find good candidate protein scaffolds in a protein-ligand database based on vector matching of key residues. Residues in the vicinity of the active site were also compared according to a similarity score between the scaffold protein and the target enzyme. Suitable scaffold proteins were selected, and the side chains of residues around the active sites were rebuilt using a previously developed side-chain packing program. Triose phosphate isomerase (TIM) was used as a validation test for enzyme design. Selected scaffold proteins were found to accommodate the enzyme active sites and successfully form a good transition state complex. This method overcomes the limitations of the current enzyme design methods that use limited number of protein scaffold and based on the position of ligands. As there are a large number of protein scaffolds available in the Protein Data Band, this method should be widely applicable for various types of enzyme design.     

A novel approach to modelling counter-current chromatography

Literature lists a number of counter-current chromatography (CCC) models that can predict the retention time and to a certain extent the peak width of a solute eluting from a CCC column. The approach described in this paper distinguishes itself from previous reports by relating all model parameters directly to column dimensions and experimental settings. Most importantly, this model can predict a chromatogram from scratch without resorting to traditional calibration using empirical values. The model validation with experimental results obtained across a range of CCC instruments demonstrated that the solute retention time, peak width, and peak resolution could be predicted within reasonable accuracy. Additionally, the effect of several process parameters, such as mobile phase flow rate, rotational speed of the column or β-value, showed that the model is robust and applicable to a wide range of CCC instruments. Overall, this model proved to be a useful tool for parameter estimation and, most significantly, separation optimisation.     

A multivariate representation and analysis of DNA sequence data

A new way to represent and analyze DNA sequence data is described. This approach complements methods currently used, in that it allows the systematic part of the variation between different sequences to be modeled. This can prove as informative as absence of variation (homology), which is the most widely used criterion for comparing sequence data. A multivariate sequence-activity model (SAM), for DNA-promoter sequences is presented, by which the relative promoter strength is modeled in terms of the primary DNA-sequence. The model is shown to have a good predictive capability. The coefficients from the model are interpreted, and used to design new structures predicted to be strong promoters in the system investigated. The approach described is also applicable to other kinds of sequence data, e.g. RNAs, proteins or peptides.     

A method for treatment of thermodesorption data

A new method for the treatment of thermodesorption data without restriction on the form of temperature programming and surface coverage has been proposed. Computer programs for the treatment of experimental data have been written.

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Supervised principal components: a new method for multivariate spectral analysis

The supervised principal components (SPC) method was proposed by Bair and Tibshirani for statistics regression problems where the number of variables greatly exceeds the number of samples. This case is extremely common in multivariate spectral analysis. The objective of this research is to apply SPC to near‐infrared and Raman spectral calibration. SPC is similar to traditional principal components analysis except that it selects the most significant part of wavelength from the high‐dimensional spectral data, which can reduce the risk of overfitting and the effect of collinearity in modeling according to a semi‐supervised strategy. In this study, four conventional regression methods, including principal component regression, partial least squares regression, ridge regression, and support vector regression, were compared with SPC. Three evaluation criteria, coefficient of determination (R²), external correlation coefficient (Q²), and root mean square error of prediction, were calculated to evaluate the performance of each algorithm on both near‐infrared and Raman datasets. The comparison results illustrated that the SPC model had a desirable ability of regression and prediction. We believe that this method might be an alternative method for multivariate spectral analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

OnPLS—a novel multiblock method for the modelling of predictive and orthogonal variation

This paper presents a new multiblock analysis method called OnPLS, a general extension of O2PLS to the multiblock case. The proposed method is equivalent to O2PLS in cases involving only two matrices, but generalises to cases involving more than two matrices without giving preference to any particular matrix: the method is fully symmetric. OnPLS extracts a minimal number of globally predictive components that exhibit maximal covariance and correlation. Furthermore, the method can be used to study orthogonal variation, i.e. local phenomena captured in the data that are specific to individual combinations of matrices or to individual matrices. The method's utility was demonstrated by its application to three synthetic data sets. It was shown that OnPLS affords a reduced number of globally predictive components and increased intercorrelations of scores, and that it greatly facilitates interpretation of the predictive model. Copyright © 2011 John Wiley & Sons, Ltd.     

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.     

A new method for the kinetic study of thermoanalytical data:: The non-parametric kinetics method

A new method, called non-parametric kinetics (NPK), for the treatment of non-isothermal thermoanalytical data has been developed. The most significant feature of this method is its ability to provide a kinetic model that fits the experimental data, without any assumptions either about the functionality of the reaction rate with the degree of conversion or the temperature. The thermal decomposition of dibenzoyl peroxide has been studied in order to validate the NPK method, and the results are compared with those of the traditional ones.     

The Law of Mixtures method for multivariate calibration

The Law of Mixtures (LM) method is a new so-called topological method for multivariate calibration. It is shown to be a very good method to predict the response for new objects that are inside the convex hull determined by the calibration data set. A method is also proposed for those that are outside the convex hull.     

GEOM: A new tool for molecular modelling based on distance geometry calculations with NMR data

Summary GEOM is a new graphics tool which allows the use of distance geometry to compute linear and cyclic structures typically arising in drug design situations. Modified amino acids or monomeric organic entities can be easily constructed in an interactive way and deposited in the library of the distance geometry program together with geometric information required for structure calculation in dihedral angle space. In addition, GEOM is able to produce all files needed to calculate a structure based on NMR data (NOE and J-coupling constraints) and it permits the graphic analysis and comparison of computed structures. The application of GEOM is demonstrated in three examples: modelling of cyclosporin A structures with and without a limited set of H-bond constraints and modelling of a cyclic hexapeptide with a full NMR data set.