Progress in statistical thermodynamics applied to fluid phase

Perturbation theories of simple fluids (proposed both for single- and multicomponent systems) and perturbation theories of molecular fluids (of polar and non-polar non-spherical molecules) are summarized with stress laid on those methods that yield relations suitable for the characterization of the thermodynamic behaviour of real liquids and their mixtures.     

Third law of thermodynamics as applied to phase diagrams

Consequences from the third law of thermodynamics are analyzed from the standpoint of low-temperature phase equilibria. The kinetics of attainment of low-temperature equilibria and some ordering and decomposition features of solid solutions are considered.     

Orthogonal control of dissociation dynamics relative to thermodynamics in a main-chain reversible polymer

A pair of homologous and soluble reversible polymers display nearly identical solution structures but dramatically different dissociation dynamics (1.0 vs ca. 100 s-1) along their main chains. The polymers are formed by organopalladium-pyridine coordination, and steric effects at the metal center control the dynamics. Importantly, the association constant is not significantly affected by the sterics. The resulting orthogonal control over dissociation kinetics provides a general tool for studying the effects of dynamics independent of thermodynamics in supramolecular systems, particularly main-chain reversible polymers.     

Generalized exponential functions applied to atomic calculations

The use of a generalized exponential function r ^v?1 exp(?ζr ^μ ) as a radial basis function in atomic calculations is studied with our special interest in the variationally optimum value of the parameter μ, since special cases of μ = 1 and μ = 2 correspond respectively to the radial parts of commonly-used Slater-type and Gaussian-type functions. Roothaan-Hartree-Fock calculations are performed for ground-state neutral atoms with atomic number Z = 2–54, singly-charged cations with Z = 3–55, and anions with Z = 1–53 within the single-zeta (or minimal basis) framework. For all the species examined, the optimtum μ values are found to be smaller than unity and increase towards unity as the atomic number increases. The present results support the use of Slater-type functions when μ is restricted to be an integer, but suggest from the variational point of view that even the exponential decay of Slater-type functions is too “strong” within the single-zeta approximation.     

Peptide retention prediction applied to proteomic data analysis

A retention prediction model was developed for peptides separated in reversed-phase chromatography. The model was utilized to identify and exclude the false positive (FP) peptide identifications obtained via database search. The selected database included human proteins, as well as decoy sequences of random proteins. The FP peptide detection rate was defined either as number of retention time outliers, or random decoy sequence identifications. The FP rate for various MASCOT scores was calculated. The peptides identified in one-dimensional (1D) and two-dimensional (2D) liquid chromatography/mass spectrometry (LC/MS) experiments were validated by prediction models. Multi-dimensional LC was based on two orthogonal reversed-phase chromatography modes; prediction models were successfully applied for data filtering in both separation dimensions.     

A point-charge representation of frost-model wave functions

A point-charge representation of Frost-model wave functions is derived from a symmetry-adapted perturbation theoretic expansion. The new point-charge model is simpler than those suggested previously yet gives good estimates of first-order molecular properties. The treatment can easily be extended to deal with second-order properties and, when this is done, formulae similar to those of the Drude theory are obtained. Using these formulae, theoretical expressions for the refractive indices of methane, ethane and water are computed and are in reasonable accord with experiment for the two hydrocarbons but less satisfactory for water.     

Machine learning based pattern recognition applied to microarray data

Motivation: Microarrays have allowed the expression level of thousands of genes or proteins to be measured simultaneously. Data sets generated by these arrays consist of a small number of observations (e.g., 20-100 samples) on a very large number of variables (e.g., 10,000 genes or proteins). The observations in these data sets often have other attributes associated with them such as a class label denoting the pathology of the subject. Finding the genes or proteins that are correlated to these attributes is often a difficult task since most of the variables do not contain information about the pathology and as such can mask the identity of the relevant features. We describe a genetic algorithm (GA) that employs both supervised and unsupervised learning to mine gene expression and proteomic data. The pattern recognition GA selects features that increase clustering, while simultaneously searching for features that optimize the separation of the classes in a plot of the two or three largest principal components of the data. Because the largest principal components capture the bulk of the variance in the data, the features chosen by the GA contain information primarily about differences between classes in the data set. The principal component analysis routine embedded in the fitness function of the GA acts as an information filter, significantly reducing the size of the search space since it restricts the search to feature sets whose principal component plots show clustering on the basis of class. The algorithm integrates aspects of artificial intelligence and evolutionary computations to yield a smart one pass procedure for feature selection, clustering, classification, and prediction.     

Charge conservation applied to experimental data for plutonium solutions

The principle of charge conservation in isolated systems is used to analyze data recorded for an academic thesis. The analysis reveals a gradual chemical reduction of the plutonium during studies of its behavior in dilute aqueous acids. The reduction effect is reproduced in several different studies. The effect was apparently unnoticed by the author.     

On the functional representation of bond energy functions

Ab initio calculations are used to test the ability of various representations to reproduce bond energies. It is found that expansion in 1/R, where R is the bond length, is remarkably efficient and is consistently better than the usual R expansion. A quadratic form in 1/R is better than a cubic representation in R and sometimes even as good as a quartic representation. A cubic function in 1/R is, in all cases studied, better performing than the quartic expansion in R. It is also found that parameters derived with the 1/R expansion are defined more sharply than those derived for the R expansion. It is suggested that the 1/R expansion may be computationally more efficient for simulations of large biomolecules and for constructions of reactive force fields than the standard bond functions. © 1994 by John Wiley & Sons, Inc.     

SIMPLISMA applied to two-dimensional wavelet compressed ion mobility spectrometry data

A modified SIMPLe-to-use Interactive Self-modeling Mixture Analysis (SIMPLISMA) algorithm, referred to as real-time (RT) SIMPLISMA has been combined with two-dimensional (2D) wavelet compression (WC²). This tool was evaluated with datasets of drugs and bacteria that were acquired from two different ion mobility spectrometers and published reference data that comprised Raman, FTIR microscopy, near-infrared (NIR) and mass spectral data. RTSIMPLISMA is amenable for real-time modeling and is able to determine the number of components automatically. The 2D wavelet compression, which compresses both acquisition and drift time dimensions of measurement, was applied to the datasets prior to RTSIMPLISMA modeling. RTSIMPLISMA models obtained from the compressed data were wavelet transformed back to the uncompressed representation. The effects of wavelet filter types and compression levels were investigated. The relative root-mean-square errors (RRMSE) of reconstruction, which calculate the relative difference between the extracted models with and without 2D compressions, were used to evaluate the effects of compression on self-modeling. The results showed that satisfactory models could be obtained when a data was compressed to 1/256 of its size.     

Discrete variable representation method applied to the determination of rotation-vibration bound states of NO2

The discrete variable representation method is applied to the determination of the rotation-vibration energy levels of the fundamental electronic state of NO₂. The Hamiltonian is expressed in Johnson hyperspherical coordinates and developed on a DVR basis for each internal coordinate, while parity-adapted linear combinations of Wigner functions are used to describe the rotational motion. The diagonalization of the Hamiltonian matrix is performed using the Lanczos algorithm for large symmetric and Hermitian matrices. Results for rovibrational states up to J = 11 for the first five vibrational energy levels are presented. © 1997 John Wiley & Sons, Inc.     

Mathematical functions for the representation of chromatographic peaks.

About ninety empirical functions for the representation of chromatographic peaks have been collected and tabulated. The table, based on almost 200 references, reports for every function: (1) the most used name; (2) the most convenient equation, with the existence intervals for the adjustable parameters and for the independent variable; (3) the applications; (4) the mathematical properties, in relation to the possible applications. The list includes also equations originally proposed to represent peaks obtained in other analytical techniques (e.g. in spectroscopy), which in many instances have proved useful in representing chromatographic peaks as well; the built-in functions employed in some commercial peak-fitting software packages were included, too. Some of the most important chromatographic functions, i.e. the Exponentially Modified Gaussian, the Poisson, the Log-normal, the Edgeworth/Cramér series and the Gram/Charlier series, have been reviewed and commented in more detail.     

An approach to thermodynamics

Suggestions are given for a new method of teaching thermodynamics starting from a minimum knowledge of quantum mechanics. For didactical reasons much reference is made to systems having only two energy levels in order to minimise difficulties in understanding the concepts of equilibrium and non-equilibrium.     

Ensemble methods and data augmentation by noise addition applied to the analysis of spectroscopic data

Near-infrared spectroscopy has gained great acceptance in the industry due to its multiple applications and versatility. Sometimes, however, the construction of accurate and robust calibration models involves the collection of a large number of samples with related reference analysis that can complicate and prolong the calibration stage.In this paper, ensemble methods and data augmentation by noise simulation have been applied to spectroscopic data in combination with PLSR to obtain robust models able to handle different types of perturbations likely to affect NIR data. Several types of noise have been investigated as well as different ensemble methods focused on obtaining robust PLS models able to predict both the original and the perturbed test data.The suitability of ensemble methods to perform robust calibration models has been investigated and compared to extended multiplicative signal correction (EMSC) and other calibration approaches in a real case of temperature compensation. Extended multiplicative signal correction (EMSC) and ensemble methods seem to be the most appropriate methods yielding the best results in terms of accuracy and prediction ability with a reduced calibration data set.     

Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann–Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2n+1 and 2n+2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self-consistent field, and second-order Møller–Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 1–52, 1998     

Instance-based regression with missing data applied to a photocatalytic oxidation process

In this paper, a modified nearest-neighbor regression method (kNN) is proposed to model a process with incomplete information of the measurements. This technique is based on the variation of the coefficients used to weight the distances of the instances. The case study selected for testing this algorithm was the photocatalytic degradation of Reactive Red 184 (RR184), a dye belonging to the group of azo compounds, which is widely used in manufacturing paint paper, leather and fabrics. The process is conducted with TiO₂ as catalyst (an inexpensive semiconductor material, completely inert chemically and biologically), in the presence of H₂O₂ (with the role of increasing the rate of photo-oxidation), at different pH values. The final concentration of RR184 is predicted accurately with the modified kNN regression method developed in this article. A comparison with other machine learning methods (sequential minimal optimization regression, decision table, reduced error pruning tree, M5 pruned model tree) proves the superiority and efficiency of the proposed algorithm, not only for its results, but for its simplicity and flexibility in manipulating incomplete experimental data.      

Orthogonal projection to latent structures solution properties for chemometrics and systems biology data

Partial least squares (PLS) is a widely used algorithm in the field of chemometrics. In calibration studies, a PLS variant called orthogonal projection to latent structures (O‐PLS) has been shown to successfully reduce the number of model components while maintaining good prediction accuracy, although no theoretical analysis exists demonstrating its applicability in this context. Using a discrete formulation of the linear mixture model known as Beer's law, we explicitly analyze O‐PLS solution properties for calibration data. We find that, in the absence of noise and for large n, O‐PLS solutions are simpler but just as accurate as PLS solutions for systems in which analyte and background concentrations are uncorrelated. However, the same is not true for the most general chemometric data in which correlations between the analyte and background concentrations are nonzero and pure profiles overlap. On the contrary, forcing the removal of orthogonal components may actually degrade interpretability of the model. This situation can also arise when the data are noisy and n is small, because O‐PLS may identify and model the noise as orthogonal when it is statistically uncorrelated with the analytes. For the types of data arising from systems biology studies, in which the number of response variables may be much greater than the number of observations, we show that O‐PLS is unlikely to discover orthogonal variation whether or not it exists. In this case, O‐PLS and PLS solutions are the same. Copyright © 2011 John Wiley & Sons, Ltd.     

Properties of the generalized master equation: Green's functions and probability density functions in the path representation

The Green's function for the master equation and the generalized master equation in path representation is an infinite sum over the length of path probability density functions (PDFs). In this paper, the properties of path PDFs are studied both qualitatively and quantitatively. The results are used in building efficient approximations for Green's function in 1D, and are relevant in modeling and in data analysis.