ASYM20: a program for force constant and normal coordinate calculations, with a critical review of the theory involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Bergmann's rule and body size in mammals

Aim: To describe the geographical pattern of mean body size of the non-volant mammals of the Nearctic and Neotropics and evaluate the influence of five environmental variables that are likely to affect body size gradients. Location: The Western Hemisphere. Methods: We calculated mean body size (average log mass) values in 110 × 110 km cells covering the continental Nearctic and Neotropics. We also generated cell averages for mean annual temperature, range in elevation, their interaction, actual evapotranspiration, and the global vegetation index and its coefficient of variation. Associations between mean body size and environmental variables were tested with simple correlations and ordinary least squares multiple regression, complemented with spatial autocorrelation analyses and split-line regression. We evaluated the relative support for each multiple-regression model using AIC. Results: Mean body size increases to the north in the Nearctic and is negatively correlated with temperature. In contrast, across the Neotropics mammals are largest in the tropical and subtropical lowlands and smaller in the Andes, generating a positive correlation with temperature. Finally, body size and temperature are nonlinearly related in both regions, and split-line linear regression found temperature thresholds marking clear shifts in these relationships (Nearctic 10.9 °C; Neotropics 12.6 °C). The increase in body sizes with decreasing temperature is strongest in the northern Nearctic, whereas a decrease in body size in mountains dominates the body size gradients in the warmer parts of both regions. Main conclusions: We confirm previous work finding strong broad-scale Bergmann trends in cold macroclimates but not in warmer areas. For the latter regions (i.e. the southern Nearctic and the Neotropics), our analyses also suggest that both local and broad-scale patterns of mammal body size variation are influenced in part by the strong mesoscale climatic gradients existing in mountainous areas. A likely explanation is that reduced habitat sizes in mountains limit the presence of larger-sized mammals.

Statistical deconvolution of enthalpic energetic contributions to MHC-peptide binding affinity

Background: MHC Class I molecules present antigenic peptides to cytotoxic T cells, which forms an integral part of the adaptive immune response. Peptides are bound within a groove formed by the MHC heavy chain. Previous approaches to MHC Class I-peptide binding prediction have largely concentrated on the peptide anchor residues located at the P2 and C-terminus positions. Results: A large dataset comprising MHC-peptide structural complexes was created by remodelling pre-determined x-ray crystallographic structures. Static energetic analysis, following energy minimisation, was performed on the dataset in order to characterise interactions between bound peptides and the MHC Class I molecule, partitioning the interactions within the groove into van der Waals, electrostatic and total non-bonded energy contributions. Conclusion: The QSAR techniques of Genetic Function Approximation (GFA) and Genetic Partial Least Squares (G/PLS) algorithms were used to identify key interactions between the two molecules by comparing the calculated energy values with experimentally-determined BL50 data. Although the peptide termini binding interactions help ensure the stability of the MHC Class I-peptide complex, the central region of the peptide is also important in defining the specificity of the interaction. As thermodynamic studies indicate that peptide association and dissociation may be driven entropically, it may be necessary to incorporate entropic contributions into future calculations.

Correlation-type structure activity relationships for the kinetics of gas-phase RO2 self-reactions and reaction with HO2

Structure activity relationships (SARs) are presented for the gas-phase reactions of RO2 with HO2, and the self- and cross-reactions of RO2. For RO2+HO2 the SAR is based upon a correlation between the logarithm of the measured rate coefficient and a calculated ionisation potential for the molecule R-CH=CH2, R being the same group in both the radical and molecular analogue. The correlation observed is strong and only for one RO2 species does the measured rate coefficient deviate by more than a factor of two from the linear least-squares regression line. For the self- and cross-reactions of RO2 radicals, the SAR is based upon a correlation between the logarithm of the measured rate coefficient and the calculated electrostatic potential (ESP) at the equivalent carbon atom in the RH molecule to which oxygen is attached in RO2, again R being the same group in the molecule and the radical. For cases where R is a simple alkyl-group, a strong linear correlation observed. For RO2 radicals which contain lone pair-bearing substituents and for which the calculated ESP<-0.05 self-reaction rate coefficients appear to be insensitive to the value of the ESP. For RO2 of this type with ESP>-0.05 a linear relationship between log k and the ESP is again observed. Using the relationships, 84 out of the 85 rate coefficients used to develop the SARs are predicted to within a factor of three of their measured values. A relationship is also presented that allows the prediction of the Arrhenius parameters for the self-reactions of simple alkyl RO2 radicals. On the basis of the correlations, predictions of room-temperature rate coefficients are made for a number of atmospherically important peroxyl-peroxyl radical reactions. (C) 2003 Elsevier Ltd. All rights reserved.

Quantitative pulsed phase thermography applied to steel plates

Pulsed Phase Thermography (PPT) has been proven effective on depth retrieval of flat-bottomed holes in different materials such as plastics and aluminum. In PPT, amplitude and phase delay signatures are available following data acquisition (carried out in a similar way as in classical Pulsed Thermography), by applying a transformation algorithm such as the Fourier Transform (FT) on thermal profiles. The authors have recently presented an extended review on PPT theory, including a new inversion technique for depth retrieval by correlating the depth with the blind frequency fb (frequency at which a defect produce enough phase contrast to be detected). An automatic defect depth retrieval algorithm had also been proposed, evidencing PPT capabilities as a practical inversion technique. In addition, the use of normalized parameters to account for defect size variation as well as depth retrieval from complex shape composites (GFRP and CFRP) are currently under investigation. In this paper, steel plates containing flat-bottomed holes at different depths (from 1 to 4.5 mm) are tested by quantitative PPT. Least squares regression results show excellent agreement between depth and the inverse square root blind frequency, which can be used for depth inversion. Experimental results on steel plates with simulated corrosion are presented as well. It is worth noting that results are improved by performing PPT on reconstructed (synthetic) rather than on raw thermal data.

Relationships between gluten rheological properties and hearth loaf characteristics

The rheological properties of fresh gluten in small amplitude oscillation in shear (SAOS) and creep recovery after short application of stress was related to the hearth breadbaking performance of wheat flours using the multivariate statistics partial least squares (PLS) regression. The picture was completed by dough mixing and extensional properties, flour protein size distribution determined by SE-HPLC, and high molecular weight glutenin subunit (HMW-GS) composition. The sample set comprised 20 wheat cultivars grown at two different levels of nitrogen fertilizer in one location. Flours yielding stiffer and more elastic glutens, with higher elastic and viscous moduli (G' and G") and lower tan 8 values in SAOS, gave doughs that were better able to retain their shape during proving and baking, resulting in breads of high form ratios. Creep recovery measurements after short application of stress showed that glutens from flours of good breadmaking quality had high relative elastic recovery. The nitrogen fertilizer level affected the protein size distribution by an increase in monomeric proteins (gliadins), which gave glutens of higher tan delta and flatter bread loaves (lower form ratio).

Wheat protein quality in relation to baking performance evaluated by the Chorleywood bread process and a hearth bread baking test

The relationships between wheat protein quality and baking properties of 20 flour samples were studied for two breadmaking processes; a hearth bread test and the Chorleywood Bread Process (CBP). The strain hardening index obtained from dough inflation measurements, the proportion of unextractable polymeric protein, and mixing properties were among the variables found to be good indicators of protein quality and suitable for predicting potential baking quality of wheat flours. By partial least squares regression, flour and dough test variables were able to account for 71-93% of the variation in crumb texture, form ratio and volume of hearth loaves made using optimal mixing and fixed proving times. These protein quality variables were, however, not related to the volume of loaves produced by the CBP using mixing to constant work input and proving to constant height. On the other hand, variation in crumb texture of CBP loaves (54-55%) could be explained by protein quality. The results underline that the choice of baking procedure and loaf characteristics is vital in assessing the protein quality of flours. (C) 2003 Elsevier Ltd. All rights reserved.

Cytenamide acetic acid solvate

In the crystal structure of the title compound (systematic name: 5H-dibenzo[a,d]cycloheptatriene-5-carboxamide ethanoic acid solvate), C16H13NO center dot C2H4O2, the cytenamide and solvent molecules form a hydrogen-bonded R-2(2)(8) dimer motif, which is further connected to form a centrosymmetric double ring motif arrangement. The cycloheptene ring adopts a boat conformation and the dihedral angle between the least-squares planes through the two aromatic rings is 54.7 (2)degrees.

Robust identification for linear-in-the-parameters models

In this paper new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness, including three algorithms using combined A- or D-optimality or PRESS statistic (Predicted REsidual Sum of Squares) with regularised orthogonal least squares algorithm respectively. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalisation scheme in orthogonal least squares or regularised orthogonal least squares has been extended such that the new algorithms are computationally efficient. A numerical example is included to demonstrate effectiveness of the algorithms. Copyright (C) 2003 IFAC.

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Sparse kernel modelling: a unified approach

A unified approach is proposed for sparse kernel data modelling that includes regression and classification as well as probability density function estimation. The orthogonal-least-squares forward selection method based on the leave-one-out test criteria is presented within this unified data-modelling framework to construct sparse kernel models that generalise well. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic sparse kernel data modelling approach.

Grey-box radial basis function modelling: the art of incorporating prior knowledge

A basic principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: the underlying data generating mechanism exhibits known symmetric property and the underlying process obeys a set of given boundary value constraints. The class of orthogonal least squares regression algorithms can readily be applied to construct parsimonious grey-box RBF models with enhanced generalisation capability.

A tunable radial basis function model for nonlinear system identification using particle swarm optimisation

A tunable radial basis function (RBF) network model is proposed for nonlinear system identification using particle swarm optimisation (PSO). At each stage of orthogonal forward regression (OFR) model construction, PSO optimises one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is computationally more efficient.