320 - canonization computer-based methods

Computer simulations of the isotherm of adsorption are frequently based on the grand canonical Monte Carlo method [40]. If the atomic structure of the solid adsorbent is known and if the adsorbate/solid and adsorbate/adsorbate energies can be computed, this algorithm makes it possible to calculate isotherms of adsorption directly. 

Computational methods have been applied to determine the connections in systems that are not well-defined by canonical pathways. This is either done by semi-automated and/or curated literature causal modeling [1] or by statistical methods based on large-scale data from expression or proteomic studies (a mostly theoretical approach is given by reference [2] and a more applied approach is in reference [3]). Many methods, including clustering, Bayesian analysis and principal component analysis have been used to find relationships and "fingerprints" in gene expression data [4]. 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

The similar accuracies of different well-parameterized continuum models implies that they will also perform similarly for the computation of partition coefficients, and that has proven to be the case in most studies to date (see, for example, Bordner, Cavasotto, and Abagyan 2002 and Curutchet et al. 2003b). In Table 11.4 the previously presented SMx results for the chloroform/water partitioning of die methylated canonical nucleic acid bases are compared to results from die MST-ST/HF/6-31G method, and also to purely electrostatic results obtained using a multipole expansion SCRF method. As the latter does not include any accounting for non-electrostatic effects, its performance is significantly degraded compared to the other two. 

There are two basic approaches to the computer simulation of liquid crystals, the Monte Carlo method and the method known as molecular dynamics. We will first discuss the basis of the Monte Carlo method. As is the case with both these methods, a small number (of the order hundreds) of molecules is considered and the difficulties introduced by this restriction are, at least in part, removed by the use of artful boundary conditions which will be discussed below. This relatively small assembly of molecules is treated by a method based on the canonical partition function approach. That is to say, the energy which appears in the Boltzman factor is the total energy of the assembly and such factors are assumed summed over an ensemble of assemblies. The summation ranges over all the coordinates and momenta which describe the assemblies. As a classical approach is taken to the problem, the summation is replaced by an integration over all these coordinates though, in the final computation, a return to a summation has to be made. If one wishes to find the probable value of some particular physical quantity, A, which is a function of the coordinates just referred to, then statistical mechanics teaches that this quantity is given by... 

The tautomers of cytosine have also been examined with continuum solvation methods. Both Miertus-Scrocco-Tomasi (MST) and PCM computations predict that 13a is the lowest energy conformer in aqueous solution. This is consistent with the explicit water computations. Aqueous solvation, therefore, substantially alters the relative energies of the tautomers of cytosine. The canonical representation of cytosine 13a, the tautomer invoked in Watson-Crick base pairing, is in fact the most favorable tautomer in solution, but not in the gas phase. 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

The Hermitian h, utilized by Westhaus and co-workers in some [103-115] of their numerical computations, is not really canonical as conditions other than (5.11) are applied to fully specify their exponential transformation operator. Suzuki [116] obtains a recursive scheme for a Hermitian h which he claims to be H. This is not the case, however, because his method is based on multiple transformations, which as mentioned above, produce a Hermitian h that differs [37] from H(-. 

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