Statistical network analysis generally

The data analysis module of ELECTRAS is twofold. One part was designed for general statistical data analysis of numerical data. The second part offers a module For analyzing chemical data. The difference between the two modules is that the module for mere statistics applies the stati.stical methods or rieural networks directly to the input data while the module for chemical data analysis also contains methods for the calculation ol descriptors for chemical structures (cl. Chapter 8) Descriptors, and thus structure codes, are calculated for the input structures and then the statistical methods and neural networks can be applied to the codes. 

Polymer networks are conveniently characterized in the elastomeric state, which is exhibited at temperatures above the glass-to-rubber transition temperature T. In this state, the large ensemble of configurations accessible to flexible chain molecules by Brownian motion is very amenable to statistical mechanical analysis. Polymers with relatively high values of such as polystyrene or elastin are generally studied in the swollen state to lower their values of to below the temperature of investigation. It is also advantageous to study network behavior in the swollen state since this facilitates the approach to elastic equilibrium, which is required for application of rubber elasticity theories based on statistical thermodynamics. ... 

The conventional analysis used for the studies of the elastic properties of swollen networks are based on models developed for dry networks and generalized to include polymer-diluent interactions. When the diluent is a very good solvent for the polymer chains, two basic assumptions, namely Gaussian statistics and mean-field approximation, are incorrect because of the excluded volume effect. The same criticism has been raised against the description of the thermodynamic behaviour of semi-dilute solutions - As... 

Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-ics. The network of signals and regulatory pathways, sources of variability, and multistep regulation that are involved in this problem is shown together with its main components. It is important to realize how between-subject and between-event variation must be addressed in a model of the system that is not purely structural, but also statistical. The power of model-based data analysis is to elucidate the (main) subsystems and their putative role in overall regulation, at a variety of life stages, species, and functional (cell to organismal) levels. Images have been selected for illustrative purposes only. See color plate.

An inexperienced user or sometimes even an avid practitioner of QSAR could be easily con-fiased by the multitude of methodologies and naming conventions used in QSAR studies. Two-dimensional (2D) and three-dimensional (3D) QSAR, variable selection and artificial neural network methods, comparative molecular field analysis (CoMFA), and binary QSAR present examples of various terms that may appear to describe totally independent approaches, which cannot be even compared to each other. In fact, any QSAR method can be generally defined as the application of mathematical and statistical methods to the problem of finding empirical relationships (QSARmod-els)of the form, D . D ), where... 

The analysis of a series of chiroptical spectra and recovery of systematic trends in a given set can be carried out in several ways. In the past, the results strongly depended on the spectroscopist s personal experience actually, this was the least objective part of the circular dichroism application. Nowadays, we can rely on general procedures of statistical data treatment like singular value decomposition, factor analysis (especially its first part, analysis of the correlation matrix and the projection of the experimental spectra onto the space of orthogonal components), cluster analysis and the use of neural networks. This field has been pioneered by Pancoska and Keiderling [72-76], and also by Johnson [77] when analyzing the chiroptical properties of biopolymers. 

A whole spectrum of statistical techniques have been applied to the analysis of DNA microarray data [26-28]. These include clustering analysis (hierarchical, K-means, self-organizing maps), dimension reduction (singular value decomposition, principal component analysis, multidimensional scaling, or correspondence analysis), and supervised classification (support vector machines, artificial neural networks, discriminant methods, or between-group analysis) methods. More recently, a number of Bayesian and other probabilistic approaches have been employed in the analysis of DNA microarray data [11], Generally, the first phase of microarray data analysis is exploratory data analysis. 

The bioactivities generally modelled are half maximal inhibitory concentration (ICjg), minimum inhibitory concentration (MIC) and half maximal effective concentration (ECjg) obtained in biological assays statistical methods used in QSAR studies are principal component analysis, partial least squares, Kohonen neural network, artificial neural network, etc. [3],... 

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