Information theory approach

A third theoretical approach, which attempts to overcome the inadequacies of the previous two statistical theories to predict population inversion, is the so-called information-theory approach 477 The latter has recently been applied to the problem of energy disposal and consumption in elementary chemical reactions. To the best of our knowledge, it has been applied to ion-neutral interactions only in the case of the collisional dissociation of H2+ (Table VI). 

The information theory approach to calculating approximate probabilities is quite general and, as we have just shown, is quite straight forward to use. One might then ask why we did not use this approach in the previous section to predict e2(0> e4(7),. .., e2J(t), and e4J(f) from and Aj(t) The answer to this question is that we did. That is, information theory predicts Gaussian transition probabilities for V and J and these were the transition probabilities that we assumed. We shall now elaborate on this remark. Let P(V, t V0,0) be the joint probability that a molecule has a velocity V at time t and a velocity V0 at t = 0. then P is related to the transition probability Pv by... 

A second interesting new theoretical development of a quite different kind has been the application of an information theory approach to the classification of experimental results [478-488]. The outcome of collisions, for example, the distribution of product translational or vibrational energies, is compared with the statistically predicted result for a closed system and the difference between the two is recorded as the surprisal. The surprisal is defined by an expression of the type found in information theory for example, if the probability of a reaction producing a molecular product in a final vibrational state v, corresponding to a fractional energy yield/,., is P fv.) and the corresponding statistical expression for a closed system is P°(fV ), then the surprisal is given by... 

The information theory approach studied here grew out of earlier studies of formation of atomic sized cavities in molecular liquids (Pohorille and Pratt, 1990 Pratt and Pohorille, 1992 1993). Since we deal with rigid and spherical solutes in the discussion we will drop the explicit indication of conformational coordinates and discuss p n) = Pa n lR ). We emphasize that the overall distribution p(n) is well described by the information theory with the first two moments, (n)o and n n — 1)/2)q. It is the prediction of the extreme member p 0) that makes the differences in these default models significant. Computing thermodynamic properties demands more than merely observing typical behavior. 

Viswanadham, V. N., Mattice, W. L. Assessment of bond rotation interdependence in polymer chains an information theory approach. Macromolecules 1987, 20, 685-688. 

Three popnlar early methods are dne to Chon and Fasman, Ganuer et al., and Lim." ° The Chon-Fasman method is based on statistical propensities of residues to form an a-helix or a P-strand, combined with a series of rules. Many methods, like Chon-Fasman, are based on statistical analyses of structural databases. The GOR method adopts an information theory approach. Although the theory is a little daunting, this is transparent to the user and the method has a firm statistical foundation that permitted extension to more subtle analyses of a larger structural database." Methods may also be based on the physico-chemical principles underlying protein structure. For example, a-helices often have a distinct pattern of hydrophobic residues, leading to a hydrophobic face that can facilitate the packing of the helix in the protein. A series of such rules forms the basis of the Lim method. ... 

D-optimal design methods [389, 403, 655, 656] calculate the determinant of the variance-covariance matrix its value is largest for substituent sets with maximum variance and minimum covariance (linear and multiple correlation) in their physicochemical properties. An information theory approach, which leads to comparable results, has been proposed by Herrmann [657]. In some other approaches synthetic accessibility has been included as an additional selection feature [656, 658, 659]. 

A. Katz, Principles of Statistical Mechanics The Information Theory Approach, W. H. Freeman, San Francisco, 1967. 

Although the information theory approach is very helpful, especially in an heuristic sense, I believe it has also somewhat obscured the central issue, relating to the second law, of how irreversible phenomena can ever occur. The fact that thermodynamic systems are incompletely specified is only part of the story, although an important part. One has also to ask questions about de fcbCto initial conditions, and how they can arise. These questions can only be answered, in my view, by referring to the pervasive irreversibility within the total environment. 

As can be seen, there is the inversion of the population OH(l) and OH(2). The P n) values marked by asterisk were obtained by the extrapolation of the experimental data on the basis of the information theory approach. 

R. D. Levine, Information theory approach to molecular reaction dynamics, Annu. Rev. Phys. Chem. 29 59 (1978). 

A recent breakthrough in molecular theory of hydrophobic effects was achieved by modeling the distribution of occupancy probabilities, the pn depicted in Figure 4, rather than applying a more difficult, direct theory of po for cavity statistics for liquid water (Pohorille and Pratt, 1990). This information theory (IT) approach (Hummer et al., 1996) focuses on the set of probabilities pn of finding n water centers inside the observation volume, with po being just one of the probabilities. Accurate estimates of the pn, and po in particular, are obtained using experimentally available information as constraints on the pn. The moments of the fluctuations in the number of water centers within the observation volume provide such constraints. 

Flow can one make practical use of these observations For some time I have advocated the use of information theory. (For more details see introductory discussions in Refs. [1] and [3], surprisal analysis in Ref. [23], applications to spectra in Refs. [24] and [30], and a recent prediction of a phase transition induced by cluster impact in Ref. [31]). What this approach seeks to do is to use the minimal dynamical input that is necessary to account for the dynamical observations of interest, the point being that one very rarely has the experimental resolution to probe the individual final quantum states. The information measured is much more coarse grained. 

The previous section concentrated on the management of a hard and soft sensors network. This is an important step since the information sources must be carefully checked before being further used. This section will be devoted to the diagnosis of the overall biological state of the process. In particular, it will illustrate that the use of the Evidence theory approach improves the fault diagnosis system in terms of modularity and d3mamical adaptation. 

The recent theoretical approach based on the information theory (IT) in studying aqueous solutions and hydration phenomena [62 66] shows such a direction. IT is a part of the system based on a probabilistic way of thinking about communication, introduced in 1948 by Sharmon and subsequently developed [114]. It consists in the quantitative description of the information by defining entropy as a function of probability... 

One of the aims of the systems approach of the information production process in the analytical laboratory was to quantify the information content of an analytical result. As a result, there was a renewed interest in applying information theory to analytical chemistry, with centers of research in the laboratories of Eckschlager in... 

N. Meinander and G. C. Tabisz. Information theory and line shape engineering approaches to spectral profiles of collision induced depolarized light scattering. Chem. Phys. Lett., 110 388, 1984. 

The RMS error of Eq. 1.13 is related to the 2-norm of the vector of differences Pi — P°, while that of Eq. 1.14 is related to the oo-norm [1], We are not asserting that the latter should replace the former as an estimate of uncertainties in calculations, but that both error estimates should be considered if the uncertainties in predicted values for which there are no standards are to be realistic. We should note that a more elaborate approach to comparing computed results to a set of standard values has been devised by Maroulis and co-workers using principles of information theory [2]. Their work has been little used in practice, but it provides a convenient way of comparing many values. 

Information complexity of copolymer sequences. A common approach to the analysis of the complexity of a system is to use concepts from information theory and information-theoretic-based techniques. 

A novel spectral processing approach based on information theory and the matrix pencil method was proposed by Lin et al.55 that enhances sensitivity and restores the baseline and phase properties, and hence is particularly useful, for example, for delayed acquisition experiments such as SPEDA spectra. 

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