Network parameters, examples

Let us consider the primary distribution network of Example 23.2 as shown in Figure 24.25(a) leeding an LT load ol 29.4 MW at 0.98 p.1. through a 33/0.4 kV transformer. The following line parameters have been considered ... 

The swelling pressure or osmotic deswelling data can be, therefore, described as the functions of n(w) by either of the theories [115]. This description can be then applied to determining the network parameters (see, for example, Ref. [22]). On the other hand, the swelling pressure which is directly connected with the chemical potential of water in the gel ... 

The SAH network parameters can be determined from the elastic modulus and the equilibrium swelling however, there are only a few examples of this approach. 

These equations allow either to predict the swelling degree (w = l/(p) as a function of external conditions or to calculate the network parameters from the correlation between the theoretical and experimental dependencies w(q) or w(p) [22, 102], An example of such a correlation is given in Fig. 2 and 5. As can be seen, theoretical predictions are in good agreement with experimental data. However, when the outer solution contains multivalent cations, only a semi-quantitative agreement is attained. 

Generally, however, A depends implicitly on other network parameters. The dependencies can be assessed by investigating the slope of G as experimental conditigns are changed. For example, if capping is irreversible (k = 0), G varies with the amount of capping protein as (cf. Equation 24)... 

The Gaussian network theory can, therefore, predict phase separation in partially swollen systems. Phase separation can be induced by increasing the degree of crosslinking or increasing the interaction parameter %. Examples are given in Fig. 16. 

After testing the results with the cross-validation set, we may end up with different descriptors and different network parameters for each of the types of protons. Since the networks have only to be trained once, we can reuse the final configuration for all predictions within the same compound class. The following section gives an example. 

Example 11.10 Bayesian network parameter estimation. Let Xu,..., X, , be continuous variables for individual genes microarray expression levels and have identically independent normal distributions with mean fij and variance of. The probability density function for the normal distribution is... 

The common and classical approach to considering pore diffusion limitations is the utilization of an effectiveness factor as a single parameter, which was developed by Damkoehler, Thiele and Zddovkh in the 1930s (Damkoehler, 1936,1937a, 1937b, 1939 Thiele, 1939 Zeldowitsch, 1939). However, an exact calculation of the effectiveness factor is only possible for simple power law kinetics, isothermal particles, or simple reaction networks, for example, for two parallel or serial reactions, as described in many textbooks (e.g., Froment and Bischoff, 1990 or Levenspiel, 1996,... 

A set of parameters indicating thermoflnctnational origin of local order domains (clnsters) was mentioned above, for example. Equation 1.12, Figure 1.8 and Figure 1.19. In the present section this question will be considered in more detail. Firstly, the interconnection between entanglement cluster network parameters and density fluctuations should be studied. Density flnctuations (Ap/p) represent the measure of disorder in polymers and are determined as follows [84, 85] ... 

Both test-set vahdation and cross-vahdation can be applied to any regression model made by either MLR, PCR, PLS or other methods. These validation methods are equally apphcable to augmented regression models like non-linear regression and neural networks, for example, and are perhaps even more important for methods that involve estimates of many parameters as these imply even greater risks of overfitting. 

VR, the inputs correspond to the value of the various parameters and the network is 1 to reproduce the experimentally determined activities. Once trained, the activity of mown compound can be predicted by presenting the network with the relevant eter values. Some encouraging results have been reported using neural networks, have also been applied to a wide range of problems such as predicting the secondary ire of proteins and interpreting NMR spectra. One of their main advantages is an to incorporate non-linearity into the model. However, they do present some problems Hack et al. 1994] for example, if there are too few data values then the network may memorise the data and have no predictive capability. Moreover, it is difficult to the importance of the individual terms, and the networks can require a considerable 1 train. 

The first is the relational model. Examples are hnear (i.e., models linear in the parameters and neural network models). The model output is related to the input and specifications using empirical relations bearing no physical relation to the actual chemical process. These models give trends in the output as the input and specifications change. Actual unit performance and model predictions may not be very close. Relational models are usebil as interpolating tools. 

Additional parameters should be taken into account for polyester networks and hyperbranched polyesters, for example, crosslink density and degree of branching. 

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