Network method

T.J. Cui and C.H. Liang, Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method, 1993, IEEE Trans. Antennas Propagat., 41, pp. 1719-1726. 

Tasks for Neural Networks and Selection of an Appropriate Neural Network Method... 

Table 9-3 can act as a guideline for the proper selection of a neural network method. It summarizes the different network types and thcii learning strategy, and lists different types of applications. 

The same structure representation as the one taken in the original study [39] is selected in order to show some possibilities evolving from working with a neural network method. Tabic 10.1-1 gives the ten descriptors chosen lor the representation of the 115 molecules of the data set. 

After selection of descriptors/NN training, the best networks were applied to the prediction of 259 chemical shifts from 31 molecules (prediction set), which were not used for training. The mean absolute error obtained for the whole prediction set was 0.25 ppm, and for 90% of the cases the mean absolute error was 0.19 ppm. Some stereochemical effects could be correctly predicted. In terms of speed, the neural network method is very fast - the whole process to predict the NMR shifts of 30 protons in a molecule with 56 atoms, starting from an MDL Molfile, took less than 2 s on a common workstation. 

The performance of the ncttral network method is remarkable considering the relatively small data set on which it was based. 

A common use of statistics in structural biology is as a tool for deriving predictive distributions of strucmral parameters based on sequence. The simplest of these are predictions of secondary structure and side-chain surface accessibility. Various algorithms that can learn from data and then make predictions have been used to predict secondary structure and surface accessibility, including ordinary statistics [79], infonnation theory [80], neural networks [81-86], and Bayesian methods [87-89]. A disadvantage of some neural network methods is that the parameters of the network sometimes have no physical meaning and are difficult to interpret. 

In spite of these important results, the two-network method has had little impact on the discussion of the role of chain entangling in cross-linked elastomers. It was therefore decided to make a more detailed examination of the method and to try to develop a simpler method which would require fewer assumptions. The present paper is a discussion of recently published and unpublished work. 

Part 2. Two-Network Method. Different Types of Strain. 

Figure 2. The principle of the two-network method for cross-linking in a state of simple extension. First network with modulus Gy is entirely due to chain entangling. Second network with modulus Gx is formed by cross-linking in the strained state. Both Gy and Gx can be calculated from the two-network theory.

The two-network method has several advantages, especially when the free energy is expressed in terms of moduli as shown in eq. 5. The following information need not be known ... 

The new method (27) has a number of advantages in comparison to the original two-network method (10). Sample dimensions and the... 

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

It is clearly shown that chain entangling plays a major role in networks of 1,2-polybutadiene produced by cross-linking of long linear chains. The two-network method should provide critical tests for new molecular theories of rubber elasticity which take chain entangling into account. 

The parsing of the transporter sequences into the TM domains shown in Fig. 1A represents the consensus result of three different methods. Average hydrophobicity was calculated with ProperTM using different window sizes and the Kyte and Doolittle scale (7). TMHMM, a hidden Markov model-based approach (8), and PHDHTM, a profile-based neural network method (9), were then utilized to refine the predictions. 

Artificial Nenral Networks Methods and Appbcations, edited by David S. Livingstone, 2008... 

B. Walczak and W. Wegscheimer, Non-linear modelling of chemical data by combinations of linear and neural networks methods. Anal. Chim. Acta., 283, 508-517 (1993). 

The challenge is therefore to develop an experiment which allows an experimental separation of the contributions from chain entangling and cross-links. The Two-Network method developed by Ferry and coworkers (17,18) is such a method. Cross-linking of a linear polymer in the strained state creates a composite network in which the original network from chain entangling and the network created by cross-linking in the strained state have different reference states. We have simplified the Two-Network method by using such conditions that no molecular theory is needed (1,21). 

The Simplified Two-Network Method and Contour Lenqth Relaxation. 

Rost, B. (1996). PHD predicting one-dimensional protein structure by profile based neural networks. Method Enzymol. 266, 525-539. 

Despite the widespread use of this machine for compounding an extensive range of polymer-based formulations, only very limited analytical work has been reported on its operational performance. In one report, a modified flow analysis network method of simulation was used to describe flow of a Newtonian... 

It is clear that the application of Langley s method in other polymer systems is essential to settle questions about Me and g in networks satisfactorily. The Ferry composite network method (223, 296) appears to be broadly applicable as well, although requiring special care to minimize slippage prior to introduction of the permanent crosslinks. (One is also still faced with the difficult question of whether g is the same for entanglements in crosslinked networks and in the plateau region of dynamic response.) Based on the limited results of these two methods in unswelled systems, Me values deduced by equilibrium and dynamic response appear to be practically the same. 

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