Staverman, A.J. Properties of Phantom Networks and Real Networks. Vol. 44, pp. 73-102. [Pg.246]

One of the key discoveries was the realization that very many real networks in nature, technology (e.g., the Internet and WWW) and human relations have similar structure and growth patterns, and can be described by the same mathematical formulas. All of them share similar properties and behavior. This discovery and the new theory have created an unprecedented opportunity for investigating resilience and vulnerabilities of the Internet and the WWW. For this reason we consider the scale-free network theory and related empirical results as being a significant development in the Cyberspace Security and Defense. [Pg.324]

It has been pointed out repeatedly that the elastic behaviour of virtually all real networks in the unswollen state deviates appreciably from Gaussian behaviour. Often these deviations depend on the history [Pg.89]

Number (or number of moles) of cross-linked or branched units (Chaps. IX and XI). Hence, also the number of chains in a perfect network structure (Chap. XI). Effective number (or number of moles) of chains in a real network (Chaps. XI and XIII). [Pg.650]

We see that, only if the parameter I is temperature independent, the entropic and energetic components of real networks with the sterical restrictions are identical to that of the phantom or affine network. [Pg.52]

Inhomogeneities in a real network may occur either because of a continuous distribution of molecular weight between crosslinks or due to the regions of different average molecular weights (as may be the case in randomly crosslinked networks). [Pg.454]

Two conditions must be met if this conclusion is to be revealed by the analysis. First, appropriate experimental procedures must be adopted to assure establishment of elastic equilibrium. Second, the contribution to the stress from restrictions on fluctuations in real networks must be properly taken into account, with due regard for the variation of this contribution with deformation and with degree of cross-linking. Otherwise, the analysis of experimental data may yield results that are quite misleading. [Pg.1]

Neurons are not used alone, but in networks in which they constitute layers. In Fig. 33.21 a two-layer network is shown. In the first layer two neurons are linked each to two inputs, x, and X2- The upper one is the one we already described, the lower one has w, = 2, W2 = 1 and also 7= 1. It is easy to understand that for this neuron, the output )>2 is 1 on and above line b in Fig. 33.22a and 0 below it. The outputs of the neurons now serve as inputs to a third neuron, constituting a second layer. Both have weight 0.5 and 7 for this neuron is 0.75. The output yfi j, of this neuron is 1 if E = 0.5 y, + 0.5 y2 > 0.75 and 0 otherwise. Since y, and y2 have as possible values 0 and 1, the condition for 7 > 0.75 is fulfilled only when both are equal to 1, i.e. in the dashed area of Fig. 33.22b. The boundary obtained is now no longer straight, but consists of two pieces. This network is only a simple demonstration network. Real networks have many more nodes and transfer functions are usually non-linear and it will be intuitively clear that boundaries of a very complex nature can be developed. How to do this, and applications of supervised pattern recognition are described in detail in Chapter 44 but it should be stated here that excellent results can be obtained. [Pg.234]

See also in sourсe #XX -- [ Pg.44 , Pg.73 ]

© 2019 chempedia.info