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As a standard consequence of the above random degree theory, we can formulate: (Random Schauder fixed point theorem).
We presented four neighbor selection schemes (random, degree, propagation-weight, and hybrid selection) and explored their feasibility.
Given the specific degree density μ(d=i), the encoding process will be relatively straightforward, which mainly involves the following three steps: 1. select a random degree according to the distribution, i.e., d∼μ(d=i); 2.
select a random degree according to the distribution, i.e., d∼μ(d=i); choose d distinct neighbors around the current input bit b k in a uniform manner, which are denoted by (b_{k}^{(1)}, b_{k}^{(2)},ldots, b_{k}^{(d)}); calculate the exclusive-OR of the d-neighbors and finally output the encoder symbol.
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The effect of recall error is uncertain, but it is more likely to have introduced random degrees of over- and underestimation than systematic error [24].
In reality, random errors are unlikely to occur at a fixed rate and the introduction of set levels of error in this study was done to simplify the modelling process, with no attempt being made to represent systematic failures (which may have been possible by simulating age heaping or more random degrees of misreporting).
The model shows that local webs with non-random degree distributions can arise from randomly structured source webs.
Nevertheless, some topological characteristics of the graphs representing the networks - namely non-random degree distribution and high clustering coefficient - are shared by networks of distantly related organisms.
To do it, we shall use the random topological degree.
Below, we collect the most important properties of the random topological degree.
The random topological degree defined in (9.1) has all the properties formulated in Theorem 9.3.
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CEO of Professional Science Editing for Scientists @ prosciediting.com