By Sapagovas M.P.

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Extra resources for A Boundary Value Problem with a Nonlocal Condition for a System of Ordinary Differential Equations

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Let us suppose that the result is navigate. Therefore we randomly choose (uniform, since in this case the random walker is not biased) one of the neighbours of x0 = 9. We take, for example, x1 = 5 and we move there. 3. At the beginning of the turn t = 2, we must choose between navigating through the edges or to be teleported. We flip a coin that with a probability of 2/3 tell us navigate and with a probability of 1/3 tell us be teleported. In this case the result is be teleported. Hence we randomly choose (uniform in this case, since we take (1/14, · · · , 1/14) ∈ R as personalization vector) any node of the 14 nodes of the network (not necessarily connected with).

25) g∈Pjk where ωg ( ) is 1 if belongs to the geodesic g and 0 otherwise. Hence if dj,k denotes the distance between j and k in the network then BE = 1 1 ∑ |E| j,k∈X njk = 1 1 ∑ |E| j,k∈X njk = 1 1 ∑ njk |E| j,k∈X ∑ njk ( ) ∈E ∑ ∑ ωg ( ) g∈Pjk ∈E ∑ g∈Pjk dj,k = n(n − 1) L(G) |E| and therefore BE (G) measures essentially the same global properties than the characteristic path length L(G). 10 Degree Distributions The degree distribution of a network G = (X, E) is a function P(k) which give us the probability of finding a node in G with degree k.

In [8] diverse real-world networks are studied, arising three classes of smallworld networks, namely scale-free, broad scale and single scale networks. , P(k) = ak−γ where a is a constant and γ is a positive exponent (this exponent, empirically varies between two and three for the majority of the real world networks). Having a P(k) that has a decaying tail in the power law means that the vast majority of nodes have low degree and that there exist few nodes, the so-called hubs, that have an extremely high connectivity.

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A Boundary Value Problem with a Nonlocal Condition for a System of Ordinary Differential Equations by Sapagovas M.P.


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