Many efforts in studying network structure and dynamics have been engaged, among which the research on the node search or navigation is one of the most important branches. With a brief analysis of the existing search strategies, the MDS (maximum degree strategy) is found not applicable to large-scale with even degree distribution networks. By importing the minimum cluster coefficient as one par...

there are three main ideas about relation between creatures and god. one of them is the theory of separation, according to this theory there's not any homogeneity between creatures and god it means the essence and existence of creatures are completely inhomogeneity with god's essence and existence. the second is the theory of oneness, according to this theory creatures and god are uni...

We determine explicit denominators for the Poincar e series of (a) the invariants of m generic N N matrices, and (b) the ring generated by m generic N N matrices and their traces, for N 4. For N 3 we prove (and for N = 4 we conjecture) that the denominators we obtain are of minimum degree. We also give explicit rational fractions for both series for small values of m and N.

We demonstrate the applicability of the polynomial degree bound technique to notions such as the nonexistence of Turing-hard sets in some relativized world, (non)uniform gap-definability, and relativized separations. This way, we settle certain open questions of Hemaspaandra, Ramachandran & Zimand [HRZ95] and Fenner, Fortnow & Kurtz [FFK94], extend results of Hemaspaandra, Jain & Vereshchagin [...

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Therefore, the degree is very important structural parameter of network topology. However, given the number of no...

The topological approaches to find solutions of a coincidence equation f1(x)= f2(x) can roughly be divided into degree and index theories. We describe how these methods can be combined. We are led to a concept of an extended degree theory for function triples which turns out to be natural in many respects. In particular, this approach is useful to find solutions of inclusion problems F(x)∈Φ(x)....