Value Of Node Research Articles

Valency-based structural properties of gamma-sheet of boron clusters.

Boron cluster sheets are two-dimensional boron atom-based formations called borophene. They are similar to the two-dimensional sheet known as graphene, which is composed of carbon atoms arranged in a hexagonal lattice. The unique electrical, mechanical, and thermal properties of borophene make it a sought-after substance for a variety of uses, such as catalysis, energy storage, and electronics. There are two ways to manufacture borophene: chemical vapor deposition and molecular beam epitaxy. Vertex-edge valency-based topological descriptors are a great example of a molecular descriptor that provides information on the connection of atoms in a molecule. These descriptions are based on the notion that a node's value in a molecular network is the sum of the valency of those atoms that are directly connected to that node. In this article, we discussed some novel vertex-edge (ve) and edge-vertex (ev) topological descriptors and found their formulations for the boron cluster or borophene sheets. Also, we show the numerical and graphical comparison of these descriptors in this article.

Novel Node-Ranking Approach and Multiple Topology Attributes-Based Embedding Algorithm for Single-Domain Virtual Network Embedding

Network virtualization (NV) is a promising approach to remove the ossification of current Internet. Virtual network embedding (VNE) is the key issue in NV which efficiently and effectively maps various of virtual networks (VNs), with different node and link resource requests, onto the shared substrate network(s) with finite underlying resources. Previous VNE algorithms in the literature are mostly heuristic. Single network topology attribute and each node’s local resources are assisted to rank nodes in most heuristic algorithms, leading to inefficient resource utilization of substrate network in the long run. To deal with this issue, we propose the network topology attribute and network resource-considered algorithm (VNE-NTANRC). The VNE-NTANRC algorithm adopts a novel node-ranking approach to rank all substrate and virtual nodes before embedding each given VN. The novel node-ranking approach has two subapproaches and considers five important network topology attributes and global network resources altogether. One subapproach is able to calculate all node values (NoV) directly. The other subapproach, stimulating from the Google PageRank website algorithm, enables to calculate NoVs in a stable state. Simulation results reveal that VNE-NTANRC algorithm outperforms typical and latest heuristic algorithms, only considering single network topology attribute and local resources.

Difference equation for tracking perturbations in systems of Boolean nested canalyzing functions.

This paper studies the spread of perturbations through networks composed of Boolean functions with special canalyzing properties. Canalyzing functions have the property that at least for one value of one of the inputs the output is fixed, irrespective of the values of the other inputs. In this paper the focus is on partially nested canalyzing functions, in which multiple, but not all inputs have this property in a cascading fashion. They naturally describe many relationships in real networks. For example, in a gene regulatory network, the statement "if gene A is expressed, then gene B is not expressed regardless of the states of other genes" implies that A is canalyzing. On the other hand, the additional statement "if gene A is not expressed, and gene C is expressed, then gene B is automatically expressed; otherwise gene B's state is determined by some other type of rule" implies that gene B is expressed by a partially nested canalyzing function with more than two variables, but with two canalyzing variables. In this paper a difference equation model of the probability that a network node's value is affected by an initial perturbation over time is developed, analyzed, and validated numerically. It is shown that the effect of a perturbation decreases towards zero over time if the Boolean functions are canalyzing in sufficiently many variables. The maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network. Percolation limits are also explored; these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied, so that the initial perturbation does not scale up with the parameters once the percolation limits are reached.

Fast Convergence for Consensus in Dynamic Networks

In this article, we study the convergence time required to achieve consensus in dynamic networks. In each timestep, a node's value is updated to some weighted average of its neighbors and its old values. We study the case when the underlying network is dynamic and investigate different averaging models. Both our analysis and experiments show that dynamic networks exhibit fast convergence behavior, even under very mild connectivity assumptions.

A solution to the GHI problem for best-first search

Best-first search algorithms usually amalgamate identical nodes for optimization reasons, meanwhile transforming the search tree into a search graph. However, identical nodes may represent different search states, e.g., due to a difference of history. So, in a search graph a node's value may be dependent on the path leading to it. This implies that different paths may result in different values. Therefore, it is difficult to determine the value of any node unambiguously. The problem is known as the graph–history-interaction (GHI) problem. This paper provides a solution for best-first search. First, we give a precise formulation of the problem. Then, for best-first search and for other searches, we review earlier proposals to overcome the problem. Next, our solution is given in detail. Here we introduce the notion of twin nodes, enabling a distinction of nodes according to their history. The implementation, called base-twin algorithm (BTA), is performed for pn search, a best-first search algorithm. It is generally applicable to other best-first search algorithms. Experimental results in the field of computer chess confirm the claim that the GHI problem has been solved for best-first search.