Solving Nonlinear Wave Equation Based on Topology

A method of solving nonlinear wave equation based on topology is proposed. Firstly, the characteristics of stochastic graph and Scaleless network are compared, and their topological characteristics are analyzed. Because of the existence of a few axis nodes, Scaleless networks have higher average aggregation than those with the same number of airport nodes and connected stochastic graphs. According to the topological structure of nonlinear wave equation, the first-order integral method is used to solve the nonlinear wave equation. According to the first integration, the threshold range is set, and the solution flow is designed in line with the division theorem. The topology of the network is analyzed according to the node degree, aggregation coefficient and reciprocity of the network, so as to verify and analyze. The experimental results show that the application of this method is 98%, which is still effective for the hyperbolic development equation of the same type.

Data Geometry and Extreme Value Distribution

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

A Stochastic Graphs Semantics for Conditionals

We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional (the global and the local interpretation, and generalizations of them) and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under these two interpretations. It also yields a powerful method of handling more complex issues (such as nested conditionals). The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the (standard) notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.

Finding the Shortest Path in Stochastic Graphs Using Learning Automata and Adaptive Stochastic Petri Nets

Shortest path problem in stochastic graphs has been recently studied in the literature and a number of algorithms has been provided to find it using varieties of learning automata models. However, all these algorithms suffer from two common drawbacks: low speed and lack of a clear termination condition. In this paper, we propose a novel learning automata-based algorithm for this problem which can speed up the process of finding the shortest path using parallelism. For this parallelism, several traverses are initiated, in parallel, from the source node towards the destination node in the graph. During each traverse, required times for traversing from the source node up to any visited node are estimated. The time estimation at each visited node is then given to the learning automaton residing in that node. Using different time estimations provided by different traverses, this learning automaton gradually learns which neighbor of the node is on the shortest path. To set a condition for the termination of the proposed algorithm, we analyze the algorithm using a recently introduced model, Adaptive Stochastic Petri Net (ASPN-LA). The results of this analysis enable us to establish a necessary condition for the termination of the algorithm. To evaluate the performance of the proposed algorithm in comparison to the existing algorithms, we apply it to find the shortest path in six different stochastic graphs. The results of this evaluation indicate that the time required for the proposed algorithm to find the shortest path in all graphs is substantially shorter than that required by similar existing algorithms.