In recent years, the direction of the study of networks in which connections correspond to the mutual influences of nodes has been developed. Many works have been devoted to the study of such complex networks, but most often they relate to the spread of one type of activity (influence). In the process of development of the newest technologies various mathematical models are developed and investigated: models with thresholds, models of independent cascades, models of distribution of epidemics, models of Markov processes. The paper proposes to use hypercomplex number systems, which are a mathematical apparatus that allows you to model some network problems and solve them at a new level, ie to consider a complex network with several properties in each node. In this paper, we consider networks where the edges correspond to the mutual influences of the nodes. It is proposed to match the number of properties in each node and the measurability of a hypercomplex number system(HNS) with the same number of basic elements. Each HNS corresponds to the Kelly table, which corresponds to the law of multiplication of these CSF. The properties of the CSF allow you to build an isomorphic transition from a filled Kelly table to a less filled one, which simplifies the calculation. To model the problem using hypercomplex number systems, we offer a specialized software package of hypercomplex computations based on the system of computer algebra Maple. All this made it easy to model a complex system with several effects.
翻译:近年来,对连接与节点相互影响的网络进行了研究。许多工作都致力于研究这种复杂的网络,但往往与一种类型的活动(影响)的传播有关。在开发最新技术的过程中,开发和调查了各种数学模型:具有阈值的模型、独立的级联模型、流行病分布模型、Markov进程模型。本文件提议使用超复合数字系统,这是一个数学机器,使您能够模拟一些网络问题,并在新的层次上解决这些问题。许多工作都致力于研究一个复杂网络,每个节点有几个属性。在本文件中,我们考虑的是边缘与结点的相互影响相对应的网络。建议将每个节点的属性数目和超相容数数系统(HNS)的可计量性与同样数量的基本要素相匹配。每个高复合数字系统与Kelly表格对应,这与这些 CSFSF的倍增法相对应。CSF的特性使您能够从一个复杂的网络网络网络网络系统从一个复杂的系统向一个不那么复杂的计算机化的计算系统转换。我们用一个不那么复杂的计算系统来计算一个基于一个简单的系统。