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Multipoint connection by long-range density interaction and short-range distance rule
Physica Scripta ( IF 2.6 ) Pub Date : 2021-02-04 , DOI: 10.1088/1402-4896/abe00c
Francesco Gentile

The performance of a system is influenced by the way its elements are connected. Networks of cells with high clustering and short paths communicate more efficiently than random or periodic networks of the same size. While many algorithms exist for generating networks from distributions of points in a plane, most of them are based on the oversimplification that a system’s components form connections in proportion to the inverse of their distance. The Waxman algorithm, which is based on a similar assumption, represents the gold standard for those who want to model biological networks from the spatial layout of cells. This assumption, however, does not allow to reproduce accurately the complexity of physical or biological systems, where elements establish both short and long-range connections, the combination of the two resulting in non-trivial topological features, including small-world characteristics. Here, we present a wiring algorithm that connects elements of a system using the logical connective between two disjoint probabilities, one correlated to the inverse of their distance, as in Waxman, and one associated to the density of points in the neighborhood of the system’s element. The first probability regulates the development of links or edges among adjacent nodes, while the latter governs interactions between cluster centers, where the density of points is often higher. We demonstrate that, by varying the parameters of the model, one can obtain networks with wanted values of small-world-ness, ranging from ∼1 (random graphs) to ∼14 (small world networks).



中文翻译:

长距离密度相互作用和短距离距离规则的多点连接

系统的性能受其元素连接方式的影响。具有高聚类和短路径的单元网络比相同大小的随机或周期性网络更有效地通信。虽然存在许多用于从平面中点的分布生成网络的算法,但大多数算法都基于过于简单化,即系统组件形成的连接与其距离的倒数成正比。基于类似假设的 Waxman 算法代表了那些想要根据细胞的空间布局对生物网络进行建模的人的黄金标准。然而,这种假设无法准确再现物理或生物系统的复杂性,其中元素建立了短程和长程连接,两者的结合产生了非平凡的拓扑特征,包括小世界特征。在这里,我们提出了一种布线算法,它使用两个不相交概率之间的逻辑连接来连接系统的元素,一个与其距离的倒数相关,如在 Waxman 中,另一个与系统元素邻域中点的密度相关. 第一个概率调节相邻节点之间链接或边的发展,而后者控制聚类中心之间的交互,其中点的密度通常更高。我们证明,通过改变模型的参数,可以获得具有小世界性所需值的网络,范围从~1(随机图)到~14(小世界网络)。我们提出了一种接线算法,该算法使用两个不相交的概率之间的逻辑连接来连接系统的元素,一个与其距离的倒数相关,如在 Waxman 中,另一个与系统元素邻域中点的密度相关。第一个概率调节相邻节点之间链接或边的发展,而后者控制聚类中心之间的交互,其中点的密度通常更高。我们证明,通过改变模型的参数,可以获得具有小世界性所需值的网络,范围从~1(随机图)到~14(小世界网络)。我们提出了一种接线算法,该算法使用两个不相交的概率之间的逻辑连接来连接系统的元素,一个与其距离的倒数相关,如在 Waxman 中,另一个与系统元素邻域中点的密度相关。第一个概率调节相邻节点之间链接或边的发展,而后者控制聚类中心之间的交互,其中点的密度通常更高。我们证明,通过改变模型的参数,可以获得具有小世界性所需值的网络,范围从~1(随机图)到~14(小世界网络)。一个与系统元素邻域中点的密度相关。第一个概率调节相邻节点之间链接或边的发展,而后者控制聚类中心之间的交互,其中点的密度通常更高。我们证明,通过改变模型的参数,可以获得具有小世界性所需值的网络,范围从~1(随机图)到~14(小世界网络)。一个与系统元素邻域中点的密度相关。第一个概率调节相邻节点之间链接或边的发展,而后者控制聚类中心之间的交互,其中点的密度通常更高。我们证明,通过改变模型的参数,可以获得具有小世界性所需值的网络,范围从~1(随机图)到~14(小世界网络)。

更新日期:2021-02-04
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