As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of pos...As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.展开更多
The spatial distribution of power facilities is uneven,thereby making the topology of geographical wiring diagrams(GWDs)based on the actual coordinates unclear.A single-line diagram has the advantage of a clear topolo...The spatial distribution of power facilities is uneven,thereby making the topology of geographical wiring diagrams(GWDs)based on the actual coordinates unclear.A single-line diagram has the advantage of a clear topology but it lacks spatial locations.A GWD has the advantage of accurate spatial locations but it lacks a clear topology.Visualizing distribution networks for planning requires both features.We proposed a new planning-oriented method for optimizing the visualization of distribution networks.From the global perspective,we proposed an improved force-directed(FD)algorithm by introducing a space restriction strategy and node–edge repulsion strategy to promote the expansion of the distance between distribution facilities within a limited buffer.We then constructed the constrained Delaunay triangulation to identify the compact districts(CDs)and used a genetic algorithm to optimize the parameters for the improved FD algorithm.A novel visualization evaluation indicator was also proposed for quantitatively assessing the visualizations.From a local perspective,the fisheye algorithm was used to optimize the CDs to further improve the visualization of the distribution network.We verified the proposed methods with real-world data.We used limited spatial displacement in exchange for maximum topology clarity to balance the accurate spatial location and topology clarity.展开更多
基金Supported by the National Natural Science Foundation of China(11671350,11571173,11801043)Natural Science Foundation for Youths of Jiangsu Province(BK20181031).
文摘As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.
基金supported by the National Natural Science Foundation of China(grant number U20A2091 and No.41771426).
文摘The spatial distribution of power facilities is uneven,thereby making the topology of geographical wiring diagrams(GWDs)based on the actual coordinates unclear.A single-line diagram has the advantage of a clear topology but it lacks spatial locations.A GWD has the advantage of accurate spatial locations but it lacks a clear topology.Visualizing distribution networks for planning requires both features.We proposed a new planning-oriented method for optimizing the visualization of distribution networks.From the global perspective,we proposed an improved force-directed(FD)algorithm by introducing a space restriction strategy and node–edge repulsion strategy to promote the expansion of the distance between distribution facilities within a limited buffer.We then constructed the constrained Delaunay triangulation to identify the compact districts(CDs)and used a genetic algorithm to optimize the parameters for the improved FD algorithm.A novel visualization evaluation indicator was also proposed for quantitatively assessing the visualizations.From a local perspective,the fisheye algorithm was used to optimize the CDs to further improve the visualization of the distribution network.We verified the proposed methods with real-world data.We used limited spatial displacement in exchange for maximum topology clarity to balance the accurate spatial location and topology clarity.
