To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successf...To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.展开更多
局部线性嵌入(Local linear embedding,LLE)算法作为一种经典的非线性降维算法,在图像识别等领域取得了很好的应用效果,但仍存在一些缺陷,如在构造邻域图时使用欧氏距离,可能会出现“短路边”的情况,同时,会受到离群点的影响,导致鲁棒...局部线性嵌入(Local linear embedding,LLE)算法作为一种经典的非线性降维算法,在图像识别等领域取得了很好的应用效果,但仍存在一些缺陷,如在构造邻域图时使用欧氏距离,可能会出现“短路边”的情况,同时,会受到离群点的影响,导致鲁棒性较差。为解决以上问题,论文基于通勤时间距离(commute time distance,CTD)和Rank-Order距离提出了CRLLE(LLE based on CTD and Rank-Order distance)算法,并在ORL人脸数据集和IMM人脸数据集上进行实验。实验设置CRLLE算法与LLE算法、等距特征映射(Isomap)算法和主成分分析降维(PCA)算法三种维数简约方法进行比较,得出改进后的CRLLE算法的降维效果优于其他三种算法的结论。展开更多
运用文献资料法、逻辑分析法,以Web of science核心合集数据库以及Google Scholar收录的26篇极限飞盘比赛相关的文献为研究对象,梳理国外有关极限飞盘比赛的研究。研究发现,国外极限飞盘在研究内容上主要集中在极限飞盘项目特征及运动...运用文献资料法、逻辑分析法,以Web of science核心合集数据库以及Google Scholar收录的26篇极限飞盘比赛相关的文献为研究对象,梳理国外有关极限飞盘比赛的研究。研究发现,国外极限飞盘在研究内容上主要集中在极限飞盘项目特征及运动员体能、极限飞盘运动员损伤、极限飞盘比赛技术统计、极限飞盘技术动作运动生物力学分析等方面。认为极限飞盘比赛要求运动员具备得分时的无氧爆发力以及在攻防过程中的有氧持续能力,是一项技战术复杂多变,对运动员体能和心智、团队协作能力要求较高的项目;在比赛过程中的运动损伤主要是运动员之间直接接触造成的,最常见的身体损伤部位为下肢;比赛球员数据统计、球队数据统计已是国外极限飞盘研究的重点;采用运动生物力学分析极限飞盘比赛时的技术动作能帮助队伍在比赛中获利。展开更多
Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtour...Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).展开更多
Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integ...Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer toT as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T iscalled arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirectedpancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and forany T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe-cial tournaments which are to be shown.展开更多
文摘To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.
文摘局部线性嵌入(Local linear embedding,LLE)算法作为一种经典的非线性降维算法,在图像识别等领域取得了很好的应用效果,但仍存在一些缺陷,如在构造邻域图时使用欧氏距离,可能会出现“短路边”的情况,同时,会受到离群点的影响,导致鲁棒性较差。为解决以上问题,论文基于通勤时间距离(commute time distance,CTD)和Rank-Order距离提出了CRLLE(LLE based on CTD and Rank-Order distance)算法,并在ORL人脸数据集和IMM人脸数据集上进行实验。实验设置CRLLE算法与LLE算法、等距特征映射(Isomap)算法和主成分分析降维(PCA)算法三种维数简约方法进行比较,得出改进后的CRLLE算法的降维效果优于其他三种算法的结论。
文摘运用文献资料法、逻辑分析法,以Web of science核心合集数据库以及Google Scholar收录的26篇极限飞盘比赛相关的文献为研究对象,梳理国外有关极限飞盘比赛的研究。研究发现,国外极限飞盘在研究内容上主要集中在极限飞盘项目特征及运动员体能、极限飞盘运动员损伤、极限飞盘比赛技术统计、极限飞盘技术动作运动生物力学分析等方面。认为极限飞盘比赛要求运动员具备得分时的无氧爆发力以及在攻防过程中的有氧持续能力,是一项技战术复杂多变,对运动员体能和心智、团队协作能力要求较高的项目;在比赛过程中的运动损伤主要是运动员之间直接接触造成的,最常见的身体损伤部位为下肢;比赛球员数据统计、球队数据统计已是国外极限飞盘研究的重点;采用运动生物力学分析极限飞盘比赛时的技术动作能帮助队伍在比赛中获利。
文摘Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).
文摘Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer toT as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T iscalled arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirectedpancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and forany T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe-cial tournaments which are to be shown.
