Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in p...Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.展开更多
Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding co...Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.展开更多
The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that ther...The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.展开更多
This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure ...This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected tir O(n)) and uses the method of path compression to find and to unite. Therefore. n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).展开更多
Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given da...Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.展开更多
This paper considers a capacity expansion problem with budget constraint. Suppose each edge in the network has two attributes: capacity and the degree of difficulty. The difficulty degree of a tree T is the maximum. d...This paper considers a capacity expansion problem with budget constraint. Suppose each edge in the network has two attributes: capacity and the degree of difficulty. The difficulty degree of a tree T is the maximum. degree of difficulty of all edges in the tree and the cost for coping with the difficulty in a tree is a nondecreasing function about the difficulty degree of the tree. The authors need to increase capacities of some edges so that there is a spanning tree whose capacity can be increased to the maximum extent, meanwhile the total cost for increasing capacity as well as overcoming the difficulty in the spanning tree does not exceed a given budget D*. Suppose the cost for increasing capacity on each edge is a linear function about the increment of capacity, they transform this problem into solving some hybrid parametric spanning tree problems([1]) and propose a strongly polynomial algorithm.展开更多
Support Vector Clustering (SVC) is a kernel-based unsupervised learning clustering method. The main drawback of SVC is its high computational complexity in getting the adjacency matrix describing the connectivity for ...Support Vector Clustering (SVC) is a kernel-based unsupervised learning clustering method. The main drawback of SVC is its high computational complexity in getting the adjacency matrix describing the connectivity for each pairs of points. Based on the proximity graph model [3], the Euclidean distance in Hilbert space is calculated using a Gaussian kernel, which is the right criterion to generate a minimum spanning tree using Kruskal's algorithm. Then the connectivity estimation is lowered by only checking the linkages between the edges that construct the main stem of the MST (Minimum Spanning Tree), in which the non-compatibility degree is originally defined to support the edge selection during linkage estimations. This new approach is experimentally analyzed. The results show that the revised algorithm has a better performance than the proximity graph model with faster speed, optimized clustering quality and strong ability to noise suppression, which makes SVC scalable to large data sets.展开更多
Aiming at the existing problems in Leach algorithm,which has short network survival time and high energy consumption,a new location-based clustering topology control algorithm is proposed.Based on Leach algorithm,impr...Aiming at the existing problems in Leach algorithm,which has short network survival time and high energy consumption,a new location-based clustering topology control algorithm is proposed.Based on Leach algorithm,improvements have been done.Firstly,when selecting cluster head,node degree,remaining energy,and the number of being cluster head,these three elements are taken into consideration.Secondly,by running the minimum spanning tree algorithm,the tree routing is constructed.Finally,selecting the next hop between clusters is done by MTE algorithm.Simulation results show that the presented control algorithm has not only a better adaptability in the large-scale networks,but also a bigger improvement in terms of some indicators of performance such as network lifetime and network energy consumption.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61962034,61862058)Longyuan Youth Innovation and Entrepreneurship Talent(Individual)Project and Tianyou Youth Talent Lift Program of Lanzhou Jiaotong Univesity。
文摘Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.
文摘Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.
文摘The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.
文摘This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected tir O(n)) and uses the method of path compression to find and to unite. Therefore. n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).
基金Supported by the Key National Natural Science Foundation of China(61035003)~~
文摘Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.
基金the partial support of National Natural ScienceFoundation (Grant 70071011 .)
文摘This paper considers a capacity expansion problem with budget constraint. Suppose each edge in the network has two attributes: capacity and the degree of difficulty. The difficulty degree of a tree T is the maximum. degree of difficulty of all edges in the tree and the cost for coping with the difficulty in a tree is a nondecreasing function about the difficulty degree of the tree. The authors need to increase capacities of some edges so that there is a spanning tree whose capacity can be increased to the maximum extent, meanwhile the total cost for increasing capacity as well as overcoming the difficulty in the spanning tree does not exceed a given budget D*. Suppose the cost for increasing capacity on each edge is a linear function about the increment of capacity, they transform this problem into solving some hybrid parametric spanning tree problems([1]) and propose a strongly polynomial algorithm.
基金TheNationalHighTechnologyResearchandDevelopmentProgramofChina (No .86 3 5 11 930 0 0 9)
文摘Support Vector Clustering (SVC) is a kernel-based unsupervised learning clustering method. The main drawback of SVC is its high computational complexity in getting the adjacency matrix describing the connectivity for each pairs of points. Based on the proximity graph model [3], the Euclidean distance in Hilbert space is calculated using a Gaussian kernel, which is the right criterion to generate a minimum spanning tree using Kruskal's algorithm. Then the connectivity estimation is lowered by only checking the linkages between the edges that construct the main stem of the MST (Minimum Spanning Tree), in which the non-compatibility degree is originally defined to support the edge selection during linkage estimations. This new approach is experimentally analyzed. The results show that the revised algorithm has a better performance than the proximity graph model with faster speed, optimized clustering quality and strong ability to noise suppression, which makes SVC scalable to large data sets.
基金Financial by program for Liaoning Outstanding Talents in University(LR2012007)
文摘Aiming at the existing problems in Leach algorithm,which has short network survival time and high energy consumption,a new location-based clustering topology control algorithm is proposed.Based on Leach algorithm,improvements have been done.Firstly,when selecting cluster head,node degree,remaining energy,and the number of being cluster head,these three elements are taken into consideration.Secondly,by running the minimum spanning tree algorithm,the tree routing is constructed.Finally,selecting the next hop between clusters is done by MTE algorithm.Simulation results show that the presented control algorithm has not only a better adaptability in the large-scale networks,but also a bigger improvement in terms of some indicators of performance such as network lifetime and network energy consumption.
