Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated...Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + n-2δ+1/((n-1)(n-3)) .展开更多
An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal...An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal identity degree based on relative positive region is proposed so that the identity degree can be computed in an objective method without any preliminary or additional information about data, which is consistent with the notion of objectivity in rough set theory and data mining theory. Subsequently, an algorithm is proposed, and in two examples, the global optimum identity degree is found out. Finally, in regard to optimum connection degree, the method of rules extraction for connection degree rough set model based on generalization function is presented by which the rules extracted from a decision table are enumerated.展开更多
In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formu...In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.展开更多
Attention deficit hyperactivity disorder（ADHD） is a pervasive psychiatric disorder that affects both children and adults. Adult male and female patients with ADHD are differentially affected, but few studies have ex...Attention deficit hyperactivity disorder（ADHD） is a pervasive psychiatric disorder that affects both children and adults. Adult male and female patients with ADHD are differentially affected, but few studies have explored the differences. The purpose of this study was to quantify differences between adult male and female patients with ADHD based on neuroimaging and connectivity analysis. Resting-state functional magnetic resonance imaging scans were obtained and preprocessed in 82 patients. Group-wise differences between male and female patients were quantified using degree centrality for different brain regions. The medial-, middle-, and inferior-frontal gyrus, superior parietal lobule, precuneus, supramarginal gyrus, superior- and middle-temporal gyrus, middle occipital gyrus, and cuneus were identified as regions with significant group-wise differences. The identified regions were correlated with clinical scores reflecting depression and anxiety and significant correlations were found. Adult ADHD patients exhibit different levels of depression and anxiety depending on sex, and our study provides insight into how changes in brain circuitry might differentially impact male and female ADHD patients.展开更多
Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and me...Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.展开更多
AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivi...AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.展开更多
Let G be a 3-connected graph with n vertices. The paper proves that if for each pair of vertices u and v of G, d(u,v)=2, has ｜N(u)∩N(v)｜≤α(α is the minimum independent set number), and then max{d(u),d(v)}≥n+12,...Let G be a 3-connected graph with n vertices. The paper proves that if for each pair of vertices u and v of G, d(u,v)=2, has ｜N(u)∩N(v)｜≤α(α is the minimum independent set number), and then max{d(u),d(v)}≥n+12, then G is a Hamilton connected graph.展开更多
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E（G）, define d（e） = d（u） ＋ d（v）. Let F denote the set of all simple 2-edge-connected graphs on n ） 4 vertices such that G∈ F if ...Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E（G）, define d（e） = d（u） ＋ d（v）. Let F denote the set of all simple 2-edge-connected graphs on n ） 4 vertices such that G∈ F if and only if d（e） ＋ d（e′） ≥ 2n for every pair of independent edges e, e′ of G. We prove in this paper that for each G ∈ F, G is not Z3-connected if and only if G is one of K2,n-2, K3,n-3, K^＋2,n-2,K^＋ 3,n-3 or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 20]0, 310： 3390-3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308： 6233-6240].展开更多
针对容迟网络中节点存储空间有限从而出现大量丢包情况的问题,本文提出了一种适用于节点环境状态的拥塞控制管理策略(congestion control management strategy suitable for the state of the node environment,NEMS):该策略由节点间位...针对容迟网络中节点存储空间有限从而出现大量丢包情况的问题,本文提出了一种适用于节点环境状态的拥塞控制管理策略(congestion control management strategy suitable for the state of the node environment,NEMS):该策略由节点间位置差异相关的控制保留策略和节点自差异相关的丢包策略构成.首先根据节点剩余缓存空间的大小判断节点是处于忙碌状态(BS)还是崩溃状态(CS),当节点处于BS状态时,节点间位置差异相关的控制保留策略结合门限度和连接活跃值的概念分析是否留存新消息.节点自差异相关的丢包策略利用熵权法动态计算各个节点中不同消息属性权重,得到消息丢弃优先级.当拥塞发生,优先删除丢弃优先级大的消息.同时,引入ACK反馈机制,消除网络中已成功投递的冗余消息.仿真结果表明,与无缓存管理的路由策略相比,加入NEMS后使得消息成功投递率增加了约100.93%~200.67%,网络负载降低了约76.05%~81.42%.展开更多
基金Supported by the Natural Science Foundation of Xinjiang University（XYl10102） Sup- ported by the of NSFXJ（2010211A06）
文摘Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + n-2δ+1/((n-1)(n-3)) .
基金supported by the National Natural Science Foundation of China (70571032)
文摘An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal identity degree based on relative positive region is proposed so that the identity degree can be computed in an objective method without any preliminary or additional information about data, which is consistent with the notion of objectivity in rough set theory and data mining theory. Subsequently, an algorithm is proposed, and in two examples, the global optimum identity degree is found out. Finally, in regard to optimum connection degree, the method of rules extraction for connection degree rough set model based on generalization function is presented by which the rules extracted from a decision table are enumerated.
基金Supported by the Department of Education Science Research Project of Hunan Province(09C470)
文摘In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.
基金supported in part by the Institute for Basic Science(to HP)No.IBS-R015-D1
文摘Attention deficit hyperactivity disorder（ADHD） is a pervasive psychiatric disorder that affects both children and adults. Adult male and female patients with ADHD are differentially affected, but few studies have explored the differences. The purpose of this study was to quantify differences between adult male and female patients with ADHD based on neuroimaging and connectivity analysis. Resting-state functional magnetic resonance imaging scans were obtained and preprocessed in 82 patients. Group-wise differences between male and female patients were quantified using degree centrality for different brain regions. The medial-, middle-, and inferior-frontal gyrus, superior parietal lobule, precuneus, supramarginal gyrus, superior- and middle-temporal gyrus, middle occipital gyrus, and cuneus were identified as regions with significant group-wise differences. The identified regions were correlated with clinical scores reflecting depression and anxiety and significant correlations were found. Adult ADHD patients exhibit different levels of depression and anxiety depending on sex, and our study provides insight into how changes in brain circuitry might differentially impact male and female ADHD patients.
文摘Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.
基金This project is supported by the National Natural Science Foundation of China
文摘AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.
文摘Let G be a 3-connected graph with n vertices. The paper proves that if for each pair of vertices u and v of G, d(u,v)=2, has ｜N(u)∩N(v)｜≤α(α is the minimum independent set number), and then max{d(u),d(v)}≥n+12, then G is a Hamilton connected graph.
基金Acknowledgements The first author was supported by the Excellent Doctorial Dissertation Cultivation Grant from Huazhong Normal University （2013YBYB42）. The second author was supported in part by the National Natural Science Foundation of China （Grant No. 11171129） and the Doctoral Fund of Ministry of Education of China （Grant No. 20130144110001）.
文摘Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E（G）, define d（e） = d（u） ＋ d（v）. Let F denote the set of all simple 2-edge-connected graphs on n ） 4 vertices such that G∈ F if and only if d（e） ＋ d（e′） ≥ 2n for every pair of independent edges e, e′ of G. We prove in this paper that for each G ∈ F, G is not Z3-connected if and only if G is one of K2,n-2, K3,n-3, K^＋2,n-2,K^＋ 3,n-3 or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 20]0, 310： 3390-3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308： 6233-6240].
文摘针对容迟网络中节点存储空间有限从而出现大量丢包情况的问题,本文提出了一种适用于节点环境状态的拥塞控制管理策略(congestion control management strategy suitable for the state of the node environment,NEMS):该策略由节点间位置差异相关的控制保留策略和节点自差异相关的丢包策略构成.首先根据节点剩余缓存空间的大小判断节点是处于忙碌状态(BS)还是崩溃状态(CS),当节点处于BS状态时,节点间位置差异相关的控制保留策略结合门限度和连接活跃值的概念分析是否留存新消息.节点自差异相关的丢包策略利用熵权法动态计算各个节点中不同消息属性权重,得到消息丢弃优先级.当拥塞发生,优先删除丢弃优先级大的消息.同时,引入ACK反馈机制,消除网络中已成功投递的冗余消息.仿真结果表明,与无缓存管理的路由策略相比,加入NEMS后使得消息成功投递率增加了约100.93%~200.67%,网络负载降低了约76.05%~81.42%.
