树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)...树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.展开更多
Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive...Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.展开更多
The extracellular matrix surrounding oligodendrocytes plays an important role during myelination and remyelination in the brain.In many cases,the microenvironment surrounding demyelination lesions contains inhibitory ...The extracellular matrix surrounding oligodendrocytes plays an important role during myelination and remyelination in the brain.In many cases,the microenvironment surrounding demyelination lesions contains inhibitory molecules,which lead to repair failure.Accordingly,blocking the activity of these inhibitory factors in the extracellular matrix should lead to more successful remyelination.In the central nervous system,oligodendrocytes form the myelin sheath.We performed primary cell culture and found that a natural increase in fibronectin promoted the proliferation of oligodendrocyte progenitors during the initial stage of remyelination while inhibiting oligodendrocyte differentiation.Poly-L-ornithine blocked these inhibitory effects without compromising fibronectin’s pro-proliferation function.Experiments showed that poly-L-ornithine activated the Erk1/2 signaling pathway that is necessary in the early stages of differentiation,as well as PI3K signaling pathways that are needed in the mid-late stages.When poly-L-ornithine was tested in a lysolecithin-induced animal model of focal demyelination,it enhanced myelin regeneration and promoted motor function recovery.These findings suggest that poly-L-ornithine has the potential to be a treatment option for clinical myelin sheath injury.展开更多
K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper propo...K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper proposes an improved K-means algorithm based on the similarity matrix. The im- proved algorithm can effectively avoid the random selection of initial center points, therefore it can provide effective initial points for clustering process, and reduce the fluctuation of clustering results which are resulted from initial points selections, thus a better clustering quality can be obtained. The experimental results also show that the F-measure of the improved K-means algorithm has been greatly improved and the clustering results are more stable.展开更多
Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal ...Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.展开更多
Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexiv...Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.展开更多
为实现对交通流局部特征的有效提取,提高交通速度预测模型的可解释性,提出基于K-means聚类与偏最小二乘(Partial Least Squares,PLS)回归的交通速度短时预测模型。模型采用时空相关矩阵挖掘路网中相邻路段交通速度之间的关联性,利用K-me...为实现对交通流局部特征的有效提取,提高交通速度预测模型的可解释性,提出基于K-means聚类与偏最小二乘(Partial Least Squares,PLS)回归的交通速度短时预测模型。模型采用时空相关矩阵挖掘路网中相邻路段交通速度之间的关联性,利用K-means聚类算法划分历史数据集,并选取实测出租车GPS数据验证模型对交通速度短时预测的准确性。实验结果表明,与ARIMA、PLS回归和LSTM模型相比,该模型的预测误差减少了约30%。展开更多
文摘树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.
基金Supported by the Education Department Foundation of Hebei Province（QN2015218） Supported by the Natural Science Foundation of Hebei Province（A2015403050）
文摘Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
基金supported by the National Nature Science Foundation of China,Nos.81371338(to HF)and 82071369(PPY)。
文摘The extracellular matrix surrounding oligodendrocytes plays an important role during myelination and remyelination in the brain.In many cases,the microenvironment surrounding demyelination lesions contains inhibitory molecules,which lead to repair failure.Accordingly,blocking the activity of these inhibitory factors in the extracellular matrix should lead to more successful remyelination.In the central nervous system,oligodendrocytes form the myelin sheath.We performed primary cell culture and found that a natural increase in fibronectin promoted the proliferation of oligodendrocyte progenitors during the initial stage of remyelination while inhibiting oligodendrocyte differentiation.Poly-L-ornithine blocked these inhibitory effects without compromising fibronectin’s pro-proliferation function.Experiments showed that poly-L-ornithine activated the Erk1/2 signaling pathway that is necessary in the early stages of differentiation,as well as PI3K signaling pathways that are needed in the mid-late stages.When poly-L-ornithine was tested in a lysolecithin-induced animal model of focal demyelination,it enhanced myelin regeneration and promoted motor function recovery.These findings suggest that poly-L-ornithine has the potential to be a treatment option for clinical myelin sheath injury.
文摘K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper proposes an improved K-means algorithm based on the similarity matrix. The im- proved algorithm can effectively avoid the random selection of initial center points, therefore it can provide effective initial points for clustering process, and reduce the fluctuation of clustering results which are resulted from initial points selections, thus a better clustering quality can be obtained. The experimental results also show that the F-measure of the improved K-means algorithm has been greatly improved and the clustering results are more stable.
文摘Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.
基金Supported by the Education Department Foundation of Hebei Province(Grant No.QN2015218).
文摘Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.
文摘为实现对交通流局部特征的有效提取,提高交通速度预测模型的可解释性,提出基于K-means聚类与偏最小二乘(Partial Least Squares,PLS)回归的交通速度短时预测模型。模型采用时空相关矩阵挖掘路网中相邻路段交通速度之间的关联性,利用K-means聚类算法划分历史数据集,并选取实测出租车GPS数据验证模型对交通速度短时预测的准确性。实验结果表明,与ARIMA、PLS回归和LSTM模型相比,该模型的预测误差减少了约30%。
