In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from au...The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.展开更多
The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder nee...The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder needs to store every ＂1＂ of the generator matrices by using huge chip area. In order to solve this problem, we need to design the protograph LDPC codes with circular generator matrices. A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed. The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix. This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices, and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem. Simulation results in ad- ditive white Gaussian noise （AWGN） channels show that the bit error rate （BER） performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金Project(51478036)supported by the National Natural Science Foundation of ChinaProject(20120009110016)supported by Research Fund for Doctoral Program of Higher EducationChina
文摘The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.
基金supported by Beijing Natural Science Foundation(4102050)the National Natural Science of Foundation of China(NSFC)-Korea Science and Engineering Foundation (KOSF) Joint Research Project of China and Korea (60811140343)
文摘The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder needs to store every ＂1＂ of the generator matrices by using huge chip area. In order to solve this problem, we need to design the protograph LDPC codes with circular generator matrices. A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed. The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix. This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices, and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem. Simulation results in ad- ditive white Gaussian noise （AWGN） channels show that the bit error rate （BER） performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.
