We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet...We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.展开更多
We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely sol...We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely soluble. In this paper, we show that the conformal mapping technique is adopted to this type of problem in the two dimensional case.展开更多
To increase airspace capacity, alleviate flight delay,and improve network robustness, an optimization method of multi-layer air transportation networks is put forward based on Laplacian energy maximization. The effect...To increase airspace capacity, alleviate flight delay,and improve network robustness, an optimization method of multi-layer air transportation networks is put forward based on Laplacian energy maximization. The effectiveness of taking Laplacian energy as a measure of network robustness is validated through numerical experiments. The flight routes addition optimization model is proposed with the principle of maximizing Laplacian energy. Three methods including the depth-first search( DFS) algorithm, greedy algorithm and Monte-Carlo tree search( MCTS) algorithm are applied to solve the proposed problem. The trade-off between system performance and computational efficiency is compared through simulation experiments. Finally, a case study on Chinese airport network( CAN) is conducted using the proposed model. Through encapsulating it into multi-layer infrastructure via k-core decomposition algorithm, Laplacian energy maximization for the sub-networks is discussed which can provide a useful tool for the decision-makers to optimize the robustness of the air transportation network on different scales.展开更多
Transport properties of a complex network can be reflected by the two-point resistance between any pair of two nodes. We systematically investigate a variety of typical complex networks encountered in nature and techn...Transport properties of a complex network can be reflected by the two-point resistance between any pair of two nodes. We systematically investigate a variety of typical complex networks encountered in nature and technology, in which we assume each link has unit resistance, and we find for non-sparse network connections a universal relation exists that the two-point resistance is equal to the sum of the inverse degree of two nodes up to a constant. We interpret our observations by the localization property of the network＇s Laplacian eigenvectors. The findings in this work can possibly be applied to probe transport properties of general non-sparse complex networks.展开更多
文摘We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.
文摘We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely soluble. In this paper, we show that the conformal mapping technique is adopted to this type of problem in the two dimensional case.
基金The National Natural Science Foundation of China(No.61573098,71401072)the Natural Science Foundation of Jiangsu Province(No.BK20130814)
文摘To increase airspace capacity, alleviate flight delay,and improve network robustness, an optimization method of multi-layer air transportation networks is put forward based on Laplacian energy maximization. The effectiveness of taking Laplacian energy as a measure of network robustness is validated through numerical experiments. The flight routes addition optimization model is proposed with the principle of maximizing Laplacian energy. Three methods including the depth-first search( DFS) algorithm, greedy algorithm and Monte-Carlo tree search( MCTS) algorithm are applied to solve the proposed problem. The trade-off between system performance and computational efficiency is compared through simulation experiments. Finally, a case study on Chinese airport network( CAN) is conducted using the proposed model. Through encapsulating it into multi-layer infrastructure via k-core decomposition algorithm, Laplacian energy maximization for the sub-networks is discussed which can provide a useful tool for the decision-makers to optimize the robustness of the air transportation network on different scales.
基金supported by the National Natural Science Foundation of China(Grant Nos.11305268 and 11465017)
文摘Transport properties of a complex network can be reflected by the two-point resistance between any pair of two nodes. We systematically investigate a variety of typical complex networks encountered in nature and technology, in which we assume each link has unit resistance, and we find for non-sparse network connections a universal relation exists that the two-point resistance is equal to the sum of the inverse degree of two nodes up to a constant. We interpret our observations by the localization property of the network＇s Laplacian eigenvectors. The findings in this work can possibly be applied to probe transport properties of general non-sparse complex networks.
