The eigenvalues of graphs play an important role in the fields of quantum chemistry, physics, computer science, communication network, and information science. Particularly, they can be interpreted in some situations ...The eigenvalues of graphs play an important role in the fields of quantum chemistry, physics, computer science, communication network, and information science. Particularly, they can be interpreted in some situations as the energy levels of an electron in a molecule or as the possible frequencies of the tone of a vibrating membrane. The diameter of a graph, the maximum distance between any two vertices of a graph, has great impact on the service quality of communication networks. So we were motivated to investigate the sharp lower bound of the least eigenvalue of graphs with given diameter. Let gn. d be the set of graphs on n vertices with diameter d. For any graph G ∈ gn, d, by considering the least eigenvalue of its connected spanning bipartite subgraph, we obtained the sharp lower bound of the least eigenvalue of graph G. Furthermore, an upper bound of Laplacian spectral radius of graph G was given.展开更多
Traditional Chinese medicine(TCM)has garnered significant global interest owing to its multi-component and multi-target theoretical framework and extensive therapeutic efficacy.However,the identification of quality ma...Traditional Chinese medicine(TCM)has garnered significant global interest owing to its multi-component and multi-target theoretical framework and extensive therapeutic efficacy.However,the identification of quality markers(Q-markers)remains a formidable challenge in TCM.Hence,this study aimed to integrate network pharmacology and chemometrics to identify Q-markers in Chinese patent medicine,with a focus on Huo-Luo-San(HLS)as a case study.HLS,a widely used powdered Chinese patent medicine in China,comprises a complex formula of 10 herbs,initially formulated during the Qing dynasty for treating fractures.Initially,13 components,chlorogenic acid,typhaneoside,isorhamnetin-3-O-neohesperidoside,cynaroside,notoginsenoside R_1,ginsenoside Rg_1,baicalin,berberine hydrochloride,ginsenoside Rb_1,dehydrocostus lactone,dioscin,imperatorin,and costunolide,were selected as phytochemical markers for each herb based on the Chinese Pharmacopoeia(2020 version),forming the“Herbs-Compounds-targets”network of HLS using network pharmacology.Subsequently,employing network pharmacology,the 13 HLS components were quantified using UPLC-QqQ-MS.Chromatographic conditions were optimized on a Waters Cortecs C_(18)column(2.1 mm×100 mm,1.6μm)with a gradient elution comprising 0.1%formic acid in water and acetonitrile.Analyte detection was performed in the multiple-reaction monitoring mode,and the method underwent validation for linearity,detection limit,precision,repeatability,stability,and accuracy.The validated method was then utilized to analyze the 13 components in 15 batches of HLS samples.Chemometric techniques,including hierarchical cluster analysis,principal component analysis,orthogonal partial least squares projection discriminant analysis,and box map analyses,were subsequently employed to identify the Q-markers.Ultimately,six components,baicalin,notoginsenoside R_1,berberine hydrochloride,dioscin,imperatorin,and chlorogenic acid,were selected as Q-markers for HLS.The integration of network pharmacology with chemometrics represented a novel approach for selecting Q-markers in Chinese patent medicine.展开更多
Most of existing works on complex network assumed that the nodes and edges were uncapacitated during the evolving process,and displayed "rich club" phenomenon.Here we will show that the "rich club"...Most of existing works on complex network assumed that the nodes and edges were uncapacitated during the evolving process,and displayed "rich club" phenomenon.Here we will show that the "rich club" could be changed to "common rich" if we consider the node capacity.In this paper,we define the node and edge attractive index with node capacity,and propose a new evolving model on the base of BBV model,with evolving simulations of the networks.In the new model,an entering node is linked with an existing node according to the preferential attachment mechanism defined with the attractive index of the existing node.We give the theoretical approximation and simulation solutions.If node capacity is finite,the rich node may not be richer further when the node strength approaches or gets to the node capacity.This is confirmed by analyzing the passenger traffic and routes of Chinese main airports.Due to node strength being function of time t,we can use the theoretical approximation solution to forecast how node strength changes and the time when node strength reaches its maximum value.展开更多
基金National Key Basic Research Programof China (973,No.2006CB805901)National Natural Science Foundationsof China (No.10671074and No.60673048)Natural Science Foundation of Education Ministry of Anhui Province,China ( No.KJ2009B002)
文摘The eigenvalues of graphs play an important role in the fields of quantum chemistry, physics, computer science, communication network, and information science. Particularly, they can be interpreted in some situations as the energy levels of an electron in a molecule or as the possible frequencies of the tone of a vibrating membrane. The diameter of a graph, the maximum distance between any two vertices of a graph, has great impact on the service quality of communication networks. So we were motivated to investigate the sharp lower bound of the least eigenvalue of graphs with given diameter. Let gn. d be the set of graphs on n vertices with diameter d. For any graph G ∈ gn, d, by considering the least eigenvalue of its connected spanning bipartite subgraph, we obtained the sharp lower bound of the least eigenvalue of graph G. Furthermore, an upper bound of Laplacian spectral radius of graph G was given.
基金The Subject of Fujian Province Science and Technology Hall of China(Grant No.2022J01867)National Key R&D Program of China(Grant No.2019YFC1710505)School Management Project of Fujian University of Traditional Chinese Medicine University(Grant No.X2021001 and No.XJC202301)。
文摘Traditional Chinese medicine(TCM)has garnered significant global interest owing to its multi-component and multi-target theoretical framework and extensive therapeutic efficacy.However,the identification of quality markers(Q-markers)remains a formidable challenge in TCM.Hence,this study aimed to integrate network pharmacology and chemometrics to identify Q-markers in Chinese patent medicine,with a focus on Huo-Luo-San(HLS)as a case study.HLS,a widely used powdered Chinese patent medicine in China,comprises a complex formula of 10 herbs,initially formulated during the Qing dynasty for treating fractures.Initially,13 components,chlorogenic acid,typhaneoside,isorhamnetin-3-O-neohesperidoside,cynaroside,notoginsenoside R_1,ginsenoside Rg_1,baicalin,berberine hydrochloride,ginsenoside Rb_1,dehydrocostus lactone,dioscin,imperatorin,and costunolide,were selected as phytochemical markers for each herb based on the Chinese Pharmacopoeia(2020 version),forming the“Herbs-Compounds-targets”network of HLS using network pharmacology.Subsequently,employing network pharmacology,the 13 HLS components were quantified using UPLC-QqQ-MS.Chromatographic conditions were optimized on a Waters Cortecs C_(18)column(2.1 mm×100 mm,1.6μm)with a gradient elution comprising 0.1%formic acid in water and acetonitrile.Analyte detection was performed in the multiple-reaction monitoring mode,and the method underwent validation for linearity,detection limit,precision,repeatability,stability,and accuracy.The validated method was then utilized to analyze the 13 components in 15 batches of HLS samples.Chemometric techniques,including hierarchical cluster analysis,principal component analysis,orthogonal partial least squares projection discriminant analysis,and box map analyses,were subsequently employed to identify the Q-markers.Ultimately,six components,baicalin,notoginsenoside R_1,berberine hydrochloride,dioscin,imperatorin,and chlorogenic acid,were selected as Q-markers for HLS.The integration of network pharmacology with chemometrics represented a novel approach for selecting Q-markers in Chinese patent medicine.
基金supported by the National Natural Science Foundation of China (Grant Nos.71171111,70771046 and 71201081)the Colleges Graduate Research and Innovation Program of Jiangsu Province (Grant Nos.CXZZ11-0220 and CX10B-102Z)
文摘Most of existing works on complex network assumed that the nodes and edges were uncapacitated during the evolving process,and displayed "rich club" phenomenon.Here we will show that the "rich club" could be changed to "common rich" if we consider the node capacity.In this paper,we define the node and edge attractive index with node capacity,and propose a new evolving model on the base of BBV model,with evolving simulations of the networks.In the new model,an entering node is linked with an existing node according to the preferential attachment mechanism defined with the attractive index of the existing node.We give the theoretical approximation and simulation solutions.If node capacity is finite,the rich node may not be richer further when the node strength approaches or gets to the node capacity.This is confirmed by analyzing the passenger traffic and routes of Chinese main airports.Due to node strength being function of time t,we can use the theoretical approximation solution to forecast how node strength changes and the time when node strength reaches its maximum value.
