Finding meaningful sets of co-purchased products allows retailers to manageinventory better and develop market strategies. Analyzing the baskets ofproducts, known as market basket analysis, is typically carried out us...Finding meaningful sets of co-purchased products allows retailers to manageinventory better and develop market strategies. Analyzing the baskets ofproducts, known as market basket analysis, is typically carried out usingassociation rule mining or community detection approach. This article usesboth methods to investigate a transaction dataset collected from a brick-andmortargrocery store. The findings reveal interesting purchasing patterns oflocal residents and prompt us to consider dynamic modeling of the productnetwork in the future.展开更多
In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. ...In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.展开更多
This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employi...This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.展开更多
The Internet of Things(IoT)has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses.Social network analysis(SNA)is a good example...The Internet of Things(IoT)has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses.Social network analysis(SNA)is a good example that has recently gained a lot of scientific attention.It has its roots in social and economic research,as well as the evaluation of network science,such as graph theory.Scientists in this area have subverted predefined theories,offering revolutionary ones regarding interconnected networks,and they have highlighted the mystery of six degrees of separation with confirmation of the small-world phenomenon.The motivation of this study is to understand and capture the clustering properties of large networks and social networks.We present a network growth model in this paper and build a scale-free artificial social network with controllable clustering coefficients.The random walk technique is paired with a triangle generating scheme in our proposed model.As a result,the clustering controlmechanism and preferential attachment(PA)have been realized.This research builds on the present random walk model.We took numerous measurements for validation,including degree behavior and the measure of clustering decay in terms of node degree,among other things.Finally,we conclude that our suggested random walk model is more efficient and accurate than previous state-of-the-art methods,and hence it could be a viable alternative for societal evolution.展开更多
ransport network in the paper is defined as follows: (1) Connected and directed network without self loop;(2) There is only one source vertex with zero in degree; (3) There is only one sink vertex with zero out de...ransport network in the paper is defined as follows: (1) Connected and directed network without self loop;(2) There is only one source vertex with zero in degree; (3) There is only one sink vertex with zero out degree;(4) The capacity of every arc is non negative integer Blocking flow is a kind of flow commonly happened in a transport network . Its formation is due to the existance of a blocking cutset in the network. In this paper the fundamental concepts and theorems of the blocking flow and the blocking cutset are introduced and a linear programming model for determining the blocking cutset in a network is set up. In order to solve the problem by graph theoretical approach a method called 'two way flow augmenting algorithm' is developed. With this method an iterative procedure of forward and backward flow augmenting process is used to determine whether a given cutset is a blocking one.展开更多
We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features...We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features related to structure, connectivity and centrality changed over time. The analysis of these metrics provides topological and data traffic information and allows to clarify some assumptions about the models concerning the evolution of the Internet graph structure. We find that the size of the Internet roughly doubled. The overall trend of the average connectivity is an increase over time, while that of the shortest path length is a decrease over time. The internal core of the Internet is composed of a small fraction of big AS and is more stable and connected the external cores. A hierarchical organization emerges where a small fraction of big hubs are connected to many regions with high internal cohesiveness, poorly connected among them and containing AS with low and medium numbers of links. Centrality measurements indicate that the average number of shortest paths crossing an AS or containing a link between two of them decreased over time.展开更多
文摘Finding meaningful sets of co-purchased products allows retailers to manageinventory better and develop market strategies. Analyzing the baskets ofproducts, known as market basket analysis, is typically carried out usingassociation rule mining or community detection approach. This article usesboth methods to investigate a transaction dataset collected from a brick-andmortargrocery store. The findings reveal interesting purchasing patterns oflocal residents and prompt us to consider dynamic modeling of the productnetwork in the future.
文摘In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.
基金supported by the National Natural Science Foundation of China (6057408860274014)
文摘This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.
基金This work was supported in part by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education under Grant NRF-2019R1A2C1006159 and Grant NRF-2021R1A6A1A03039493in part by the 2021 Yeungnam University Research Grant。
文摘The Internet of Things(IoT)has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses.Social network analysis(SNA)is a good example that has recently gained a lot of scientific attention.It has its roots in social and economic research,as well as the evaluation of network science,such as graph theory.Scientists in this area have subverted predefined theories,offering revolutionary ones regarding interconnected networks,and they have highlighted the mystery of six degrees of separation with confirmation of the small-world phenomenon.The motivation of this study is to understand and capture the clustering properties of large networks and social networks.We present a network growth model in this paper and build a scale-free artificial social network with controllable clustering coefficients.The random walk technique is paired with a triangle generating scheme in our proposed model.As a result,the clustering controlmechanism and preferential attachment(PA)have been realized.This research builds on the present random walk model.We took numerous measurements for validation,including degree behavior and the measure of clustering decay in terms of node degree,among other things.Finally,we conclude that our suggested random walk model is more efficient and accurate than previous state-of-the-art methods,and hence it could be a viable alternative for societal evolution.
文摘ransport network in the paper is defined as follows: (1) Connected and directed network without self loop;(2) There is only one source vertex with zero in degree; (3) There is only one sink vertex with zero out degree;(4) The capacity of every arc is non negative integer Blocking flow is a kind of flow commonly happened in a transport network . Its formation is due to the existance of a blocking cutset in the network. In this paper the fundamental concepts and theorems of the blocking flow and the blocking cutset are introduced and a linear programming model for determining the blocking cutset in a network is set up. In order to solve the problem by graph theoretical approach a method called 'two way flow augmenting algorithm' is developed. With this method an iterative procedure of forward and backward flow augmenting process is used to determine whether a given cutset is a blocking one.
文摘We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features related to structure, connectivity and centrality changed over time. The analysis of these metrics provides topological and data traffic information and allows to clarify some assumptions about the models concerning the evolution of the Internet graph structure. We find that the size of the Internet roughly doubled. The overall trend of the average connectivity is an increase over time, while that of the shortest path length is a decrease over time. The internal core of the Internet is composed of a small fraction of big AS and is more stable and connected the external cores. A hierarchical organization emerges where a small fraction of big hubs are connected to many regions with high internal cohesiveness, poorly connected among them and containing AS with low and medium numbers of links. Centrality measurements indicate that the average number of shortest paths crossing an AS or containing a link between two of them decreased over time.
文摘目的探讨阿尔茨海默病(Alzheimer's disease,AD)患者大脑灰质体积、灰质皮层厚度及基于皮层厚度的结构协变网络(structural covariance network,SCN)的拓扑属性改变。材料与方法本研究共筛选了250例来自ADNI数据库的被试,包括AD组100人,健康对照(healthy controls,HCs)组150人。首先,利用基于体素的形态学分析方法(voxel-based morphometry,VBM)和基于表面的形态学分析方法(surface-based morphometry,SBM)分别计算每组被试的灰质体积和皮层厚度并比较其组间差异。其次,将有组间差异的脑区定义为感兴趣区(region of interest,ROI),提取每一个ROI的灰质体积和皮层厚度值,与认知量表进行偏相关分析。最后,构建基于皮层厚度的SCN并利用图论分析方法分析该网络的全局属性及局部属性的变化特征。结果第一,相较于HCs组,AD组的灰质体积和皮层厚度显著下降[体素和顶点水平总体误差(family-wise error,FWE)校正后P<0.001]。AD组灰质体积下降的脑区主要包括双侧海马、双侧眶额皮层、左侧岛叶、右侧枕下回、左侧楔前叶、左侧中央前回、左侧中央扣带回。AD组皮层厚度变薄的脑区主要包括双侧颞叶、双侧额叶、双侧顶叶、双侧扣带回、双侧梭状回、双侧岛回、双侧楔前叶等。第二,偏相关分析表明,AD组简易精神状态检查量表(Mini-Mental State Examination,MMSE)得分分别与右侧海马体积[rs=0.35,错误发现率(false discovery rate,FDR)校正后P<0.001]、左侧海马体积(r_(s)=0.38,FDR校正后P<0.001)、右侧梭状回皮层厚度(r_(s)=0.38,FDR校正后P<0.001)呈正相关;临床痴呆评定量表(Clinical Dementia Rating Sum of Boxes,CDR-SB)评分与左侧梭状回皮层厚度(r_(s)=-0.39,FDR校正后P<0.001)呈负相关。第三,脑网络分析表明,AD组SCN的全局效率(P<0.001)、局部效率(P=0.03)及小世界属性(P<0.001)高于HCs组,最短路径低于HCs组(P<0.001)。结论联合VBM、SBM的形态学分析及SCN的图论分析有助于全面理解AD患者脑网络的重组及其意义,进而为AD患者神经影像学改变提供新的见解和证据。
