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Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
www.druid.dk Innovation Clusters in Technological Systems: A Network Analysis of 15 OECD Countries for the Middle ‘90s
"... The paper aims at investigating how innovations cluster in different technological systems (TSs) when their “technoeconomic", rather than “territorial " space is considered. Innovation clusters of economic sectors are identified by applying network analysis to the intersectoral R&D fl ..."
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The paper aims at investigating how innovations cluster in different technological systems (TSs) when their “technoeconomic", rather than “territorial " space is considered. Innovation clusters of economic sectors are identified by applying network analysis to the intersectoral R&D flows matrices of 15 OECD countries in the middle '90s. Different clusterization models are first tested in order to detect the way sectors group on the basis of the embodied R&D flows they exchange. Actual clusters are then mapped in the different TSs by looking for intersectoral relationships which can be qualified to constitute “reducedTSs " (ReTSs). In all the 15 TSs investigated the technoeconomic space appears organized in hierarchies, along which its constitutive sectors group into clusters with different density and composition. Once ReTSs are looked for, the 15 TSs display highly heterogeneous structures, but with some interesting similarity on the basis of which different clusters of TSs can be identified in turn. Key words: Innovation clusters; technological systems; R&D expenditure; embodied innovation flows
THE EUROPEAN PHYSICAL JOURNAL B Role models for complex networks
, 2007
"... Abstract. We present a framework for automatically decomposing (“blockmodeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the netwo ..."
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Abstract. We present a framework for automatically decomposing (“blockmodeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both twomode and onemode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is nonparametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy. PACS. 89.75.Fb Structures and organization in complex systems – 89.75.Hc Networks and genealogical trees – 89.65.Gh Economics; econophysics, financial markets, business and management – 89.65.Ef Social organizations; anthropology 1
Contents
, 903
"... We consider an Abelian Gauge Theory in R 4 equipped with the Minkowski metric. This theory leads to a system of equations, the KleinGordonMaxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the ene ..."
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We consider an Abelian Gauge Theory in R 4 equipped with the Minkowski metric. This theory leads to a system of equations, the KleinGordonMaxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momentum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortexsolutions.