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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
Topologicallyaware overlay construction and server selection
, 2002
"... A number of largescale distributed Internet applications could potentially benefit from some level of knowledge about the relative proximity between its participating host nodes. For example, the performance of large overlay networks could be improved if the applicationlevel connectivity between ..."
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Cited by 343 (5 self)
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A number of largescale distributed Internet applications could potentially benefit from some level of knowledge about the relative proximity between its participating host nodes. For example, the performance of large overlay networks could be improved if the applicationlevel connectivity between the nodes in these networks is congruent with the underlying IPlevel topology. Similarly, in the case of replicated web content, client nodes could use topological information in selecting one of multiple available servers. For such applications, one need not find the optimal solution in order to achieve significant practical benefits. Thus, these applications, and presumably others like them, do not require exact topological information and can instead use sufficiently informative hints about the relative positions of Internet hosts. In this paper, we present a binning scheme whereby nodes partition themselves into bins such that nodes that fall within a given bin are relatively close to one another in terms of network latency. Our binning strategy is simple (requiring minimal support from any measurement infrastructure), scalable (requiring no form of global knowledge, each node only needs knowledge of a small number of wellknown landmark nodes) and completely distributed (requiring no communication or cooperation between the nodes being binned). We apply this binning strategy to the two applications mentioned above: overlay network construction and server selection. We test our binning strategy and its application using simulation and Internet measurement traces. Our results indicate that the performance of these applications can be significantly improved by even the rather coarsegrained knowledge of topology offered by our binning scheme.
THE KARP COMPLEXITY OF UNSTABLE CLASSES
"... Abstract. A class K of structures is controlled if, for all cardinals λ, the relation of L∞,λequivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudoelementary class with th ..."
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Abstract. A class K of structures is controlled if, for all cardinals λ, the relation of L∞,λequivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudoelementary class with the ωindependence property is not controlled. 560 revision:20001031 modified:20001031 1.
The Vaught Conjecture Do uncountable models count?
, 2006
"... We give a model theoretic proof, replacing admissible set theory by the LopezEscobar theorem, of Makkai’s theorem: Every counterexample to Vaught’s conjecture has an uncountable model which realizes only countably many Lω1,ωtypes. The following result is new. Theorem. If a first order theory is a ..."
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Cited by 2 (2 self)
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We give a model theoretic proof, replacing admissible set theory by the LopezEscobar theorem, of Makkai’s theorem: Every counterexample to Vaught’s conjecture has an uncountable model which realizes only countably many Lω1,ωtypes. The following result is new. Theorem. If a first order theory is a
KARP COMPLEXITY AND CLASSES WITH THE INDEPENDENCE PROPERTY
"... Abstract. A class K of structures is controlled if for all cardinals λ, the relation of L∞,λequivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that no pseudoelementary class with the independence property is controlled. By contrast, there is a pseud ..."
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Cited by 2 (0 self)
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Abstract. A class K of structures is controlled if for all cardinals λ, the relation of L∞,λequivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that no pseudoelementary class with the independence property is controlled. By contrast, there is a pseudoelementary class with the strict order property that is controlled (see [4]). 687 revision:20021003 modified:20021004 1.
A CONSTRUCTION OF MANY UNCOUNTABLE RINGS USING SFP DOMAINS AND ARONSZAJN TREES
, 1991
"... The paper is in two parts. In Part I we describe a construction of a certain kind of subdirect product of a family of rings. We endow the index set of the family with the partial order structure of an SFP domain, as introduced by Plotkin, and provide a commuting system of homomorphisms between those ..."
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. The construction needs only ZFC, and uses Aronszajn trees to build many different SFP domains with bases of cardinality K,.
Results 1  10
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