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9,680
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 ..."
Abstract

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
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
Abstract

Cited by 1772 (10 self)
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How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
Abstract

Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
 C. R. Acad. Sci. Paris Ser. I Math
, 2001
"... Abstract. We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolationrelated quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of t ..."
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Cited by 272 (9 self)
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Abstract. We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolationrelated quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance
of Percolation Clusters
, 2008
"... We study random networks of nonlinear resistors, which obey a generalized Ohm’s law, V ∼ I r. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is presented in detail. By considering distinct values of the nonlin ..."
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of the nonlinearity r, we calculate several fractal dimensions characterizing percolation clusters. For the dimension associated with the red bonds we show that dred = 1/ν at least to order O ( ǫ 4) , with ν being the correlation length exponent, and ǫ = 6 − d, where d denotes the spatial dimension. This result
Gossipbased ad hoc routing
, 2002
"... Abstract—Many ad hoc routing protocols are based on some variant of flooding. Despite various optimizations, many routing messa ges are propagated unnecessarily. We propose a gossipingbased approa ch, where each node forwards a message with some probability, to reduce the ov erhead of the routing p ..."
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Cited by 371 (4 self)
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Abstract—Many ad hoc routing protocols are based on some variant of flooding. Despite various optimizations, many routing messa ges are propagated unnecessarily. We propose a gossipingbased approa ch, where each node forwards a message with some probability, to reduce the ov erhead of the routing protocols. Gossiping exhibits bimodal behavio r in sufficiently large networks: in some executions, the gossip dies out quic kly and hardly any node gets the message; in the remaining executions, a sub stantial fraction of the nodes gets the message. The fraction of execution s in which most nodes get the message depends on the gossiping probability a nd the topology of the network. In the networks we have considered, using g ossiping probability between 0.6 and 0.8 suffices to ensure that almost every node gets the message in almost every execution. For large networ ks, this simple gossiping protocol uses up to 35 % fewer messages than flood ing, with improved performance. Gossiping can also be combined with va rious optimizations of flooding to yield further benefits. Simulations show that adding gossiping to AODV results in significant performance improv ement, even in networks as small as 150 nodes. We expect that the improvemen t should be even more significant in larger networks. I.
Results 1  10
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