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893
Complex networks: Structure and dynamics
, 2006
"... Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is t ..."
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Cited by 428 (9 self)
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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks ’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines,
Critical Behavior in the Satisfiability of Random Boolean Formulae
 Science
, 1994
"... The satisfiability of randomly generated Boolean formulae with k variables per clause is a popular testbed for the performance of search algorithms in artificial intelligence and computer science. For k = 2, formulae are almost aways satisfiable when the ratio of clauses to variables is less than ..."
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Cited by 178 (10 self)
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The satisfiability of randomly generated Boolean formulae with k variables per clause is a popular testbed for the performance of search algorithms in artificial intelligence and computer science. For k = 2, formulae are almost aways satisfiable when the ratio of clauses to variables is less than 1; for ratios larger than 1, the formulae are almost never satisfiable. We present data showing a similar threshold behavior for higher values of k. We also show how finitesize scaling, a method from statistical physics, can be used to characterize size dependent effects near the threshold. Finally, we comment on the relationship between thresholds and computational complexity. This work was done during a 1993 sabbatical at the Racah Institute of Physics and Center for Neural Computation, Hebrew University, Jerusalem, 91904 Israel. A portion of the work was carried out at the Salk Institute, with support from the McDonnellPew Foundation. Properties of randomly generated combinatoria...
Quantifying landscape spatial pattern: What is the state of the art
 Ecosystems
, 1998
"... Ecosystems is currently published by Springer. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 172 (3 self)
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Ecosystems is currently published by Springer. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Complexity and robustness
 Proceedings of the National Academy of Sciences 99(Suppl
, 2002
"... Highly Optimized Tolerance (HOT) was recently introduced as a conceptual framework to study fundamental aspects of complexity. HOT is motivated primarily by systems from biology and engineering and emphasizes 1) highly structured, nongeneric, selfdissimilar internal configurations and 2) robust, yet ..."
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Cited by 153 (9 self)
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Highly Optimized Tolerance (HOT) was recently introduced as a conceptual framework to study fundamental aspects of complexity. HOT is motivated primarily by systems from biology and engineering and emphasizes 1) highly structured, nongeneric, selfdissimilar internal configurations and 2) robust, yet fragile external behavior. HOT claims these are the most important features of complexity and are not accidents of evolution or artifices of engineering design, but are inevitably intertwined and mutually reinforcing. In the spirit of this collection, our paper contrasts HOT with alternative perspectives on complexity, drawing on both real world examples and also model systems, particularly those from SelfOrganized Criticality (SOC).
Estimating fractal dimension
 Journal of the Optical Society of America A
, 1990
"... Fractals arise from a variety of sources and have been observed in nature and on computer screens. One of the exceptional characteristics of fractals is that they can be described by a noninteger dimension. The geometry of fractals and the mathematics of fractal dimension have provided useful tools ..."
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Cited by 120 (4 self)
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Fractals arise from a variety of sources and have been observed in nature and on computer screens. One of the exceptional characteristics of fractals is that they can be described by a noninteger dimension. The geometry of fractals and the mathematics of fractal dimension have provided useful tools for a variety of scientific disciplines, among which is chaos. Chaotic dynamical systems exhibit trajectories in their phase space that converge to a strange attractor. The fractal dimension of this attractor counts the effective number of degrees of freedom in the dynamical system and thus quantifies its complexity. In recent years, numerical methods have been developed for estimating the dimension directly from the observed behavior of the physical system. The purpose of this paper is to survey briefly the kinds of fractals that appear in scientific research, to discuss the application of fractals to nonlinear dynamical systems, and finally to review more comprehensively the state of the art in numerical methods for estimating the fractal dimension of a strange attractor. Confusion is a word we have invented for an order which is not understood.Henry Miller, "Interlude," Tropic of Capricorn Numerical coincidence is a common path to intellectual perdition in our quest for meaning. We delight in catalogs of disparate items united by the same number, and often feel in our gut that some unity must underlie it all.
Nonequilibrium critical phenomena and phase transitions into absorbing states
 ADVANCES IN PHYSICS
, 2000
"... ..."
Why stock market crash
, 2003
"... The young science of complexity, which studies systems as diverse as the human body, the earth and the universe, offers novel insights on the question raised in the title. The science of complexity explains largescale collective behavior, such as wellfunctioning capitalistic markets, and also pre ..."
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Cited by 107 (13 self)
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The young science of complexity, which studies systems as diverse as the human body, the earth and the universe, offers novel insights on the question raised in the title. The science of complexity explains largescale collective behavior, such as wellfunctioning capitalistic markets, and also predicts that financial crashes and depressions are intrinsic properties resulting from the repeated nonlinear interactions between investors. Applying concepts and methods from complex theory and statistical physics, we have developed mathematical measures to successfully predict the emergence and development of speculative bubbles as well as depressions. This essay attempts to capture and extend the essence of the book with the same title published in January 2003 by Princeton University Press. Recent novelties and live predictions are available at
A community based mobility model for ad hoc network research
 in Proceedings of ACM REALMAN
, 2006
"... Validation of mobile ad hoc network protocols relies almost exclusively on simulation. The value of the validation is, therefore, highly dependent on how realistic the movement models used in the simulations are. Since there is a very limited number of available real traces in the public domain, syn ..."
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Cited by 102 (7 self)
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Validation of mobile ad hoc network protocols relies almost exclusively on simulation. The value of the validation is, therefore, highly dependent on how realistic the movement models used in the simulations are. Since there is a very limited number of available real traces in the public domain, synthetic models for movement pattern generation must be used. However, most widely used models are currently very simplistic, their focus being ease of implementation rather than soundness of foundation. As a consequence, simulation results of protocols are often based on randomly generated movement patterns and, therefore, may differ considerably from those that can be obtained by deploying the system in real scenarios. Movement is strongly affected by the needs of humans to socialise or cooperate, in one form or another. Fortunately, humans are known to associate in particular ways that can be mathematically modelled and that have been studied in social sciences for years. In this paper we propose a new mobility model founded on social network theory. The model allows collections of hosts to be grouped together in a way that is based on social relationships among the individuals. This grouping is then mapped to a topographical space, with movements influenced by the strength of social ties that may also change in time. We have validated our model with real traces by showing that the synthetic mobility traces are a very good approximation of human movement patterns. We have also run simulations of AODV and DSR routing protocols on the mobility model and show how the message delivery ratio is affected by this type of mobility. 1.
The Load, Capacity and Availability of Quorum Systems
, 1998
"... A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is th ..."
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Cited by 100 (12 self)
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A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is the minimal access probability of the busiest element, minimizing over the strategies. The capacity Cap(S) is the highest quorum accesses rate that S can handle, so Cap(S) = 1=L(S).
An Algorithm for Two Dimensional Rigidity Percolation: The Pebble Game
 Journal of Computational Physics
, 1997
"... Many important macroscopic properties of materials depend upon the number of microscopic degrees of freedom. The task of counting the number of such degrees of freedom can be computationally very expensive. We describe a new approach for this calculation which is appropriate for two dimensional, gla ..."
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Cited by 100 (1 self)
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Many important macroscopic properties of materials depend upon the number of microscopic degrees of freedom. The task of counting the number of such degrees of freedom can be computationally very expensive. We describe a new approach for this calculation which is appropriate for two dimensional, glasslike networks, building upon recent work in graph rigidity. This purely combinatorial algorithm is formulated in terms of a simple pebble game. It has allowed for the first studies of the rigidity transition in generic networks, which are models of amorphous materials and glasses. In the context of generic rigidity percolation, we show how to calculate the number of internal degrees of freedom, identify all rigid clusters and locate the overconstrained regions. For a network of n sites the pebble game has a worst case performance of O(n 2 ). In our applications its performance scaled as n 1:15 at the rigidity transition, while away from the transition region it grew linearly. y ja...