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47
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 1959 (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
Traffic and related selfdriven manyparticle systems
, 2000
"... Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? ..."
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Cited by 312 (40 self)
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Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? What are the mechanisms behind stopandgo traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ‘‘freeze by heating’’? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to selfdriven manyparticle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particlebased), mesoscopic (gaskinetic), and macroscopic (fluiddynamic) models. Attention is also paid to the formulation of a micromacro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for selfdriven manyparticle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socioeconomic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.
Universality classes in nonequilibrium lattice systems
, 2003
"... This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second se ..."
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Cited by 36 (0 self)
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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section
A Percolation Model of Innovation in Complex Technology Spaces
, 2002
"... Innovations are known to arrive more highly clustered than if they were purely random, and their rate of arrival has been increasing nearly exponentially for several centuries. Their distribution of importance is highly skewed and appears to obey a power law or lognormal distribution. Technological ..."
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Cited by 15 (1 self)
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Innovations are known to arrive more highly clustered than if they were purely random, and their rate of arrival has been increasing nearly exponentially for several centuries. Their distribution of importance is highly skewed and appears to obey a power law or lognormal distribution. Technological change has been seen by many scholars as following technological trajectories and being subject to ‘paradigm ’ shifts from time to time. To address these empirical observations, we introduce a complex technology space based on percolation theory. This space is searched randomly in local neighborhoods of the current bestpractice frontier. Numerical simulations demonstrate that with increasing radius of search, the probability of becoming deadlocked declines and the mean rate of innovation increases until a plateau is reached. The distribution of innovation sizes is highly skewed and heavy tailed. For percolation probabilities near the critical value, it seems to resemble an infinitevariance Pareto distribution in the tails. For higher values, the lognormal appears to be preferred.
Evolution of random networks
 Advances in Physics
, 2002
"... We review a recent fast progress in statistical physics of evolving networks. Interest focuses mainly on the structure properties of random hierarchically organized networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind were created r ..."
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Cited by 7 (0 self)
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We review a recent fast progress in statistical physics of evolving networks. Interest focuses mainly on the structure properties of random hierarchically organized networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind were created recently. This opens a wide field for research of their topology, evolution, and complex processes proceeding in them. Such networks possess a rich set of scaling properties. A number of them is scalefree and show striking resilience against random breakdowns. In spite of huge sizes of these networks, the distances between most of nodes of the networks are short – the “smallworld” effect. Their features make them appropriate for numerous applications. We discuss how growing networks selforganize into scalefree structure and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in networks. We present a number of models demonstrating the main features of evolving networks and discuss existing approaches to their simulation and analytical study. Applications of the general results to the particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of nonequilibrium physics, econophysics,
Counting lattice animals: a parallel attack
 Journal of Statistical Physics
, 1992
"... A parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented. The algorithm has been implemented on 17 RISCbased workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersize s = 21. New data for perimeter polynomi ..."
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A parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented. The algorithm has been implemented on 17 RISCbased workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersize s = 21. New data for perimeter polynomials D s up to D21, total number of clusters gs up to g22, and coefficients b ~ in the lowdensity series expansion of the mean cluster size up to b21 are given.
Measures of critical exponents in the fourdimensional site percolation
"... Using finitesize scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also obtain the leading correctionstoscaling exponent and, with great ..."
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Using finitesize scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also obtain the leading correctionstoscaling exponent and, with great accuracy, the critical density.
Lattice animals: A fast enumeration algorithm and new perimeter polynomials
 J. STAT. PHYS
, 1990
"... A fast computer algorithm for enumerating isolated connected clusters on a regular lattice and its Fortran implementation are presented. New perimeter polynomials are calculated for the square, the triangular, the simple cubic, and the square lattice with next nearest neighbors. ..."
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Cited by 6 (1 self)
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A fast computer algorithm for enumerating isolated connected clusters on a regular lattice and its Fortran implementation are presented. New perimeter polynomials are calculated for the square, the triangular, the simple cubic, and the square lattice with next nearest neighbors.
Review Piezoresistive Strain Sensors Made from Carbon Nanotubes Based Polymer Nanocomposites
, 2011
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MITCTP3331 From boom to bust and back again: the complex dynamics of trends and fashions
, 2008
"... Social trends or fashions are spontaneous collective decisions made by large portions of a community, often without an apparent good reason. The spontaneous formation of trends provides a well documented mechanism for the spread of information across a population, the creation of culture and the sel ..."
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Cited by 2 (1 self)
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Social trends or fashions are spontaneous collective decisions made by large portions of a community, often without an apparent good reason. The spontaneous formation of trends provides a well documented mechanism for the spread of information across a population, the creation of culture and the selfregulation of social behavior. Here I introduce an agent based dynamical model that captures the essence of trend formation and collapse. The resulting population dynamics alternates states of great diversity (large configurational entropy) with the dominance by a few trends. This behavior displays a kind of selforganized criticality, measurable through cumulants analogous to those used to study percolation. I also analyze the robustness of trend dynamics subject to external influences, such as population growth or contraction and in the presence of explicit information biases. The resulting population response gives insights about the fragility of public opinion in specific circumstances and suggests how it may be driven to produce social consensus or dissonance.