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Abstract
We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process ...
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Abstract
Conflicting interests among group members are common when making collective decisions, yet failure to achieve consensus can be costly. Under these circumstances individuals may be susceptible to manipulation by a strongly opinionated, or extremist, minority. It has previously been argued, for humans and animals, that social groups containing individuals who are uninformed, or exhibit weak preferences, are particularly vulnerable to such manipulative agents. Here, we use theory and experiment to demonstrate that, for a wide range of conditions, a strongly opinionated ...
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Abstract
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more components or species to vanish. Although there are many random paths to an extinct state, there is an optimal path that maximizes the probability to extinction. In this paper, we ...
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Abstract
Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching. ...
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posted to cooperation economics game-theory
by rincedd
on 2011-11-22 10:34:00
Abstract
This paper proposes a novel framework that generalizes the timing structure of games. Building on alternating move games and models of rational inattention, the players' actions may be rigid, i.e., infrequent. This rigidity in the timing of moves makes the game more dynamic and asynchronous, acting as a commitment mechanism. Therefore, it can enhance cooperation and often eliminate inefficient equilibrium outcomes present in the static (normal form) game. Interestingly, (i) this can happen even in a finite game (possibly as short ...
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In Theoretical neuroscience (2005)
Abstract
Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory. The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of ...
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Abstract
Growth of collateral vessels is potentially able to preserve structure and a variable degree of function in subtended tissues in the presence of arterial occlusions. The process of transformation of a small arteriole into much larger conductance artery is called arteriogenesis. Small arterioles that interconnect side branches proximal from the arterial occlusion with distal ones experience increased fluid shear stress because of the increased blood flow velocity attributable to the pressure gradient along the bridging collaterals. This activates the endothelium and ...
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Abstract
We study the realizability of scale-free networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse. ...
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Abstract
We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters: members of the same cluster share the same opinion but are no longer influenced by members of other clusters. ...
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Abstract
Over the past decade, there has been an explosion of interest in network research across the physical and social sciences. For social scientists, the theory of networks has been a gold mine, yielding explanations for social phenomena in a wide variety of disciplines from psychology to economics. Here, we review the kinds of things that social scientists have tried to explain using social network analysis and provide a nutshell description of the basic assumptions, goals, and explanatory mechanisms prevalent in the ...
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Abstract
We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a stochastic cascade model, we construct the excess kinetic energy as the sum over the energy transfers at different levels of the cascade. We find an asymmetric distribution that strongly resembles the experimental data. The asymmetry is an explicit consequence of intermittency and the global measure is dominated ...
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Abstract
A statistical treatment of three-dimensional turbulent flow continues to pose a challenge to theorists1,2. One suggestion invokes an analogy with equilibrium phase transitions3. Here we approach this idea experimentally, presenting evidence of a strong analogy between the statistical behaviour of a confined turbulent flow andthat of a model of the critical behaviour of a ferromagnet. Both systems experience large fluctuations limited only by the system size. We find that the power consumption measured in turbulent-flow experiments and the magnetization at the ...
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Abstract
We present a mean-field model for the phase diagram of a community of micro-organisms, interacting through their metabolism so that they are, in effect, engaging in a cooperative social game. We show that as a function of the concentration of the nutrients glucose and histidine, the community undergoes a phase transition separating a state in which one strain is dominant to a state which is characterized by coexisting populations. Our results are in good agreement with recent experimental results, correctly reproducing ...
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(07 May 2007)
Abstract
The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, ...
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Abstract
We show that the intelligence of a swarm of cooperative units (birds) emerges at criticality, as an effect of the joint action of frequent organizational collapses and of spatial correlation as extended as the flock size. The organizational collapses make the birds become independent of one another, thereby allowing the flock to follow the direction of the lookout birds. Long-range correlation violates the principle of locality, making the lookout birds transmit information on either danger or resources with a time delay ...
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Abstract
We investigate the formulation of mean-field (MF) approaches for co-evolving dynamic model systems, focusing on the accuracy and validity of different schemes in closing MF equations. Within the context of a recently introduced co-evolutionary snowdrift game in which rational adaptive actions are driven by dissatisfaction in the payoff, we introduce a method to test the validity of closure schemes and analyse the shortcomings of previous schemes. A previous scheme suitable for adaptive epidemic models is shown to be invalid for the ...
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Abstract
The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to scripting the paths of each bird individually. The simulated flock is an elaboration of a particle systems, with the simulated birds being the particles. The aggregate motion of the ...
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Abstract
The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ?functorial? mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through ...
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(23 July 2004)
Abstract
Ideas about social structure and social networks are very old. People have always believed that biological and social links among individuals are important. But it wasn't until the early 1930s that systematic research that explored the patterning of social ties linking individuals emerged. And it emerged, not once, but several times in several different social science fields and in several places. This book reviews these developments and explores the social processes that wove all these "schools" of ...
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Abstract
We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with ...
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Abstract
In order to characterize networks in the scale-free network class we study the frequency of cycles of length h that indicate the ordering of network structure and the multiplicity of paths connecting two nodes. In particular we focus on the scaling of the number of cycles with the system size in off-equilibrium scale-free networks. We observe that each off-equilibrium network model is characterized by a particular scaling in general not equal to the scaling found in equilibrium scale-free networks. We claim ...
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Abstract
In this paper we study the impact of degree correlations in the subgraph statistics of scale-free networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the ...
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Abstract
The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number Nh(t) of loops of size h as a function of the system size. In particular, we have found the analytic expression for the scaling of Nh(t) in the Barabási-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for Nh(t) in the BA network and in other growing scale-free networks, such as the bosonic network and the aging nodes network. We show ...
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Abstract
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free networks valid at fixed number of nodes N and for any length L of the loops. We bring evidence that the most frequent loop size in a scale-free network of N nodes is of the ...
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Abstract
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value pc≈10%, there is a dramatic decrease in the time Tc taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p<pc, Tc~exp[α(p)N], whereas for ...
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Abstract
Social organisms form striking aggregation patterns, displaying cohesion, polarization, and collective intelligence. Determining how they do so in nature is challenging; a plethora of simulation studies displaying life-like swarm behavior lack rigorous comparison with actual data because collecting field data of sufficient quality has been a bottleneck. Here, we bridge this gap by gathering and analyzing a high-quality dataset of flocking surf scoters, forming well-spaced groups of hundreds of individuals on the water surface. By reconstructing each individual's position, velocity, and ...
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Abstract
Similarity breeds connection. This principle—the homophily principle—structures network ties of every type, including marriage, friendship, work, advice, support, information transfer, exchange, comembership, and other types of relationship. The result is that people's personal networks are homogeneous with regard to many sociodemographic, behavioral, and intrapersonal characteristics. Homophily limits people's social worlds in a way that has powerful implications for the information they receive, the attitudes they form, and the interactions they experience. Homophily in race and ethnicity creates the strongest divides in ...
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Abstract
SUMMARYTwo species compete for territory along their mutual boundary. The species are fairly matched and the result of conflict is the invasion by one of the species of territory held by the other. A simple stochastic model for this process is described and rules are given for the calculation, as a function of time, of the probabilities that individual territories and groups of territories are held by a single species. Asymptotic results are given for the pattern of territories held by ...
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Abstract
We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs, i.e., highly connected nodes, in the network modifies the linear system size scaling law ...
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Abstract
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model using a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise- and density-driven order–disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a non-spatial model suggests that spatial geometry may have less of an impact ...
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Abstract
We show that the two-dimensional voter model, usually considered to be only a marginal coarsening system, represents a broad class of models for which phase ordering takes place without surface tension. We argue that voter-like growth is generically observed at order-disorder nonequilibrium transitions solely driven by interfacial noise between dynamically symmetric absorbing states. ...
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Abstract
Based on a signaling process of complex networks, a method for identification of community structure is proposed. For a network with n nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken as the initial signal source to excite the whole network one time. Then the source node is associated with an n-dimensional vector which records the effects of the signaling process. By this process, the topological relationship of nodes on ...
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Abstract
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis. ...
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Abstract
A fast community detection algorithm based on a q-state Potts model is presented. Communities (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overlapping (“fuzzy”) communities and quantifying the association of nodes with multiple communities as well as the robustness ...
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In Reviews of Nonlinear Dynamics and Complexity, Vol. 2 (April 2009)
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Abstract
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of ...
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Abstract
We study the dynamics of the voter and Moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects. For each elementary dynamical step the first node is chosen at random and the second is selected with probability proportional to the weight of the connecting edge. We present a heterogeneous mean-field approach allowing to identify conservation laws and to calculate exit probabilities along with consensus times. In the ...
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(01 July 1998)
Abstract
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph ...
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Abstract
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. In our model there is neither growth of new connections nor growth of new nodes. We start from a well connected network and implement a probabilistic purely depletion procedure. The resulting degree distribution exponent is typically less than two (5/3) as opposed to the case of the growth models studied before where the exponents are larger. We investigate the most important properties characterizing these networks, as ...
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Abstract
The rate of deployment and adoption issues of new network technologies, IPv6 in particular, have recently been hotly debated in the research community. However, the question of how protocols migrate, especially the dynamics of migration, to new paradigms is still largely open. In this paper, we address the issue from a game theoretic point of view. We model and analyze the profit maximizing strategies of Autonomous Systems (ASes); both the properties of ASes and the topology of the Internet is considered. ...
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Abstract
In this paper, we consider asynchronous update scheme for a variant of graph rewriting systems called graph-rewriting automata, and show that synchronous update can be simulated by asynchronous update using a constructed rule set from the one for synchronous update. It is well known that such rule construction is possible on cellular automata or other automata networks whose structures are fixed, but graph rewriting automata induce structural changes and additional mechanism of communication and local synchronization is required. Some simple examples ...
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Abstract
Insights into what stabilizes natural food webs have always been limited by a fundamental dilemma: Studies either need to make unwarranted simplifying assumptions, which undermines their relevance, or only examine few replicates of small food webs, which hampers the robustness of findings. We used generalized modeling to study several billion replicates of food webs with nonlinear interactions and up to 50 species. In this way, first we show that higher variability in link strengths stabilizes food webs only when webs are ...
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Abstract
We analyze the properties of seven community food webs from a variety of environments, including freshwater, marine-freshwater interfaces, and terrestrial environments. We uncover quantitative unifying patterns that describe the properties of the diverse trophic webs considered and suggest that statistical physics concepts such as scaling and universality may be useful in the description of ecosystems. Specifically, we find that several quantities characterizing these diverse food webs obey functional forms that are universal across the different environments considered. The empirical results are ...
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Abstract
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of ...
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Abstract
We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree ...
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Abstract
We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ...
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Abstract
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's dynamics. We also found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this ...
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