Dynamics on complex networks
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Dynamics on complex networks
Investigating how agents influence each other through a coupling network
Curated by Shaolin Tan
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PLoS Computational Biology: Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

PLoS Computational Biology: Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability | Dynamics on complex networks | Scoop.it

Dynamically critical systems are those which operate at the border of a phase transition between two behavioral regimes often present in complex systems: order and disorder. Critical systems exhibit remarkable properties such as fast information processing, collective response to perturbations or the ability to integrate a wide range of external stimuli without saturation. Recent evidence indicates that the genetic networks of living cells are dynamically critical. This has far reaching consequences, for it is at criticality that living organisms can tolerate a wide range of external fluctuations without changing the functionality of their phenotypes. Therefore, it is necessary to know how genetic criticality emerged through evolution. Here we show that dynamical criticality naturally emerges from the delicate balance between two fundamental forces of natural selection that make organisms evolve: (i) the existing phenotypes must be resilient to random mutations, and (ii) new phenotypes must emerge for the organisms to adapt to new environmental challenges. The joint effect of these two forces, which are essential for evolvability, is sufficient in our computational models to generate populations of genetic networks operating at criticality. Thus, natural selection acting as a tinkerer of evolvable systems naturally generates critical dynamics.

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Ecological Populations of Bacteria Act as Socially Cohesive Units of Antibiotic Production and Resistance

Cooperation among individuals of the same population directed against competing populations (cooperative warfare) is widespread in animals and plants. What happens in the microbial world is much less understood. Microbes can interact with one another through chemical signals, but little is known about the nature of their interactions, particularly outside the laboratory. On page 1228 of this issue, Cordero et al. (1) present a detailed analysis of ecological interaction networks, population structures, and genetic relatedness of microbes in the wild. They suggest that cooperative warfare is common in the microbial world.

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Evolutionary shift dynamics on a cycle

Evolutionary shift dynamics on a cycle | Dynamics on complex networks | Scoop.it

We present a new model of evolutionary dynamics in one-dimensional space. Individuals are arranged on a cycle. When a new offspring is born, another individual dies and the rest shift around the cycle to make room. This rule, which is inspired by spatial evolution in somatic tissue and microbial colonies, has the remarkable property that, in the limit of large population size, evolution acts to maximize the payoff of the whole population. Therefore, social dilemmas, in which some individuals benefit at the expense of others, are resolved. We demonstrate this principle for both discrete and continuous games. We also discuss extensions of our model to other one-dimensional spatial configurations. We conclude that shift dynamics in one dimension is an unusually strong promoter of cooperative behavior.


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Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead to high levels of cooperation. Instead we observe perpetual oscillations between cooperation and defection, with defection being substantially more frequent than cooperation. The reason for this is that “indirect invasions” remove equilibrium strategies: every strategy has neutral mutants, which in turn can be invaded by other strategies. However, reciprocity is not the only way to promote cooperation. Another mechanism for the evolution of cooperation, which has received as much attention, is assortment because of population structure. Here we develop a theory that allows us to study the synergistic interaction between direct reciprocity and assortment. This framework is particularly well suited for understanding human interactions, which are typically repeated and occur in relatively fluid but not unstructured populations. We show that if repeated games are combined with only a small amount of assortment, then natural selection favors the behavior typically observed among humans: high levels of cooperation implemented using conditional strategies.

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Long-Range Navigation on Complex Networks using Lévy Random Walks

We introduce a new strategy of navigation in undirected networks, including regular, random and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time and the average time to reach a node on the network. We found that the long-range navigation using the L\'evy random walk strategy, in comparison with the normal random walk strategy, is more efficient to reduce the time to cover the network. The dynamical effect of using the L\'evy walk strategy is to transform a large-world network into a small world. Our exact results provide a general framework that connects two important fields: L\'evy navigation strategies and dynamics in complex networks.

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Online Social Networks can be Tipped by as Little as 0.8% of their Population | The Central Node

In a "tipping" model, each node in a social network, representing an individual, adopts a behavior if a certain number of his incoming neighbors previously held that property. A key problem for viral marketers is to determine an initial "seed" set in a network such that if given a property then the entire network adopts the behavior. Here we introduce a method for quickly finding seed sets that scales to very large networks. Our approach finds a set of nodes that guarantees spreading to the entire network under the tipping model. After experimentally evaluating 31 real-world networks, we found that our approach often finds such sets that are several orders of magnitude smaller than the population size. Our approach also scales well - on a Friendster social network consisting of 5.6 million nodes and 28 million edges we found a seed sets in under 3.6 hours. We also find that highly clustered local neighborhoods and dense network-wide community structure together suppress the ability of a trend to spread under the tipping model.

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Science Magazine: Sign In

Although people often tend to consider themselves and others as unique individuals, there are many situations in which they think, feel, and act primarily as group members. This can bring out the best in them, as when they are inspired to help fellow citizens in need, or the worst, as when they show hostility against others simply because they represent another religious or ethnic group. Understanding when and why the group self becomes more important than the individual self, and how this affects people’s thoughts, feelings, and behaviors, can help to prevent and redirect unwelcome aspects of human behavior by addressing them at the appropriate level of self

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It's the network!

A new article by a Northwestern University complex networks expert discusses how networks governing processes in nature and society are becoming increasingly amenable to modeling, forecast and control.
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PLoS Computational Biology: The Impact of Imitation on Vaccination Behavior in Social Contact Networks

PLoS Computational Biology: The Impact of Imitation on Vaccination Behavior in Social Contact Networks | Dynamics on complex networks | Scoop.it

Both infectious diseases and behavioral traits can spread via social contacts. Using network-based mathematical models, our study addresses the interplay between these two processes, as disease spreads through a population and individuals copy their social contacts when making vaccination decisions. Imitation can produce clusters of non-vaccinating, susceptible individuals that facilitate relatively large outbreaks of infectious diseases despite high overall vaccination coverage. This may explain, for example, recent measles outbreaks observed in many countries with universal measles vaccination policies. Given that vaccine decisions are likely to be influenced by social contacts and that such imitation can have detrimental epidemiological effects, it is important that policy makers understand its causes, magnitude and implications for disease eradication.

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If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation : Scientific Reports : Nature Publishing Group

If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation : Scientific Reports : Nature Publishing Group | Dynamics on complex networks | Scoop.it
Spatial reciprocity is a well known tour de force of cooperation promotion. A thorough understanding of the effects of different population densities is therefore crucial.
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The Structure of Mutations and the Evolution of Cooperation

The Structure of Mutations and the Evolution of Cooperation | Dynamics on complex networks | Scoop.it

Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are n strategies a single mutation can result in any strategy with probability 1/n . However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoner's dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the “model-less” approach to mutations in evolutionary dynamics.


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A model balancing cooperation and competition can explain our right-handed world and the dominance of left-handed athletes

An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here, we present a novel mathematical model and use it to test the idea that population-level hand preference represents a balance between selective costs and benefits arising from cooperation and competition in human evolutionary history. We use the selection of elite athletes as a test-bed for our evolutionary model and find evidence for the validity of this idea. Our model gives the first quantitative explanation for the distribution of handedness both across and within many professional sports. It also predicts strong lateralization of hand use in social species with limited combative interaction, and elucidates the absence of consistent population-level ‘pawedness’ in some animal species.


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An analysis of fixation probability of a mutant on class of weighted networks under neutral selection - RMIT Research Repository

An analysis of fixation probability of a mutant on class of weighted networks under neutral selection - RMIT Research Repository | Dynamics on complex networks | Scoop.it

Recently, evolutionary dynamics on structured population has attracted an increasing attention in various fields. This paper aims at investigating the fixation probability of a mutant under random drift on a class of weighted networks. In particular, we have attained the analytical solutions of fixation probability of mutants on the weighted networks with three different updating rules, including link dynamics, Moran process, and voter model. It should be especially pointed out that the above analytical solutions can be used to further understand and control the evolution processes. Numerical simulations are also given to validate the above analytical solutions.

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The automatic chemist

The automatic chemist | Dynamics on complex networks | Scoop.it

Bartosz Grzybowski of Northwestern University in Illinois, US – who has already established himself as one of our most inventive chemists – has unveiled a ‘chemo-informatic’ scheme, Chematica, that can stake a reasonable claim to being paradigm-changing. Grzybowski and his colleagues have spent years assembling the transformations that link chemical species into a vast network that codifies and organises the known pathways through chemical space. The nodes of the network – molecules, elements and chemical reactions – are linked together by connecting reactants to products via the nexus of a known reaction. The full network contains around 7 million compound nodes and about the same number of reaction nodes. Grzybowski calls it a ‘collective chemical brain’.

 

The automatic chemist
Philip Ball

Chemistry World 22 August 2012

http://www.rsc.org/chemistryworld/2012/08/automatic-chemist


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Exploring evolutionary dynamics in a class of structured populations

Exploring evolutionary dynamics in a class of structured populations | Dynamics on complex networks | Scoop.it

It is well known that the selection of fixation probability is the fundamental problem for the evolutionary dynamics in structured populations. This paper aims to introduce a general approach for investigating the evolutionary dynamics in a class of structured populations. It includes the evolutionary game dynamics and constant selection dynamics with different asynchronous updating rules, such as ‘birth-death’, ‘voter model’, ‘death-birth’, and ‘imitation’. It should be pointed out that the proposed method provides an effective way to resolve the evolutionary dynamics on general graphs. In particular, it introduces a useful calculating tool to analyze various evolutionary dynamics on small order graphs.

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PLoS ONE: Dynamics of Opinion Forming in Structurally Balanced Social Networks

PLoS ONE: Dynamics of Opinion Forming in Structurally Balanced Social Networks | Dynamics on complex networks | Scoop.it

A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.

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Identifying Influential and Susceptible Members of Social Networks

Identifying social influence in networks is critical to understanding how behaviors spread. We present a method for identifying influence and susceptibility in networks that avoids biases in traditional estimates of social contagion by leveraging in vivo randomized experimentation. Estimation in a representative sample of 1.3 million Facebook users showed that younger users are more susceptible than older users, men are more influential than women, women influence men more than they influence other women, and married individuals are the least susceptible to influence in the decision to adopt the product we studied. Analysis of influence and susceptibility together with network structure reveals that influential individuals are less susceptible to influence than non-influential individuals and that they cluster in the network, which suggests that influential people with influential friends help spread this product.

 

Identifying Influential and Susceptible Members of Social Networks
Sinan Aral, Dylan Walker

Science http://dx.doi.org/10.1126/science.1215842


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Information Diffusion and External Influence in Networks

Social networks play a fundamental role in the diffusion of information. However, there are two different ways of how information reaches a person in a network. Information reaches us through connections in our social networks, as well as through the influence of external out-of-network sources, like the mainstream media. While most present models of information adoption in networks assume information only passes from a node to node via the edges of the underlying network, the recent availability of massive online social media data allows us to study this process in more detail. We present a model in which information can reach a node via the links of the social network or through the influence of external sources.

 

Information Diffusion and External Influence in Networks

Seth A. Myers, Chenguang Zhu, Jure Leskovec

http://arxiv.org/abs/1206.1331


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Networks thrive in complexity | Harold Jarche

Networks thrive in complexity | Harold Jarche | Dynamics on complex networks | Scoop.it

In complex environments, weak hierarchies and strong networks are the best organizing principle. One good example of complexity that we can try to fathom is nature itself. Networks thrive in nature. As Howard Bloom stated in a speech at Yale University.

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[1205.4282] The relationship between structure and function in complex networks observed locally

The study of complex networks has drawn much attention over the last years, mainly by virtue of its potential to characterize the most diverse systems through unified mathematical and computational tools. Not long ago the emphasis on this field mostly focused on the effects of the structural properties on the global behavior of a dynamical process taking place in the system. Recently, some studies started to unveil the richness of interactions that occur between groups of nodes when we look at the small scale of interactions occurring in the network. Such findings call for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we present a first step towards this direction, in which we define a new measurement that, based on dynamical characteristics obtained for a large set of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measurement we find the high capacity of networks, generated by the geographic and Barab\'asi-Albert models, to exhibit groups of nodes with distinct dynamics compared to the rest of the network. We also present a practical application of the methodology by using the neuronal network of the nematode \emph{Caenorhabditis elegans}, where we show that the interneurons of the ventral cord presents a very large dynamical differentiation when compared to the rest of the network

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Universal features of correlated bursty behaviour

Universal features of correlated bursty behaviour | Dynamics on complex networks | Scoop.it

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution for a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems.

 

Universal features of correlated bursty behaviour

Márton Karsai, Kimmo Kaski, Albert-László Barabási & János Kertész

Scientific Reports 2, Article number: 397 http://dx.doi.org/10.1038/srep00397


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The organization of strong links in complex networks

The organization of strong links in complex networks | Dynamics on complex networks | Scoop.it

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

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Competing activation mechanisms in epidemics on networks : Scientific Reports : Nature Publishing Group

Competing activation mechanisms in epidemics on networks : Scientific Reports : Nature Publishing Group | Dynamics on complex networks | Scoop.it

In contrast to previous common wisdom that epidemic activity in heterogeneous networks is dominated by the hubs with the largest number of connections, recent research has pointed out the role that the innermost, dense core of the network plays in sustaining epidemic processes

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Sexual selection enables long-term coexistence despite ecological equivalence

Empirical data indicate that sexual preferences are critical for maintaining species boundaries, yet theoretical work has suggested that, on their own, they can have only a minimal role in maintaining biodiversity. This is because long-term coexistence within overlapping ranges is thought to be unlikely in the absence of ecological differentiation9. Here we challenge this widely held view by generalizing a standard model of sexual selection to include two ubiquitous features of populations with sexual selection: spatial variation in local carrying capacity, and mate-search costs in females.

 

Sexual selection enables long-term coexistence despite ecological equivalence

Leithen K. M’Gonigle, Rupert Mazzucco, Sarah P. Otto & Ulf Dieckmann
Nature 484, 506–509 (26 April 2012) http://dx.doi.org/10.1038/nature10971


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Different Reactions to Adverse Neighborhoods in Games of Cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods.

 

Zhang C, Zhang J, Weissing FJ, Perc M, Xie G, et al. (2012) Different Reactions to Adverse Neighborhoods in Games of Cooperation. PLoS ONE 7(4): e35183. http://dx.doi.org/10.1371/journal.pone.0035183


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