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Register a new userMutual selection in network evolution: the role of the intrinsic fitness
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We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, a vertex $i$ is assigned a fitness $x_i$, drawn from a given probability distribution function $f(x)$. During network evolution, with rate $p$ we add a vertex $j$ of fitness $x_j$ and connect to an existing vertex $i$ of fitness $x_i$ selected preferentially to a linking probability function $g(x_i,x_j)$ which depends on the fitnesses of the two vertices involved and, with rate $1-p$ we create an edge between two already existed vertices with fitnesses $x_i$ and $x_j$, with a probability also preferential to the connection function $g(x_i,x_j)$. For the proper choice of $g$, the resulting networks have generalized power laws, irrespective of the fitness distribution of vertices.
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Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) sim k^{-1}$ and $C sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resilience with an error of 5%.
In this paper we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving social network where agents are made to interact, possibly update their beliefs and modify the social relationships according to the opinion exchange.
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $mu_N$, and each beneficial mutation increases the individuals fitness by $s_N$. Each individual dies at rate one, and when a death occurs, an individual is chosen with probability proportional to the individuals fitness to give birth. Under certain conditions on the parameters $mu_N$ and $s_N$, we obtain rigorous results for the rate at which mutations accumulate in the population and the distribution of the fitnesses of individuals in the population at a given time. Our results confirm predictions of Desai and Fisher (2007).
We discuss two different ways of chromosomes and genomes evolution. Purifying selection dominates in large panmictic populations, where Mendelian law of independent gene assortment is valid. If the populations are small, recombination processes are not effective enough to ensure an independent assortment of linked genes and larger clusters of genes could be inherited as the genetic units. There are whole clusters of genes which tend to complement in such conditions instead of single pairs of alleles like in the case of purifying selection. Computer simulations have shown that switching in-between complementation and purification strategies has a character of a phase transition. This is also responsible for specific distribution of recombination events observed along eukaryotic chromosomes - higher recombination rate is observed in subtelomeric regions than in central parts of chromosomes - for sympatric speciation and probably for non-monotonous relation between reproduction potential and genetic distance between parents.
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