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Approximating evolutionary dynamics on networks using a Neighbourhood Configuration model
Evolutionary dynamics have been traditionally studied on homogeneously mixed and infinitely large populations. However, real populations are usually finite and characterised by complex interactions among individuals. Recent studies have shown that the outcome of the evolutionary process might be significantly affected by the population structure. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. In this paper, we adopt an approximation method which has been recently used for the modelling of infectious disease transmission, to model evolutionary game dynamics on complex networks. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the process and the improved accuracy that it provides when, for example, compared to well-known pair approximation methods. This modelling framework offers a flexible way to carry out a systematic analysis of evolutionary game dynamics on graphs and to establish the link between network topology and potential system behaviours. As an example, we investigate how the Hawk and Dove strategies in a Hawk-Dove game spread in a population represented by a random regular graph, a random graph and a scale-free network, and we examine the features of the graph which affect the evolution of the population in this particular game
Power-law weighted networks from local attachments
This letter introduces a mechanism for constructing, through a process of
distributed decision-making, substrates for the study of collective dynamics on
extended power-law weighted networks with both a desired scaling exponent and a
fixed clustering coefficient. The analytical results show that the connectivity
distribution converges to the scaling behavior often found in social and
engineering systems. To illustrate the approach of the proposed framework we
generate network substrates that resemble steady state properties of the
empirical citation distributions of (i) publications indexed by the Institute
for Scientific Information from 1981 to 1997; (ii) patents granted by the U.S.
Patent and Trademark Office from 1975 to 1999; and (iii) opinions written by
the Supreme Court and the cases they cite from 1754 to 2002.Comment: 18 pages, 3 figures; Proceedings of the IEEE Conference on Decision
and Control and the European Control Conference, Orlando, FL, Dec. 2011;
Added references; We modified the model in order to take into account
extended power-law distributions which better fit to the citations data sets;
Added proofs of theorems; Shorten version; Updated plo
A Network Model characterized by a Latent Attribute Structure with Competition
The quest for a model that is able to explain, describe, analyze and simulate
real-world complex networks is of uttermost practical as well as theoretical
interest. In this paper we introduce and study a network model that is based on
a latent attribute structure: each node is characterized by a number of
features and the probability of the existence of an edge between two nodes
depends on the features they share. Features are chosen according to a process
of Indian-Buffet type but with an additional random "fitness" parameter
attached to each node, that determines its ability to transmit its own features
to other nodes. As a consequence, a node's connectivity does not depend on its
age alone, so also "young" nodes are able to compete and succeed in acquiring
links. One of the advantages of our model for the latent bipartite
"node-attribute" network is that it depends on few parameters with a
straightforward interpretation. We provide some theoretical, as well
experimental, results regarding the power-law behaviour of the model and the
estimation of the parameters. By experimental data, we also show how the
proposed model for the attribute structure naturally captures most local and
global properties (e.g., degree distributions, connectivity and distance
distributions) real networks exhibit. keyword: Complex network, social network,
attribute matrix, Indian Buffet processComment: 34 pages, second version (date of the first version: July, 2014).
Submitte
From innovation to diversification: a simple competitive model
Few attempts have been proposed in order to describe the statistical features
and historical evolution of the export bipartite matrix countries/products. An
important standpoint is the introduction of a products network, namely a
hierarchical forest of products that models the formation and the evolution of
commodities. In the present article, we propose a simple dynamical model where
countries compete with each other to acquire the ability to produce and export
new products. Countries will have two possibilities to expand their export:
innovating, i.e. introducing new goods, namely new nodes in the product
networks, or copying the productive process of others, i.e. occupying a node
already present in the same network. In this way, the topology of the products
network and the country-product matrix evolve simultaneously, driven by the
countries push toward innovation.Comment: 8 figures, 8 table
Causal connectivity of evolved neural networks during behavior
To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics
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