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Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…
Power-law distributions are widely recognized in complex systems physics as indicative of underlying complexity in interaction networks and critical macroscopic behavior. Previous studies, notably those of Newman and others, have emphasized…
We study noisy majority-rule dynamics on annealed hypergraphs to clarify how variability in group interaction sizes reshapes collective ordering. At each update, a group is sampled from a prescribed size distribution and either follows the…
Most random graph models are locally tree-like - do not contain short cycles - rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the…
We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Egu\'{\i}luz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)].…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…
How does social network structure amplify or stifle behavior diffusion? Existing theory suggests that when social reinforcement makes the adoption of behavior more likely, it should spread more -- both farther and faster -- on clustered…
The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to…
A cluster theory based mathematical model was developed and used to simulate the dynamics of a system composed of a large number of interacting agents-clusters with different size. The case of a system formed by a constant total number of…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own…
We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
Complex systems contain a lot of individuals and some interactions between them. The structure of interactions can be modeled to be a network: nodes represent individuals and links to be interaction between two individuals. This paper tries…
A generic communication model of a boolean network with transmission errors is proposed to explore the power-law scaling of states' evolution in small-world networks. In the model, the power spectrum of the population difference between…
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…