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We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite…
In addition to the well known common properties such as small world and community structures, recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability…
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map…
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
Information spread through social networks is ubiquitous. Influence maximiza- tion (IM) algorithms aim to identify individuals who will generate the greatest spread through the social network if provided with information, and have been…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
In today's world, individuals interact with each other in more complicated patterns than ever. Some individuals engage through online social networks (e.g., Facebook, Twitter), while some communicate only through conventional ways (e.g.,…
We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For…
A model algorithm is proposed to study subsequent partitions of complex networks describing social structures. The partitions are supposed to appear as actions of rivaling leaders corresponding to nodes with large degrees. The condition of…
Understanding the process by which the individuals of a society make up their minds and reach opinions about different issues can be of fundamental importance. In this work we propose an idealized model for competitive cluster growth in…
Human communities have self-organizing properties in which specific Dunbar Numbers may be invoked to explain group attachments. By analyzing Wikipedia editing histories across a wide range of subject pages, we show that there is an emergent…
We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling…
The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…
In this paper, we revisit the problem of influence maximization with fairness, which aims to select k influential nodes to maximise the spread of information in a network, while ensuring that selected sensitive user attributes are fairly…
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…
The traditional approach to the quantitative study of segregation is to employ indices that are selected by ``desirable properties''. Here, we detail how information theory underpins entropy-based indices and demonstrate how desirable…