Optimal learning paths in information networks.

Each sphere of knowledge and information could be depicted as a complex mesh of correlated items. By properly exploiting these connections, innovative and more efficient navigation strategies could be defined, possibly leading to a faster learning process and an enduring retention of information. In this work we investigate how the topological structure embedding the items to be learned can affect the efficiency of the learning dynamics. To this end we introduce a general class of algorithms that simulate the exploration of knowledge/information networks standing on well-established findings on educational scheduling, namely the spacing and lag effects. While constructing their learning schedules, individuals move along connections, periodically revisiting some concepts, and sometimes jumping on very distant ones. In order to investigate the effect of networked information structures on the proposed learning dynamics we focused both on synthetic and real-world graphs such as subsections of Wikipedia and word-association graphs. We highlight the existence of optimal topological structures for the simulated learning dynamics whose efficiency is affected by the balance between hubs and the least connected items. Interestingly, the real-world graphs we considered lead naturally to almost optimal learning performances.

The dynamics of correlated novelties.

Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called "expanding the adjacent possible". The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose a simple mathematical model that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs. The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (Heaps' law) and for the probability distribution on the space explored (Zipf's law), as well as signatures of the process by which one novelty sets the stage for another. We test these predictions on four data sets of human activity: the edit events of Wikipedia pages, the emergence of tags in annotation systems, the sequence of words in texts, and listening to new songs in online music catalogues. By quantifying the dynamics of correlated novelties, our results provide a starting point for a deeper understanding of the adjacent possible and its role in biological, cultural, and technological evolution.

Structural disorder and anomalous diffusion in random packing of spheres.

Nowadays Nuclear Magnetic Resonance diffusion (dNMR) measurements of water molecules in heterogeneous systems have broad applications in material science, biophysics and medicine. Up to now, microstructural rearrangement in media has been experimentally investigated by studying the diffusion coefficient (D(t)) behavior in the tortuosity limit. However, this method is not able to describe structural disorder and transitions in complex systems. Here we show that, according to the continuous time random walk framework, the dNMR measurable parameter α, quantifying the anomalous regime of D(t), provides a quantitative characterization of structural disorder and structural transition in heterogeneous systems. To demonstrate this, we compare α measurements obtained in random packed monodisperse micro-spheres with Molecular Dynamics simulations of disordered porous media and 3D Monte Carlo simulation of particles diffusion in these kind of systems. Experimental results agree well with simulations that correlate the most used parameters and functions characterizing the disorder in porous media.

Preferential attachment in the growth of social networks: the internet encyclopedia Wikipedia.

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.