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.

Dynamically correlated mutations drive human Influenza A evolution.

Human Influenza A virus undergoes recurrent changes in the hemagglutinin (HA) surface protein, primarily involved in the human antibody recognition. Relevant antigenic changes, enabling the virus to evade host immune response, have been recognized to occur in parallel to multiple mutations at antigenic sites in HA. Yet, the role of correlated mutations (epistasis) in driving the molecular evolution of the virus still represents a challenging puzzle. Further, though circulation at a global geographic level is key for the survival of Influenza A, its role in shaping the viral phylodynamics remains largely unexplored. Here we show, through a sequence based epidemiological model, that epistatic effects between amino acids substitutions, coupled with a reservoir that mimics worldwide circulating viruses, are key determinants that drive human Influenza A evolution. Our approach explains all the up-to-date observations characterizing the evolution of H3N2 subtype, including phylogenetic properties, nucleotide fixation patterns, and composition of antigenic clusters.