In a bipartite rating network, edges represent reviews of products purchased by consumers and are weighted by the numerical score received (i.e. Amazon review system). We provide theoretical tools for their analysis extending the procedure in [1, 2, 3]. Given an observed rating network, its random counterpart is given by a gran canonical ensemble of graphs, which probability distribution is defined maximising the entropy over a set of constraints per node, i.e. the observed degree for each possible score (Bipartite Score Configuration Model, BiSCM).
Other applications of Complex Systems
In this work we take advantage of the availability of Twitter data gathered during two electoral campaigns  that are very close in time (the Spanish general elections held on the 20th of December 2015 and the repetition of the elections on the 26th of July 2016) to compare the collective user behavior manifested in two analogous social systems with a similar context. Our objective is to study and characterize emergent behaviors that are recurrently manifested in political contexts.
The dynamics of teams can be investigated by agent based modelling where team behaviour emerges from the actions and interactions of individual team members as autonomous agents. Let xi be an individual agent with state st(xi) at time t. Let the set y = <x1, …, xn> be the set of agents in the team. Let st(y) be the state of the team at time t. Let the changes in state st1(xi) → st2(xi) and st1(y) → st2(y) be called events. et2t1(xi) = st2(xi) – st1(xi) is Level-1 event and et2t1(y) = st2(yj) – st1(yj) is Level-2 event.
The growing importance of citation-based bibliometric indicators in shaping the prospects of academic careers incentivizes scientists to boost the numbers of citations they receive. Whereas the exploitation of self-citations has been extensively documented, “higher order” manipulation strategies of bibliometric indicators have not yet been studied.
Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors.