Community structure in real-world networks from a non-parametrical synchronization-based dynamical approach

[EN]This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic Rössler oscillators each one characterized by a defined natural frequency, and coupled according to a predefined network topology. The interaction scheme contemplates an uniformly increasing coupling force to simulate a society in which the association between the agents grows in time. To enhance the stability of the correlated states that could emerge from the synchronization process, we propose a parameterless mechanism that adapts the characteristic frequencies of coupled oscillators according to a dynamic connectivity matrix deduced from correlated data. We show that the characteristic frequency vector that results from the adaptation mechanism reveals the underlying community structure present in the network.

The propagation of nerve pulses: From the Hodgkin-Huxley model to the soliton theory

The present project aims to describe and study the nature and transmission of nerve pulses. First we review a classical model by Hodgkin-Huxley which describes the nerve pulse as a pure electric signal which propagates due to the opening of some time- and voltage-dependent ion channels. Although this model was quite successful when introduced, it fails to provide a satisfactory explanation to other phenomena that occur in the transmission of nerve pulses, therefore a new theory seems to be necessary. The soliton theory is one such theory, which we explain after introducing two topics that are important for its understanding: (i) the lipid melting of membranes, which are found to display nonlinearity and dispersion during the melting transition, and (ii) the discovery and the conditions required for the existence of solitons. In the soliton theory, the pulse is presented as an electromechanical soliton which forces the membrane through the transition while propagating. The action of anesthesia is also explained in the new framework by the melting point depression caused by anesthetics. Finally, we present a comparison between the two models.