Guillermo Cecchi

Computational Biology Center, IBM

 The local structure of biological and man-made complex systems can be studied by enumerating network motifs. Since searching for large size arbitrary motifs is cumbersome, we limit our focus on cycles and utilize a parallelized program to search for large-size cycles and characterize their statistical properties in different networks. Studying biological complex systems and man-made complex systems abstracted to directed networks, we will show that the statistics of directional correlations (i.e. links coming in and out of each node) can be captured by a simple physical model, a Pott's spin system. Most of the networks display strong negative correlations in the directions of links along cycles, and are locally described as ``anti-ferromagnets'', i.e. nodes tend to be either sources of sinks of directional links. However, this negative correlation is determined not only by local properties, but also by global ones, as architectural randomizations tend to be more positively correlated than the original networks. We will also present an evolutive algorithm that recreates most of these novel topological properties, along with traditional ones, and emphasizes the interplay of local and global interactions in the determination of directionality. Finally, we will show that this particular topological feature has a dramatic impact on the dynamics of the networks, as it tends to minimize dynamical interference of signals reverberating across nodes, and in particular significantly reduces the number of feedback loops.