Synchronization, Diversity, and Topology of Networks of Integrate and Fire Oscillators

We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention in the interplay between networks topological disorder and its synchronization features. Firstly, we analyze synchronization time $T$ in random networks, and find a scaling law which relates $T$ to networks connectivity. Then, we carry on comparing synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than any other disordered network. The fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to have a non-random topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.Comment: 6 pages, 8 figures, LaTeX 209, uses RevTe

On pseudorandom generators in NC 0

Abstract. In this paper we consider the question of whether NC 0 circuits can generate pseudorandom distributions. While we leave the general question unanswered, we show • Generators computed by NC 0 circuits where each output bit depends on at most 3 input bits (i.e, NC 0 3 circuits) and with stretch factor greater than 4 are not pseudorandom. • A large class of “non-problematic ” NC 0 generators with superlinear stretch (including all NC 0 3 generators with superlinear stretch) are broken by a statistical test based on a linear dependency test combined with a pairwise independence test. • There is an NC 0 4 generator with a super-linear stretch that passes the linear dependency test as well as k-wise independence tests, for any constant k.