6 research outputs found
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 in random networks, and find a scaling law
which relates 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.