A guide to time-resolved and parameter-free measures of spike train synchrony

Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain analytic expressions for the expectation values of the ISI-distance and SPIKE-Synchronization for Poisson spike trains. For the SPIKE-distance we present an empirical formula deduced from numerical evaluations. These expectation values are crucial for interpreting the synchronization of spike trains measured in experiments or numerical simulations, as they represent the point of reference for fully randomized spike trains.Comment: 8 pages, 4 figure

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

Global synchronization algorithms for the Intel iPSC/860

In a distributed memory multicomputer that has no global clock, global processor synchronization can only be achieved through software. Global synchronization algorithms are used in tridiagonal systems solvers, CFD codes, sequence comparison algorithms, and sorting algorithms. They are also useful for event simulation, debugging, and for solving mutual exclusion problems. For the Intel iPSC/860 in particular, global synchronization can be used to ensure the most effective use of the communication network for operations such as the shift, where each processor in a one-dimensional array or ring concurrently sends a message to its right (or left) neighbor. Three global synchronization algorithms are considered for the iPSC/860: the gysnc() primitive provided by Intel, the PICL primitive sync0(), and a new recursive doubling synchronization (RDS) algorithm. The performance of these algorithms is compared to the performance predicted by communication models of both the long and forced message protocols. Measurements of the cost of shift operations preceded by global synchronization show that the RDS algorithm always synchronizes the nodes more precisely and costs only slightly more than the other two algorithms