Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems

Improving files availability for BitTorrent using a diffusion model

The BitTorrent mechanism effectively spreads file fragments by copying the rarest fragments first. We propose to apply a mathematical model for the diffusion of fragments on a P2P in order to take into account both the effects of peer distances and the changing availability of peers while time goes on. Moreover, we manage to provide a forecast on the availability of a torrent thanks to a neural network that models the behaviour of peers on the P2P system. The combination of the mathematical model and the neural network provides a solution for choosing file fragments that need to be copied first, in order to ensure their continuous availability, counteracting possible disconnections by some peers