10 research outputs found
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio
Rough Paths based Numerical Algorithms in Computational Finance.
The paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probably earlier, is based on locally deriving and solving random ordinary differential equations. A sufficient condition on the accuracy of the numerical ODE solver is given to ensure the global order is g1/2 if the local order is g. We also point out some practical solutions which make the high order schemes tractable