We present a novel, general construction to abstractly interpret higher-order automatic differentiation (AD). Our construction allows one to instantiate an abstract interpreter for computing derivatives up to a chosen order. Furthermore, since our construction reduces the problem of abstractly reasoning about derivatives to abstractly reasoning about real-valued straight-line programs, it can be instantiated with almost any numerical abstract domain, both relational and non-relational. We formally establish the soundness of this construction. We implement our technique by instantiating our construction with both the non-relational interval domain and the relational zonotope domain to compute both first and higher-order derivatives. In the latter case, we are the first to apply a relational domain to automatic differentiation for abstracting higher-order derivatives, and hence we are also the first abstract interpretation work to track correlations across not only different variables, but different orders of derivatives. We evaluate these instantiations on multiple case studies, namely robustly explaining a neural network and more precisely computing a neural network’s Lipschitz constant. For robust interpretation, first and second derivatives computed via zonotope AD are up to 4.76× and 6.98× more precise, respectively, compared to interval AD. For Lipschitz certification, we obtain bounds that are up to 11,850× more precise with zonotopes, compared to the state-of-the-art interval-based tool.

In vehicular ad-hoc networks, physical parameters of traffic flow (traffic density and velocities), directly relate to networking parameters (node degree and duration of communication). While existing research on these relations has mainly focused on simulative work or on the free-flow regime of traffic, we discuss these relations for both free-flow and congested traffic and provide an analytical framework for the computation of relevant networking parameters. We also discuss some results and analyze their impact on vehicular communications.

The ongoing process of globalization leads to a huge demand for highly scalable applications that are able to deal with millions of participants distributed all over the world. Peer-to-peer (P2P) technology enables an arbitrary large number of users to participate in distributed services like content distribution or collaboration tools. In order to verify a new protocol's performance and scalability simulation is a commonly used tool. First, predicting the network and peer behavior in the real world is only feasible if the simulation, i.e. all applied models as well as the peer state, is as realistic as possible. Second, many properties of the system only become observable when the number of participants is sufficiently large. Therefore, verifying the scalability of a system requires simulating huge worldwide networks. Due to limited processing power, central memory and availabe time, both requirements can only be fullfilled if the applied models are very efficient. In this paper we take a closer look at the network layer. We compare the most commonly-used network models and present a very efficient model for applying real-world network transmission times in large scale simulations