The index of differential-algebraic equations is one measure for the numerical problems in electric circuit simulation. The index depends on the mathematical model in different ways: setup of equations, classical or charge-oriented formulation and modelling of basic elements and semiconductor...

In electrical circuit simulation, a refined network approach is used to describe secondary and parasitic effects. This ansatz yields initial-boundary value problems of mixed partial-differential and differential-algebraic equations, so-called PDAE systems. One requirement for method-of-lines...

We analyze the general risk-neutral valuation for counterparty risk embedded in a Credit Default Swap (CDS) contract by adapting the recent findings of Brigo and Capponi (2009) to allow for simultaneous defaults among the two parties and the underlying reference credit, while the counterparty...

We present a model of opinion formation where individuals repeatedly engage in discussion and update their opinion in a social network similarly to the DeGroot model. Abstracting from the standard assumption that individuals always report their opinion truthfully, agents in our model interact...

We study the evolution of R&D networks in a Cournot model where firms may lower marginal costs due to bilateral R&D collaborations. Stochastically stable R&D networks exhibit the dominant group architecture, and, contrary to the existing literature, generically unique predictions about the size...

We study a dynamic model of opinion formation in social networks. In our model, boundedly rational agents update opinions by averaging over their neighbors’ expressed opinions, but may misrepresent their own opinion by conforming or counter-conforming with their neighbors. We show that an...

Modeling the evolution of networks is central to our understanding of modern large communication systems, such as the World-Wide-Web, as well as economic and social networks. The research on social and economic networks is truly interdisciplinary and the number of modeling strategies and...

We study the structure of pairwise stable networks from a very general point. Rather than assuming a particular functional form of utility, we simply assume that the society is homogeneous, i.e. that agents’ utilities differ only with respect to their network position while their names do not...

We study a dynamic model of opinion formation in social networks. In our model, boundedly rational agents update opinions by averaging over their neighbors' expressed opinions, but may misrepresent their own opinion by conforming or counter-conforming with their neighbors. We show that an...

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a...