Diese Woche wird es bei unserem Algorithmus um die Berechnung von physikalischen Effekten gehen. Computer können nämlich auch verwendet werden, um natürliche Vorgänge zu simulieren. Das wird in der Wissenschaft immer wichtiger, weil man damit oft besser verstehen kann, wie die Natur funktioniert. Unsere Wettervorhersage beruht z.B. auf einer Simulation, bei der es auf die möglichst genaue Abbil...

In [10] Michel Talagrand gave a rigorous proof of the Parisi formula in the SherringtonKirkpatrick model. In this paper we build upon the methodology developed in [10] and extend Talagrand’s result to a more general class of mean field models with spins distributed according to an arbitrary probability measure on the bounded subset of the real line and with external field term given by an arbit...

A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle θ and sufficiently large n there are at most 2n−...