Thus, a little reflection on the axioms of Zermelo-Fraenkel set theory (ZF) shows that Vù, the first transfinite level of the hierarchy, is a model of all the axioms of ZF with the exception of the axiom of infinity. And, in general, one finds that if κ is a strongly inaccessible ordinal, then Vκ is a model of all of the axioms of ZF.1 (For all these models, we take ∈ to be the standard element...

In this paper, we derive a second order mean field theory for directed graphical probability models. By using an information theoretic argument it is shown how this can be done in the absense of a partition function. This method is the direct generalisation of the well-known TAP approximation for Boltzmann Machines. In a numerical example, it is shown that the method greatly improves the first ...

We attempt to generalize the familiar covariantly conserved Bel-Robinson tensor Bμναβ ∼ RR of GR and its recent topologically massive third derivative order counterpart B ∼ RDR, to quadratic curvature actions. Two very different models of current interest are examined: fourth order D = 3 “new massive”, and second order D > 4 Lanczos-Lovelock, gravity. On dimensional grounds, the candidates here...

Energy balance method EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the firstand second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreemen...

Starting from discrete event simulations based on sampled data we simulate the interplay between product density and flux. Data-fitting helps to determine the right parameters for clearing functions to close first and second order conservation laws. For the first order case well-known relations from M/M/1-queuing theory can be reproduced and numerically extended to transient behavior. To includ...

Most variable selection techniques focus on first-order linear regression models. Often, interaction and quadratic terms are also of interest, but the number of candidate predictors grows very fast with the number of original predictors, making variable selection more difficult. Forward selection algorithms are thus developed that enforce natural hierarchies in second-order models to control th...