We prove universal recursive formulas for Branson’s Q-curvature of order eight in terms of lower-order Q-curvatures, lower-order GJMSoperators and holographic coefficients. The results confirm a special case of a conjecture in [On conformally covariant powers of the Laplacian, arXiv:0905.3992v3].

In this paper a globally convergent first–order training algorithm is proposed that uses sign–based information of the batch error measure in the framework of the nonlinear Jacobi process. This approach allows us to equip the recently proposed Jacobi–Rprop method with the global convergence property, i.e. convergence to a local minimiser from any initial starting point. We also propose a strate...

We describe a second-order double precision finite volume Boussinesq code implemented using the CUDA platform. We perform detailed validation of the code on a variety of Rayleigh-Benard convection problems and show second order convergence. We obtain matching results with a Fortran code running on a high-end eight-core CPU. The CUDA-accelerated code achieves approximately an eight-time speedup ...

Nešetřil and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if (Gi)i∈N is a sequence of graphs with M being their first order limit and v is a vertex of M , then there exists a sequence (vi)i∈N of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this ...

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the BenjaminiSchramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this resul...