arXiv subjects

Christian Knoll

Publications and source records attributed to Christian Knoll.

22 records · Page 2Linked to original sources

arXiv2018

Slowly damped quasinormal modes of the massive Dirac field in d-dimensional Tangherlini spacetime

We consider quasinormal modes of the massive Dirac field in the background of a Schwarzschild- Tangherlini black hole. Different dimensions of the spacetime are considered, from d = 4 to d = 9. The quasinormal modes are calculated using two independent methods: WKB and continued fraction. We obtain the spectrum of quasinormal modes for different values of the overtone number and angular quantum number. An analytical approximation of the spectrum valid in the case of large values of the angular quantum number and mass is calculated. Although we don't find unstable modes in the spectrum, we show that for large values of the mass, the quasinormal modes can become very slowly damped, giving rise to quasistationary perturbations.

gr-qc↗

arXiv2017

Cepstral Analysis of Random Variables: Muculants

An alternative parametric description for discrete random variables, called muculants, is proposed. In contrast to cumulants, muculants are based on the Fourier series expansion, rather than on the Taylor series expansion, of the logarithm of the characteristic function. We utilize results from cepstral theory to derive elementary properties of muculants, some of which demonstrate behavior superior to those of cumulants. For example, muculants and cumulants are both additive. While the existence of cumulants is linked to how often the characteristic function is differentiable, all muculants exist if the characteristic function satisfies a Paley-Wiener condition. Moreover, the muculant sequence and, if the random variable has finite expectation, the reconstruction of the characteristic function from its muculants converge. We furthermore develop a connection between muculants and cumulants and present the muculants of selected discrete random variables. Specifically, it is shown that the Poisson distribution is the only distribution where only the first two muculants are nonzero.

math.PR↗

arXiv2017

Fixed Points of Belief Propagation -- An Analysis via Polynomial Homotopy Continuation

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed points. In this work, we formulate a set of polynomial equations, the solutions of which correspond to BP fixed points. To solve such a nonlinear system we present the numerical polynomial-homotopy-continuation (NPHC) method. Experiments on binary Ising models and on error-correcting codes show how our method is capable of obtaining all BP fixed points. On Ising models with fixed parameters we show how the structure influences both the number of fixed points and the convergence properties. We further asses the accuracy of the marginals and weighted combinations thereof. Weighting marginals with their respective partition function increases the accuracy in all experiments. Contrary to the conjecture that uniqueness of BP fixed points implies convergence, we find graphs for which BP fails to converge, even though a unique fixed point exists. Moreover, we show that this fixed point gives a good approximation, and the NPHC method is able to obtain this fixed point.

stat.ML↗

arXiv2015

Charged rotating dilaton black holes with Kaluza-Klein asymptotics

We construct a class of stationary and axisymmetric solutions to the 5D Einstein-Maxwell-dilaton gravity, which describe configurations of charged rotating black objects with Kaluza-Klein asymptotics. The solutions are constructed by uplifting a vacuum seed solution to six dimensions, performing a boost, and a subsequent circle reduction. We investigate the physical properties of the charged solutions, and obtain their general relations to the properties of the vacuum seed. We also derive the gyromagnetic ratio and the Smarr-like relations. As particular cases we study three solutions, which describe a charged rotating black string, a charged rotating black ring on Kaluza-Klein bubbles, and a superposition of two black holes and a Kaluza-Klein bubble.

gr-qc↗