Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes

We present an approximate Bayesian inference approach for estimating the intensity of a inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and Polya--Gamma random variables we obtain a representation of the likelihood which is conjugate to the GP prior. We estimate the posterior using a variational free--form mean field optimisation together with the framework of sparse GPs. Furthermore, as alternative approximation we suggest a sparse Laplace's method for the posterior, for which an efficient expectation--maximisation algorithm is derived to find the posterior's mode. Both algorithms compare well against exact inference obtained by a Markov Chain Monte Carlo sampler and standard variational Gauss approach solving the same model, while being one order of magnitude faster. Furthermore, the performance and speed of our method is competitive with that of another recently proposed Poisson process model based on a quadratic link function, while not being limited to GPs with squared exponential kernels and rectangular domains.DFG, 318763901, Approximative Bayes’sche Schätzung und Modellauswahl für stochastische Differentialgleichungen (A06)DFG, 318763901, SFB 1294: Datenassimilation: Die nahtlose Verschmelzung von Daten und Modelle

Validität und Reliabilität von Entscheidungsregeln bei akuten Halsschmerzen

In dieser Arbeit werden vier Entscheidungsregeln zur Differenzierung zwischen Streptokokkeninfekt und anderen Racheninfekten auf ihre Validität in einer hausärztlichen Praxis überprüft und vergleichend beurteilt. (Validitätsstudie) Zudem wird untersucht, wie häufig zwei Untersucher am selben Patienten einen übereinstimmenden Befund erheben. (Reliabilitätsstudie

Relaxation of dynamically disordered tetragonal platelets in the relaxor ferroelectric 0.964Na1/2Bi1/2TiO3−0.036BaTiO30.964\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3-0.036\mathrm{BaTiO}_3

The local dynamics of the lead-free relaxor $0.964\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3-0.036\mathrm{BaTiO}_3$ (NBT-3.6BT) have been investigated by a combination of quasielastic neutron scattering (QENS) and ab initio molecular dynamics simulations. In a previous paper, we were able to show that the tetragonal platelets in the microstructure are crucial for understanding the dielectric properties of NBT-3.6BT [F. Pforr et al., Phys. Rev. B 94, 014105 (2016)]. To investigate their dynamics, ab initio molecular dynamics simulations were carried out using $\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3$ with 001 cation order as a simple model system for the tetragonal platelets in NBT-3.6BT. Similarly, 111-ordered $\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3$ was used as a model for the rhombohedral matrix. The measured single crystal QENS spectra could be reproduced by a linear combination of calculated spectra. We find that the relaxational dynamics of NBT-3.6BT are concentrated in the tetragonal platelets. Chaotic stages, during which the local tilt order changes incessantly on the timescale of several picoseconds, cause the most significant contribution to the quasielastic intensity. They can be regarded as an excited state of tetragonal platelets, whose relaxation back into a quasistable state might explain the frequency dependence of the dielectric properties of NBT-3.6BT in the 100 GHz to THz range. This substantiates the assumption that the relaxor properties of NBT-3.6BT originate from the tetragonal platelets.Comment: 27 pages, 9 figure

Semantische Klassifizierung von 3D-Punktwolken

Für die automatisierte Überwachung technischer Einbauten in untertägigen Bergwerksanlagen auf Basis dreidimensionaler Punktwolken wurde ein Geomonitoringverfahren, bestehend aus Datenaufnahme und -analyse, entwickelt. Es werden zwei Ansätze zur semantischen Klassifizierung von dreidimensionalen Punktwolken betrachtet, die Multi-Skalen-Feature-Extraktion und die Anwendung eines dreidimensionalen Faltenden Neuronalen Netzes. Die Methode der Multi-Skalen-Feature-Extraktion bestimmt durch festgelegte Berechnungsvorschriften Features allein aus den Koordinaten eines Punktes und seiner Nachbarn auf mehreren Längenskalen. Diese werden zu Feature-Vektoren zusammengefasst und dienen als Input für einen Random Forest-Klassifizierer. Die Anwendung eines dreidimensionalen Faltenden Neuronalen Netzes erfordert nur die Vorverarbeitung der Punktwolke zu einem Voxel-Grid und liefert dann direkt Klassifizierungsergebnisse. In einer exemplarischen Anwendung beider Ansätze zur Detektion von Stempeln, Schienen und Stößen in einer untertägigen Szene werden Klassifizierungsgenauigkeiten von über 90 % erreicht

Generative inverse design of multimodal resonant structures for locally resonant metamaterials

In the development of locally resonant metamaterials, the physical resonator design is often omitted and replaced by an idealized mass-spring system. This paper presents a novel approach for designing multimodal resonant structures, which give rise to multi-bandgap metamaterials with predefined band gaps. Our method uses a conditional variational autoencoder to identify nontrivial patterns between design variables of complex-shaped resonators and their modal effective parameters. After training, the cost of generating designs satisfying arbitrary criteria - frequency and mass of multiple modes - becomes negligible. An example of a resonator family with six geometric variables and two targeted modes is further elaborated. We find that the autoencoder performs well even when trained with a limited dataset, resulting from a few hundred numerical modal analyses. The method generates several designs that very closely approximate the desired modal characteristics. The accuracy of the best designs, proposed by the auto-encoder, is confirmed in tests of 3D-printed resonator prototypes. Further experiments demonstrate the close agreement between the measured and desired dispersion relation of a sample metamaterial beam