Tails of Localized Density of States of Two-dimensional Dirac Fermions

The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m^2, where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.Comment: 8 pages, REVTeX, 1 eps figure; to appear in Annalen der Physi

Anomaly Detection in the Latent Space of VAEs

One of the most important challenges in the development of autonomous driving systems is to make them robust against unexpected or unknown objects. Many of these systems perform really good in a controlled environment where they encounter situation for which they have been trained. In order for them to be safely deployed in the real world, they need to be aware if they encounter situations or novel objects for which the have not been sufficiently trained for in order to prevent possibly dangerous behavior. In reality, they often fail when dealing with such kind of anomalies, and do so without any signs of uncertainty in their predictions. This thesis focuses on the problem of detecting anomalous objects in road images in the latent space of a VAE. For that, normal and anomalous data was used to train the VAE to fit the data onto two prior distributions. This essentially trains the VAE to create an anomaly and a normal cluster. This structure of the latent space makes it possible to detect anomalies in it by using clustering algorithms like k-means. Multiple experiments were carried out in order to improve to separation of normal and anomalous data in the latent space. To test this approach, anomaly data from multiple datasets was used in order to evaluate the detection of anomalies. The approach described in this thesis was able to detect almost all images containing anomalous objects but also suffers from a high false positive rate which still is a common problem of many anomaly detection methods

Aspects of integrability in a classical model for non-interacting fermionic fields

In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle