Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.Comment: Reformulation of main theorem, minor changes in the proo

Moment-Based Variational Inference for Markov Jump Processes

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning (ICML 2019

Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: - The classes of the Boolean hierarchy over level $\Sigma_1$ of the dot-depth hierarchy are decidable in $NL$ (previously only the decidability was known). The same remains true if predicates mod $d$ for fixed $d$ are allowed. - If modular predicates for arbitrary $d$ are allowed, then the classes of the Boolean hierarchy over level $\Sigma_1$ are decidable. - For the restricted case of a two-letter alphabet, the classes of the Boolean hierarchy over level $\Sigma_2$ of the Straubing-Th\'erien hierarchy are decidable in $NL$. This is the first decidability result for this hierarchy. - The membership problems for all mentioned Boolean-hierarchy classes are logspace many-one hard for $NL$. - The membership problems for quasi-aperiodic languages and for $d$-quasi-aperiodic languages are logspace many-one complete for $PSPACE$

Soil Ecological Impact of a Hotspot Copper Contamination

In the experimental farm of the Fachhochschule Osnabrück an area (15 m x 20 m) of eutric cambisol over limestone is covered with a 0.3 m layer of very humous sandy substrate with an extremely high copper contamination (> 20 000 mg/kg). In the field the extremely contaminated place was well vegetated but recognisable by its spontaneous vegetation (high dominance of Urtica dioica) and a mor / moder like humus form with plant residues and a dense root mat of nettles overlaying the mineral soil. Soil microbial parameters (field respiration, basal respiration, microbial biomass) and decomposition of plant residues in litter bags differed not significantly between the hot spot and an adjacent reference plot with low Cu contamination. Toxicity tests confirmed that the soil contamination is very adverse to earthworms, is depressing plant growth (Lepidum sativum), and is inhibiting substrate induced respiration. It is concluded that the contamination disrupted the soil ecological system. A decomposer refuge and shortcut nutrient cycle developed in the litter layer on top of the contamination. Bioturbation is the most affected soil biological process, therefore the spread of the contaminated substrate into the surrounding soil is minimized. Trees are probably able to circumvent the contaminated zone with their root system