The Complexity of Combinations of Qualitative Constraint Satisfaction Problems

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathrm{CSP}(T_1)$ and $\mathrm{CSP}(T_2)$ are decidable (or polynomial-time decidable). We show that for a large class of $\omega$-categorical theories $T_1, T_2$ the Nelson-Oppen conditions are not only sufficient, but also necessary for polynomial-time tractability of $\mathrm{CSP}(T_1 \cup T_2)$ (unless P=NP)

Bidirectional Text Compression in External Memory

Bidirectional compression algorithms work by substituting repeated substrings by references that, unlike in the famous LZ77-scheme, can point to either direction. We present such an algorithm that is particularly suited for an external memory implementation. We evaluate it experimentally on large data sets of size up to 128 GiB (using only 16 GiB of RAM) and show that it is significantly faster than all known LZ77 compressors, while producing a roughly similar number of factors. We also introduce an external memory decompressor for texts compressed with any uni- or bidirectional compression scheme

Three-band Hubbard model for Na2_2IrO3_3: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material

Na$_2$IrO$_3$ was one of the first materials proposed to feature the Kane-Mele type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.Comment: 5 pages, 3 figures; v2 (as published): added discussion about kinetic energy scale C; more realistic values of C shift the zigzag AFM phase to larger values of

Catalytic Asymmetric Pictet-Spengler Reactions toward Tetrahydroisoquinolines

The Pictet-Spengler reaction of 2-arylethylamines with aldehydes is a powerful methodology for the redox-neutral synthesis of partly hydrogenated nitrogen heterocycles. Especially tetrahydro-β-carbolines and tetrahydroisoquinolines represent valuable synthetic targets due to the prevalence of the respective molecular frameworks in naturally occurring alkaloids. The work presented within this thesis describes the development of a catalytic asymmetric Pictet-Spengler reaction toward tetrahydroisoquinolines – a product class that had been largely inaccessible via this route. Furthermore, the utilization of the available products in the biomimetic formal or total synthesis of eleven distinct natural products from diverse alkaloid classes was accomplished. Key to the development of a general methodology was the design and synthesis of bespoke imidodiphosphorimidate catalysts featuring electron-rich substituents that offered unprecedentedly high reactivity and selectivity in the system under study. The mechanistic nuances of the reaction were studied experimentally through in-depth kinetic analyses. Our investigation thus provides insights into the overall reaction mechanism as well as specific interactions offered by the optimal catalysts. Finally, further studies were directed toward the development of a catalytic asymmetric Pictet-Spengler reaction of electronically unbiased phenethylamines

N-loop running should be combined with N-loop matching

We investigate the high-scale behaviour of Higgs sectors beyond the Standard Model, pointing out that the proper matching of the quartic couplings before applying the renormalisation group equations (RGEs) is of crucial importance for reliable predictions at larger energy scales. In particular, the common practice of leading-order parameters in the RGE evolution is insufficient to make precise statements on a given model's UV behaviour, typically resulting in uncertainties of many orders of magnitude. We argue that, before applying N-loop RGEs, a matching should even be performed at N-loop order in contrast to common lore. We show both analytical and numerical results where the impact is sizeable for three minimal extensions of the Standard Model: a singlet extension, a second Higgs doublet and finally vector-like quarks. We highlight that the known two-loop RGEs tend to moderate the running of their one-loop counterparts, typically delaying the appearance of Landau poles. For the addition of vector-like quarks we show that the complete two-loop matching and RGE evolution hints at a stabilisation of the electroweak vacuum at high energies, in contrast to results in the literature.Comment: 16 pages, 11 figures; v2: title changed, accepted for publication in PR

Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model

In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength $U$ and various antiferromagnetic insulators at large $U$, we find an intermediate-$U$ antiferromagnetic metal. Most interestingly, we also identify a non-magnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the large-$U$ limit, we establish the phase diagram of the corresponding $J_1$-$J_2$-$J_3$ Heisenberg model. This is qualitatively confirmed - including the non-magnetic region - using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the $J_1$-$J_2$ square-lattice Heisenberg model, suggesting that the non-magnetic region hosts a 3D spin-liquid phase.Comment: 5 pages, 4 figures; final version incl. discussion about material

Visual Analysis of Spatio-Temporal Event Predictions: Investigating the Spread Dynamics of Invasive Species

Invasive species are a major cause of ecological damage and commercial losses. A current problem spreading in North America and Europe is the vinegar fly Drosophila suzukii. Unlike other Drosophila, it infests non-rotting and healthy fruits and is therefore of concern to fruit growers, such as vintners. Consequently, large amounts of data about infestations have been collected in recent years. However, there is a lack of interactive methods to investigate this data. We employ ensemble-based classification to predict areas susceptible to infestation by D. suzukii and bring them into a spatio-temporal context using maps and glyph-based visualizations. Following the information-seeking mantra, we provide a visual analysis system Drosophigator for spatio-temporal event prediction, enabling the investigation of the spread dynamics of invasive species. We demonstrate the usefulness of this approach in two use cases