Faster Sorting Networks for 1717, 1919 and 2020 Inputs

We present new parallel sorting networks for $17$ to $20$ inputs. For $17, 19,$ and $20$ inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on $17, 19,$ and $20$ channels. The networks were obtained using a combination of hand-crafted first layers and a SAT encoding of sorting networks

Avoiding and Enforcing Repetitive Structures in Words

The focus of this thesis is on the study of repetitive structures in words, a central topic in the area of combinatorics on words. The results presented in the thesis at hand are meant to extend and enrich the existing theory concerning the appearance and absence of such structures. In the first part we examine whether these structures necessarily appear in infinite words over a finite alphabet. The repetitive structures we are concerned with involve functional dependencies between the parts that are repeated. In particular, we study avoidability questions of patterns whose repetitive structure is disguised by the application of a permutation. This novel setting exhibits the surprising behaviour that avoidable patterns may become unavoidable in larger alphabets. The second and major part of this thesis deals with equations on words that enforce a certain repetitive structure involving involutions in their solution set. Czeizler et al. (2009) introduced a generalised version of the classical equations u` Æ vmwn that were studied by Lyndon and Schützenberger. We solve the last two remaining and most challenging cases and thereby complete the classification of these equations in terms of the repetitive structures appearing in the admitted solutions. In the final part we investigate the influence of the shuffle operation on words avoiding ordinary repetitions. We construct finite and infinite square-free words that can be shuffled with themselves in a way that preserves squarefreeness. We also show that the repetitive structure obtained by shuffling a word with itself is avoidable in infinite words

Non-remote reference noise cancellation - using reference data in the presence of surface-NMR signals

Surface-NMR measurements commonly suffer from low signal-to-noise ratios. In recent years, with the introduction of multi-channel surface-NMR instruments, the technique of remote-reference noise cancellation (RNC) was developed and significantly improved the applicability of surface-NMR. The current formulation of RNC requires a reference loop to be placed a remote distance from the transmitter loop such that no NMR signal is recorded. Reference loops placed at non-remote distances have been envisaged to provide both improved noise cancellation performance and field efficiency; however, the concept has not been previously applied because the theoretical framework was missing. In this paper, the theoretical framework is presented. It is demonstrated that reference loops placed at non-remote distances provide superior noise cancellation performance. Considerations for placing the reference loop relative to the transmitter loop are provided, and the theoretical framework is evaluated based on a semi-synthetic example using real field noise and synthetic surface-NMR data. © 202

Super-resolution microscopy reveals specific recruitment of HIV-1 envelope proteins to viral assembly sites dependent on the envelope C-terminal tail

The inner structural Gag proteins and the envelope (Env) glycoproteins of human immunodeficiency virus (HIV-1) traffic independently to the plasma membrane, where they assemble the nascent virion. HIV-1 carries a relatively low number of glycoproteins in its membrane, and the mechanism of Env recruitment and virus incorporation is incompletely understood. We employed dual-color super-resolution microscopy visualizing Gag assembly sites and HIV-1 Env proteins in virus-producing and in Env expressing cells. Distinctive HIV-1 Gag assembly sites were readily detected and were associated with Env clusters that always extended beyond the actual Gag assembly site and often showed enrichment at the periphery and surrounding the assembly site. Formation of these Env clusters depended on the presence of other HIV-1 proteins and on the long cytoplasmic tail (CT) of Env. CT deletion, a matrix mutation affecting Env incorporation or Env expression in the absence of other HIV-1 proteins led to much smaller Env clusters, which were not enriched at viral assembly sites. These results show that Env is recruited to HIV-1 assembly sites in a CT-dependent manner, while Env(ΔCT) appears to be randomly incorporated. The observed Env accumulation surrounding Gag assemblies, with a lower density on the actual bud, could facilitate viral spread . Keeping Env molecules on the nascent virus low may be important for escape from the humoral immune response, while cell-cell contacts mediated by surrounding Env molecules could promote HIV-1 transmission through the virological synapse

Application of adiabatic pulses for magnetic Resonance Sounding – Pulse shapes and resolution

Magnetic Resonance Sounding (MRS) can image the spatial distribution of hydrologically relevant parameters in in the subsurface. However, the application of MRS is often limited by its low signal-to-noise ratio. The use of adiabatic excitation pulses show promising features to overcome this limitation. In this work, we study practical considerations when applying adiabatic pulses for MRS, i.e. calculation of the sensitivity kernel for varying pulse shapes and vertical resolution. The pulse shape is crucial for the performance of adiabatic pulses. We investigate the shapes of adiabatic pulses recorded during a MRS and observe small systematic deviations from the theoretical predicted pulse shape and variations between different pulse strengths. We show that the overall impact on the obtained sounding curve and inversion result was small. This enables to limit the time consuming modelling of the spin dynamic to one representative pulse shape, which significantly speeds up the calculation of the sensitivity kernel, necessary for the interpretation of MRS. Additionally, we show that on-resonance excitation generally outperforms adiabatic excitation concerning vertical resolution and depth of investigation (both up to a factor of two). This is true for a wide range of noise conditions. For a very shallow depth interval compared to the loop size, however, adiabatic excitation features improved imaging capabilities. © 2020 The Author