Vacuum polarization in heavy atoms

We formulate the Hartree-Fock method using a functional integral approach. Then we consider a nonperturbative component of the vacuum polarization. For the Dirac-Coulomb operator the renormalization flow of the vacuum polarization is calculated numerically. For the Hartree-Fock operator the polarization is obtained by integrating an appropriately rescaled flow. The text includes an approximate calculation of the vacuum polarization in Uranium

A User-Centric Approach to Explainable AI in Corporate Performance Management

Machine learning (ML) applications have surged in popularity in the industry, however, the lack of transparency of ML-models often impedes the usability of ML in practice. Especially in the corporate performance management (CPM) domain, transparency is crucial to support corporate decision-making processes. To address this challenge, approaches of explainable artificial intelligence (XAI) provide solutions to reduce the opacity of ML-based systems. This design science study further builds on prior user experience (UX) and user interface (UI) focused XAI-research, to develop a user-centric approach to XAI for the CPM field. As key results, we identify design principles in three decomposition layers, including ten explainability UI-elements that we developed and evaluated through seven interviews. These results complement prior research by focusing it on the CPM domain and provide practitioners with concrete guidelines to foster ML adoption in the CPM field

Fabrication and application of hydrophilic-hydrophobic micropatterned polymer surfaces

Surface patterning is important in a wide spectrum of applications ranging from microelectronics, sensors design and material science to high throughput screening, tissue engineering and cell biology. A number of methods for specific patterning applications, such as photolithography, soft lithography, or electron beam and dip-pen nanolithography, have been developed. However, there is still a clear need for the development of novel methods permitting patterning of different cell types, nano- and microparticles as well as hydrogels incorporating cells. These novel patterning methods are vital for the advancement of such research fields as tissue engineering, biomaterials and for fundamental investigation of cell-cell communication, tissue and organ development. The aims of this PhD thesis were: a) develop a technique for creating droplets of liquid with defined geometries that can be used for patterning water soluble components; b) optimize the conditions for the fabrication of porous polymer surfaces for the liquid patterning; c) characterize the produced patterned polymer surfaces; d) further develop the technique for maskless generation of liquid patterns with arbitrary geometry; e) optimize the method for the patterning of different materials (chemicals, hydrogels, microparticles); f) show an application of the method for patterning of living cells and characterize their behavior on the composite surface during cultivation; g) show an application of the technology to mimic natural cell-cell communication in vitro via signaling protein propagation between patterned cell populations in co-culture. The first part of the work was devoted to the development of porous polymer layers with precise micropatterns of hydrophilic and hydrophobic areas. In order to fabricate these patterns, UV-initiated photografting of 2,2,3,3,3-pentafluoropropyl methacrylate (PFPMA) on porous poly(2-hydroxyethyl methacrylate-co-ethylene dimethacrylate) (HEMA-EDMA) was optimized. Before and after photografting, both polymer substrates were thoroughly characterized using water contact angle measurement, UV-Vis spectroscopy, scanning electron microscopy (SEM) and time of flight secondary ion mass spectrometry (ToF-SIMS). Porous properties were characterized by UV-Vis spectroscopy, SEM and dynamic light scattering techniques (DLS). Due to the high difference in wettability of the hydrophilic HEMA-EDMA polymer film and hydrophobic regions coated with PFPMA polymer brushes, aqueous solutions can be trapped in the hydrophilic areas, taking the shape of these areas. The transparency of the HEMA-EDMA monolith originated from porous properties of the polymer makes it suitable for microscopic monitoring of liquid patterns during experiments. The method was for the first time applied for the simultaneous micropatterning of multiple cell types. More than ten different cell populations separated by hydrophobic borders could be cultured in microreservoirs. After adhesion, the cells could be placed in the mutual culture medium, allowing cell-cell communication among populations. During 3 days co-culture in the mutual medium, cross-contamination was shown to be less than 1,5%, although the cells were pre-patterned in the hydrophilic areas separated by hydrophobic borders of only two to three cell diameters. The capability of cell patterning and long term cultivation opens the way for many interesting bio-applications, such as in vitro mimicking important biological processes that involve and depend on the organization of multiple cell types into complex micropatterns in vivo. As a case study, I together with Dr. Steffen Scholpp and Dipl. Eliana Stanganello (ITG, KIT) used the developed technique to visualize spreading of signaling molecules (Wnt protein) from one micropatterned population of fibroblast cells to another fibroblast population by activation of the reporter system. Thus, we were able to simulate paracrine signaling system in vitro. In addition, I further developed our technique into a new type of mask-less liquid patterning or digital liquid patterning (DLP) method. The idea of this method is similar to the working principle of a digital score board. A digital score board consists of many small bulbs, which generate light symbols on it. In the case of DLP, instead of the bulbs, small liquid droplets (digits) form a more complex liquid pattern on a substrate. The substrate for DLP is a composite surface, consisting of a grid of hydrophilic HEMA-EDMA spots divided by hydrophobic PFPMA barriers. The method allows on-demand fabrication of liquid patterns without the need to change the substrate and use an additional photomask. Patterns with customized geometries can be prepared manually by simply pipetting liquid inside the spots and successively coalescing the generated droplets to form a liquid micropattern. The DLP does not require clean room or high-precision microfabrication and allows the manual positioning of microdroplets in the range of micrometer scale. It was also shown that using superhydrophilic/superhydrophobic patterned surfaces leads to spontaneous dewetting of the coalesced microdroplets on the interface of the superhydrophobic border and the superhydrophilic spot. Hence, the usage of hydrophilic/hydrophobic patterned surface ensures the stability of liquid patterns during manipulations. Furthermore, the developed technique enables patterning of not only solutions, e.g. different chemicals, but also suspensions of living cells and microparticles, hydrogels, or formation of liquid multi-component gradients with complex geometries. Thus, this method will be especially useful for biological studies, which require the generation of complex patterns of different or the same cell types, or bioactive materials and cellular gradients without the need for sophisticated microfluidic and printing equipment, or for designing additional mask

A Solvent Model for Simulations of Peptides in Bilayers. II. Membrane-Spanning α-Helices

AbstractWe describe application of the implicit solvation model (see the first paper of this series), to Monte Carlo simulations of several peptides in bilayer- and water-mimetic environments, and in vacuum. The membrane-bound peptides chosen were transmembrane segments A and B of bacteriorhodopsin, the hydrophobic segment of surfactant lipoprotein, and magainin2. Their conformations in membrane-like media are known from the experiments. Also, molecular dynamics study of surfactant lipoprotein with different explicit solvents has been reported (Kovacs, H., A. E. Mark, J. Johansson, and W. F. van Gunsteren. 1995. J. Mol. Biol. 247:808–822). The principal goal of this work is to compare the results obtained in the framework of our solvation model with available experimental and computational data. The findings could be summarized as follows: 1) structural and energetic properties of studied molecules strongly depend on the solvent; membrane-mimetic media significantly promote formation of α-helices capable of traversing the bilayer, whereas a polar environment destabilizes α-helical conformation via reduction of solvent-exposed surface area and packing; 2) the structures calculated in a membrane-like environment agree with the experimental ones; 3) noticeable differences in conformation of surfactant lipoprotein assessed via Monte Carlo simulation with implicit solvent (this work) and molecular dynamics in explicit solvent were observed; 4) in vacuo simulations do not correctly reproduce protein-membrane interactions, and hence should be avoided in modeling membrane proteins

A Solvent Model for Simulations of Peptides in Bilayers. I. Membrane-Promoting α-Helix Formation

AbstractWe describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting α-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides—poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation—were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of α-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed

Controlled expansion of shell-shaped Bose–Einstein condensates

Motivated by the recent experimental realization of ultracold quantum gases in shell topology, we propose a straightforward implementation of matter-wave lensing techniques for shell-shaped Bose–Einstein condensates. This approach allows to significantly extend the free evolution time of the condensate shell after release from the trap and enables the study of novel quantum many-body effects on curved geometries. With both analytical and numerical methods we derive optimal parameters for realistic schemes to conserve the shell shape of the condensate for times up to hundreds of milliseconds

Shell-shaped Bose-Einstein condensates realized with dual-species mixtures

Confining Bose-Einstein condensates (BECs) in shell-shaped trapping potentials enables the generation of hollow quasi-2D topologies with superfluid properties. Motivated by recent microgravity experiments, these shell-shaped BECs are nowadays actively studied both theoretically and experimentally, with radio-frequency (rf) dressing being the main trapping mechanism under study. Here we present an alternative approach that utilizes the repulsive interaction in a dual-species mixture to achieve shell-shaped BECs, which could be realized in the future BECCAL mission. In contrast to the rf case, which relies on a dynamical transition from a filled to a hollow condensate, the mixture approach is based on realizing the shell structure as the ground state of the system, where one species is located at the center of the trap surrounded by the other and kept in place by the repulsive inter-species interaction. We compare both approaches by analyzing the initial states, the free expansion dynamics, and the collective excitation spectrum with analytical and numerical methods. In all three categories the mixture performs similar to the rf approach. Moreover, the interaction-driven expansion of the mixture allows to increase the size of the shell during time-of-flight without distorting its shape and therefore magnifying the dynamics within the shell; a mechanism not realizable in the rf case. We conclude by performing a feasibility analysis for both approaches that takes residual gravitational effects and possible trap asymmetries into account, which currently are the main obstacles to experimentally realize shell-shaped BECs