Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Coarse-graining methods and polymer dynamics

This thesis studies molecular dynamics simulations on two levels of resolution: the detailed level of atomistic simulations, where the motion of explicit atoms in a many-particle system is considered, and the coarse-grained level, where the motion of superatoms composed of up to 10 atoms is modeled. While atomistic models are capable of describing material specific effects on small scales, the time and length scales they can cover are limited due to their computational costs. Polymer systems are typically characterized by effects on a broad range of length and time scales. Therefore it is often impossible to atomistically simulate processes, which determine macroscopic properties in polymer systems. Coarse-grained (CG) simulations extend the range of accessible time and length scales by three to four orders of magnitude. However, no standardized coarse-graining procedure has been established yet. Following the ideas of structure-based coarse-graining, a coarse-grained model for polystyrene is presented. Structure-based methods parameterize CG models to reproduce static properties of atomistic melts such as radial distribution functions between superatoms or other probability distributions for coarse-grained degrees of freedom. Two enhancements of the coarse-graining methodology are suggested. Correlations between local degrees of freedom are implicitly taken into account by additional potentials acting between neighboring superatoms in the polymer chain. This improves the reproduction of local chain conformations and allows the study of different tacticities of polystyrene. It also gives better control of the chain stiffness, which agrees perfectly with the atomistic model, and leads to a reproduction of experimental results for overall chain dimensions, such as the characteristic ratio, for all different tacticities. The second new aspect is the computationally cheap development of nonbonded CG potentials based on the sampling of pairs of oligomers in vacuum. Static properties of polymer melts are obtained as predictions of the CG model in contrast to other structure-based CG models, which are iteratively refined to reproduce reference melt structures. The dynamics of simulations at the two levels of resolution are compared. The time scales of dynamical processes in atomistic and coarse-grained simulations can be connected by a time scaling factor, which depends on several specific system properties as molecular weight, density, temperature, and other components in mixtures. In this thesis the influence of molecular weight in systems of oligomers and the situation in two-component mixtures is studied. For a system of small additives in a melt of long polymer chains the temperature dependence of the additive diffusion is predicted and compared to experiments.

Highly accurate quantum chemistry : spin-orbit splittings via multireference coupled-cluster methods and applications in heavy-atom main-group chemistry

Diese Dissertation demonstriert und verbessert die Vorhersagekraft der Coupled-Cluster-Theorie im Hinblick auf die hochgenaue Berechnung von Moleküleigenschaften. Die Demonstration erfolgt mittels Extrapolations- und Additivitätstechniken in der Single-Referenz-Coupled-Cluster-Theorie, mit deren Hilfe die Existenz und Struktur von bisher unbekannten Molekülen mit schweren Hauptgruppenelementen vorhergesagt wird. Vor allem am Beispiel von cyclischem SiS_2, einem dreiatomigen Molekül mit 16 Valenzelektronen, wird deutlich, dass die Vorhersagekraft der Theorie sich heutzutage auf Augenhöhe mit dem Experiment befindet: Theoretische Überlegungen initiierten eine experimentelle Suche nach diesem Molekül, was schließlich zu dessen Detektion und Charakterisierung mittels Rotationsspektroskopie führte. Die Vorhersagekraft der Coupled-Cluster-Theorie wird verbessert, indem eine Multireferenz-Coupled-Cluster-Methode für die Berechnung von Spin-Bahn-Aufspaltungen erster Ordnung in 2^Pi-Zuständen entwickelt wird. Der Fokus hierbei liegt auf Mukherjee's Variante der Multireferenz-Coupled-Cluster-Theorie, aber prinzipiell ist das vorgeschlagene Berechnungsschema auf alle Varianten anwendbar. Die erwünschte Genauigkeit beträgt 10 cm^-1. Sie wird mit der neuen Methode erreicht, wenn Ein- und Zweielektroneneffekte und bei schweren Elementen auch skalarrelativistische Effekte berücksichtigt werden. Die Methode eignet sich daher in Kombination mit Coupled-Cluster-basierten Extrapolations-und Additivitätsschemata dafür, hochgenaue thermochemische Daten zu berechnen.

Methods and strategies to identify the mode of action of phytoactive compounds

Small molecules affecting biological processes in plants are widely used in agricultural practice as herbicides or plant growth regulators and in basic plant sciences as probes to study the physiology of plants. Most of the compounds were identified in large screens by the agrochemical industry, as phytoactive natural products and more recently, novel phytoactive compounds originated from academic research by chemical screens performed to induce specific phenotypes of interest. The aim of the present PhD thesis is to evaluate different approaches used for the identification of the primary mode of action (MoA) of a phytoactive compound. Based on the methodologies used for MoA identification, three approaches are discerned: a phenotyping approach, an approach based on a genetic screen and a biochemical screening approach.rnFour scientific publications resulting from my work are presented as examples of how a phenotyping approach can successfully be applied to describe the plant MoA of different compounds in detail.rnI. A subgroup of cyanoacrylates has been discovered as plant growth inhibitors. A set of bioassays indicated a specific effect on cell division. Cytological investigations of the cell division process in plant cell cultures, studies of microtubule assembly with green fluorescent protein marker lines in vivo and cross resistant studies with Eleusine indica plants harbouring a mutation in alpha-tubulin, led to the description of alpha-tubulin as a target site of cyanoacrylates (Tresch et al., 2005).rnII. The MoA of the herbicide flamprop-m-methyl was not known so far. The studies described in Tresch et al. (2008) indicate a primary effect on cell division. Detailed studies unravelled a specific effect on mitotic microtubule figures, causing a block in cell division. In contrast to other inhibitors of microtubule rearrangement such as dinitroanilines, flamprop-m-methyl did not influence microtubule assembly in vitro. An influence of flamprop-m-methyl on a target within the cytoskeleton signalling network could be proposed (Tresch et al., 2008).rnIII. The herbicide endothall is a protein phosphatase inhibitor structurally related to the natural product cantharidin. Bioassay studies indicated a dominant effect on dark-growing cells that was unrelated to effects observed in the light. Cytological characterisation of the microtubule cytoskeleton in corn tissue and heterotrophic tobacco cells showed a specific effect of endothall on mitotic spindle formation and ultrastructure of the nucleus in combination with a decrease of the proliferation index. The observed effects are similar to those of other protein phosphatase inhibitors such as cantharidin and the structurally different okadaic acid. Additionally, the observed effects show similarities to knock-out lines of the TON1 pathway, a protein phosphatase-regulated signalling pathway. The data presented in Tresch et al. (2011) associate endothall’s known in vitro inhibition of protein phosphatases with in vivo-effects and suggest an interaction between endothall and the TON1 pathway.rnIV. Mefluidide as a plant growth regulator induces growth retardation and a specific phenotype indicating an inhibition of fatty acid biosynthesis. A test of the cuticle functionality suggested a defect in the biosynthesis of very-long-chain fatty acids (VLCFA) or waxes. Metabolic profiling studies showed similarities with different groups of VLCFA synthesis inhibitors. Detailed analyses of VLCFA composition in tissues of duckweed (Lemna paucicostata) indicated a specific inhibition of the known herbicide target 3 ketoacyl-CoA synthase (KCS). Inhibitor studies using a yeast expression system established for plant KCS proteins verified the potency of mefluidide as an inhibitor of plant KCS enzymes. It could be shown that the strength of inhibition varied for different KCS homologues. The Arabidopsis Cer6 protein, which induces a plant growth phenotype similar to mefluidide when knocked out, was one of the most sensitive KCS enzymes (Tresch et al., 2012).rnThe findings of my own work were combined with other publications reporting a successful identification of the MoA and primary target proteins of different compounds or compound classes.rnA revised three-tier approach for the MoA identification of phytoactive compounds is proposed. The approach consists of a 1st level aiming to address compound stability, uniformity of effects in different species, general cytotoxicity and the effect on common processes like transcription and translation. Based on these findings advanced studies can be defined to start the 2nd level of MoA characterisation, either with further phenotypic characterisation, starting a genetic screen or establishing a biochemical screen. At the 3rd level, enzyme assays or protein affinity studies should show the activity of the compound on the hypothesized target and should associate the in vitro effects with the in vivo profile of the compound.

High-mass Drell-Yan cross-section and search for new phenomena in multi-electron/positron final states with the ATLAS detector

The Standard Model of particle physics is a very successful theory which describes nearly all known processes of particle physics very precisely. Nevertheless, there are several observations which cannot be explained within the existing theory. In this thesis, two analyses with high energy electrons and positrons using data of the ATLAS detector are presented. One, probing the Standard Model of particle physics and another searching for phenomena beyond the Standard Model.rnThe production of an electron-positron pair via the Drell-Yan process leads to a very clean signature in the detector with low background contributions. This allows for a very precise measurement of the cross-section and can be used as a precision test of perturbative quantum chromodynamics (pQCD) where this process has been calculated at next-to-next-to-leading order (NNLO). The invariant mass spectrum mee is sensitive to parton distribution functions (PFDs), in particular to the poorly known distribution of antiquarks at large momentum fraction (Bjoerken x). The measurementrnof the high-mass Drell-Yan cross-section in proton-proton collisions at a center-of-mass energy of sqrt(s) = 7 TeV is performed on a dataset collected with the ATLAS detector, corresponding to an integrated luminosity of 4.7 fb-1. The differential cross-section of pp -> Z/gamma + X -> e+e- + X is measured as a function of the invariant mass in the range 116 GeV < mee < 1500 GeV. The background is estimated using a data driven method and Monte Carlo simulations. The final cross-section is corrected for detector effects and different levels of final state radiation corrections. A comparison isrnmade to various event generators and to predictions of pQCD calculations at NNLO. A good agreement within the uncertainties between measured cross-sections and Standard Model predictions is observed.rnExamples of observed phenomena which can not be explained by the Standard Model are the amount of dark matter in the universe and neutrino oscillations. To explain these phenomena several extensions of the Standard Model are proposed, some of them leading to new processes with a high multiplicity of electrons and/or positrons in the final state. A model independent search in multi-object final states, with objects defined as electrons and positrons, is performed to search for these phenomenas. Therndataset collected at a center-of-mass energy of sqrt(s) = 8 TeV, corresponding to an integrated luminosity of 20.3 fb-1 is used. The events are separated in different categories using the object multiplicity. The data-driven background method, already used for the cross-section measurement was developed further for up to five objects to get an estimation of the number of events including fake contributions. Within the uncertainties the comparison between data and Standard Model predictions shows no significant deviations.