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A mathematical analysis of a family of rotating shallow water models in semigeostrophic scaling
No full textWe prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of PV-conserving balanced models for rapidly rotating shallow water includes the model derived by R. Salmon in 1985 and its 2006 generalization by M. Oliver. The results are, under the physical restriction that the initial potential vorticity is positive, as strong as those available for the 2D Euler equations. Our results are based on careful estimates which show that, although the potential vorticity inversion is nonlinear, bounds on the potential vorticity inversion operator remain linear in derivatives of the potential vorticity. This permits the adaptation of an argument based on elliptic theory, proposed by Yudovich in 1963 for proving existence and uniqueness of weak solutions for the two-dimensional Euler equations, to our particular nonlinear situation. We note that our work, besides the nonlinearity of the potential vorticity inversion operator, differs also from earlier works with respect to the fact that the velocity is not divergence-free in our case. Moreover, we prove existence, uniqueness and continuous dependence on initial data of global weak solutions. Radon-measured potential vorticities as can be shown to make sense in Euler- case, however, appear to break down altogether here. Finally, as a first step towards model justification we prove that, for balanced initial data, solutions of the rotating shallow water model stay -accurately close to the solution of the model on finite time intervals of order 1
A classification of postcritically finite Newton maps
No full textOne of the most important open problems in rational dynamics is understanding the structure of the space of rational functions. Newton maps of polynomials form an interesting subset of the space of rational maps that is more accessible for studying than the full space of rational maps. For every postcritically finite Newton map N_p of a polynomial p we construct a finite connected graph that contains the postcritical set of N_p. We show that such graphs characterize Newton maps uniquely up to Moebius conjugation. Conversely, we show that every graph with an associated map that satisfies particular conditions is realized by a unique postcritically finite Newton map. We show that there is a mapping from the set of postcritically finite Newton maps up to Moebius equivalence to the set of abstract extended Newton graphs with the corresponding equivalence relation on them. We show that this mapping is one to one, giving thereby a combinatorial classification of postcritically finite Newton maps in terms of finite connected graphs
Protein design of the mammalian DNA methyltransferase Dnmt3a
No full textThe catalytic domain of the Dnmt3a DNA-(cytosine C5)-methyltransferase (Dnmt3a-C) is active in isolated form but like full-length Dnmt3a it shows only weak DNA methylation activity. To improve this activity by directed evolution, we set up a selection system in which Dnmt3a-C methylate its own expression plasmid in E. coli and protect it from cleavage with methylation specific restriction enzymes. However, despite screening about 400 clones which were selected in 3 rounds from a library of 60000 clones, we were not able to isolate a variant with improved activity, most likely because of a background of uncleaved plasmids and plasmids which have lost the restriction site. We also showed that the catalytic domain of mouse Dnmt3a DNA methyltransferase is able to transfer the methyl group from S-adenosyl-L-methionine (AdoMet) to a cysteine residue in its catalytic centre. This reaction is reversible and slow. The yield of auto-methylation is increased by addition of Dnmt3L, which functions as a stimulator of Dnmt3a AdoMet complexes. In the presence of CpG containing double stranded DNA, the transfer of the methyl group from AdoMet to the flipped target base was preferred and auto-methylation was not detected. This reaction might constitute a regulatory mechanism which could inactivate unused Dnmt3a in the cell
Synthesis and Structural Characterization of Lanthanide-Containing Polyoxometalates
No full textPolyoxometalates (POMs) represent a large class of nanosized metal-oxo anions. POMs are remarkable not only in terms of molecular and electronic structural versatility, but also due to their reactivity and relevance in fields such as photochemistry, analytical chemistry, clinical chemistry, magnetism, catalysis, biology, medicine and materials science. Lanthanide-containing POMs have been investigated less than those containing 3d-transition metals. The former have shown interesting properties in the areas of photoluminescence, catalysis, electrochemistry, and magnetism.
Chapter I contains an extensive introduction to the class of POMs. Chapter II describes the synthetic procedures for some POM precursors and presents the different experimental techniques used for the characterization of the products. Chapter III comprises the lanthanide-containing polyoxotungstates results, divided into two sections, the lanthanide isopolytungstates and the lanthanide heteropolytungstates. In the first section, the polyanions [Ln2(H2O)10W22O71(OH)2]8− (Ln = La, Ce, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y) {Ln2W22} and the V-shaped polyanions [Ln2(H2O)10W28O93(OH)2]14− (Ln = Sm, and Eu) {Ln2W28} were discussed. The {Ln2W22} family consists of the [H2W22O74]14− fragment and two {Ln(H2O)5}3+ supporting units while the {Ln2W28} consists of the [H2W28O95]20− unit and two {Ln(H2O)n}3+ supporting groups. The [H2W22O74]14− cluster is made up of two undecatungstate fragments while the [H2W28O95]20− cluster consists of two undecatungstate and a hexatungstate fragment. In the second section, the mono- and di-lanthanide derivatives of the tungstoarsenates(III) [Yb(H2O)2K(H2O)2As2W19O67(H2O)]10− {YbAs2W19}; [La2(H2O)6As2W19O67(H2O)]8− {La2As2W19}, the mono- and di-lanthanide derivatives of the tungstoantimonates(III) [Ln(H2O)3Sb2W21O72(OH))]10− (Ln = Yb, Lu, Y) {LnSb2W21}; [Ln2(H2O)6Sb2W20O70)]8− (Yb, Lu, Y) {Ln2Sb2W20}, and the acetate sandwich-type tungstogermanates [(Ln(GeW11O39)(H2O))2(m-CH3COO)2]12− (Ln = Eu, Gd, Lu) have been presented. Polyanions {YbAs2W19}, {La2As2W19}, {LnSb2W21} and {Ln2Sb2W20} were synthesized in simple, one-pot reactions of Ln3+ ions with the lone pair containing polyanion precursors ([As2W19O67(H2O)]14−, [B-α-AsW9O33]9−, [Sb2W22O74(OH)2]12−, [B-α-SbW9O33]9−).
Chapter IV describes the mixed lanthanide/d-transition metal containing POMs, the novel open-ring shaped polyanions [Fe16O2(OH)23(H2O)9(P8W49O189)Ln4(H2O)20]11− {Ln4Fe16P8W49}(Ln = Eu and Gd) which have been synthesized by reaction of the known [H7P8W48O184]33− {P8W48} cyclic precursor with Fe3+ and Ln3+ ions in acidic aqueous medium in the presence of hydrogen peroxide. The unique novel open-ring tungstophosphate(V) unit {P8W48O188(WO3)}44− exists in the structure of the {Ln4Fe16P8W49}compounds in addition to the {Fe16O2(OH)20(H2O)12}21+ nanocluster and four {Ln(H2O)5}3+ grafted units.
Chapter V comprises non-lanthanide-containing POMs, divided into two sections, tellurium and d-transition metal containing POMs. The tungstotellurates(IV) [H2Te4W20O80]22− and [NaTeW15O54]13− and the molybotellurate(IV) [H2Te24Mo44O198]34− are described in the first section. In the second section, the sandwich-type tungstogermanates [Cu3(H2O)(B-β-GeW9O33(OH))(B-β-GeW8O30(OH))]12−, [Co(H2O)2{Co3(B-β-GeW9O33(OH))(B-β-GeW8O30(OH))}2]22− and [Mn(H2O)2{Mn3(H2O)(B-β-GeW9O33(OH))(B-β-GeW8O30(OH))}2]22− are presented.
All obtained compounds have been characterized in the solid state by FTIR, single-crystal XRD, TGA and elemental analyses. Furthermore, solution studies of the diamagnetic derivatives (La, Lu and Y analogues) by 183W and 89Y NMR spectroscopy were also performed, in addition to 13C NMR and 1H NMR spectroscopy for the acetate containing POMs
Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration
No full textMathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents with a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows. The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contribution of existing knowledge collections to the Web of Data.Mathematik wird mehr und mehr kollaborativ, aber Software unterstützt das nur unzureichend: Social-Web-Anwendungen machen mathematisches Wissen bisher automatisierten Agenten nicht zugänglich, die ein tieferes Verständnis für mathematische Strukturen haben. Solche Agenten gibt es, aber aber sie beschränken sich auf einzelne Arbeitsaufgaben, wie z.B. Schreiben, Publizieren, Begutachtung oder Verifikation, an Stelle komplexer kollaborativer Arbeitsabläufe. Diese Arbeit ermöglicht es, sie wirklich zu integrieren – durch einen Brückenschlag zwischen der dokumentenorientierten Sicht des mathematischen Schreibens und Publizierens und der netzorientierten Sicht der Diskussions-Threads und des Information Retrievals. Sie erreicht dies, indem sie vorhandene Repräsentationen mathematischen und relevanten verwandten Wissens über Anwendungen, Projekte und Personen auf eine gemeinsame Semantic-Web-Grundlage stellt. Dienst-Integration wird von zwei Seiten betrachtet: Anreicherung publizierter Dokumente durch Einbettung unterstützender Dienste, und Übersetzung zwischen unterschiedlichen Wissensrepräsentationen in Wissensdatenbanken. Eine Evaluation der Gebrauchstauglichkeit eines semantischen Wikis, das Wissensproduktion und -Konsum zusammenhängend integriert, zeigt die verbleibenden Herausforderungen dabei auf, mit solch heterogen integrierten Umgebungen realistische Arbeitsabläufe zu unterstützen. Die Ergebnisse dieser Arbeit werden bald auch kollaborativen Wissenserwerb ermöglichen, sowie den Beitrag vorhandener Wissenssammlungen zum Web of Data
Investment, Unbundling, and Vertical Governance in Electric Power Systems
No full textAbstract Unbundling, the vertical separation of electricity networks from generation and retail, and liberalization have been common features of electricity market reform around the world. As a consequence, the structure of electric power systems is becoming increasingly decentralized. Electricity supply is an interrelated system that requires careful coordination between supply and demand. This applies especially to system operation. But also in the long term coordination exhibits considerable benefit since the siting of generators has considerable influence on the network and may defer/ or increase investment need. With unbundling, firm-internal coordination across the entire supply chain is no longer possible. Coordination problems can arise because of lacking information or because of incentive problems. Since lack of coordination can cause efficiency losses, alternative governance mechanisms are needed to restore coordination in a market environment. This PhD thesis explores the coordination problem and possible solutions in five related articles. The first paper focuses on operational coordination and analyses the option of an independent system operator as a governance form for future actively managed smart distribution networks. The second paper examines whether costless information exchange ("cheap talk") can achieve coordination of investment decisions. Cheap talk may fail because of incentives problems. However, deep charging can serve to restore incentive compatibility. The third paper studies locational charging as price mechanism to coordinate distribution network and network users analytically. The fourth paper extends the theoretical analysis with a more in-depth investigation of the possibilities for locational pricing in Germany based on contractual solutions between network operator and user. The fifth paper shows that such optional and voluntary contracts can achieve a pareto-improvement
Gerechtigkeit in der Gesundheitsversorgung: eine empirische Untersuchung über die Verteilungspräferenzen medizinischer Laien
No full textSimilar to other industrial countries, Germanys health care system is confronted with budget constraints and not everything what is possible from a medical point of view can be paid for. Although a fair allocation of health care resources requires generally accepted prioritization criteria, only few attemps have been made to involve the general public in the process of priority setting in medicine. The present study investigates public preferences for the allocation of medical resources whereat it focuses on differences in the preferences of individuals with different social status, age, sex and health. A mixed-methods design is used for combining a qualitative interview study, inferential statistics, and a conjoint analysis. The interview study explores in detail the criteria and underlying principles of justice used to allocate medical services. 32 purposefully selected medical laypersons were interviewed, following a semi-structured questionnaire. The results show that in addition to medical criteria such as therapeutic benefit or severity of illness, the interviewees also draw upon issues such as lifestyle or the patients age. The criteria refer to different principles of justice, such as need or efficiency, and are highly disputed in parts. The conjoint analysis estimates the relative importance of selected priority setting criteria explored in the interview study. 120 purposefully selected participants were asked to rank order hypothetical patients who differed in age, lifestyle, type and severity of illness, improvement in health and treatment costs by priority of treatment. The findings show that the patients age is the most important criterion for the allocation of health care recources, followed by "severity of illness" and "improvement in health". Preferences vary among participants with different social status and sex, which refer to different attitudes towards distributive justice and may reflect different socialization experiences and self-interests
Structural characterization of porins in the presence of antibiotics
No full textThe main goal of my PhD work was to try to elucidate the major pathways of antibiotics into the bacterial cell, and their interaction at the molecular level with bacterial membrane components. Bacterial membranes show high structural complexity. The outer membrane of Gram-negative bacteria, acting as a selectively permeable barrier, enables the bacterial cell to survive in various hostile environments. Restricted permeability is one important factor in determining antibiotic resistance as no antimicrobial agent will be effective unless it can penetrate the cell wall, so that knowledge of their composition and function becomes essential to the design and development of effective antibiotics. Channel forming proteins are a very important membrane component involved in the influx of several hydrophilic compounds, including different families of antibiotics. In the present work, fluorescence techniques are combined with high-resolution conductance measurements (black lipid bilayer technique) to characterize these biological structures in the presence and in the absence of antibiotics. Results obtained from fluorescence measurements can be successfully combined with bilayer measurements revealing details of the molecular interactions between the antibiotic and the the major porins of Escherichia coli. Cephalosporin studies proved the importance of the use of these two techniques and show that these interactions were higher for OmpF than for OmpC. Studies on single mutated OmpF porins demonstrated the drastic effect on channel permeation by substitution of a single amino acid. The replacement of a positively charged residue by a neutral one in the channel constriction zone results in a much lower main effective barrier for the translocation of antibiotics. Our studies with enrofloxacin not only corroborate this fact but also show that the replacement of an aminoacid residue away from the constriction zone also affects the antibiotic transport. The comprehensive information provided by the complementary and wide-ranging studies of drug-porin interactions can provide a thorough understanding of the mechanisms of drug intake and resistance, which can enable refinement of the current drug therapies and the design of new types of antibiotics to target resistant organisms
The Bacterial Community of Marine Copepods
No full textMarine copepods form one of the most abundant mesozooplankton groups in the oceans. They are important components of the marine food web and are a significant link between primary producers and higher trophic levels. They and are associated with various numbers of different bacteria, but to date little effort has been made to obtain an overview of the whole bacterial community associated with these animals. Therefore, this thesis aims to provide more information about their whole bacterial community. After determining the best suited DNA extraction technique for investigating the copepod-bacteria-consortia for further analysis with denaturing gradient gel electrophoresis (DGGE), four copepod key genera were investigated over a sampling period of two years in the German Bight, North Sea. The bacterial community-fingerprints of these different copepod taxa were compared for determining differences in the community composition and for temporal changes in community structure. To identify the members of the bacterial community associated with marine copepods, bacterial phylotypes of four copepod key- and three less frequently appearing genera were identified by 16S rRNA gene sequencing. Neither differences of the bacterial community-patterns among different copepod genera nor seasonal changes or succession were found throughout the survey. From the phylogenetic analysis, it could be concluded that the investigated marine copepods were associated with bacteria of four phyla: Proteobacteria, Bacteroidetes, Actinobacteria and Firmicutes. Roseovarius spp., Sulfitobacter spp., Psychrobacter spp. and Photobacterium spp. were the most abundant bacterial genera. This study contributes the first detailed insights of the whole bacterial community of different marine copepod genera. Additionally it provides insights whether the bacterial community composition is copepod genera-specific and/or whether it changes seasonally. These findings can provide a new platform for identifying bacterial symbionts and parasites of the copepods by investigating the function and abilities of the detected bacteria
Exploring the Marine Virosphere: From Genome Context to Content
No full textOver the last decade, we have witnessed the dawn of marine phage genomics. Since the first genome was sequenced just over ten years ago, nearly thirty additional marine phage genomes and eleven marine virus metagenomes have offered a small glimpse into the genomic underpinnings of phage in the oceans. Genomics has revealed their role in host metabolism, as phage genomes harbor environmentally relevant functional genes, such as those involved in photosynthesis, nutrient stress response, nucleotide scavenging, and vitamin biosynthesis, some of which are expressed during infection. Furthermore, due to evidence of phage activity in host genomic islands, phages are now thought to be important drivers of microbial niche adaptation and diversification in the oceans. In recent years, advances in sequencing technologies and falling costs have led to sequence generation at an unprecedented rate. However, with this input, our ability to analyze and interpret new sequence data in attempt to garner biological insights (as those described above) is under serious threat. The role of bioinformatics in the current age is to keep this data accessible, or we risk serious loss in its value. For this reason the development of contextual data standards becomes crucial. The power of context to a biologist touches upon the core tenets of comparative genomics by expanding the dimensions among which comparisons and inferences can be made. This thesis addresses bioinformatic themes of contextual data development and implementation as a means to enhance marine phage genomics. This puts into practice the ultimate role of bioinformatics: to facilitate the capture and collection of various data sources, enabling in silico biological predictions that lead to acute, solvable laboratory experiments