Spectrum of stochastic adding machines and fibered Julia sets

Consider the basic algorithm to perform the transformation n--> n+1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through sucessive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enable us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains.Comment: 26pages, 2 figure

Local dynamics for fibered holomorphic transformations

Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case

Cartographic generalization

This short paper gives a subjective view on cartographic generalization, its achievements in the past, and the challenges it faces in the future

Biosynthetic plasticity as a means for the discovery and diversification of natural products

Naturstoffe inspirieren fortwährend die Arzneistoffentwicklung, da sie zentrale Ausgangspunkte für die Strukturmodifikation und -optimierung darstellen. Daher ist die Entdeckung neuer Sekundärstoffe und ihrer biologischen Aktivität von zentraler Bedeutung, ebenso wie Studien zu entsprechenden Struktur-Wirkungsbeziehungen. Diese Arbeit zeigt, wie Präkursor-gesteuerte Biosynthese als universell einsetzbare Methode zur Untersuchung diverser Forschungsfragen eingesetzt werden kann. Die Derivatisierung der myxobakteriellen Naturstoffe Myxochelin B, Pseudochelin A, sowie Aurachin D gibt Einblicke in die natürliche Promiskuität der Biosynthesewege. Durch Zugabe von Benzoesäureanaloga in einem rekom- binanten Myxococcus xanthus Stamm, wurde die Produktion von Myxochelin B und Pseudochelin A gesteigert, sowie auch 14 Derivate dieser Naturstoffe erzeugt. Es wurde gezeigt, dass diese Produkte eine ähnliche oder bessere Bioaktivität bezüglich der humanen 5-Lipoxygenasehemmung aufweisen als die zuvor getesteten Myxochelin A-Analoga. Auf diese Weise konnte das bisherige Wissen über ihre Struktur-Wirkungsbeziehungen erweitert werden. Zudem wurde Stigmatella erecta genutzt, um drei fluorierte Aurachin D Analoga zu generieren, welche eine vergleichbare antibiotische Potenz hatten wie die in der Natur gebildete Verbindung. Ferner wurde in zwei Modellstämmen eine Methode zur Wirkstoffsuche entwickelt und getestet, die auf dem biosynthetischen Einbau von nicht natürlich vorkommenden, acetylenischen Präkursoren in Naturstoffe, der anschließenden Derivatisierung durch Click Chemie und UV/VIS Visualisierung beruht. Untersuchungen an M. xanthus, aber auch an Ralstonia solanacearum zeigten, dass sich Aminosäuren als biosynthetische Bausteine nur selten durch Analoga mit acetylenischen Funktionen ersetzen lassen. Die Zufuhr von Fettsäuren mit terminaler Alkinylgruppe war jedoch erfolgreicher und einige wurden in quantitativen Ausbeuten inkorporiert. Dies gelang u.a. in der Biosynthese des Antibiotikums Micacocidin, in welcher ein 5-Hexinsäure-haltiges Derivat generiert werden konnte. Dagegen war der Ralsolamycin-Biosyntheseweg weniger tolerant gegenüber den Fettsäureanaloga, lieferte aber dennoch messbare Mengen der alkinylhaltigen Produkte. Dieser Einsatz als chemische Sonden lieferte Erkenntnisse über die möglichen Inkorporationsmöglichkeiten, zeigte jedoch auch die Grenzen der Derivatisierung von Rohextraktproben auf.Natural products continuously inspire drug development as they represent key starting points for structural modification and optimization. Therefore, the discovery of new secondary metabolites and their biological activity is of vital importance, as are studies of corresponding structure-activity relationships. This work demonstrates how precursor-directed biosynthesis can be used as a universally applicable method to investigate diverse research questions. Derivatization of the myxobacterial natural products myxochelin B, pseudochelin A, as well as aurachin D provides insight into the natural promiscuity of biosynthetic pathways. Addition of benzoic acid analogs in a recombinant Myxococcus xanthus strain, increased the production of myxochelin B and pseudochelin A, and also generated 14 derivatives of these natural products. These compounds were shown to have similar or improved bioactivity with respect to human 5 lipoxygenase inhibition than the previously tested myxochelin A analogs. In this way, previous knowledge of their structure-activity relationships was expanded. Furthermore, Stigmatella erecta was used to generate three fluorinated aurachin D analogs that had equivalent antibiotic potency to the compound formed in nature. In addition, a drug discovery method based on the biosynthetic incorporation of non-naturally occurring acetylenic precursors into natural products, their subsequent derivatization by Click chemistry and UV/VIS visualization was developed and tested in two model strains. Studies on M. xanthus and Ralstonia solanacearum showed that amino acids as biosynthetic building blocks can rarely be replaced by analogs with acetylenic functions. However, the supply of fatty acids with terminal alkynyl groups was more successful and some were incorporated in quantitative yields. Among others, this was successful for the biosynthesis of the antibiotic micacocidin, in which case a 5-hexynoic acid-containing derivative could be generated. In contrast, the ralsolamycin biosynthetic pathway was less tolerant of the fatty acid analogs, but still yielded measurable amounts of the alkynyl-containing products. This application as chemical probes provided insights into the potential incorporation possibilities, but also demonstrated the limitations of derivatizing crude extract samples

Analysis of mobility data–A focus on Mobile Mapping Systems

The increasing availability of devices to capture the position of moving objects (and other environmental information) leads to a very large amount and variety of mobility data. In order to obtain important information about the objects, their behavior or the environment of the objects, an automatic analysis is required. This article highlights current research questions in the context of the analysis of mobility data and presents them on the basis of work carried out at the Institute of Cartography and Geoinformatics (ikg) at Leibniz University of Hannover, Germany. A focus is put on the analysis and exploitation of information from Mobile Mapping vehicles

The ECB's Controversial Securities Market Programme(SMP) and its role in relation to the modified EFSF andthe future ESM

The article analyzes how the role of the European Central Bank (ECB) has developed throughout the sovereign debt crisis. The author concludes that the ECB acted, so far, within the limits of its competences. However, he recognizes that this judgment is built on a rather "aggressive” interpretation of the TFEU and the statute of the ECB. The author is very sceptical that the existence of the modified EFSF and ESM will allow the ECB to stop buying sovereign bonds in secondary markets. He outlines the structure of a potential future Fiscal Union including Eurobond