Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist. Assuming that the systems are in continuous times, stemming from stochastic-differential-equation-based models and random discrete events, switching diffusions come into being. In such systems, continuous states and discrete events (discrete states) coexist and interact. A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points). When the discrete component takes a value $i$ (i.e., $\alpha(t)=i$), the continuous component $X(t)$ evolves according to the diffusion process whose drift and diffusion coefficients depend on $i$. Until very recently, in most of the literature $\alpha(t)$ was assumed to be a process taking values in a finite set, and that the switching rates of $\alpha(t)$ are either independent or depend only on the current state of $X(t)$. To be able to treat more realistic models and to broaden the applicability, this dissertation undertakes the task of investigating the dynamics of $(X(t),\alpha(t))$ in a much more general setting in which $\alpha(t)$ has a countable state space and its switching intensities depend on the history of the continuous component $X(t)$. We systematically established important properties of this system: well-posedness, the Markov Feller property, and the recurrence and ergodicity of the associated function-valued process. We have also studied several types of stability for the system

Anaerobic O-demethylation in acetobacterium dehalogenans: interaction mediated by O-demethylase components

The gram positive bacterium Acetobacterium dehalogenans belongs to the group of acetogens. The anaerobe utilizes the methyl group of phenyl methyl ethers, which are products of the lignin degradation process, as a carbon and energy source. The O-demethylation reaction in which the methyl group of the substrate is transferred to tetrahydrofolate is mediated by the key enzymes, the O-demethylases, in the methylotrophic metabolism. The O-demethylase enzyme complex consists of four components: a methyltransferase I (MT I) transfers the methyl group of a phenyl methyl ether to a super-reduced corrinoid protein ([CoI]-CP) to form methylcobalamin (CH3-[CoIII]-CP). The second methyltransferase (MT II) mediates the methyl transfer from CH3-[CoIII]-CP to tetrahydrofolate forming methyltetrahydrofolate. The inactive form of the corrinoid protein ([CoII]-CP), which is occasionally generated by inadvertent oxidation, is reduced by the activating enzyme (AE) in an ATP dependent reaction. Four different O-demethylase enzyme systems were identified as guaiacol-, syringate-, vanillate-, and veratrol-O-demethylase. In the work presented here, the interactions of the O-demethylase components were studied using two-hybrid assays, gel shift experiments and far-Western blot analyses. Emphasis was laid on studies on the interaction of AE and CP. With the exception of the yeast two-hybrid assay (Y2H), an interaction between AE and CP was always observed. In gel shift experiments, the presence of the corrinoid cofactor was a prerequisite for the interaction of the two components. On native PAGE, AE appeared as dimer. The Y2H experiments pointed to an involvement of the N-terminal fragment of AE (AE 1-133) in the oligomerization of the protein. Interaction studies in the presence of the other O-demethylase components revealed interactions of CP and the two MTs which is in accordance to the proposed reaction mechanism of the O-demethylases. The reductive activation of CP catalyzed by AE in an ATP dependent reaction was also studied. It was shown that AE is able to reduce the corrinoid cofactor of different CPs and therefore, AE seems to be an universal reductive activator of corrinoid enzymes of A. dehalogenans. The physiological electron donor for the corrinoid reduction is unknown so far. In this study two genes of A. dehalogenans encoding putative ferredoxins (Fds) were cloned and heterologously expressed in Escherichia coli. The reconstituted Fds I and II showed typical UV/Vis spectra for the presence of iron-sulfur clusters. The amino acid sequence analyses and iron determinations indicated that Fd I contains 4 [4Fe-4S] clusters while Fd II harbors two of these. However, the involvement of the two ferredoxins in corrinoid activation could not be demonstrated by the biochemical assays used.Der gram-positive Mikroorganismus Acetobacterium dehalogenans gehört zur Gruppe der acetogenen Bakterien. Er verwendet die Methylgruppe von Phenylmethylethern, Abbauprodukten des Lignins, als Kohlenstoff- und Energiequelle. Die Methylgruppe der Substrate wird durch O-Demethylasen, die Schlüsselenzyme des methylotrophen Stoffwechsels, auf Tetrahydrofolat übertragen. O-Demethylasen sind Enzymkomplexe und bestehen aus vier Proteinen: die Methyltransferase I (MT I) überträgt die Methylgruppe vom Phenylmethylether auf das super-reduzierte Corrinoidprotein ([CoI]-CP) unter Bildung von Methylcobalamin (CH3-[CoIII]-CP). Die Methyltransferase II (MT II) katalysiert den Methylgruppentransfer von CH3-[CoIII]-CP auf Tetrahydrofolat. Methyltetrahydrofolat wird gebildet. Die inaktive Form des Corrinoidproteins ([CoII]-CP), die aufgrund von Autoxidation entsteht, wird in einer ATP-abhängigen Reaktion durch das Aktivierende Enzym (AE) reduziert. Vier verschiedene O-Demethylase-Systeme – die Guaiacol-, die Syringat-, die Vanillat- und die Veratrol-O-Demethylase – wurden bisher in A. dehalogenans identifiziert. In der vorliegenden Arbeit wurde die Interaktion der O-Demethylasekomponenten unter Verwendung von Two-Hybrid-Systemen, Gel-Shift- sowie Far-Western Blot-Experimenten untersucht. Schwerpunkt war hierbei die Interaktion von AE und CP, die mit Ausnahme des Yeast Two-Hybrid-Systems (Y2H) für alle Methoden nachgewiesen werden konnte. In Gel-Shift-Experimenten war das Vorhandensein des Corrinoid-Cofaktors Voraussetzung für die Interaktion dieser beiden Proteinkomponenten. Auf nativen Gelen wurde AE als Dimer detektiert. Y2H-Analysen zeigten, dass für die Oligomerisierung wahrscheinlich ein N-terminales AE-Fragment verantwortlich ist. Interaktionsstudien in Anwesenweit weiterer O-Demethylasekomponenten führten zum Nachweis der Interaktion von CP mit beiden MT-Proteinen. Dieses Ergebnis stimmt mit dem postulierten Reaktionsmechanismus überein. Die Reduktion von inaktivem CP, die durch AE in einer ATP-abhängigen Reaktion katalysiert wird, war ebenfalls Bestandteil der hier durchgeführten Untersuchungen. Es wurde gezeigt, dass AE verschiedene Corrinoidproteine reduzieren kann. Somit scheint AE in A. dehalogenans als universeller reduktiver Aktivitator von Corrinoidproteinen zu fungieren. Der physiologische Elektronendonor dieses Prozesses ist bisher nicht bekannt. Es wurden zwei mutmaßliche Ferredoxingene von A. dehalogenans heterolog in Escherichia coli exprimiert. Die rekombinanten Ferredoxine (Fd) I und II wiesen nach Rekonstituion typische UV/Vis-Spektren für Eisen/Schwefel-Cluster-enthaltende Proteine auf. Sequenzanalysen sowie die Bestimmung von Eisen zeigten, dass Fd I vier und Fd II zwei [4Fe-4S]-Cluster enthält. Eine Beteiligung der Ferredoxine bei der Corrinoidaktivierung konnte bisher jedoch nicht gezeigt werden

Questions and conjectures about the modular representation theory of the general linear group GLn(F2) and the Poincar\'e series of unstable modules

This note is devoted to some questions about the representation theory over the finite field $\mathbb{F}_2$ of the general linear groups $\mathbb{GL_n(F_2)}$ and Poincar\'e series of unstable modules. The first draft was describing two conjectures. They were presented during talks made at VIASM in summer 2013. Since then one conjecture has been disproved, the other one has been proved. These results naturally lead to new questions which are going to be discussed. In winter 2013, Nguyen Dang Ho Hai proved the second conjecture, he disproved the first one in spring 2014. Up to now, the proof of the second one depends on a major topological result: the Segal conjecture. This discussion could be extended to an odd prime, but we will not do it here, just a small number of remarks will be made

Phenolic glucosides from the leaves of Desmodium gangeticum (L.) DC

From the water-soluble extract of the leaves of Desmodium gangeticum, three phenolic glucosides were isolated. By means of spectroscopic methods they were identified as methyl salicylate β-D-glucopyranoside (1), leonuriside A (2) and syringaresinol-4'-O-β-D-glucopyranoside (3). These compounds were isolated for the first time from the genus Desmodium. Compound 1 significantly inhibited a-glucosidase in comparison with diabetic drug acarbose

The First Record of Metaphire Birmanica (Rosa, 1888) in Vietnam, with Notes on Several Earthworm Species

The Amynthas and Metaphire species recorded in Vietnam have been rechecked based on original descriptions and preserved specimens. As a result, Metaphire birmanica (Rosa, 1888) is recorded in Vietnam for the first time. The species is recognized by having three pairs of spermathecal pores in 5/6/7/8, male pores in xviii, presence of copulatory pouches, no genial markings, and manicate intestinal caeca. In addition, three species have been rechecked and re-assigned to different genera, namely Amynthas tripidoporophoratus (Thai & Nguyen, 1993) comb. nov., Metaphire dranfocana (Do & Huynh, 1993) comb. nov., Metaphire anhumalatana (Thai & Huynh, 1993) comb. nov