Algebraic Discrete Morse Theory and Applications to Commutative Algebra

In dieser Doktorarbeit verallgemeinern wir die Diskrete Morse Theorie von Forman auf eine algebraische Version, die wir Algebraische Diskrete Morse- Theorie nennen. Ziel der Theorie ist es zu einem gegebenem algebraischem Kettenkomplex freier R-Moduln einen Homotopie-äquivalenten Kettenkomplex zu konstruieren, dessen Ränge in den einzelnen homologischen Graden kleiner sind. Die Idee unserer Theorie ist es den Komplex als gerichteten Graphen zu interpretieren, und dann in diesem Graphen nach möglichst großen azyklischen Matchings zu suchen. Mit Hilfe dieser azyklischen Matchings wird ein sogenannter Morse-Graph konstruiert und wir beweisen, dass dessen zugehöriger Kettenkomplex dieselbe Homologie wie der Ausgangskomplex hat. Der Hauptteil der Arbeit besteht aus Anwendungen unserer Theorie in der Kommutativen Algebra. Wir verwenden unser Verfahren zur Konstruktion von minimalen multigraduierten freien Auflösungen verschiedener Moduln. In erster Linie beschäftigen wir uns mit der Konstruktion von minimalen freien Auflösungen des Restklassenkörpers über Quotientenringen aus dem (nicht notwendig kommutativen) Polynomring und einem beliebigen Ideal. Hier bekommen wir für verschiedene Klassen von Ringen neue minimale Auflösungen des Restklassenkörpers. Unter anderem können wir damit eine Vermutung von Sturmfels beweisen und ein Resultat von BACH zur Berechnung der Hochschild-Homologie deutlich verallgemeinern. Für den Fall, dass der Quotientenring aus einem kommutativen Polynomring und einem monomialen Ideal gebildet wird sind wir insbesondere an der Poincare-Betti Reihe interessiert. Bekannt ist, dass in diesem Fall die Poincare-Betti Reihe eine rationale Funktion ist. Eine konkrete Gestalt war jedoch bis jetzt nicht bekannt. Mit Hilfe der Algebraischen Diskreten Morse-Theorie konstruieren wir einen graduierten Vektorraum von dem wir vermuten, dass er als Vektorraum isomorph zur minimalen Auflösung des Körpers ist. Da wir die Hilbertreihe dieses Vektorraums ausrechnen können, bekommen wir eine explizite Gestalt der multigraduierten Poincare-Betti Reihe für solche Ringe. Unsere Form der Poincare-Betti Reihe präzisiert eine Vermutung von Charalambous und Reeves. Wir beweisen unsere Vermutung über die minimale Auflösung des Restklassenkörpers für verschiedene Klassen von monomialen Ringen. Da die Golod-Eigenschaft von monomialen Ringen durch eine spezielle Form der Poincare-Betti Reihe charakterisiert werden kann, bekommen wir mit unserer Gestalt der Poincare-Betti Reihe neue kombinatorische Kriterien für die Golod-Eigenschaft von monomialen Ringen, die nur von den Erzeugern des herausdividierten Ideals abhängen. Ein weiterer Teil der Arbeit beschäftigt sich mit der Konstruktion minimaler Auflösungen von Borel bzw. p-Borel fixed Idealen. Über Auflösungen von p-Borel fixed Idealen war bislang sehr wenig bekannt. Wir beweisen die Existenz von zellulären minimalen Auflösungen für eine neue, relativ große, Klasse von p-Borel fixed Idealen und geben Formeln für deren Poincare-Betti Reihe sowie deren Regularität. Diese Formeln verallgemeinern bestehende Resultate. Zum Schluss werden zwei verwandte Probleme aus der algebraischen Kombinatorik diskutiert. Das erste Problem beschäftigt sich mit Homologien von nilpotenten Lie-Algebren und das zweite behandelte Problem ist die Neggers-Stanley Vermutung über die Unimodalität spezieller Polynome. Für beide Probleme präsentieren wir einige Resultate und Lösungsansätze für den allgemeinen Fall

Baseline MELD score predicts hepatic decompensation during antiviral therapy in patients with chronic hepatitis C and advanced cirrhosis

Background and Aims: In patients with advanced liver cirrhosis due to chronic hepatitis C virus (HCV) infection antiviral therapy with peginterferon and ribavirin is feasible in selected cases only due to potentially life-threatening side effects. However, predictive factors associated with hepatic decompensation during antiviral therapy are poorly defined. Methods: In a retrospective cohort study, 68 patients with HCV-associated liver cirrhosis (mean MELD score 9.18±2.72) were treated with peginterferon and ribavirin. Clinical events indicating hepatic decompensation (onset of ascites, hepatic encephalopathy, upper gastrointestinal bleeding, hospitalization) as well as laboratory data were recorded at baseline and during a follow up period of 72 weeks after initiation of antiviral therapy. To monitor long term sequelae of end stage liver disease an extended follow up for HCC development, transplantation and death was applied (240weeks, ±SD 136weeks). Results: Eighteen patients (26.5%) achieved a sustained virologic response. During the observational period a hepatic decompensation was observed in 36.8%. Patients with hepatic decompensation had higher MELD scores (10.84 vs. 8.23, p14, respectively. Baseline MELD score was significantly associated with the risk for transplantation/death (p<0.001). Conclusions: Our data suggest that the baseline MELD score predicts the risk of hepatic decompensation during antiviral therapy and thus contributes to decision making when antiviral therapy is discussed in HCV patients with advanced liver cirrhosis

The Significance of the Theological Declaration of Barmen 1934 and “Christophobia in Europe” Today

The article delves into the enduring significance of theological declarations such as the Barmen Declaration of 1934 and their relevance in contemporary discourse, particularly regarding issues like Christophobia in Europe. It explores the historical contexts and theological underpinnings of declarations like Barmen, Belhar, and the Heidelberg Disputation, highlighting their confrontations with oppressive political and ecclesiastical powers. Additionally, it examines critiques of European attitudes towards Christianity by scholars such as Joseph H.H. Weiler and discusses the transformative potential of movements emphasizing the power of the Holy Spirit, such as Pentecostalism. The article underscores the ongoing theological dialogue surrounding liberation, social justice, and the enduring relevance of biblical theology in addressing contemporary challenges

Growth and Survival of Larval Fishes: The Role of Zooplankton Abundance and Competition

Interactions among larval gizzard shad, bluegill and zooplankton prey were examined via a controlled mesocosm experiment and field sampling in Lake Shelbyville, Illinois. In the mesocosm experiment gizzard shad growth and survival were negatively correlated with shad density and positively correlated with macrozooplankton prey. Bluegill growth was also positively correlated with prey availability, but survival was uniformly high despite differences in zooplankton abundance and fish density. Declines in macrozooplankton and copepod biomass were related to fish density. In Lake Shelbyville limnetic overlap of larval gizzard shad and bluegill was limited to a three week period, with the interval of greatest shad abundance preceding the appearance of bluegill. Zooplankton abundance declined greatly following the peak in shad abundance, and remained low when bluegill were present-a pattern documented in previous studies. Growth rates of gizzard shad were highest early and declined throughout the summer, whereas bluegill growth was highest during mid to late summer. Growth rates of gizzard shad and bluegill were not correlated with fish density. However, as predicted from the mesocosm experiment, bluegill growth was correlated with available zooplankton prey. Diet overlap was high as gizzard shad and bluegill fed selectively on smaller prey items in June, switching to larger bodied cladocerans and copepods by July. As in the mesocosm experiment, zooplankton biomass was negatively correlated with fish density. We found no evidence of differential survival of larval bluegill over time in juveniles collected from the littoral zone in the fall. Our results suggest that growth and survival of planktivorous larval gizzard shad and bluegill are affected by availability of zooplankton prey, and that both intra- and interspecific exploitative competition can occur when resources become limiting

Application of precise genome editing tools in the zebrafish model to elucidate protein function with regards to developmental phenotypes

Genetic engineering is a powerful tool for biologists and geneticists to study the natural world. In general, it allows for asking and answering precise gene or DNA level questions about biological systems. The drawback of genetic engineering is that many applications requires a deep knowledge of multiple disciplines from biology to chemistry, which can make it inaccessible. Here I give a brief history of the field and define four tenets of necessary actions to begin engineering DNA, and four classes of applications using genetic engineering. I present three papers that define an accessible method of genome editing using CRISPR/Cas called GeneWeld, and describe two series of tools pGTag and pPRISM that reduce the materials cost of beginning genetic engineering experiments. I describe use cases for each tool, and finally present an expansion of the methodology and tools to generate synthetic alleles and examine their function in living zebrafish. We expect that these tools and methods will increase the accessibility of genetic engineering using and enable new kinds of research questions

Cristologia do Espírito: do triplo ministério de Cristo à tripla feição do Reino de Deus

a ser enviadoThe article analyzes the relation between the power of the creator and recreator God and the power of the Holy Spirit in Jesus Christ and through him. To analyze the theme, it proposes two key concepts proposed by the Geneva reformer, John Calvin. According to Calvin, the Holy Spirit needs to be understood within a strict relationship with Christology: Jesus Christ is the Holy Spirit. From this centrality of Christ comes forth the question: For what reason was Christ sent to the world? The answer to this is given by Calvin through the doctrine of the triple ministry of Christ (munus triplex Christi), which makes it possible to understand the public and eschatological work of Christ, bringing up connections with the Old Testament tradition, demonstrating lines of continuity between the pre-paschal and post-paschal actions of Jesus Christ, but also the work of kings, priest and prophets, evoked in the New Testament.O artigo analisa a relação entre o poder de Deus criador e recriador e o poderdo Espírito Santo em Jesus Cristo e por meio dele. Para analisar o tema, propõe duas noções-chave propostas pelo reformador de Genebra, João Calvino. Segundo Calvino, o Espírito Santo precisa ser compreendido em estreita relação com a cristologia: Jesus Cristo é o Espírito Santo. Dessa centralidade de Cristo segue a pergunta: Para que Cristo foi enviado ao mundo? A resposta a isso é dada por Calvino através da doutrina do triplo ministério de Cristo (munus triplex Christi), que possibilita a compreensão da atuação pública e escatológica de Cristo, afl orando conexões com a tradição veterotestamentária, evidenciando linhas de continuidade entre as atuações pré-pascal e pós-pascal de Jesus Cristo, mas também a atuação de reis, sacerdotes e profetas, evocados no Novo Testamento

Gottes Gerechtigkeit

Der Beitrag thematisiert angesichts evidenter Unrechtsverhältnisse in aller Welt zunächst zahlreiche Vorbehalte gegenüber jeder Rede von Gottes Gerechtigkeit. Er zeigt dann die Schwierigkeiten auf, unter dem Titel "Naturrecht" normative Zusammenhänge zu behaupten zwischen Gottes Gerechtigkeit, Regularitäten und Ordnungen in Natur und Kosmos und politischen, rechtlichen und moralischen Bemühungen um die Errichtung zwischenmenschlicher Wohlordnung. Die Annahme eines "Naturrechts" muss sich über die intrinsisch räuberische Verfassung von Natur und Leben hinwegsetzen. Nicht die Kräfte natürlichen Lebens, das auf Kosten von anderem Leben leben muss, sondern die gegenläufigen Kräfte der Liebe und der Barmherzigkeit, der freien, schöpferischen Selbstzurücknahme zugunsten anderen Lebens, die uns ebenso umgeben wie die Kräfte der Natur, verweisen auf Gottes Gerechtigkeit, die durch Gottes Wort und Gottes Geist den Menschen zuteil wird