Regularity of solutions of the p-Laplace equation in the Heisenberg group

tbd

Dispersive wave solutions of the klein-gordon equation in cosmology

L'equazione di Klein-Gordon descrive una ampia varietà di fenomeni fisici come la propagazione delle onde in Meccanica dei Continui ed il comportamento delle particelle spinless in Meccanica Quantistica Relativistica. Recentemente, la forma dissipativa di questa equazione si è rivelata essere una legge di evoluzione fondamentale in alcuni modelli cosmologici, in particolare nell'ambito dei cosiddetti modelli di k-inflazione in presenza di campi tachionici. L'obiettivo di questo lavoro consiste nell'analizzare gli effetti del parametro dissipativo sulla dispersione nelle soluzioni dell'equazione d'onda. Saranno inoltre studiati alcuni tipici problemi al contorno di particolare interesse cosmologico per mezzo di grafici corrispondenti alle soluzioni fondamentali (Funzioni di Green).

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Der Renormierungsgruppen-Fluß der konform-reduzierten Quantengravitation

Wir analysieren die Rolle von "Hintergrundunabhängigkeit" im Zugang der effektiven Mittelwertwirkung zur Quantengravitation. Wenn der nicht-störungstheoretische Renormierungsgruppen-(RG)-Fluß "hintergrundunabhängig" ist, muß die Vergröberung durch eine nicht spezifizierte, variable Metrik definiert werden. Die Forderung nach "Hintergrundunabhängigkeit" in der Quantengravitation führt dazu, daß die funktionale RG-Gleichung von zusätzlichen Feldern abhängt; dadurch unterscheidet sich der RG-Fluß in der Quantengravitation deutlich von dem RG-Fluß einer gewöhnlichen Quantentheorie, deren Moden-Cutoff von einer starren Metrik abhängt. Beispielsweise kann in der "hintergrundunabhängigen" Theorie ein Nicht-Gauß'scher Fixpunkt existieren, obwohl die entsprechende gewöhnliche Quantentheorie keinen solchen entwickelt. Wir untersuchen die Bedeutung dieses universellen, rein kinematischen Effektes, indem wir den RG-Fluß der Quanten-Einstein-Gravitation (QEG) in einem "konform-reduzierten" Zusammenhang untersuchen, in dem wir nur den konformen Faktor der Metrik quantisieren. Alle anderen Freiheitsgrade der Metrik werden vernachlässigt. Die konforme Reduktion der Einstein-Hilbert-Trunkierung zeigt exakt dieselben qualitativen Eigenschaften wie in der vollen Einstein-Hilbert-Trunkierung. Insbesondere besitzt sie einen Nicht-Gauß'schen Fixpunkt, der notwendig ist, damit die Gravitation asymptotisch sicher ist. Ohne diese zusätzlichen Feldabhängigkeiten ist der RG-Fluß dieser Trunkierung der einer gewöhnlichen $phi^4$-Theorie. Die lokale Potentialnäherung für den konformen Faktor verallgemeinert den RG-Fluß in der Quantengravitation auf einen unendlich-dimensionalen Theorienraum. Auch hier finden wir sowohl einen Gauß'schen als auch einen Nicht-Gauß'schen Fixpunkt, was weitere Hinweise dafür liefert, daß die Quantengravitation asymptotisch sicher ist. Das Analogon der Metrik-Invarianten, die proportional zur dritten Potenz der Krümmung ist und die die störungstheoretische Renormierbarkeit zerstört, ist unproblematisch für die asymptotische Sicherheit der konform-reduzierten Theorie. Wir berechnen die Skalenfelder und -imensionen der beiden Fixpunkte explizit und diskutieren mögliche Einflüsse auf die Vorhersagekraft der Theorie. Da der RG-Fluß von der Topologie der zugrundeliegenden Raumzeit abhängt, diskutieren wir sowohl den flachen Raum als auch die Sphäre. Wir lösen die Flußgleichung für das Potential numerisch und erhalten Beispiele für RG-Trajektorien, die innerhalb der Ultraviolett-kritischen Mannigfaltigkeit des Nicht-Gauß'schen Fixpunktes liegen. Die Quantentheorien, die durch einige solcher Trajektorien definiert sind, zeigen einen Phasenübergang von der bekannten (Niederenergie-) Phase der Gravitation mit spontan gebrochener Diffeomorphismus-Invarianz zu einer neuen Phase von ungebrochener Diffeomorphismus-Invarianz. Diese Hochenergie-Phase ist durch einen verschwindenden Metrik-Erwartungswert charakterisiert.

Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.

The Complex Monge-Ampère Equation

In questa trattazione si studia la regolarità delle soluzioni viscose plurisubarmoniche dell’equazione di Monge-Ampère complessa. Si tratta di un’equazione alle derivate parziali del secondo ordine completamente non lineare il cui termine del secondo ordine è il determinante della matrice hessiana complessa di una funzione incognita a valori reali u. Il principale risultato della tesi è un nuovo controesempio di tipo Pogorelov per questa equazione. Si prova cioè l’esistenza di soluzioni viscose plurisubarmoniche e non classiche per un equazione di Monge-Ampère complessa.

Impact of Bone Harvesting Techniques on Cell Viability and the Release of Growth Factors of Autografts

Background: Autogenous bone grafts obtained by different harvesting techniques behave differently during the process of graft consolidation; the underlying reasons are however not fully understood. One theory is that harvesting techniques have an impact on the number and activity of the transplanted cells which contribute to the process of graft consolidation. Materials and Methods: To test this assumption, porcine bone grafts were harvested with four different surgical procedures: bone mill, piezosurgery, bone drilling (bone slurry), and bone scraper. After determining cell viability, the release of molecules affecting bone formation and resorption was assessed by reverse transcription polymerase chain reaction and immunoassay. The mitogenic and osteogenic activity of the conditioned media was evaluated in a bioassay with isolated bone cells. Results: Cell viability and the release of molecules affecting bone formation were higher in samples harvested by bone mill and bone scraper when compared with samples prepared by bone drilling and piezosurgery. The harvesting procedure also affected gene expression, for example, bone mill and bone scraper samples revealed significantly higher expression of growth factors such as bone morphogenetic protein-2 and vascular endothelial growth factor compared with the two other modalities. Receptor activator of nuclear factor kappa B ligand expression was lowest in bone scraper samples. Conclusion: These data can provide a scientific basis to better understand the impact of harvesting techniques on the number and activity of transplanted cells, which might contribute to the therapeutic outcome of the augmentation procedure.

Cancer therapy modulates VEGF signaling and viability in adult rat cardiac microvascular endothelial cells and cardiomyocytes

This work was motivated by the incomplete characterization of the role of vascular endothelial growth factor-A (VEGF-A) in the stressed heart in consideration of upcoming cancer treatment options challenging the natural VEGF balance in the myocardium. We tested, if the cytotoxic cancer therapy doxorubicin (Doxo) or the anti-angiogenic therapy sunitinib alters viability and VEGF signaling in primary cardiac microvascular endothelial cells (CMEC) and adult rat ventricular myocytes (ARVM). ARVM were isolated and cultured in serum-free medium. CMEC were isolated from the left ventricle and used in the second passage. Viability was measured by LDH-release and by MTT-assay, cellular respiration by high-resolution oxymetry. VEGF-A release was measured using a rat specific VEGF-A ELISA-kit. CMEC were characterized by marker proteins including CD31, von Willebrand factor, smooth muscle actin and desmin. Both Doxo and sunitinib led to a dose-dependent reduction of cell viability. Sunitinib treatment caused a significant reduction of complex I and II-dependent respiration in cardiomyocytes and the loss of mitochondrial membrane potential in CMEC. Endothelial cells up-regulated VEGF-A release after peroxide or Doxo treatment. Doxo induced HIF-1α stabilization and upregulation at clinically relevant concentrations of the cancer therapy. VEGF-A release was abrogated by the inhibition of the Erk1/2 or the MAPKp38 pathway. ARVM did not answer to Doxo-induced stress conditions by the release of VEGF-A as observed in CMEC. VEGF receptor 2 amounts were reduced by Doxo and by sunitinib in a dose-dependent manner in both CMEC and ARVM. In conclusion, these data suggest that cancer therapy with anthracyclines modulates VEGF-A release and its cellular receptors in CMEC and ARVM, and therefore alters paracrine signaling in the myocardium.

Perinatal care at the limit of viability between 22 and 26 completed weeks of gestation in Switzerland. 2011 revision of the Swiss recommendations

Perinatal care of pregnant women at high risk for preterm delivery and of preterm infants born at the limit of viability (22-26 completed weeks of gestation) requires a multidisciplinary approach by an experienced perinatal team. Limited precision in the determination of both gestational age and foetal weight, as well as biological variability may significantly affect the course of action chosen in individual cases. The decisions that must be taken with the pregnant women and on behalf of the preterm infant in this context are complex and have far-reaching consequences. When counselling pregnant women and their partners, neonatologists and obstetricians should provide them with comprehensive information in a sensitive and supportive way to build a basis of trust. The decisions are developed in a continuing dialogue between all parties involved (physicians, midwives, nursing staff and parents) with the principal aim to find solutions that are in the infant's and pregnant woman's best interest. Knowledge of current gestational age-specific mortality and morbidity rates and how they are modified by prenatally known prognostic factors (estimated foetal weight, sex, exposure or nonexposure to antenatal corticosteroids, single or multiple births) as well as the application of accepted ethical principles form the basis for responsible decision-making. Communication between all parties involved plays a central role. The members of the interdisciplinary working group suggest that the care of preterm infants with a gestational age between 22 0/7 and 23 6/7 weeks should generally be limited to palliative care. Obstetric interventions for foetal indications such as Caesarean section delivery are usually not indicated. In selected cases, for example, after 23 weeks of pregnancy have been completed and several of the above mentioned prenatally known prognostic factors are favourable or well informed parents insist on the initiation of life-sustaining therapies, active obstetric interventions for foetal indications and provisional intensive care of the neonate may be reasonable. In preterm infants with a gestational age between 24 0/7 and 24 6/7 weeks, it can be difficult to determine whether the burden of obstetric interventions and neonatal intensive care is justified given the limited chances of success of such a therapy. In such cases, the individual constellation of prenatally known factors which impact on prognosis can be helpful in the decision making process with the parents. In preterm infants with a gestational age between 25 0/7 and 25 6/7 weeks, foetal surveillance, obstetric interventions for foetal indications and neonatal intensive care measures are generally indicated. However, if several prenatally known prognostic factors are unfavourable and the parents agree, primary non-intervention and neonatal palliative care can be considered. All pregnant women with threatening preterm delivery or premature rupture of membranes at the limit of viability must be transferred to a perinatal centre with a level III neonatal intensive care unit no later than 23 0/7 weeks of gestation, unless emergency delivery is indicated. An experienced neonatology team should be involved in all deliveries that take place after 23 0/7 weeks of gestation to help to decide together with the parents if the initiation of intensive care measures appears to be appropriate or if preference should be given to palliative care (i.e., primary non-intervention). In doubtful situations, it can be reasonable to initiate intensive care and to admit the preterm infant to a neonatal intensive care unit (i.e., provisional intensive care). The infant's clinical evolution and additional discussions with the parents will help to clarify whether the life-sustaining therapies should be continued or withdrawn. Life support is continued as long as there is reasonable hope for survival and the infant's burden of intensive care is acceptable. If, on the other hand, the health car...