A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

Untersuchungen zur Genauigkeit adaptiver unstetiger Galerkin-Simulationen mit Hilfe von Luftblasen-Testfällen

Allgemein erlaubt adaptive Gitterverfeinerung eine Steigerung der Effizienz numerischer Simulationen ohne dabei die Genauigkeit des Ergebnisses signifikant zu verschlechtern. Es ist jedoch noch nicht erforscht, in welchen Bereichen des Rechengebietes die räumliche Auflösung tatsächlich vergröbert werden kann, ohne die Genauigkeit des Ergebnisses signifikant zu beeinflussen. Diese Frage wird hier für ein konkretes Beispiel von trockener atmosphärischer Konvektion untersucht, nämlich der Simulation von warmen Luftblasen. Zu diesem Zweck wird ein neuartiges numerisches Modell entwickelt, das auf diese spezielle Anwendung ausgerichtet ist. Die kompressiblen Euler-Gleichungen werden mit einer unstetigen Galerkin Methode gelöst. Die Zeitintegration geschieht mit einer semi-implizite Methode und die dynamische Adaptivität verwendet raumfüllende Kurven mit Hilfe der Funktionsbibliothek AMATOS. Das numerische Modell wird validiert mit Hilfe einer Konvergenzstudie und fünf Standard-Testfällen. Eine Methode zum Vergleich der Genauigkeit von Simulationen mit verschiedenen Verfeinerungsgebieten wird eingeführt, die ohne das Vorhandensein einer exakten Lösung auskommt. Im Wesentlichen geschieht dies durch den Vergleich von Eigenschaften der Lösung, die stark von der verwendeten räumlichen Auflösung abhängen. Im Fall einer aufsteigenden Warmluftblase ist der zusätzliche numerische Fehler durch die Verwendung der Adaptivität kleiner als 1% des gesamten numerischen Fehlers, wenn die adaptive Simulation mehr als 50% der Elemente einer uniformen hoch-aufgelösten Simulation verwendet. Entsprechend ist die adaptive Simulation fast doppelt so schnell wie die uniforme Simulation.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Improved virological outcome in White patients infected with HIV-1 non-B subtypes compared to subtype B

Antiretroviral compounds have been predominantly studied in human immunodeficiency virus type 1 (HIV-1) subtype B, but only ~10% of infections worldwide are caused by this subtype. The analysis of the impact of different HIV subtypes on treatment outcome is important.

Auditory motion direction encoding in auditory cortex and high-level visual cortex

The aim of this functional magnetic resonance imaging (fMRI) study was to identify human brain areas that are sensitive to the direction of auditory motion. Such directional sensitivity was assessed in a hypothesis-free manner by analyzing fMRI response patterns across the entire brain volume using a spherical-searchlight approach. In addition, we assessed directional sensitivity in three predefined brain areas that have been associated with auditory motion perception in previous neuroimaging studies. These were the primary auditory cortex, the planum temporale and the visual motion complex (hMT/V5+). Our whole-brain analysis revealed that the direction of sound-source movement could be decoded from fMRI response patterns in the right auditory cortex and in a high-level visual area located in the right lateral occipital cortex. Our region-of-interest-based analysis showed that the decoding of the direction of auditory motion was most reliable with activation patterns of the left and right planum temporale. Auditory motion direction could not be decoded from activation patterns in hMT/V5+. These findings provide further evidence for the planum temporale playing a central role in supporting auditory motion perception. In addition, our findings suggest a cross-modal transfer of directional information to high-level visual cortex in healthy humans.

A brief update on lung stereology

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema-like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant-producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well-established classical stereological methods, these design-based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene-manipulated mice, at the light and electron microscopic level.

Effect of voluntary exercise on number and volume of cardiomyocytes and their mitochondria in the mouse left ventricle

Voluntary exercise (VE) has a beneficial influence on the heart and mean lifespan. The present study evaluates structural adaptations of cardiomyocytes and their mitochondria due to VE by new, unbiased stereological methods. Female, 7-9-week-old mice were randomly assigned to a control (CG, n = 7) or VE group (EG, n = 7). EG animals were housed in cages with free access to a running wheel and had a mean running distance of 6.7 (1.8) km per day. After 4 weeks, the hearts of all mice were processed for light and electron microscopy. We estimated the number and volume of cardiomyocytes by the disector method and the number and volume of mitochondria by estimation of the Euler number. In comparison to CG, VE did not have an effect on the myocardial volume of the left ventricle (CG: 93 (10), EG: 103 (17) (mm(3))), the number of cardiomyocytes (CG: 2.81 (0.27), EG: 2.82 (0.43) (x10(6))) and their number-weighted mean volume. However, the composition of the cardiomyocytes changed due to VE. The total volume of mitochondria (CG: 21.8 (4.9), EG: 32.2 (4.3) (mm(3)), P < 0.01) and the total number (CG: 3.76 (0.44), EG: 7.02 (1.13) (x10(10)), P < 0.001) were significantly higher in EG than in CG. The mean number-weighted mitochondrial volume was smaller in EG than in CG (P < 0.05). In summary, VE does not alter ventricular volume nor cardiomyocyte volume or number but the oxidative capacity of cardiomyocytes by an increased mitochondrial number and total volume in the left ventricle. These structural changes may participate in the beneficial effects of VE.

Contractile performance of adult ventricular rat cardiomyocytes is not directly jeopardized by NO/cGMP-dependent induction of pro-apoptotic pathways

The activation of NO/cGMP pathways can induce pro-apoptotic pathways in cardiomyocytes although only a small number of cardiomyocytes fulfill the criteria of apoptosis. The same pathways reduce the contractile performance of cardiomyocytes. In the present study, we tested the hypothesis that exposure of cells to NO/cGMP for 24 h decrease their contractile performance due to an activation of pro-apoptotic pathways. Experiments were performed on freshly isolated and cultured adult ventricular rat cardiomyocytes. Cells were incubated with 8-bromo-cyclo-GMP (100 nmol/L-1 micromol/L), the NO donor SNAP (1 nmol/L-100 micromol/L), or the guanylyl cyclase activator YC-1 (3 micromol/L). Cell shortening, contraction and relaxation velocities, and diastolic cell lengths were determined at beating frequencies of 0.5, 1, and 2 Hz 24 h later. The activation of pro-apoptotic pathways was determined by staining of cardiomyocytes with an antibody directed against active caspase-3 and quantification of the number of apoptotic cells (annexin staining). Caspase-3 activation and an increase in the number of apoptotic cells was observed, but only at the highest concentrations tested (8-bromo-cyclo-GMP: 1-10 mmol/L; SNAP: 1-100 micromol/L). At these concentrations, none of the drugs decreased the mean cell shortening of cardiomyocytes. However, at concentrations lower than those required for induction of apoptotic cell death, the diastolic cell lengths and sarcomere lengths increased but cell shortening decreased. In conclusion, low concentrations of either NO or cGMP cause a desensitization of myofibrils, as indicated by elongated cell shapes, increased sarcomere lengths and reduced load-free cell shortening. High concentrations of NO/cGMP induce caspase-3 activation and increase the number of cells fulfilling the criteria of apoptotic cell death but did not impair cell function. Therefore, induction of apoptotic cell death per se seems not to contribute to the loss of contractile efficiency on the cellular level.