Near critical catalyst reactant branching processes with controlled immigration

Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. Such models are motivated by problems in chemical kinetics where one wants to keep the level of a catalyst above a certain threshold in order to maintain a desired level of reaction activity. A diffusion limit theorem for the scaled processes is presented, in which the catalyst limit is described through a reflected diffusion, while the reactant limit is a diffusion with coefficients that are functions of both the reactant and the catalyst. Stochastic averaging principles under fast catalyst dynamics are established. In the case where the catalyst evolves "much faster" than the reactant, a scaling limit, in which the reactant is described through a one dimensional SDE with coefficients depending on the invariant distribution of the reflected diffusion, is obtained. Proofs rely on constrained martingale problem characterizations, Lyapunov function constructions, moment estimates that are uniform in time and the scaling parameter and occupation measure techniques.Comment: Published in at http://dx.doi.org/10.1214/12-AAP894 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic Behavior of Near Critical Branching Processes and Modeling of Cell Growth Data

This dissertation is composed of two parts, a theoretical part, in which certain asymptotic properties of near critical branching processes are studied, and an applied part, consisting of statistical analysis of cell growth data. First, near critical single type Bienaym&eacute-Galton-Watson (BGW) processes are considered. It is shown that, under appropriate conditions, Yaglom distributions of suitably scaled BGW processes converge to that of the corresponding diffusion approximation. Convergences of stationary distributions for Q processes and models with immigration to the corresponding distributions of the associated diffusion approximations are established as well. Moreover, convergence of Yaglom distributions of suitably scaled multitype subcritical BGW processes to that of the associated diffusion model is established. Next, near critical catalyst-reactant branching processes with controlled immigration are considered. The catalyst population evolves according to a classical continuous time branching process, while the reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. A diffusion limit theorem for the scaled processes is established, in which the catalyst limit is a reflected diffusion and the reactant limit is a diffusion with coefficients depending on the reactant. Stochastic averaging under fast catalyst dynamics are considered next. In the setting where both catalyst and reactant evolve according to the above described (reflected) diffusions, but where the evolution of the catalyst is accelerated by a factor of n, we establish a scaling limit theorem, in which the reactant process is asymptotically described through a one dimensional SDE with coefficients depending on the invariant distribution of the catalyst reflected diffusion. Convergence of the stationary distribution of the scaled catalyst branching process (with immigration) to that of the limit reflected diffusion is established as well. Finally, results from a collaborative proof-of-principle study, relating cell growth to the stiffness of the surrounding environment, are presented.Doctor of Philosoph

The Early Universe : Probing Primordial Magnetic Fields, Dark Matter Models and the First Supermassive Black Holes

The goal of this work is to better understand the universe between recombination and reionization and to outline new possibilities to explore it in more detail. This concerns the stellar population, the physics of the early universe, and the formation of the first supermassive black holes. With the reionization optical depth from WMAP 5, I derive upper limits for the strength of primordial magnetic fields and dark matter annihilation / decay, as well as constraints for stellar population models. Further constraints can be found from the gamma-ray and neutrino background, which rule out s-wave annihilation of light dark matter. It was shown that future 21 cm observations will constrain primor- dial magnetic fields even further. To improve our understanding of the origin of the first supermassive black holes and their high metallicity, I explore how they can be observed with ALMA and JWST between redshift 5 and 15. For this purpose, I estimated and classified the available observables, and I provide several independent estimates for the expected number of high-redshift black holes. In spite of large model uncertainties, one can expect to find at least a few sources in a solid angle similar to the Hubble-Deep-Field

Acupuncture in Seasonal Allergic Rhinitis (ACUSAR) - Design and Protocol of a Randomised Controlled Multi-Centre Trial

Background: We report on the study design and protocol of a randomised controlled trial (Acupuncture in Seasonal Allergic Rhinitis, ACUSAR) that investigates the efficacy of acupuncture in the treatment of seasonal allergic rhinitis (SAR). Objective: To investigate whether acupuncture is non-inferior or superior to (a) penetrating sham acupuncture and (b) rescue medication in the treatment of SAR. Design: 3-armed, randomised controlled multi-centre trial with a total follow-up time of 16 weeks in the 1st year and 8 weeks in the 2nd year. Setting: 41 physicians in 37 out-patient units in Germany specialised in acupuncture treatment. Patients: 400 seasonal allergic rhinitis patients with clinical symptoms and test-positive (skin-prick test and/or specific IgE) to both birch and grass pollen. Interventions: Patients will be randomised in a 2:1:1 ratio to one of three groups: (a) semi-standardised acupuncture plus rescue medication (cetirizine); (b) penetrating sham acupuncture at non-acupuncture points plus rescue medication; or (c) rescue medication alone for 8 weeks (standard treatment group). Acupuncture and sham acupuncture will consist of 12 treatments per patient over 8 weeks. Main Outcome Measures: Average means of the Rhinitis Quality of Life Questionnaire (RQLQ) overall score and the Rescue Medication Score (RMS) between weeks 6 and 8 in the first year, adjusted for baseline values. Outlook: The results of this trial available in 2011 will have a major impact on the decision of whether acupuncture should be considered as a therapeutic option in the treatment of SAR

Physiologically Based Pharmacokinetic Modeling to Describe the CYP2D6 Activity Score-Dependent Metabolism of Paroxetine, Atomoxetine and Risperidone

The cytochrome P450 2D6 (CYP2D6) genotype is the single most important determinant of CYP2D6 activity as well as interindividual and interpopulation variability in CYP2D6 activity. Here, the CYP2D6 activity score provides an established tool to categorize the large number of CYP2D6 alleles by activity and facilitates the process of genotype-to-phenotype translation. Compared to the broad traditional phenotype categories, the CYP2D6 activity score additionally serves as a superior scale of CYP2D6 activity due to its finer graduation. Physiologically based pharmacokinetic (PBPK) models have been successfully used to describe and predict the activity score-dependent metabolism of CYP2D6 substrates. This study aimed to describe CYP2D6 drug–gene interactions (DGIs) of important CYP2D6 substrates paroxetine, atomoxetine and risperidone by developing a substrate-independent approach to model their activity score-dependent metabolism. The models were developed in PK-Sim®, using a total of 57 plasma concentration–time profiles, and showed good performance, especially in DGI scenarios where 10/12, 5/5 and 7/7 of DGI AUClast ratios and 9/12, 5/5 and 7/7 of DGI Cmax ratios were within the prediction success limits. Finally, the models were used to predict their compound’s exposure for different CYP2D6 activity scores during steady state. Here, predicted DGI AUCss ratios were 3.4, 13.6 and 2.0 (poor metabolizers; activity score = 0) and 0.2, 0.5 and 0.95 (ultrarapid metabolizers; activity score = 3) for paroxetine, atomoxetine and risperidone active moiety (risperidone + 9-hydroxyrisperidone), respectively

Negative Posttraumatic Cognitions Color the Pathway from Event Centrality to Posttraumatic Stress Disorder Symptoms

Background: The centrality of an event indicates the extent to which it becomes a core part of identity and life story. Event centrality (EC) has been shown to have a strong relationship with PTSD symptoms, which seems to be indirectly influenced by negative posttraumatic cognitions (PTC). However, research on this potential mediation and its causal links particularly with clinical samples is limited and essential to derive treatment implications. Methods: Pre- and posttreatment data of 103 day-unit patients with PTSD was examined using mediation analyses and structural equation modeling. Results: Negative PTC mediated the relationship between EC and PTSD symptoms, partially pre- and completely posttreatment. Within extended longitudinal analyses causal directions of the mediation pathways were not adequately interpretable due to unexpected suppression effects. Conclusions: The results suggest that EC may only have an indirect effect on PTSD symptoms through negative PTC. Thus, decreasing negative PTC which are connected to centralized events might be a key element for PTSD treatment. Thereby, transforming the cognitions' valence to more positive and constructive forms could be crucial rather than mere decentralization. Although suppression effects limited causal inferences, they do not contradict the mediation and further indicate potential interactional terms and a transformation of EC