Universal properties of distorted Kerr-Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.Comment: 7 page

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8\pi J)2+(4\pi Q2)2=A+ A-, where A+ and A- denote the areas of event and Cauchy horizon respectively

Convergence Rates of Gaussian ODE Filters

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives \emph{a priori} as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. This article establishes worst-case local convergence rates of order $q+1$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyses how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we show that, in the globally convergent case, the posterior credible intervals are well calibrated in the sense that they globally contract at the same rate as the truncation error. We illustrate these theoretical results by numerical experiments which might indicate their generalizability to $q \in \{2,3,\dots\}$.Comment: 26 pages, 5 figure

Influence of mirtazapine on salivary cortisol in depressed patients

Unlike other antidepressants, mirtazapine does not inhibit the reuptake of norepinephrine or serotonin but acts as an antagonist at presynaptic alpha(2)-receptors, at postsynaptic 5-HT2 and 5-HT3 receptors, and at histaminergic H1 receptors. Furthermore, mirtazapine has been shown to acutely inhibit cortisol secretion in healthy subjects. In the present study, the impact of mirtazapine treatment on salivary cortisol secretion was investigated in 12 patients (4 men, 8 women) suffering from major depression according to DSM-IV criteria. Patients were treated with mirtazapine for 3 weeks, receiving 15 mg mirtazapine on day 0, 30 mg on day 1 and 45 mg per day from day 2 up to the end of the study (day 21). Response to mirtazapine treatment was defined by a reduction of at least 50% in the Hamilton Rating Scale for Depression after 3 weeks of therapy. Salivary cortisol concentrations were measured before treatment (day -1), at the beginning of treatment (day 0), after 1 week (day 7) and after 3 weeks (day 21) of treatment with mirtazapine. Saliva samples were collected hourly from 08.00 until 20.00 h. The area under the curve values served as parameter for the salivary cortisol secretion. Following analysis of variance with a repeated measures design, tests with contrasts revealed a significant reduction of cortisol concentrations already after 1 day of mirtazapine treatment that was comparable in responders and nonresponders. In addition to new pharmacological approaches such as CRH1 receptor antagonists, mirtazapine therefore appears to be an effective strategy to decrease hypercortisolism and restore HPA system dysregulation in depression. However, the importance of the acute inhibitory effects of mirtazapine on cortisol secretion for its antidepressant efficacy has to be further clarified. Copyright (C) 2003 S. Karger AG, Basel

Charge transport in a nonlinear, three--dimensional DNA model with disorder

We study the transport of charge due to polarons in a model of DNA which takes in account its 3D structure and the coupling of the electron wave function with the H--bond distortions and the twist motions of the base pairs. Perturbations of the ground states lead to moving polarons which travel long distances. The influence of parametric and structural disorder, due to the impact of the ambient, is considered, showing that the moving polarons survive to a certain degree of disorder. Comparison of the linear and tail analysis and the numerical results makes possible to obtain further information on the moving polaron properties.Comment: 9 pages, 2 figures. Proceedings of the conference on "Localization and energy transfer in nonlinear systems", June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. To be publishe

Nonlinear charge transport mechanism in periodic and disordered DNA

We study a model for polaron-like charge transport mechanism along DNA molecules with emphasis on the impact of parametrical and structural disorder. Our model Hamiltonian takes into account the coupling of the charge carrier to two different kind of modes representing fluctuating twist motions of the base pairs and H-bond distortions within the double helix structure of $\lambda-$DNA. Localized stationary states are constructed with the help of a nonlinear map approach for a periodic double helix and in the presence of intrinsic static parametrical and/or structural disorder reflecting the impact of ambient solvent coordinates. It is demonstrated that charge transport is mediated by moving polarons respectively breather compounds carrying not only the charge but causing also local temporal deformations of the helix structure through the traveling torsion and bond breather components illustrating the interplay of structure and function in biomolecules.Comment: 23 pages, 13 figure

Cell seeding chamber for bone graft substitutes

There is an increasing demand for bone graft substitutes that are used as osteoconductive scaffolds in the treatment of bone defects and fractures. Achieving optimal bone regeneration requires initial cell seeding of the scaffolds prior to implantation. The cell seeding chamber is a closed assembly. It works like a sandglass. The position of the scaffold is between two reservoirs containing the fluid (e. g. blood). The fluid at the upper reservoir flows through the scaffold driven by gravity. Fluid is collected at the lower reservoir. If the upper reservoir is empty the whole assembly turned and the process starts again. A new compact cell seeding chamber for initial cell seeding has been developed that can be used in the operating theater