A coupling approach to Doob's theorem

We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\mu$ converge to $\mu$ in the total variation distance. In addition we show that non-singularity (rather than equivalence) of the transition probabilities suffices to ensure convergence of the transition probabilities for $\mu$-almost all initial conditions

Generalized couplings and ergodic rates for SPDEs and other Markov models

We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtained results to show exponential ergodicity of a variety of nonlinear stochastic partial differential equations with additive forcing, including 2D stochastic Navier-Stokes equations. Our main tool is a new version of the generalized coupling method

Competitive Scavenging of Trace Metals by HFO and HMO during Redox-driven Early Diagenesis of Ferromanganese Nodules (11 pp)

-: Dedicated to Prof. Dr. Ulrich Förstner on his 65th birthday Background: Surface complexation models (SCM) alone have yet less successfully reproduced sorption isotherms of hydrous manganese oxides (HMO). This is in part due to the fact that the HMO structure may vary with pH, and also because microbially formed natural HMO has an oxidation number O/Mn 〈 2, i.e. is of non-stoichiometrical composition. The former effect has often led to severe artefacts, such as an under-prediction of metal sequestration at low pH, and non-comparable pK and pHZPC values in literature. The latter effect is of particular importance for environments of varying redox conditions like sediments. Objectives: We propose therefore a new sorption model comprising of amphoteric site SCM, ion exchange due to permanent charge compensation, and solid solution formation, in order to comply at least in part with the redox complexity of HMO phases of stable birnessite- and buserite-type structures. Methods: The model is run by a new Gibbs energy minimization code which is shown to be particularly suitable for such a sorption continuum approach. Results and Discussion: Initial calibration of the model was performed by experimental literature data on simple laboratory systems. Thus parameterised, we simulated on the basis of available field data the effect of redox-driven dissolution of a ferromanganese nodule on the partitioning of metals between the interacting HMO, HFO, and marine water phases. Our scenario model suggests that significant fraction of Mn and other metals, probably 50% or more, may be recycled to water column from the surface of the ferromanganese nodule upon gradual development of the bottom water stagnation, except of Zn for which a by far stronger net retention was found. Conclusion and Outlook: Our model, even if only a first approximation, clearly shows that stagnation in the marine bottom water, once occurring, can drastically change primary element proxy records in ferromanganese nodules, smoothing out any anomalous patterns in the most recent recor

Nucleation and Growth of the Superconducting Phase in the Presence of a Current

We study the localized stationary solutions of the one-dimensional time-dependent Ginzburg-Landau equations in the presence of a current. These threshold perturbations separate undercritical perturbations which return to the normal phase from overcritical perturbations which lead to the superconducting phase. Careful numerical work in the small-current limit shows that the amplitude of these solutions is exponentially small in the current; we provide an approximate analysis which captures this behavior. As the current is increased toward the stall current J*, the width of these solutions diverges resulting in widely separated normal-superconducting interfaces. We map out numerically the dependence of J* on u (a parameter characterizing the material) and use asymptotic analysis to derive the behaviors for large u (J* ~ u^-1/4) and small u (J -> J_c, the critical deparing current), which agree with the numerical work in these regimes. For currents other than J* the interface moves, and in this case we study the interface velocity as a function of u and J. We find that the velocities are bounded both as J -> 0 and as J -> J_c, contrary to previous claims.Comment: 13 pages, 10 figures, Revte

SpEYEders: Adults’ and children’s affective responses during immersive playful gaze interactions transforming virtual spiders

Specific phobias like spider phobia represent a frequent mental health problem in children and adolescents, demanding innovative prevention and treatment approaches. We therefore develop an eye tracking supported Virtual Reality serious game for school-aged children, realizing gaze interactions to promote attention towards, and positive experiences during exposure to spiders. Within pilot studies in adults (n=30) and children (n=14) without fear of spiders, we assessed positive and negative affect during prototype gaze feedback through five different variants: If gazed for few seconds, the virtual spider changed into a shrunk, a rainbow coloured, or dying spider, or morphed into a smileyball, or speaks friendly. We found the highest positive affect for the rainbow and smileyball variant, followed by the shrunk and friendly speaking variant. In contrast, the dying variant was excluded due to the possible induction of negative affect. Findings indicate eligible variants for the further development of the VR serious game

Heterologous expression, purification and characterization of nitrilase from Aspergillus niger K10

<p>Abstract</p> <p>Background</p> <p>Nitrilases attract increasing attention due to their utility in the mild hydrolysis of nitriles. According to activity and gene screening, filamentous fungi are a rich source of nitrilases distinct in evolution from their widely examined bacterial counterparts. However, fungal nitrilases have been less explored than the bacterial ones. Nitrilases are typically heterogeneous in their quaternary structures, forming short spirals and extended filaments, these features making their structural studies difficult.</p> <p>Results</p> <p>A nitrilase gene was amplified by PCR from the cDNA library of <it>Aspergillus niger </it>K10. The PCR product was ligated into expression vectors pET-30(+) and pRSET B to construct plasmids pOK101 and pOK102, respectively. The recombinant nitrilase (Nit-ANigRec) expressed in <it>Escherichia coli </it>BL21-Gold(DE3)(pOK101/pTf16) was purified with an about 2-fold increase in specific activity and 35% yield. The apparent subunit size was 42.7 kDa, which is approx. 4 kDa higher than that of the enzyme isolated from the native organism (Nit-ANigWT), indicating post-translational cleavage in the enzyme's native environment. Mass spectrometry analysis showed that a C-terminal peptide (Val₃₂₇- Asn₃₅₆) was present in Nit-ANigRec but missing in Nit-ANigWT and Asp₂₉₈-Val₃₁₃peptide was shortened to Asp₂₉₈-Arg₃₁₀in Nit-ANigWT. The latter enzyme was thus truncated by 46 amino acids. Enzymes Nit-ANigRec and Nit-ANigWT differed in substrate specificity, acid/amide ratio, reaction optima and stability. Refolded recombinant enzyme stored for one month at 4°C was fractionated by gel filtration, and fractions were examined by electron microscopy. The late fractions were further analyzed by analytical centrifugation and dynamic light scattering, and shown to consist of a rather homogeneous protein species composed of 12-16 subunits. This hypothesis was consistent with electron microscopy and our modelling of the multimeric nitrilase, which supports an arrangement of dimers into helical segments as a plausible structural solution.</p> <p>Conclusions</p> <p>The nitrilase from <it>Aspergillus niger </it>K10 is highly homologous (≥86%) with proteins deduced from gene sequencing in <it>Aspergillus </it>and <it>Penicillium </it>genera. As the first of these proteins, it was shown to exhibit nitrilase activity towards organic nitriles. The comparison of the Nit-ANigRec and Nit-ANigWT suggested that the catalytic properties of nitrilases may be changed due to missing posttranslational cleavage of the former enzyme. Nit-ANigRec exhibits a lower tendency to form filaments and, moreover, the sample homogeneity can be further improved by <it>in vitro </it>protein refolding. The homogeneous protein species consisting of short spirals is expected to be more suitable for structural studies.</p