Boundary non-crossings of Brownian pillow

Let B_0(s,t) be a Brownian pillow with continuous sample paths, and let h,u:[0,1]^2\to R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability \psi(u;h):=P{B_0(s,t)+h(s,t) \le u(s,t), \forall s,t\in [0,1]}. Further we investigate the asymptotic behaviour of $\psi(u;\gamma h)$ with $\gamma$ tending to infinity, and solve a related minimisation problem.Comment: 14 page

An optimal series expansion of the multiparameter fractional Brownian motion

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal.Comment: 21 pages, no figures, final version, to appear in Journal of Theoretical Probabilit

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Occupational exposure to chemicals and fetal growth: the Generation R Study

Background Developmental diseases, such as birth defects, growth restriction and preterm delivery, account for >25 of infant mortality and morbidity. Several studies have shown that exposure to chemicals during pregnancy is associated with adverse birth outcomes. The aim of this study was to identify whether occupational exposure to various chemicals might adversely influence intrauterine growth patterns and placental weight.Methods Associations between mat

Industry/University Collaboration at the University of Michigan-Dearborn: A Focus on Relevant Technology

https://deepblue.lib.umich.edu/bitstream/2027.42/154106/1/kampfner1998.pd

High efficient electrical stimulation of hippocampal slices with vertically aligned carbon nanofiber microbrush array

Long-term neuroprostheses for functional electrical stimulation must efficiently stimulate tissue without electrolyzing water and raising the extracellular pH to toxic levels. Comparison of the stimulation efficiency of tungsten wire electrodes (W wires), platinum microelectrode arrays (PtMEA), as-grown vertically aligned carbon nanofiber microbrush arrays (VACNF MBAs), and polypyrrole coated (PPy-coated) VACNF MBAs in eliciting field potentials in the hippocampus slice indicates that, at low stimulating voltages that preclude the electrolysis of water, only the PPy-coated VACNF MBA is able to stimulate the CA3 to CA1 pathway. Unlike the W wires, PtMEA, as-grown VACNF MBA, and the PPy-coated VACNF MBA elicit only excitatory postsynaptic potentials (EPSPs). Furthermore, the PPy-coated VACNF MBA evokes somatic action potentials in addition to EPSPs. These results highlight the PPy-coated VACNF’s advantages in lower electrode impedance, ability to stimulate tissue through a biocompatible chloride flux, and stable vertical alignment in liquid that enables access to spatially confined regions of neuronal cells

Replication of Wiener-Transformable Stochastic Processes with Application to Financial Markets with Memory

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 271)Daphne Jackson fellowship funded by EPSRC; Australian Research Council (project number DP150102758); ToppForsk project nr. 274410 of the Research Council of Norway with title STORM: Stochastics for Time-Space Risk Models

Impact of EU regulatory label changes for diclofenac in people with cardiovascular disease in four countries:interrupted time series regression analysis

Objective: Due to cardiovascular safety concerns, the European Medicines Agency (EMA) recommended new contraindications and changes to product information for diclofenac across Europe in 2013. This study aims to measure their impact among targeted populations. Method: Quarterly interrupted time series regression (ITS) analyses of diclofenac initiation among cohorts with contraindications (congestive cardiac failure [CHF], ischaemic heart disease [IHD], peripheral arterial disease [PAD], cerebrovascular disease [CVD]) and cautions (hypertension, hyperlipidaemia, diabetes) from Denmark, the Netherlands, England and Scotland. Results: The regulatory action was associated with significant immediate absolute reductions in diclofenac initiation in all countries for IHD (Denmark −0.08%, 95%CI −0.13, −0.03; England −0.09%, 95%CI −0.13 to −0.06%; the Netherlands −1.84%, 95%CI −2.51 to −1.17%; Scotland −0.34%, 95%CI −0.38 to −0.30%), PAD and hyperlipidaemia, the Netherlands, England and Scotland for hypertension and diabetes, and England and Scotland for CHF and CVD. Post-intervention there was a significant negative trend in diclofenac initiation in the Netherlands for IHD (−0.12%, 95%CI −0.19 to −0.04), PAD (−0.13%, 95%CI −0.22 to −0.05), hypertension, hyperlipidaemia and diabetes, and in Scotland for CHF (−0.01%, 95%CI −0.02 to −0.007%), IHD (−0.017, 95%CI −0.02, −0.01%), PAD and hypertension. In England, diclofenac initiation rates fell less steeply. In Denmark changes were more strongly associated with the earlier EMA 2012 regulatory action. Conclusion: Although significant reductions in diclofenac initiation occurred, patients with contraindications continued to be prescribed diclofenac, the extent of which varied by country and target condition. Understanding reasons for such variation may help to guide the design or dissemination of future safety warnings