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Author: Wolf, Sebastian × Version: publishedVersion ×

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Now showing 1 - 4 of 4
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    Highly Sensitive Detection of the Antibiotic Ciprofloxacin by Means of Fiber Enhanced Raman Spectroscopy
    (Basel : MDPI, 2019) Wolf, Sebastian; Frosch, Timea; Popp, Juergen; Pletz, Mathias W.; Frosch, Torsten
    Sepsis and septic shock exhibit a rapid course and a high fatality rate. Antibiotic treatment is time-critical and precise knowledge of the antibiotic concentration during the patients’ treatment would allow individual dose adaption. Over- and underdosing will increase the antimicrobial efficacy and reduce toxicity. We demonstrated that fiber enhanced Raman spectroscopy (FERS) can be used to detect very low concentrations of ciprofloxacin in clinically relevant doses, down to 1.5 µM. Fiber enhancement was achieved in bandgap shifted photonic crystal fibers. The high linearity between the Raman signals and the drug concentrations allows a robust calibration for drug quantification. The needed sample volume was very low (0.58 µL) and an acquisition time of 30 s allowed the rapid monitoring of ciprofloxacin levels in a less invasive way than conventional techniques. These results demonstrate that FERS has a high potential for clinical in-situ monitoring of ciprofloxacin levels.
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    Variational Monte Carlo - Bridging concepts of machine learning and high dimensional partial differential equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Eigel, Martin; Trunschke, Philipp; Schneider, Reinhold; Wolf, Sebastian
    A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range of problems. A general unified convergence analysis is derived, which takes into account the approximation and the statistical errors. By this, a combination of theoretical results from numerical analysis and statistics is obtained. Numerical experiments illustrate the performance of the method with the model class of hierarchical tensors.
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    Stochastic topology optimisation with hierarchical tensor reconstruction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian
    A novel approach for risk-averse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common risk-aware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such high-dimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach.
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    Non-intrusive tensor reconstruction for high dimensional random PDEs
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian
    This paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high dimensional parametric random PDEs which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to Monte Carlo sampling.