In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ to waves requires polynomial type bounds for operators related to the operator − s 2 in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and -hard obstacles, by homogeneous and non-homogeneous obstacles.
In this paper we propose and analyze a fully discrete method for a direct boundary integral formulation of the scattering of a transient acoustic wave by a sound-soft obstable. The method uses Galerkin-BEM in the space variables and three different choices of time-stepping strategies based on Convolution Quadrature. The numerical analysis of the method is carried out directly in the time domain, not reverting to Laplace transform techniques.
Kirchhoff's formula is the equivalent to Green's Third Theorem for transient waves, representing the solution of the three-dimensional wave equation in terms of its boundary data. In this classical result two retarded layer potentials appear. We show in this paper a precise description of these potentials as time convolution with adequate tempered distributions with values on operator spaces. With these potentials in hands we give a selfcontained proof of the formula with minimal smoothness requirements.
Background: Electronic fetal monitoring (EFM) is the universal method for the surveillance of fetal well-being in intrapartum. Our objective was to predict acidemia from fetal heart signal features using machine learning algorithms. Methods: A case–control 1:2 study was carried out compromising 378 infants, born in the Miguel Servet University Hospital, Spain. Neonatal acidemia was defined as pH < 7.10. Using EFM recording logistic regression, random forest and neural networks models were built to predict acidemia. Validation of models was performed by means of discrimination, calibration, and clinical utility. Results: Best performance was attained using a random forest model built with 100 trees. The discrimination ability was good, with an area under the Receiver Operating Characteristic curve (AUC) of 0.865. The calibration showed a slight overestimation of acidemia occurrence for probabilities above 0.4. The clinical utility showed that for 33% cutoff point, missing 5% of acidotic cases, 46% of unnecessary cesarean sections could be prevented. Logistic regression and neural networks showed similar discrimination ability but with worse calibration and clinical utility. Conclusions: The combination of the variables extracted from EFM recording provided a predictive model of acidemia that showed good accuracy and provides a practical tool to prevent unnecessary cesarean sections.
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