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Impedance Measurement System for Determination of Capacitive Electrode Coupling

Capacitive electrodes have been studied as an alternative to gel electrodes, as they allow measurement of biopotentials without conductive contact with the patient. However, because the skin interface is not as precisely defined as with gel electrodes, this could lead to signal deformation and misdiagnoses. Thus, measurement of a capacitive coupling of the electrodes may allow to draw conclusions about the applicability of such systems. In addition, combining capacitive biosignal sensing with an impedance measurement unit may enable bioimpedance measurements, from which additional information on the hydration status can be extracted. A prototype system is introduced which measures impedance over capacitive electrodes in parallel with biopotential measurements. Also presented are the first results on characterization of the skin electrode coupling achieved with the system.

Motion Artifact Removal from Capacitive ECG Measurements by Means of Adaptive Filtering

Capacitive ECG sensing is not just a very promising alternative to conventional ECG but also allows for new applications, in which recording a conventional ECG is not imaginable due to practical aspects. This way, integration into car seats for monitoring of the heart rate of the driver or a usage in a home monitoring scenario is no longer unimaginable. Nevertheless, capacitive ECG measurements are very prone to motion artifacts, which need to be eliminated. For this purpose, this paper introduces adaptive filtering as a method for signal enhancement by using a second signal, which is correlated with the interfering signal. The approach is validated in a setting with an additional acceleration signal during car drive.

Discrete and continuous adjoint approaches to estimate boundary heat fluxes in falling films

A wavy falling film simulation is considered in which a liquid travels along one side of a thin metal foil that is heated electrically from the opposite side. The direct problem consists of a three-dimensional heat conduction equation on a cuboid domain representing the foil with suitable initial and boundary conditions. The inverse problem consists of determining the heat flux on the film side of the foil from a given distribution of the temperature on the heating side. Two different adjoint approaches for the solution of this inverse problem are compared. In the continuous adjoint approach, the adjoint problem is analytically derived from the direct problem and then discretized. In the discrete adjoint approach, the direct problem is discretized, from which an adjoint code is generated by means of the reverse mode of automatic differentiation. Numerical experiments are reported, demonstrating the advantages and disadvantages of the two approaches.

Using exact Jacobians in an implicit Newton method for solving multiphase flow in porous media

We present a new numerical approach to solve the fully coupled equations for two-phase flow in porous media with exact Jacobians. The method is based on a space and time discretisation and a linearisation of the arising non-linear algebraic system with Newtons method, where the required Jacobians are obtained with automatic differentiation (AD), providing the exact derivatives. We compare the forward AD differentiation mode to the standard finite difference method and the complex variable method in terms of precision and performance. It turns out that AD performs favourably compared to both methods. We also illustrate the advantages of exact Jacobians in a test example for two-phase flow in porous media investigating the evolution of pressure and saturation in a CO

A new user interface for ADiMat: toward accurate and efficient derivatives of MATLAB programmes with ease of use

Various techniques in computational science and engineering benefit from accurate and efficient derivative computation. ADiMat is a software tool that transforms a numerical program written in MATLAB into another MATLAB programme for the computation of derivatives that are free from truncation error. We introduce a new and easy-to-use interface for ADiMat and present case studies from geophysics and fluid mechanics to quantify the performance of the code generated by ADiMat.

The Impact of Dynamic Data Reshaping on Adjoint Code Generation for Weakly-Typed Languages Such as Matlab

Productivity-oriented programming languages typically emphasize convenience over syntactic rigor. A well-known example is Matlab, which employs a weak type system to allow the user to assign arbitrary types and shapes to a variable, and it provides various shortcuts in programming that result in implicit data reshapings. Examples are scalar expansion, where a scalar is implicitly expanded to a matrix of the appropriate size filled with copies of the scalar value, the use of row vectors in place of column vectors and vice versa, and the automatic expansion of arrays when indices outside of the previously allocated range are referenced. These features need to be addressed at runtime when generating adjoint code, as Matlab does not provide required information about types, shapes and conversions at compile time. This fact, and the greater scope of reshaping possible, is a main distinguishing feature of Matlab compared to traditional programming languages, some of which, e.g. Fortran 90, also support vector expressions. In this paper, in the context of the AdiMAT source transformation tool for Matlab, we develop techniques generally applicable for adjoint code generation in the face of dynamic data reshapings occurring both on the left- and right-hand side of assignments. Experiments show that in this fashion correct adjoint code can be generated also for very dynamic language scenarios at moderate additional cost.

RIOS: efficient I/O in reverse direction

The reverse mode of automatic differentiation executes the adjoint statements induced by each statement in the original program in the reverse order of the original program flow. This program flow reversal commonly requires storage of information on the control flow of the original program. In addition, intermediate values of variables that are overwritten have to be recorded, as these values may later be needed to compute the partial derivatives of the corresponding statement. The stored information will be accessed in reverse order of being written. This runs contrary to many assumptions made in standard implementations of file systems, operating systems, and input/output (I/O) libraries. A common buffering strategy aimed at speeding up future read requests is to employ read‐ahead. This strategy is useful for accesses in forward direction but is considered to be harmful to the performance of the reverse mode. To increase the performance of the reverse mode, it is also advantageous to interleave computations with the data storage and retrieval operations, which can be achieved using multithreading. To this end, we design and implement a novel software called reverse‐mode I/O stream (RIOS) that is adapted to these particular requirements of the reverse mode. We show the advantages of RIOS in two empirical case studies, an artificially constructed example of a typical I/O pattern in the reverse mode and a real‐world example arising from fluid mechanics, which is studied in Fortran90 and in Matlab where the reverse mode is generated via the automatic differentiation tools Tapenade and ADiMat, respectively. Copyright

Estimating the expansion coefficients of a geomagnetic field model using first-order derivatives of associated Legendre functions

The associated Legendre functions are defined on a closed interval. Thus, their derivatives do not exist at the endpoints of the interval. However, one-sided derivatives may exist at the endpoints if the ordinary limit is replaced by a one-sided limit. When computer models that evaluate associated Legendre functions at an endpoint are transformed by automatic differentiation, an approach is needed that is tailored to one-sided derivatives. Rather than employing a black-box approach of automatic differentiation, a hierarchical approach is introduced that is based on analytic first-order one-sided derivatives of the associated Legendre functions at the endpoints. This hierarchical approach is implemented in the automatic differentiation software ADiMat and its feasibility is demonstrated in a parameter estimation problem arising from geomagnetic field modelling.

Source Transformation for the Optimized Utilization of the Matlab Runtime System for Automatic Differentiation

Operator overloading in Matlab allows for user-defined types to semantically augment existing Matlab codes without changes. However, given sufficient knowledge about types and operand semantics, operator overloading can be replaced by equivalent function calls. The ADiMat software tool provides automatic differentiation of Matlab functions using a hybrid approach that combines source transformation and operator overloading. It can also be used as a general framework for user-defined transformations of Matlab codes. Tests showed the potential for performance improvement in a derivative class providing essential linear algebra functionality for ADiMat. The Matlab runtime environment was benchmarked regarding function and method call overheads as well as property access overhead with Matlab’s objects. These tests identify the access to class properties of type cell array as the main performance culprit. Hence, an automatic method, transforming the XML based abstract syntax tree created with ADiMat’s toolchain through a set of stylesheets, was developed. This process completely removes the derivative object usage and hence the operator overloading and the property access overhead from any derivative function created with ADiMat. Experimental results show that performance is improved considerably depending on the data container storing the derivative directions.

Parallel summation of symmetric inter-particle forces in smoothed particle hydrodynamics

In the smoothed particle hydrodynamics (SPH) method, the forces between all particles are efficiently summed up in a serial environment as follows. Each pair of particles is considered once. The resulting inter-particle force is computed and then the contributions to both particles are updated, taking into account the symmetry of the problem. This algorithm is difficult to parallelise when concurrently accessing the same memory location in a multi-threaded process. We develop a parallel 1D summation algorithm consisting of two passes on a Cartesian grid of cells in which particles move freely. In a first pass, we consider all cells with an even index n. We compute the inter-particle forces for all pairs of particles located in cell n and those pairs where a particle is located in cell n and another particle is located in cell n + 1. Each cell n is handled by a different thread since no data race can occur. In a second pass, we do the same for cells with odd n. This way, all interparticle forces are computed. We generalise this algorithm to 2D, 3D, and arbitrarily high dimensions and report performance results on three different shared-memory platforms using the OpenMP programming paradigm.