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The goal of this work is improving existing and suggesting novel filtering algorithms for nonlinear dynamic state estimation. Nonlinearity is considered in two ways: First, propagation is improved by proposing novel methods for approximating continuous probability distributions by discrete distributions defined on the same continuous domain. Second, nonlinear underlying domains are considered by proposing novel filters that inherently take the underlying geometry of these domains into account.

Sensordatenfusion --- Richtungsstatistik --- Directional Statistics --- Stochastische Filterung --- Sensor Data Fusion --- DichteapproximationStochastic Filtering --- Density Approximation

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In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart.

Oberflächenrekonstruktion --- Sensordatenfusion --- Richtungsstatistik --- Directional Statistics --- Medical Robotics --- Bildstabilisierung --- Surface Reconstruction --- Sensor Data Fusion --- Image Stabilization --- Medizinrobotik

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“Computational Mathematics, Algorithms, and Data Processing” of MDPI consists of articles on new mathematical tools and numerical methods for computational problems. Topics covered include: numerical stability, interpolation, approximation, complexity, numerical linear algebra, differential equations (ordinary, partial), optimization, integral equations, systems of nonlinear equations, compression or distillation, and active learning.

Research & information: general --- Mathematics & science --- interpolation --- constraints --- embedded constraints --- generalized multiscale finite element method --- multiscale model reduction --- deep learning --- Deep Neural Nets --- ReLU Networks --- Approximation Theory --- radial basis functions --- native spaces --- truncated function --- approximation --- surface modeling --- second order initial value problems --- linear multistep methods --- Obrechkoff schemes --- trigonometrically fitted --- Darcy-Forchheimer model --- flow in porous media --- nonlinear equation --- heterogeneous media --- finite element method --- multiscale method --- mixed generalized multiscale finite element method --- multiscale basis functions --- two-dimensional domain --- Thiele-like rational interpolation continued fractions with parameters --- unattainable point --- inverse difference --- virtual point --- polynomial chaos --- Szegő polynomials --- directional statistics --- Rogers-Szegő --- state estimation --- clustering

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• Reference Manager
• EndNote
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“Computational Mathematics, Algorithms, and Data Processing” of MDPI consists of articles on new mathematical tools and numerical methods for computational problems. Topics covered include: numerical stability, interpolation, approximation, complexity, numerical linear algebra, differential equations (ordinary, partial), optimization, integral equations, systems of nonlinear equations, compression or distillation, and active learning.

Research & information: general --- Mathematics & science --- interpolation --- constraints --- embedded constraints --- generalized multiscale finite element method --- multiscale model reduction --- deep learning --- Deep Neural Nets --- ReLU Networks --- Approximation Theory --- radial basis functions --- native spaces --- truncated function --- approximation --- surface modeling --- second order initial value problems --- linear multistep methods --- Obrechkoff schemes --- trigonometrically fitted --- Darcy-Forchheimer model --- flow in porous media --- nonlinear equation --- heterogeneous media --- finite element method --- multiscale method --- mixed generalized multiscale finite element method --- multiscale basis functions --- two-dimensional domain --- Thiele-like rational interpolation continued fractions with parameters --- unattainable point --- inverse difference --- virtual point --- polynomial chaos --- Szegő polynomials --- directional statistics --- Rogers-Szegő --- state estimation --- clustering --- interpolation --- constraints --- embedded constraints --- generalized multiscale finite element method --- multiscale model reduction --- deep learning --- Deep Neural Nets --- ReLU Networks --- Approximation Theory --- radial basis functions --- native spaces --- truncated function --- approximation --- surface modeling --- second order initial value problems --- linear multistep methods --- Obrechkoff schemes --- trigonometrically fitted --- Darcy-Forchheimer model --- flow in porous media --- nonlinear equation --- heterogeneous media --- finite element method --- multiscale method --- mixed generalized multiscale finite element method --- multiscale basis functions --- two-dimensional domain --- Thiele-like rational interpolation continued fractions with parameters --- unattainable point --- inverse difference --- virtual point --- polynomial chaos --- Szegő polynomials --- directional statistics --- Rogers-Szegő --- state estimation --- clustering