Adaptive eigenspace for inverse problems in the frequency domain

Inverse scattering problems are used in a vast number of applications, such as geophysical exploration and medical imaging. The goal is to recover unknown media using wave prop- agation. The inverse problem is designed to minimize simulated data with observation data, using partial differential equations (PDE) as constrains. The resulting minimiza- tion problem is often severely ill-posed and contains a large number of local minima. To tackle ill-posedness, several optimization and regularization techniques have been explored. However, the applications are still asking for improvement and stability. In this thesis, a nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton- type method. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. We actually show how to build an AE from the gradients of Tikhonov-regularization functionals. Both analytical and numerical evidence underpin the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion (AEI) method. We also consider missing frequency data and apply the AEI to the multi-parameter inverse scattering problem

Adaptive eigenspace regularization for inverse scattering problems

A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation, each parameter is projected to a separate finite-dimensional subspace, which is iteratively adapted during the optimization. Each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori. The (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi-parameter problems, including the well-known Marmousi problem from geophysics

RAG: RNA-As-Graphs web resource

BACKGROUND: The proliferation of structural and functional studies of RNA has revealed an increasing range of RNA's structural repertoire. Toward the objective of systematic cataloguing of RNA's structural repertoire, we have recently described the basis of a graphical approach for organizing RNA secondary structures, including existing and hypothetical motifs. DESCRIPTION: We now present an RNA motif database based on graph theory, termed RAG for RNA-As-Graphs, to catalogue and rank all theoretically possible, including existing, candidate and hypothetical, RNA secondary motifs. The candidate motifs are predicted using a clustering algorithm that classifies RNA graphs into RNA-like and non-RNA groups. All RNA motifs are filed according to their graph vertex number (RNA length) and ranked by topological complexity. CONCLUSIONS: RAG's quantitative cataloguing allows facile retrieval of all classes of RNA secondary motifs, assists identification of structural and functional properties of user-supplied RNA sequences, and helps stimulate the search for novel RNAs based on predicted candidate motifs

High Agreement between Barrett Universal II Calculations with and without Utilization of Optional Biometry Parameters

Purpose: To examine the contribution of anterior chamber depth (ACD), lens thickness (LT), and white-to-white (WTW) measurements to intraocular lens (IOL) power calculations using the Barrett Universal II (BUII) formula. Methods: Measurements taken with the IOLMaster 700 (Carl Zeiss, Meditec AG, Jena, Germany) swept-source biometry of 501 right eyes of 501 consecutive patients undergoing cataract extraction surgery between January 2019 and March 2020 were reviewed. IOL power was calculated using the BUII formula, first through the inclusion of all measured variables and then by using partial biometry data. For each calculation method, the IOL power targeting emmetropia was recorded and compared for the whole cohort and stratified by axial length (AL) of the measured eye. Results: The mean IOL power calculated for the entire cohort using all available parameters was 19.50 ± 5.11 diopters (D). When comparing it to the results obtained by partial biometry data, the mean absolute difference ranged from 0.05 to 0.14 D; p < 0.001. The optional variables (ACD, LT, WTW) had the least effect in long eyes (AL ≥ 26 mm; mean absolute difference ranging from 0.02 to 0.07 D; p < 0.001), while the greatest effect in short eyes (AL ≤ 22 mm; mean absolute difference from 0.10 to 0.21 D; p < 0.001). The percentage of eyes with a mean absolute IOL dioptric power difference more than 0.25 D was the highest (32.0%) among the short AL group when using AL and keratometry values only. Conclusions: Using partial biometry data, the BUII formula in small eyes (AL ≤ 22 mm) resulted in a clinically significant difference in the calculated IOL power compared to the full biometry data. In contrast, the contribution of the optional parameters to the calculated IOL power was of little clinical importance in eyes with AL longer than 22 mm

High Agreement between Barrett Universal II Calculations with and without Utilization of Optional Biometry Parameters

Purpose: To examine the contribution of anterior chamber depth (ACD), lens thickness (LT), and white-to-white (WTW) measurements to intraocular lens (IOL) power calculations using the Barrett Universal II (BUII) formula. Methods: Measurements taken with the IOLMaster 700 (Carl Zeiss, Meditec AG, Jena, Germany) swept-source biometry of 501 right eyes of 501 consecutive patients undergoing cataract extraction surgery between January 2019 and March 2020 were reviewed. IOL power was calculated using the BUII formula, first through the inclusion of all measured variables and then by using partial biometry data. For each calculation method, the IOL power targeting emmetropia was recorded and compared for the whole cohort and stratified by axial length (AL) of the measured eye. Results: The mean IOL power calculated for the entire cohort using all available parameters was 19.50 ± 5.11 diopters (D). When comparing it to the results obtained by partial biometry data, the mean absolute difference ranged from 0.05 to 0.14 D; p < 0.001. The optional variables (ACD, LT, WTW) had the least effect in long eyes (AL ≥ 26 mm; mean absolute difference ranging from 0.02 to 0.07 D; p < 0.001), while the greatest effect in short eyes (AL ≤ 22 mm; mean absolute difference from 0.10 to 0.21 D; p < 0.001). The percentage of eyes with a mean absolute IOL dioptric power difference more than 0.25 D was the highest (32.0%) among the short AL group when using AL and keratometry values only. Conclusions: Using partial biometry data, the BUII formula in small eyes (AL ≤ 22 mm) resulted in a clinically significant difference in the calculated IOL power compared to the full biometry data. In contrast, the contribution of the optional parameters to the calculated IOL power was of little clinical importance in eyes with AL longer than 22 mm

Differences in autophagy marker levels at birth in preterm vs. term infants.

BACKGROUND Preterm infants are susceptible to oxidative stress and prone to respiratory diseases. Autophagy is an important defense mechanism against oxidative-stress-induced cell damage and involved in lung development and respiratory morbidity. We hypothesized that autophagy marker levels differ between preterm and term infants. METHODS In the prospective Basel-Bern Infant Lung Development (BILD) birth cohort we compared cord blood levels of macroautophagy (Beclin-1, LC3B), selective autophagy (p62) and regulation of autophagy (SIRT1) in 64 preterm and 453 term infants. RESULTS Beclin-1 and LC3B did not differ between preterm and term infants. However, p62 was higher (0.37, 95% confidence interval (CI) 0.05;0.69 in log2-transformed level, p = 0.025, padj = 0.050) and SIRT1 lower in preterm infants (-0.55, 95% CI -0.78;-0.31 in log2-transformed level, padj < 0.001). Furthermore, p62 decreased (padj-value for smoothing function was 0.018) and SIRT1 increased (0.10, 95% CI 0.07;0.13 in log2-transformed level, padj < 0.001) with increasing gestational age. CONCLUSION Our findings suggest differential levels of key autophagy markers between preterm and term infants. This adds to the knowledge of the sparsely studied field of autophagy mechanisms in preterm infants and might be linked to impaired oxidative stress response, preterm birth, impaired lung development and higher susceptibility to respiratory morbidity in preterm infants. IMPACT To the best of our knowledge, this is the first study to investigate autophagy marker levels between human preterm and term infants in a large population-based sample in cord blood plasma This study demonstrates differential levels of key autophagy markers in preterm compared to term infants and an association with gestational age This may be linked to impaired oxidative stress response or developmental aspects and provide bases for future studies investigating the association with respiratory morbidity

Adaptive Eigenspace for Multi-Parameter Inverse Scattering Problems

A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation, each parameter is projected to a separate finite-dimensional subspace, which is iteratively adapted during the optimization. Each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori. The (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi-parameter problems, including the well-known Marmousi model from geosciences

Adaptive eigenspace method for inverse scattering problems in the frequency domain

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method