Structure Preserving Model Order Reduction by Parameter Optimization

Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non structure preserving counterparts. In this paper, we present a framework for MOR based on direct parameter optimization. This means that the elements of the system matrices are iteratively varied to minimize an objective functional that measures the difference between the FOM and the reduced order model (ROM). Structural constraints are encoded in the parametrization of the ROM. The method only depends on frequency response data and can thus be applied to a wide range of dynamical systems. We illustrate the effectiveness of our method on a port-Hamiltonian and on a symmetric second order system in a comparison with other structure preserving MOR algorithms.Comment: 26 pages, 7 figure

Clinical Outcomes of Root-Analogue Implants Restored with Single Crowns or Fixed Dental Prostheses: A Retrospective Case Series

The objective was to investigate clinical and radiological outcomes of rehabilitations with root-analogue implants (RAIs). Patients restored with RAIs, supporting single crowns or fixed dental prostheses, were recruited for follow-up examinations. Besides clinical and esthetical evaluations, X-rays were taken and compared with the records. Patients were asked to evaluate the treatment using Visual Analogue Scales (VAS). For statistical analyses, mixed linear models were used. A total of 107 RAIs were installed in one dental office. Of these, 31 were available for follow-up examinations. For those remaining, survival has been verified via phone. RAIs were loaded after a mean healing time of 6.6 ± 2.5 months. 12.1 ± 6.9 months after loading, a mean marginal bone loss (MBL) of 1.20 ± 0.73 mm was measured. Progression of MBL significantly decreased after loading (p = 0.013). The mean pink and white esthetic score (PES/WES) was 15.35 ± 2.33 at follow-up. A survival rate of 94.4% was calculated after a mean follow-up of 18.9 ± 2.4 months after surgery. Immediate installation of RAIs does not seem to reduce MBL, as known from the literature regarding screw-type implants, and might not be recommended for daily routine. Nevertheless, they deliver esthetically satisfying results

Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive coupling of physical systems across different physical domains, scales, and accuracies. This makes pH models well-suited building-blocks for component-wise modeling of large system networks. In this context, it is often necessary to preserve the pH structure during MOR. We discuss current projection-based and structure-preserving MOR algorithms for pH systems and present a new optimization-based framework for that task. The benefits of our method include a simplified treatment of algebraic constraints and often a higher accuracy of the resulting reduced-order model, which is demonstrated by several numerical examples.Comment: 11 pages, 4 figure

Structure-Preserving Model Reduction for Dissipative Mechanical Systems

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model order reduction to construct easy-to-evaluate surrogates for the original dynamical system having the same structure. In our work, we present an overview of recently developed structure-preserving model reduction methods for second-order systems. These methods are based on modal and balanced truncation in different variants, as well as on rational interpolation. Numerical examples are used to illustrate the effectiveness of all described methods.Comment: 21 pages, 8 figure

Cutting Edge: Protein Arginine Deiminase 2 and 4 Regulate NLRP3 Inflammasome-Dependent IL-1β Maturation and ASC Speck Formation in Macrophages

Protein arginine deiminase (PAD) enzymes catalyze the conversion of protein-bound arginine into citrulline, an irreversible posttranslational modification with loss of a positive charge that can influence protein-protein interactions and protein structure. Protein arginine deiminase activity depends on high intracellular calcium concentrations occurring in dying cells. In this study, we demonstrate that protein citrullination is common during pyroptotic cell death in macrophages and that inhibition of PAD enzyme activity by Cl-amidine, a pan-PAD inhibitor, blocks NLRP3 inflammasome assembly and proinflammatory IL-1β release in macrophages. Genetic deficiency of either PAD2 or PAD4 alone in murine macrophages does not impair IL-1β release; however, pharmacological inhibition or small interfering RNA knockdown of PAD2 within PAD4-/-macrophages does. Our results suggest that PAD2 and 4 activity in macrophages is required for optimal inflammasome assembly and IL-1β release, a finding of importance for autoimmune diseases and inflammation