On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints

We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints

Modellierung und Lösung parametrischer Packungsprobleme mittels semi-infiniter Optimierung: Angewandt auf die Verwertung von Edelsteinen

Die vorliegende Dissertation ist motiviert durch eine praktische Aufgabenstellung: der Verwertung von Edelsteinen. Liegt der Fokus dabei auf der Volumenmaximierung der zu fertigenden Schmucksteine, handelt es sich aus mathematischer Sicht um eine Aufgabe der maximalen Materialausbeute mit veränderlichen Designs. In der Arbeit wird gezeigt, dass sich derartige Probleme bei funktionaler Beschreibung aller involvierten Objekte als allgemeines semi-infinites Optimierungsproblem (GSIP) formulieren lassen. Für das numerische Lösen von GSIPs mit konvexen Problemen der unteren Stufe werden zwei Methoden entwickelt und deren Konvergenz nachgewiesen. Das erste Verfahren basiert auf der Approximation der infiniten Indexmenge mittels verschobener entropischer Glättung, das zweite kombiniert die Transformation in ein gewöhnliches semi-infinites Problem sowie die Diskretisierbarkeit dessen geschickt miteinander. Abschließend werden die beiden Methoden mit dem Verfahren von Stein numerisch verglichen und gezeigt, dass sich kleine bis mittlere Probleminstanzen der Edelstein-Verwertungsaufgabe mittels des transformationsbasierten Diskretisierungsverfahrens auf einem Standard-PC in annehmbarer Zeit lösen lassen

On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints

We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints

A quantitative and site-specific chemoenzymatic glycosylation approach for PEGylated MUC1 peptides

Full control over complex post-translational modifications (PTMs), such as O-glycosylation, is a prerequisite for testing and understanding the biological role of these modifications in protein function. Despite considerable progress over the last years, high throughput and easy-to-use methods for the synthesis of complex glycosylated peptides are still missing. We present here an efficient methodology to produce homogeneous site-specifically O-glycosylated peptides. Sequential chemoenzymatic glycosylation and separation from the reaction components are achieved via the temporary attachment of a monodisperse polyethylene glycol (PEG) polymer to the N-terminus of these peptides. Subsequent proteolytic removal of the PEG moiety allows quantitative recovery of homogeneous O-glycopeptides, suitable as building blocks for glycoprotein synthesis. Here, we demonstrate the preparation of glucuronylated variants of MUC1, a well-known member of the human mucin family. Homogeneously O-glycosylated variants were synthesized and will be used to study the role of O-linked glucuronic acid epitopes within the functional environment of the human MUC1 tandem repeat

Greybox models - new opportunities for the optimization of entire processes

The use of process optimization is often limited due to missing models for certain process steps. The systematic combination of available operating data with previous knowledge in so called graybox models helps to bridge this gap. Following the concept of incremental model identification it will be shown how the workflow has been integrated into a simulation software environment. It will be applied to a cumene process

Myocardial transcriptome analysis of human arrhythmogenic right ventricular cardiomyopathy

Gaertner A, Schwientek P, Ellinghaus P, et al. Myocardial transcriptome analysis of human arrhythmogenic right ventricular cardiomyopathy. Physiological Genomics. 2012;44(1):99-109.Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited cardiomyopathy primarily of the right ventricle characterized through fibrofatty replacement of cardiomyocytes. The genetic etiology in ARVC patients is most commonly caused by dominant inheritance and high genetic heterogeneity. Though histological examinations of ARVC-affected human myocardium reveals fibrolipomatous replacement, the molecular mechanisms leading to loss of cardiomyocytes are largely unknown. We therefore analyzed the transcriptomes of six ARVC hearts and compared our findings to six nonfailing donor hearts (NF). To characterize the ARVC-specific transcriptome, we compared our findings to samples from seven patients with idiopathic dilated cardiomyopathy (DCM). The myocardial DCM and ARVC samples were prepared from hearts explanted during an orthotopic heart transplantation representing myocardium from end-stage heart failure patients (NYHA IV). From each heart, left (LV) and right ventricular (RV) myocardial samples were analyzed by Affymetrix HG-U133 Plus 2.0 arrays, adding up to six sample groups. Unsupervised cluster analyses of the groups revealed a clear separation of NF and cardiomyopathy samples. However, in contrast to the other samples, the analyses revealed no distinct expression pattern in LV and RV of myocardial ARVC samples. We further identified differentially expressed transcripts using t-tests and found transcripts separating diseased and NF ventricular myocardium. Of note, in failing myocardium only 15-16% of the genes are commonly regulated compared with NF samples. In addition both cardiomyopathies are clearly distinct on the transcriptome level. Comparison of the expression patterns between the failing RV and LV using a paired t-test revealed a lack of major differences between LV and RV gene expression in ARVC hearts. Our study is the first analysis of specific ARVC-related RV and LV gene expression patterns in terminal failing human hearts

Decision support by multicriteria optimization in process development: An integrated approach for robust planning and design of plant experiments

In simulation-based process design, model parameters, like thermodynamic data, are affected by uncertainties. Optimized process designs should, among different other objectives, also be robust to uncertainties of the model parameters. In industrial practise, it is important to know the trade-off between an increase in robustness and the other objectives – like minimizing costs or maximizing product purities. This contribution describes a practical procedure how to incorporate robustness as an objective into a multicriteria optimization framework. The general procedure is illustrated by a concrete example. Finally, we argue that the same approach is useable for an optimal design of plant experiments

A single-cell genomics pipeline for environmental microbial eukaryotes.

Single-cell sequencing of environmental microorganisms is an essential component of the microbial ecology toolkit. However, large-scale targeted single-cell sequencing for the whole-genome recovery of uncultivated eukaryotes is lagging. The key challenges are low abundance in environmental communities, large complex genomes, and cell walls that are difficult to break. We describe a pipeline composed of state-of-the art single-cell genomics tools and protocols optimized for poorly studied and uncultivated eukaryotic microorganisms that are found at low abundance. This pipeline consists of seven distinct steps, beginning with sample collection and ending with genome annotation, each equipped with quality review steps to ensure high genome quality at low cost. We tested and evaluated each step on environmental samples and cultures of early-diverging lineages of fungi and Chromista/SAR. We show that genomes produced using this pipeline are almost as good as complete reference genomes for functional and comparative genomics for environmental microbial eukaryotes

A single-cell genomics pipeline for environmental microbial eukaryotes.

Single-cell sequencing of environmental microorganisms is an essential component of the microbial ecology toolkit. However, large-scale targeted single-cell sequencing for the whole-genome recovery of uncultivated eukaryotes is lagging. The key challenges are low abundance in environmental communities, large complex genomes, and cell walls that are difficult to break. We describe a pipeline composed of state-of-the art single-cell genomics tools and protocols optimized for poorly studied and uncultivated eukaryotic microorganisms that are found at low abundance. This pipeline consists of seven distinct steps, beginning with sample collection and ending with genome annotation, each equipped with quality review steps to ensure high genome quality at low cost. We tested and evaluated each step on environmental samples and cultures of early-diverging lineages of fungi and Chromista/SAR. We show that genomes produced using this pipeline are almost as good as complete reference genomes for functional and comparative genomics for environmental microbial eukaryotes