Dictionary-based Online-adaptive Structure-preserving Model Order Reduction for Parametric Hamiltonian Systems

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally, Hamiltonian structure of dynamical systems may be available and should be preserved during the reduction. In the current presentation, we address these two aspects by proposing a corresponding dictionary-based, online-adaptive MOR approach. The method requires dictionaries for the state-variable, non-linearities and discrete empirical interpolation (DEIM) points. During the online simulation, local basis extensions/simplifications are performed in an online-efficient way, i.e. the runtime complexity of basis modifications and online simulation of the reduced models do not depend on the full state dimension. Experiments on a linear wave equation and a non-linear Sine-Gordon example demonstrate the efficiency of the approach.Comment: 29 pages, 13 figure

Emotionale Ambivalenz bei chronischem Schmerz. Psychometrische Qualität der deutschen Fassung des „Ambivalence over Emotional Expression Questionnaire“ (Fragebogen zur Emotionalen Ambivalenz)

In der vorliegenden Arbeit wurde die deutsche Version (AmbEE) eines amerikanischen Fragebogens zur Ambivalenz gegenüber emotionaler Expressivität (AEQ) bezüglich der Gütekriterien Reliabilität und Validität untersucht. Die Testung des AmbEE erfolgte an einer Stichprobe aus chronischen Schmerzpatienten (N = 135), die sich zum Zeitpunkt der Erhebung aufgrund ihrer Schmerzen in stationärer Behandlung befanden. Als Maß für die Kriteriumsvalidität des AmbEE wurden folgende Fragebögen eingesetzt: die Visuelle Analogskala (VAS) zur Messung der Schmerzintensität, die Schmerzempfindungsskala (SES), der Pain Disability Index (PDI) zur Erfassung der Behinderungseinschätzung durch die Schmerzen, die Allgemeine Depressionsskala (ADS) und der SF-36 zur Beurteilung der gesundheitsbezogenen Lebensqualität Der AmbEE zeichnet sich durch eine sehr hohe Reliabilität mit einer inneren Konsistenz von Cronbachs- = .96 und einer zufriedenstellenden Retestreliabilität von rtt = .69 aus. Die Mittelwerte und Standardabweichungen der einzelnen Items liegen im Wertebereich des AEQ. Bei der Mehrzahl der Items fällt eine linksschiefe Verteilung auf. Die Kurtosis der Items zeigt, dass die Daten aus einer nicht normalverteilten Grundgesamtheit stammten und ergab eine schmalgipflige Verteilung der Items. Die Trennschärfe der Items ist sehr hoch, während die Schwierigkeiten der Items im mittleren Bereich liegt. Die Faktorenanalyse ergibt eine Ein-Faktorenlösung mit 45,8% Varianzaufklärung, nachdem Lösungen mit mehreren Faktoren (fünf, drei und zwei Faktoren) inhaltlich nicht interpretierbar waren und daher verworfen werden mussten. Kriteriumsvalidität zeigt der AmbEE in signifikanten positiven Pearsonkorrelationen zu affektivem Schmerzempfinden, gemessen mit dem SES, zum PDI und zur ADS, sowie in signifikanten negativen Pearsonkorrelationen zur psychischen Summenskala des SF-36. Keine Korrelation zeigt der AmbEE mit dem sensorischen Schmerzempfinden der SES und der körperlichen Summenskala des SF-36. Die Spearmann-Rangkorrelation der durchschnittlichen, momentanen und erträglichen Schmerzstärke, gemessen mit der VAS und dem AmbEE, ergeben ebenfalls keine signifikanten Ergebnisse. Folglich ist der AmbEE ein gutes Instrument zur Erfassung des Konflikts über den Ausdruck von Emotionen. Es zeigt sich ein geringer klinisch relevanter Einfluss von Emotionaler Ambivalenz auf chronischen Schmerz. In Anbetracht der bisher wenig vorhandenen Literatur auf diesem Gebiet wird weitere Forschungsarbeit empfohlen, die Emotionale Ambivalenz zu anderen Persönlichkeitsmerkmalen abgrenzt und den Einfluss von Emotionaler Ambivalenz auf Krankheit und Gesundheit näher beleuchtet

Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for representing the high-dimensional system states in a reduced-dimensional coordinate system. While these approximations respect the symplectic nature of Hamiltonian systems, linear basis approximations can suffer from slowly decaying Kolmogorov $N$-width, especially in wave-type problems, which then requires a large basis size. We propose two different model reduction methods based on recently developed quadratic manifolds, each presenting its own advantages and limitations. The addition of quadratic terms to the state approximation, which sits at the heart of the proposed methodologies, enables us to better represent intrinsic low-dimensionality in the problem at hand. Both approaches are effective for issuing predictions in settings well outside the range of their training data while providing more accurate solutions than the linear symplectic reduced-order models

Symplectic model order reduction with non-orthonormal bases

Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g. structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such a ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction

A simple statistical test of taxonomic or functional homogeneity using replicated microbiome sequencing samples

One important question in microbiome analysis is how to assess the homogeneity of the microbial composition in a given environment, with respect to a given analysis method. Do different microbial samples taken from the same environment follow the same taxonomic distribution of organisms, or the same distribution of functions? Here we provide a non-parametric statistical “triangulation test” to address this type of question. The test requires that multiple replicates are available for each of the biological samples, and it is based on three-way computational comparisons of samples. To illustrate the application of the test, we collected three biological samples taken from different locations in one piece of human stool, each represented by three replicates, and analyzed them using MEGAN. (Despite its name, the triangulation test does not require that the number of biological samples or replicates be three.) The triangulation test rejects the null hypothesis that the three biological samples exhibit the same distribution of taxa or function (error probability ≤0.05), indicating that the microbial composition of the investigated human stool is not homogenous on a macroscopic scale, suggesting that pooling material from multiple locations is a reasonable practice. We provide an implementation of the test in our open source program MEGAN Community Edition

Gut microbial species and metabolic pathways associated with response to treatment with immune checkpoint inhibitors in metastatic melanoma

In patients with metastatic cancer, gut microbiome composition differs between responder and non-responders to immune checkpoint inhibitors. However, there is little consensus on the microbiome taxa associated with response or lack of response. Additionally, recognized confounders of gut microbiome composition have generally not been taken into account. In this study, metagenomic shotgun sequencing was performed on freshly frozen pre-treatment stool samples from 25 patients (12 responders and 13 non-responders) with unresectable metastatic melanoma treated with immune checkpoint inhibitors. We observed no significant differences in alpha-diversity and bacterial prevalence between responders and non-responders (P > 0.05). In a zero-inflated multivariate analysis, correcting for important confounders such as age, BMI and use of antibiotics, 68 taxa showed differential abundance between responders and non-responders (false-discovery rate <0.05). Cox-regression analysis showed longer overall survival for carriers of Streptococcus parasanguinis [hazard ratio (HR): 6.9] and longer progression-free survival for carriers of Bacteroides massiliensis (HR: 3.79). In contrast, carriership of Peptostreptococcaceae (unclassified species) was associated with shorter overall survival (HR 0.18) and progression-free survival (HR 0.11). Finally, 17 microbial pathways differentially abundant between responder and non-responders were observed. These results underline the association between gut microbiome composition and response to immune checkpoint inhibitor therapy in a cohort of patients with cutaneous melanoma

Transkingdom Networks: A Systems Biology Approach to Identify Causal Members of Host-Microbiota Interactions

Improvements in sequencing technologies and reduced experimental costs have resulted in a vast number of studies generating high-throughput data. Although the number of methods to analyze these "omics" data has also increased, computational complexity and lack of documentation hinder researchers from analyzing their high-throughput data to its true potential. In this chapter we detail our data-driven, transkingdom network (TransNet) analysis protocol to integrate and interrogate multi-omics data. This systems biology approach has allowed us to successfully identify important causal relationships between different taxonomic kingdoms (e.g. mammals and microbes) using diverse types of data