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Thermoviscoelasticity in Kelvin-Voigt rheology at large strains.
No full textThe frame-indifferent thermodynamically-consistent model of thermoviscoelasticity
at large strain is formulated in the reference configuration by using the concept
of the second-grade nonsimple materials. We focus on physically correct viscous
stresses that are frame indifferent under time-dependent rotations. Also elastic
stresses are frame indifferent under rotations and respect positivity of the determinant
of the deformation gradient. The heat transfer is governed by the Fourier law
in the actual deformed configuration, which leads to a nontrivial description when
pulled back to the reference configuration. The existence of weak solutions in the
quasistatic setting, that is inertial forces are ignored, is shown by time discretizatio
Coarse-graining via EDP-convergence for linear fast-slow reaction systems
Get PDFWe consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarse-grained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system can be written as a gradient flow with respect to the relative entropy. Focusing on the physically relevant cosh-type gradient structure we show how an effective limit gradient structure can be rigorously derived and that the coarse-grained equation again has a cosh-type gradient structure. We obtain the strongest version of convergence in the sense of the Energy-Dissipation Principle (EDP), namely EDP-convergence with tilting
Coarse graining molecular dynamics with graph neural networks
No full textABSTRACT
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems
Annotation und Interpretation von Varianten und Polymorphismen im humanen Genom
No full textDas Gesamtvolumen genomischer Sequenzierungsdaten nimmt, dank der Entwicklung der DNA-Hochdurchsatz-Sequenziertechniken, in den letzten Jahren in unglaublichem Tempo zu. Dies erweitert unser Wissen des humanen Genoms über dessen Aufbau, die Struktur und die räumliche Organisation. Die Erkenntnis um den komplexen Aufbau wird in naher Zukunft in die Interpretation von Variationen auch im klinischen Kontext einfließen müssen, birgt sie doch zahlreiche potentielle Möglichkeiten in der Diagnostik. Whole Genome Sequencing hat schon jetzt den Sprung aus den Forschungslaboren in die angewandte Diagnostik von Krankenhäusern geschafft und erlaubt damit die Einführung der Präzisionsmedizin für alle Patienten. Für eine optimale klinische Interpretation genomischer Varianten ist es wichtig, konsistente und passende Referenzen zu verwenden. Hierzu zählt neben der Auswahl des Referenzgenoms auch die verwendete Datenbank zur Annotierung von funktionalen Einheiten auf der DNA. Diese Arbeit geht auf zwei wichtige Schritte auf dem Weg zum Einsatz des WGS im klinischen Alltag ein. Der erste Schritt beinhaltet, möglichst schnell die gefundenen Varianten zu genomischen Eigenschaften und Featu- res (in Relation zu einer Referenz) zuzuordnen. Dies ist aufgrund der großen Datenmengen ein zunehmendes Problem geworden. Mit Jannovar wird hier eine Softwarebibliothek vorgestellt, welche hervorragend an diese Ansprüche angepasst ist. Die Bibliothek ist schnell, flexibel und kann leicht in Annotationspipelines und eigene Programme integriert werden. Die so annotierten und charakterisierten Veränderungen des Genotyps bilden eine Basis für die weitere Interpretation und Beurteilung durch andere Programme. Die Repräsentation der Genomreferenz entwickelt sich hin zu einem Graphengenom, um die populationsspezifische Variabilität zumindest ansatzweise abzubilden. Diese kann einen enormen Einfluss auf die Interpretation von Varianten haben. Im zweiten Schritt geht es darum, diese populationsspezifische Komplexität zu erläutern. Mit ASDPex wird ein heuristischer Algorithmus vorgestellt, welcher für WGS-Daten eines Individuums das Auftreten von alternativen Haplotypsequenzen vorhersagt. Dafür verwendet es die Verteilung der Allelfrequenzen der individuellen Varianten und gleicht sie mit einer Art Fingerabdruck aus haplotypspezifischen Varianten ab. Das Wissen um die alternativen Sequenzen kann die Verlässlichkeit der klinischen Interpretation weiter verbessern. Zukünftig wird es darum gehen, noch mehr Daten in die Varianteninterpretation zu integrieren, um noch mehr falsch positive/falsch negative Assoziationen zu verhindern und irrelevante Varianten herauszufiltern
Lern- und Erfahrungsmöglichkeiten durch Bewegung. Ausgewählte Befunde zu Wunsch und Wirklichkeit
No full textComputational strategies to combat COVID-19: useful tools to accelerate SARS-CoV-2 and coronavirus research
No full textSARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) is a novel virus of the family Coronaviridae. The virus causes the infectious disease COVID-19. The biology of coronaviruses has been studied for many years. However, bioinformatics tools designed explicitly for SARS-CoV-2 have only recently been developed as a rapid reaction to the need for fast detection, understanding and treatment of COVID-19. To control the ongoing COVID-19 pandemic, it is of utmost importance to get insight into the evolution and pathogenesis of the virus. In this review, we cover bioinformatics workflows and tools for the routine detection of SARS-CoV-2 infection, the reliable analysis of sequencing data, the tracking of the COVID-19 pandemic and evaluation of containment measures, the study of coronavirus evolution, the discovery of potential drug targets and development of therapeutic strategies. For each tool, we briefly describe its use case and how it advances research specifically for SARS-CoV-2. All tools are free to use and available online, either through web applications or public code repositories
Uncertainty quantification
No full textUncertainty quantification (UQ) is concerned with including and characterising uncertainties in mathematical models. Major steps comprise proper description of system uncertainties, analysis and efficient quantification of uncertainties in predictions and design problems, and statistical inference on uncertain parameters starting from available measurements. Research in UQ addresses fundamental mathematical and statistical challenges, but has also wide applicability in areas such as engineering, environmental, physical and biological applications. This workshop focussed on mathematical challenges at the interface of applied mathematics, probability and statistics, numerical analysis, scientific computing and application domains. The workshop served to bring together experts from those disciplines in order to enhance their interaction, to exchange ideas and to develop new, powerful methods for UQ
Transfer as a reciprocal process: How to foster receptivity to results of transdisciplinary research
No full textTransdisciplinary research (TDR) seeks to address real-world problems and aims to be socially transformative. This normative objective extends beyond particular TDR projects, as real-world problems are embedded in concrete contexts but, at the same time, are also related to wider societal challenges that are not restricted to one context. Therefore, TDR generally entails transfer of knowledge and results to other contexts. However, the TDR discourse has mainly treated transfer efforts from the perspective of scientific generalization, translation and packaging of knowledge. Within this understanding of transfer, little attention has been paid to interplay between contexts and the role of new contexts themselves.
This article is based on qualitative explorative research on four TDR projects. Its results were iteratively derived through project analysis, reflection on insights from the literature and discussions with TDR experts. We propose that transfer is a complex reciprocal process in which different types of knowledge are provided and transferred to other contexts, where knowledge is adapted, enriched and modified. In addition to project researchers, actors in other (pick-up) contexts also play an important role for successful transfer and appropriation of TDR results. Generating transfer potential within the duration of a project depends on being aware of potential pick-up contexts. To address the interdependent aspects of transfer (results, mediation, and appropriation in other contexts), we present a comprehensive model outlining TDR transfer processes. To support projects seeking to raise their transfer potential in a more conscious manner, we also formulate three overarching recommendations: 1) process results for transfer adequately, 2) identify and support intermediaries and, 3) increase awareness of and address other contexts. Considering these recommendations while also being aware of their interdependence may increase potential for transfer of knowledge and results to other contexts. Our conceptual understanding acknowledges the complexity and non-linearity of endeavors to take advantage of case-specifically gained knowledge and results in other contexts or at other scales
On the relationship between offshore geodetic coverage and slip model uncertainty: Analog megathrust earthquake case studies.
No full textWe apply a geodetic slip inversion technique to analog subduction megathrust earthquakes to demonstrate how limited offshore geodetic coverage affects coseismic slip models. We analyzed two archetypical megathrust earthquakes: trench‐breaking and non‐trench‐breaking earthquakes. Slip inversion models of analog earthquakes show quantitative and qualitative changes as a function of offshore coverage. Shallow slip cannot be resolved if the observation coverage of the offshore segment is <50%. Moreover, the slip pattern of shallow event flips from landward to trenchward skewed as offshore coverage reduces to <40%. The estimated slip for both event types converges to a similar unimodal pattern when there is no offshore coverage. We infer 5‐20% slip overestimation when the observations are above the high slipping zone during trench‐breaking events versus 5‐10% underestimation during non‐trench‐breaking events if observations are land‐limited. The moment magnitude derived for trench‐breaking ruptures might be significantly affected (ΔM w ~ 0.5)
Error bounds for PDE-regularized learning
Get PDFIn this work we consider the regularization of a supervised learning problem by partial differential equations (PDEs) and derive error bounds for the obtained approximation in terms of a PDE error term and a data error term. Assuming that the target function satisfies an unknown PDE, the PDE error term quantifies how well this PDE is approximated by the auxiliary PDE used for regularization. It is shown that this error term decreases if more data is provided. The data error term quantifies the accuracy of the given data. Furthermore, the PDE-regularized learning problem is discretized by generalized Galerkin discretizations solving the associated minimization problem in subsets of the infinite dimensional functions space, which are not necessarily subspaces. For such discretizations an error bound in terms of the PDE error, the data error, and a best approximation error is derived