Neural and spectral operator surrogates: unified construction and expression rate bounds

Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising e.g. as data-to-solution maps of linear and nonlinear partial differential equations. Specifically, we study approximation rates for Deep Neural Operator and Generalized Polynomial Chaos (gpc) Operator surrogates for nonlinear, holomorphic maps between infinite-dimensional, separable Hilbert spaces. Operator in- and outputs from function spaces are assumed to be parametrized by stable, affine representation systems. Admissible representation systems comprise orthonormal bases, Riesz bases or suitable tight frames of the spaces under consideration. Algebraic expression rate bounds are established for both, deep neural and spectral operator surrogates acting in scales of separable Hilbert spaces containing domain and range of the map to be expressed, with finite Sobolev or Besov regularity. We illustrate the abstract concepts by expression rate bounds for the coefficient-to-solution map for a linear elliptic PDE on the torus

Die Bedeutung Der Deutschen Nato-Politik In Libyen Als Herausforderung Für Die Weiterentwicklung Der Transatlantischen Zusammenarbeit

The present paper addresses the question whether in light of its security policy Germany is still to be considered an integral part of the NATO community. Furthermore, this essay analyzes which implications the German NATO policy will have on future transatlantic cooperation within the alliance. To this end, the experiences made in the surroundings of the international military mission in Libya will be exemplifi ed and drawn upon.Serving as the article’s theoretical background, the so called “Communities of Practice” approach permits to establish to what extent Germany is to be characterized as a member or a non-member of the transatlantic alliance. In this context, NATO is perceived as a community of practice, within which common discursive principles are being developed and joint actions are being executed by its members. In the course of this study, primarily Germany’s and NATO’s reasoning concerning Libya will be compared by conducting a discourse analysis. Subsequently, all concrete actions which have been taken by the entities in question will be contrasted with each other. Consequently, a light will be shone on the manifest differences between Germany and NATO with regard to both the discourse and their respective practical politics. Against the background of the Libyan case, Germany can no longer be considered a part of NATO as a community of practice which can in turn be taken as evidence for a tendency towards less dedication to multilateralism and less commitment in the field of military missions on the part of Germany. Thus, within the relation between NATO and Germany, a lacking sense of community can clearly be detected which potentially poses a threat to any future transatlantic cooperation

Filme als Träger strategischer Kultur - Eine filmpolitologische Analyse normativ-kultureller Grundlagen europäischer Sicherheits- und Verteidigungspolitik

Innerhalb Europas herrschen sehr unterschiedliche Vorstellungen darüber vor, wann, wie und ob militärische Mittel eingesetzt werden sollen. Deutlich wird dies insbesondere in den Diskussionen über die Gemeinsame Sicherheits- und Verteidigungspolitik der Europäischen Union (GSVP). Solche unterschiedlichen Herangehensweisen von Staaten an sicherheitspolitische Fragestellungen möchte der Strategic-Culture-Ansatz erklären, der sich mit kollektiven, kulturell verwurzelten Vorstellungen von Sicherheitspolitik und dem Einsatz militärischer Mittel befasst. Er kann daher einen grundlegenden Erklärungsfaktor liefern, warum es sich immer wieder als schwierig erweist, in sicherheits- und verteidigungspolitischen Fragen zu einer vertieften Integration zu gelangen, weswegen der Erforschung der nationalen Vorstellungen und Legitimationsgrundlagen des Einsatzes militärischer Mittel und deren Kompatibilität, deren Gemeinsamkeiten und Unterschiede eine besondere Relevanz zuerkannt werden kann. Bisher völlig ausgeblendet in der Strategic-Culture-Literatur wurde allerdings die Frage, inwieweit strategische Kultur auch in der Populärkultur, konkret Filmen, repräsentiert ist, da sich in bisherigen Studien nur auf klassische Untersuchungsgegenstände wie Elitendiskurse, Strategiepapiere oder Bevölkerungsumfragen zur Herausarbeitung strategischer Kultur bezogen wurde. Dies ist insofern als Forschungslücke anzusehen, da sich in den letzten Jahren eine rege Debatte innerhalb der Internationalen Beziehungen (IB) zur Rolle von Filmen entfaltet hat. Grundannahme dieser Forschungsagenda ist, dass durch Filme soziale Ordnungen repräsentiert, konstruiert und letztlich normalisiert werden, weswegen solche Untersuchungsgegenstände relevant für politikwissenschaftliche Fragestellungen sind. Gleichzeitig haben auch die filmorientierten IB noch nicht auf den Strategic-Culture-Ansatz zurückgegriffen. Vor diesem Hintergrund verfolgt diese Arbeit die folgenden vier Leitfragen: 1.(Wie) kann der Strategic-Culture-Ansatz für die Analyse von Filmen genutzt werden? 2.Welche Vorstellungen militärischer Gewaltanwendung und damit Ausprägungen strategischer Kulturen finden sich in Filmen aus Deutschland, Frankreich und Großbritannien? 3.In welchem Zusammenhang stehen die filmischen Repräsentationen mit der „realen“ strategischen Kultur dieser Länder? 4.Wie wirken Filme in den gesellschaftlichen Resonanzraum der Debatte zum Einsatz militärischer Mittel? Das forschungsleitende Interesse dieser Studie liegt damit insgesamt gesehen darin, Filme als Repräsentationen und letztlich Träger strategischer Kulturen zu untersuchen, um so die normativ-kulturellen Grundlagen europäischer Sicherheitspolitik besser zu verstehen. Die Studie argumentiert, dass sich Filme als Träger strategischer Kulturen konzeptualisieren lassen und damit ein großes Potenzial für eine solche Forschungsagenda entfalten können

P2Y2R Signaling Is Involved in the Onset of Glomerulonephritis

Endogenously released adenosine-5’-triphosphate (ATP) is a key regulator of physiological function and inflammatory responses in the kidney. Genetic or pharmacological inhibition of purinergic receptors has been linked to attenuation of inflammatory disorders and hence constitutes promising new avenues for halting and reverting inflammatory renal diseases. However, the involvement of purinergic receptors in glomerulonephritis (GN) has only been incompletely mapped. Here, we demonstrate that induction of GN in an experimental antibody-mediated GN model results in a significant increase of urinary ATP-levels and an upregulation of P2Y2R expression in resident kidney cells as well as infiltrating leukocytes pointing toward a possible role of the ATP/P2Y2R-axis in glomerular disease initiation. In agreement, decreasing extracellular ATP-levels or inhibition of P2R during induction of antibody-mediated GN leads to a reduction in all cardinal features of GN such as proteinuria, glomerulosclerosis, and renal failure. The specific involvement of P2Y2R could be further substantiated by demonstrating the protective effect of the lack of P2Y2R in antibody-mediated GN. To systematically differentiate between the function of P2Y2R on resident renal cells versus infiltrating leukocytes, we performed bone marrow-chimera experiments revealing that P2Y2R on hematopoietic cells is the main driver of the ATP/P2Y2R-mediated disease progression in antibody-mediated GN. Thus, these data unravel an important pro-inflammatory role for P2Y2R in the pathogenesis of GN

A communal catalogue reveals Earth's multiscale microbial diversity

Our growing awareness of the microbial world's importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth's microbial diversity.Peer reviewe

A communal catalogue reveals Earth’s multiscale microbial diversity

Our growing awareness of the microbial world’s importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth’s microbial diversity

Timing of glacial retreat in the Wicklow Mountains, Ireland, conditioned by glacier size and topography

This paper presents 170 Schmidt Hammer exposure ages from moraine boulders and glacially-sculpted bedrock to reveal the post-Last Glacial Maximum (LGM) history of the Wicklow Mountains, Ireland. These data suggest that large ice masses survived for 4-7 ka after retreat of the Irish Sea Ice Stream and were sustained by summit ice-fields until ~16.6 ka. Post-LGM retreat was dynamic, with re-advance moraines deposited in response to Heinrich Stadial 1. However, these events reflect short-term ice front oscillations (≤ 1 ka) during the long-term retreat phase. Retreat from re-advance positions was synchronous across the range and paced by climate, with time-progressive deglaciation from low to high elevation. In contrast, marked asynchroneity in the timing of Younger Dryas deglaciation is closely linked to snow redistribution and indicates that for small cirque glaciers (≤ 1 km2 ), topography can exert the primary control on glacier survival. This result has important implications for palaeoclimate econstructions as cirque glacier dynamics may be unrelated to climate. This is further complicated by post-depositional processes which can result in moraine ages (e.g. 10Be) which post-date retreat. Future palaeoclimate studies should prioritise cirque glaciers where snow contributing areas are small and where postdepositional disturbance is limited (matrix-poor, boulder-rich moraines)

The importance of the German policy in Libya NATO as a challenge for further development of transatlantic cooperation

The present paper addresses the question whether in light of its security policy Germany is still to be considered an integral part of the NATO community. Furthermore, this essay analyzes which implications the German NATO policy will have on future transatlantic cooperation within the alliance. To this end, the experiences made in the surroundings of the international military mission in Libya will be exemplified and drawn upon. Serving as the article’s theoretical background, the so called “Communities of Practice” approach permits to establish to what extent Germany is to be characterized as a member or a non-member of the transatlantic alliance. In this context, NATO is perceived as a community of practice, within which common discursive principles are being developed and joint actions are being executed by its members. In the course of this study, primarily Germany’s and NATO’s reasoning concerning Libya will be compared by conducting a discourse analysis. Subsequently, all concrete actions which have been taken by the entities in question will be contrasted with each other. Consequently, a light will be shone on the manifest differences between Germany and NATO with regard to both the discourse and their respective practical politics. Against the background of the Libyan case, Germany can no longer be considered a part of NATO as a community of practice which can in turn be taken as evidence for a tendency towards less dedication to multilateralism and less commitment in the field of military missions on the part of Germany. Thus, within the relation between NATO and Germany, a lacking sense of community can clearly be detected which potentially poses a threat to any future transatlantic cooperation

Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions

ISSN:2166-252

Sediment transport models to simulate erosion of overtopped earth-dikes

An accurate simulation of the erosion of an earth-dike by overtopping is directly linked to the choice of the sediment transport model. The model should account for rather high sediment transport on the steep downstream slope. This study presents two different numerical approaches to simulate the overtopping of a river embankment. The first approach is based on the classical coupled Saint-Venant-Exner equations, as-suming one layer of pure water over a movable bed that can undergo erosion or deposition. Several empirical formulations are used to estimate the sediment transport capacity. The second approach assumes a fluid layer composed of a mixture of water and sediment, characterised by a depth-averaged density, for which the bed deformation rate is modelled as a function of both the erosion and deposition rates. These two models are compared with laboratory experiments on a one-dimensional dike failure due to overtopping, for which both the temporal water and sediment level evolutions were measured