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Derivation and characterization of a new filter for nonlinear high-dimensional data assimilation
(2015)
Data assimilation (DA) combines model forecasts with real-world observations to achieve an optimal estimate of the state of a dynamical system. The quality of predictions in nonlinear and chaotic systems such as atmospheric or oceanic circulation is strongly sensitive to the initial conditions. Therefore, beyond the consistent reconstruction of past states, a primary relevance of advanced DA methods concerns the proper model initialization. The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational DA schemes. They are applied in a wide range of research and operations. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the mean and covariance of the analysis ensemble are biased and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) relies on Bayes' theorem without further assumptions, which guarantees an exact asymptotic behavior. However, it is exposed to weight collapse, particularly in higher-dimensional settings, known as the curse of dimensionality.
This work presents a new method to obtain an analysis ensemble with mean and covariance that exactly match the corresponding Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The forecast step remains as in the ETKF. The algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF). The limitation with respect to fully-nonlinear filtering is that the NETF only considers the mean and covariance of the Bayesian analysis density, neglecting higher-order moments.
The properties and performance of the proposed algorithm are investigated via a set of experiments. The results indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. They also confirm that localization enhances the applicability of this PF-inspired scheme in larger-dimensional systems. Finally, the novel filter is coupled to a large-scale ocean general circulation model with a realistic observation scenario. The NETF remains stable with a small ensemble size and shows a consistent behavior. Additionally, its analyses exhibit low estimation errors, as revealed by a comparison with a free ensemble integration and the ETKF. The results confirm that, in principle, the filter can be applied successfully and as simple as the ETKF in high-dimensional problems. No further modifications are needed, even though the algorithm is only based on the particle weights. Thus, it is able to overcome the curse of dimensionality, even in deterministic systems. This proves that the NETF constitutes a promising and user-friendly method for nonlinear high-dimensional DA.
A new global synthesis and biomization of long (> 40 kyr) pollen-data records is presented, and used with simulations from the HadCM3 and FAMOUS climate models to analyse the dynamics of the global terrestrial biosphere and carbon storage over the last glacial–interglacial cycle. Global modelled (BIOME4) biome distributions over time generally agree well with those inferred from pollen data. The two climate models show good agreement in global net primary productivity (NPP). NPP is strongly influenced by atmospheric carbon dioxide (CO2) concentrations through CO2 fertilization. The combined effects of modelled changes in vegetation and (via a simple model) soil carbon result in a global terrestrial carbon storage at the Last Glacial Maximum that is 210–470 Pg C less than in pre-industrial time. Without the contribution from exposed glacial continental shelves the reduction would be larger, 330–960 Pg C. Other intervals of low terrestrial carbon storage include stadial intervals at 108 and 85 kaBP, and between 60 and 65 kaBP during Marine Isotope Stage 4. Terrestrial carbon storage, determined by the balance of global NPP and decomposition, influences the stable carbon isotope composition (δ 13C) of seawater because terrestrial organic carbon is depleted in 13C. Using a simple carbon-isotope mass balance equation we find agreement in trends between modelled ocean δ 13C based on modelled land carbon storage, and palaeo-archives of ocean δ 13C, confirming that terrestrial carbon storage variations may be important drivers of ocean δ 13 C changes.
Künstliche Ribonucleasen, die sequenzspezifisch und effizient die Spaltung von RNA-Phosphordiesterbindungen katalysieren, könnten potenziell nicht nur als biochemische Werkzeuge dienen, sondern auch als Wirkstoffe gegen eine Vielzahl von Erkrankungen, bei denen mRNA oder miRNA involviert sind, eine wichtige Rolle spielen. Obwohl in den letzten beiden Jahrzehnten zahlreiche sequenzspezifische RNA-Spalter entwickelt wurden, bleibt die Spaltaktivität dieser Verbindungen nach wie vor deutlich hinter der ihrer natürlichen Äquivalente zurück. Die Optimierung künstlicher Ribonucleasen und grundlegend dafür die Erforschung der Faktoren, die die Spaltaktivität einer Verbindung beeinflussen, sind daher weiterhin von großem Interesse. Zwar enthalten die meisten künstlichen Ribonucleasen Metallionen, doch sind auch metallfreie RNA-Spalter, zum Beispiel auf der Basis heterocyclischer Guanidine, bekannt. Prinzipiell kann die Hydrolyse des RNA-Rückgrates durch Deprotonierung der nucleophil am Phosphoratom angreifenden 2‘-OH-Gruppe, durch Protonierung der als Abgangsgruppe fungierenden 5‘-OH-Gruppe sowie durch Stabilisierung des bei der Spaltung durchlaufenen dianionischen Phosphorans katalysiert werden. Daher sollten potenzielle RNA-Spalter in der Lage sein, sowohl als Base als auch als Säure wirken zu können, was bei einem pKa-Wert im Bereich von 7 am besten gegeben ist. Fungiert ein und dasselbe Molekül als Protonenakzeptor und -donor, so kommt es im Fall von Guanidinanaloga zu einer Tautomerisierung vom Amino- zum Iminoisomer. Eine möglichst kleine Energiedifferenz zwischen beiden Formen sollte sich daher positiv auf die Spaltaktivität auswirken. In der vorliegenden Arbeit wurde eine Reihe heterocyclischer Guanidine synthetisiert, deren pKa-Werte bestimmt und die jeweiligen Energiedifferenzen zwischen Amino- und Iminotautomer grob mittels AM1-Rechnungen abgeschätzt. In Spaltexperimenten wurden Cy5-markierte RNA-Substrate mit den verschiedenen Verbindungen inkubiert (Spalter-Konzentration: 2 bzw. 10 mM). Die Analyse und Quantifizierung der Spaltprodukte erfolgten anschließend mithilfe eines DNA-Sequenziergerätes. Alle untersuchten und ausreichend löslichen Substanzen, die sowohl einen geeigneten pKa-Wert (6 – 8) als auch eine niedrige Energiedifferenz zwischen Amino- und Iminotautomer (≤ 5 kcal/mol) aufwiesen bzw. bei denen nur der pKa-Wert oder nur die Energiedifferenz in geringem Maße vom Idealwert abwich, spalteten RNA, wenn auch teilweise nur mit einer geringen Aktivität. In den Spaltexperimenten erwiesen sich Guanidinanaloga mit einem großen aromatischen System als besonders aktiv, allen voran 2-Aminoperimidin und seine Derivate, die auch bei Konzentrationen unter 50 µM Spaltaktivität zeigten. Gleichzeitig offenbarten diese Verbindungen in Fluoreszenzkorrelationsspektroskopie Experimenten eine große Tendenz zur Aggregation mit RNA, so dass die Spaltung in diesen Fällen möglicherweise nicht durch Einzelmoleküle, sondern durch Aggregate erfolgte. Um RNA-Substrate auch sequenzspezifisch spalten zu können, wurden PNA-Konjugate des bereits bekannten RNA-Spalters Tris(2-aminobenzimidazol) hergestellt, wobei der Spalter über eine neue, quecksilberfreie Route synthetisiert wurde. Es konnte gezeigt werden, dass diese PNA-Konjugate RNA sequenzspezifisch mit einer Halbwertszeit von etwa 11 h spalten, was im Rahmen der Halbwertszeit vergleichbarer DNA-Konjugate liegt. Um zu untersuchen, ob 2-Aminoperimidine auch als Einzelverbindungen aktiv sind, wurden zwei PNA-Konjugate von am Naphthylring substituierten 2-Aminoperimidin-Derivaten synthetisiert. Beide Konjugate zeigten keinerlei Spaltaktivität, was darauf hindeuten könnte, dass die Hydrolyse des RNA-Rückgrates nur durch mehrere Spalter-Einheiten – kovalent verknüpft oder in Form von Aggregaten – effizient katalysiert werden kann.
The c-MYC proto-oncogene is a regulator of fundamental cellular processes such as cell cycle progression and apoptosis. The development of novel c-MYC inhibitors that can act by targeting the c-MYC DNA G-quadruplex at the level of transcription would provide potential insight into structure-based design of small molecules and lead to a promising arena for cancer therapy. Herein we report our finding that two simple bis-triazolylcarbazole derivatives can inhibit c-MYC transcription, possibly by stabilizing the c-MYC G-quadruplex. These compounds are prepared using a facile and modular approach based on Cu(I) catalysed azide and alkyne cycloaddition. A carbazole ligand with carboxamide side chains is found to be microenvironment-sensitive and highly selective for "turn-on" detection of c-MYC quadruplex over duplex DNA. This fluorescent probe is applicable to visualize the cellular nucleus in living cells. Interestingly, the ligand binds to c-MYC in an asymmetric fashion and selects the minor-populated conformer via conformational selection.
Ausländische Pflegekräfte in deutschen Privathaushalten : ein Interview mit Prof. Dr. Helma Lutz
(2015)
Helma Lutz ist Professorin am Fachbereich Gesellschaftswissenschaften der Goethe-Universität Frankfurt am Main. Seit 15 Jahren beschäftigt sie sich in ihrer Forschung mit "neuen Dienstmädchen" – Migrantinnen, die Haus-, Erziehungs- und Versorgungsarbeit ("Care-Arbeit") in deutschen Haushalten verrichten. Die Redaktion von focus Migration hat sie zu diesem Thema befragt.
As a surrogate of live cells, proteo-lipobeads are presented, encapsulating functional membrane proteins in a strict orientation into a lipid bilayer. Assays can be performed just as on live cells, for example using fluorescence measurements. As a proof of concept, we have demonstrated proton transport through cytochrome c oxidase.
Projected demographic changes in industrialized and developing countries vary in extent and timing but will reduce the share of the population in working age everywhere. Conventional wisdom suggests that this will increase capital intensity with falling rates of return to capital and increasing wages. This decreases welfare for middle aged asset rich households. This paper takes the perspective of the three demographically oldest European nations — France, Germany and Italy — to address three important adjustment channels to dampen these detrimental effects of aging in these countries: investing abroad, endogenous human capital formation and increasing the retirement age. Our quantitative finding is that endogenous human capital formation in combination with an increase in the retirement age has strong implications for economic aggregates and welfare, in particular in the open economy. These adjustments reduce the maximum welfare losses of demographic change for households alive in 2010 by about 2.2 percentage points in terms of a consumption equivalent variation.
When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations. We derive the equilibrium dynamics in closed form and show that joint presence of both risks leads to over-proportional risk exposure for households. This implies that the whole benefit from insurance through social security is greater than the sum of the benefits from insurance against each of the two risks in isolation. We measure this through interaction effects which appear even though the two risks are orthogonal by construction. While the interactions unambiguously increase the welfare benefits from insurance, they can in- or decrease the welfare costs from crowding out of capital formation. The net effect depends on the relative strengths of the opposing forces.
n this paper we compute the optimal tax and education policy transition in an economy where progressive taxes provide social insurance against idiosyncratic wage risk, but distort the education decision of households. Optimally chosen tertiary education subsidies mitigate these distortions. We highlight the importance of two different channels through which academic talent is transmitted across generations (persistence of innate ability vs. the impact of parental education) for the optimal design of these policies and model different forms of labor as imperfect substitutes, thereby generating general equilibrium feedback effects from policies to relative wages of skilled and unskilled workers. We show that subsidizing higher education has important redistributive benefits, by shrinking the college wage premium in general equilibrium. We also argue that a full characterization of the transition path is crucial for policy evaluation. We find that optimal education policies are always characterized by generous tuition subsidies, but the optimal degree of income tax progressivity depends crucially on whether transitional costs of policies are explicitly taken into account and how strongly the college premium responds to policy changes in general equilibrium.