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We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and transient aseismic processes. Although the origin of the first two sources is known, transient aseismic processes are more difficult to detect. However, the knowledge of the associated changes of the earthquake activity is of great interest, because it might help identify natural aseismic deformation patterns such as slow-slip events, as well as the occurrence of induced seismicity related to human activities. For this goal, we develop a Bayesian approach to identify change-points in seismicity data automatically. Using the Bayes factor, we select a suitable model, estimate possible change-points, and we additionally use a likelihood ratio test to calculate the significance of the change of the intensity. The approach is extended to spatiotemporal data to detect the area in which the changes occur. The method is first applied to synthetic data showing its capability to detect real change-points. Finally, we apply this approach to observational data from Oklahoma and observe statistical significant changes of seismicity in space and time.
Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.
Cell-free protein synthesis as a novel tool for directed glycoengineering of active erythropoietin
(2018)
As one of the most complex post-translational modification, glycosylation is widely involved in cell adhesion, cell proliferation and immune response. Nevertheless glycoproteins with an identical polypeptide backbone mostly differ in their glycosylation patterns. Due to this heterogeneity, the mapping of different glycosylation patterns to their associated function is nearly impossible. In the last years, glycoengineering tools including cell line engineering, chemoenzymatic remodeling and site-specific glycosylation have attracted increasing interest. The therapeutic hormone erythropoietin (EPO) has been investigated in particular by various groups to establish a production process resulting in a defined glycosylation pattern. However commercially available recombinant human EPO shows batch-to-batch variations in its glycoforms. Therefore we present an alternative method for the synthesis of active glycosylated EPO with an engineered O-glycosylation site by combining eukaryotic cell-free protein synthesis and site-directed incorporation of non-canonical amino acids with subsequent chemoselective modifications.
Frühe mathematische Bildung
(2018)
Im vorliegenden Beitrag werden aktuelle Forschungstrends im Bereich der frühen mathematischen Bildung im Kontext jüngst formulierter Zieldimensionen für die frühe mathematische Bildung (siehe Benz et al., 2017) dargestellt. Es wird auf spielbasierte Fördermaßnahmen, Kompetenzen im Bereich „Raum und Form“, den Einfluss sprachlicher Parameter auf die Entwicklung mathematischer Kompetenzen sowie auf mathematikbezogene Kompetenzen frühpädagogischer Fachkräfte eingegangen. Darüber hinaus werden die Ergebnisse einer aktuellen Feldstudie zur Förderung früher mathematischer Kompetenzen (siehe Dillon, Kannan, Dean, Spelke & Duflo, 2017) vorgestellt. Abschließend wird die Entwicklung und Implementierung anschlussfähiger Bildungskonzepte als eine der zentralen Herausforderungen zukünftiger Forschungs- und Bildungsbemühungen diskutiert
We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.
We consider a statistical inverse learning (also called inverse regression) problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X-i , superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set.
Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun. 3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 mu Nm(-1) was exerted at the base even when the fluid shear rate was applied at about 0.1 s(-1). The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future.
Genetic and environmental factors both contribute to cognitive test performance. A substantial increase in average intelligence test results in the second half of the previous century within one generation is unlikely to be explained by genetic changes. One possible explanation for the strong malleability of cognitive performance measure is that environmental factors modify gene expression via epigenetic mechanisms. Epigenetic factors may help to understand the recent observations of an association between dopamine-dependent encoding of reward prediction errors and cognitive capacity, which was modulated by adverse life events. The possible manifestation of malleable biomarkers contributing to variance in cognitive test performance, and thus possibly contributing to the "missing heritability" between estimates from twin studies and variance explained by genetic markers, is still unclear. Here we show in 1475 healthy adolescents from the IMaging and GENetics (IMAGEN) sample that general IQ (gIQ) is associated with (1) polygenic scores for intelligence, (2) epigenetic modification of DRD2 gene, (3) gray matter density in striatum, and (4) functional striatal activation elicited by temporarily surprising reward-predicting cues. Comparing the relative importance for the prediction of gIQ in an overlapping subsample, our results demonstrate neurobiological correlates of the malleability of gIQ and point to equal importance of genetic variance, epigenetic modification of DRD2 receptor gene, as well as functional striatal activation, known to influence dopamine neurotransmission. Peripheral epigenetic markers are in need of confirmation in the central nervous system and should be tested in longitudinal settings specifically assessing individual and environmental factors that modify epigenetic structure.
In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.