Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Handling Uncertainty in Tsunami Early Warning: Interaction between Decision Support and Multi-Sensor Simulation System

The new InaTEWS/GITEWS tsunami early warning system has been designed to work reliably and quickly in the special case of near-field tsunamis with extremely short warning times. In order to avoid false warnings this system is equipped with a multi-sensor simulation system which can evaluate multiple online measurement values simultaneously. With this system, within short time a reliable small number of scenarios can be selected to serve as an early situation assessment. However, in order to support a decision maker for issuing warning products, a thorough analysis of the simulation results and a blending with additional geographic and socio-economic information is necessary. In this paper the interplay between decision support system and simulation system is illustrated

Substrate determinants of signal peptide peptidase-like 2a (SPPL2a)-mediated intramembrane proteolysis of the invariant chain CD74

The presenilin homologue signal peptide peptidase-like 2a (SPPL2a) is an intramembrane protease of lysosomes/late endosomes which cleaves type II transmembrane proteins. We recently identified CD74, the invariant chain of the MHCII complex, as the first in vivo validated substrate of this protease. In endosomal compartments, CD74 undergoes sequential proteolysis leading to the generation of a membrane-bound N-terminal fragment (NTF) that requires cleavage by SPPL2a for its turnover. In SPPL2a−/− mice, this fragment accumulates in B-cells and significantly disturbs their maturation and functionality. To date, the substrate requirements of the protease SPPL2a have not been investigated. In the present study, we systematically analysed the molecular determinants of CD74 with regard to the intramembrane cleavage by SPPL2a. Using domain-exchange experiments, we demonstrate that the intracellular domain (ICD) of CD74 can be substituted without affecting cleavability by SPPL2a. Based on IP-MS analysis of the cleavage product, we report identification of the primary SPPL2a cleavage site between Y52 and F53 within the CD74 transmembrane segment. Furthermore, systematic alanine-scanning mutagenesis of the transmembrane and membrane-proximal parts of the CD74 NTF has been performed. We show that none of the analysed determinants within the CD74 NTF including the residues flanking the primary cleavage site are absolutely essential for SPPL2a cleavage. Importantly, we found that alanine substitution of helix-destabilizing glycines within the transmembrane segment and distinct residues within the luminal membrane-proximal segment led to a reduced efficiency of SPPL2a-mediated processing. Therefore we propose that elements within the transmembrane segment and the luminal juxtamembrane domain facilitate intramembrane proteolysis of CD74 by SPPL2a.</jats:p