Search

Assume that a family of (non-normal) matrices has stable spectra contained in the complex unit circle. This does not necessarily imply that the 2-norm of such matrices is small, and the question is under what 'natural' similarity transformation the transformed matrices will have 2-norm smaller or equal to 1. Already for the 2×2 - case this is a nontrivial question, involving the analysis of a function in two complex variables (the eigenvalues) and a positive scaling parameter. We discuss and explain an approach to this problem which has been used before in the analysis of companion matrices. For the 3D case we present a numerical example. [ABSTRACT FROM AUTHOR]

We compare adaptive time integrators for the numerical solution of linear Schrödinger equations where the Hamiltonian explicitly depends on time. The approximation methods considered are splitting methods, where the time variable is split off and advanced separately, and commutator-free Magnus-type methods. The time-steps are chosen adaptively based on asymptotically correct estimators of the local error in both cases. It is found that splitting methods are more efficient when the Hamiltonian naturally suggests a separation into kinetic and potential part, whereas Magnus-type integrators excel when the structure of the problem only allows to advance the time variable separately., (© The Author(s) 2020.)

Identification of antibody-binding epitopes is crucial to understand immunological mechanisms. It is of particular interest for allergenic proteins with high cross-reactivity as observed in the lipid transfer protein (LTP) syndrome, which is characterized by severe allergic reactions. Art v 3, a pollen LTP from mugwort, is frequently involved in this cross-reactivity, but no antibody-binding epitopes have been determined so far. To reveal human IgE-binding regions of Art v 3, we produced three murine high-affinity mAbs, which showed 70-90% coverage of the allergenic epitopes from mugwort pollen-allergic patients. As reliable methods to determine structural epitopes with tightly interacting intact antibodies under native conditions are lacking, we developed a straightforward NMR approach termed hydrogen/deuterium exchange memory (HDXMEM). It relies on the slow exchange between the invisible antigen-mAb complex and the free 15 N-labeled antigen whose 1 H- 15 N correlations are detected. Due to a memory effect, changes of NH protection during antibody binding are measured. Differences in H/D exchange rates and analyses of mAb reactivity to homologous LTPs revealed three structural epitopes: two partially cross-reactive regions around α-helices 2 and 4 as well as a novel Art v 3-specific epitope at the C terminus. Protein variants with exchanged epitope residues confirmed the antibody-binding sites and revealed strongly reduced IgE reactivity. Using the novel HDXMEM for NMR epitope mapping allowed identification of the first structural epitopes of an allergenic pollen LTP. This knowledge enables improved cross-reactivity prediction for patients suffering from LTP allergy and facilitates design of therapeutics., (Copyright © 2020 © 2020 Di Muzio et al. Published by Elsevier Inc. All rights reserved.)

An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on the error, in contrast to existing asymptotical approximations. It can be computed economically in the underlying Krylov space. In view of time-stepping applications, assuming that the given matrix is scaled by a time step, it is shown that the bound is asymptotically correct (with an order related to the dimension of the Krylov space) for the time step tending to zero. This means that the deviation of the error estimate from the true error tends to zero faster than the error itself. Furthermore, this result is extended to Krylov approximations of φ -functions and to improved versions of such approximations. The accuracy of the derived bounds is demonstrated by examples and compared with different variants known from the literature, which are also investigated more closely. Alternative error bounds are tested on examples, in particular a version based on the concept of effective order. For the case where the matrix exponential is used in time integration algorithms, a step size selection strategy is proposed and illustrated by experiments., (© The Author(s) 2019.)

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom (DOFs) are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates the healthy human knee joint as a compound hinge joint with minimal varus/valgus rotation. Most of these optimizations involve an orthogonality constraint. This contribution compares the effect of a model with and without orthogonality constraint on the obtained joint rotation angles. For this purpose, knee joint motion is simulated to generate kinematic data without noise and with normally distributed noise of varying size. For small noise the unconstrained model provides more accurate results, whereas for larger noise this is the case for the constrained model. This can be attributed to the shape of the objective function of the unconstrained model near its minimum.