Stability of subdivision schemes

The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined

Shape preserving C2C^2 interpolatory subdivision schemes

Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least $C^2$. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate $C^2$ limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to $C^2$ limit functions is introduced. As the algebra is far too complicated for an analytical proof of smoothness, validation has been performed by a simple numerical methodology

A linear approach to shape preserving spline approximation

This report deals with approximation of a given scattered univariate or bivariate data set that possesses certain shape properties, such as convexity, monotonicity, and/or range restrictions. The data are approximated for instance by tensor-product B-splines preserving the shape characteristics present in the data. Shape preservation of the spline approximant is obtained by additional linear constraints. Constraints are constructed which are local {\em linear sufficient\/} conditions in the unknowns for convexity or monotonicity. In addition, it is attractive if the objective function of the minimization problem is also linear, as the problem can be written as a linear programming problem then. A special linear approach based on constrained least squares is presented, which reduces the complexity of the problem in case of large data sets in contrast with the $\ell_\infty$ and the $\ell_1$-norms. An algorithm based on iterative knot insertion which generates a sequence of shape preserving approximants is given. It is investigated which linear objective functions are suited to obtain an efficient knot insertion method

Mutational analysis of the carbohydrate binding activity of the tobacco lectin

At present the three-dimensional structure of the tobacco lectin, further referred to as Nictaba, and its carbohydrate-binding site are unresolved. In this paper, we propose a three-dimensional model for the Nictaba domain based on the homology between Nictaba and the carbohydrate-binding module 22 of Clostridium thermocellum Xyn10B. The suggested model nicely fits with results from circular dichroism experiments, indicating that Nictaba consists mainly of beta-sheet. In addition, the previously identified nuclear localization signal is located at the top of the protein as a part of a protruding loop. Judging from this model and sequence alignments with closely related proteins, conserved glutamic acid and tryptophan residues in the Nictaba sequence were selected for mutational analysis. The mutant DNA sequences as well as the original Nictaba sequence have been expressed in Pichia pastoris and the recombinant proteins were purified from the culture medium. Subsequently, the recombinant proteins were characterized and their carbohydrate binding properties analyzed with glycan array technology. It was shown that mutation of glutamic acid residues in the C-terminal half of the protein did not alter the carbohydrate-binding activity of the lectin. In contrast, mutation of tryptophan residues in the N-terminal half of the Nictaba domain resulted in a complete loss of carbohydrate binding activity. These results suggest that tryptophan residues play an important role in the carbohydrate binding site of Nictaba