Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Conserved hydrophobic clusters on the surface of the Caf1A usher C-terminal domain are important for F1 antigen assembly

The outer membrane usher protein Caf1A of the plague pathogen Yersinia pestis is responsible for the assembly of a major surface antigen, the F1 capsule. The F1 capsule is mainly formed by thin linear polymers of Caf1 (capsular antigen fraction 1) protein subunits. The Caf1A usher promotes polymerization of subunits and secretion of growing polymers to the cell surface. The usher monomer (811 aa, 90.5 kDa) consists of a large transmembrane β-barrel that forms a secretion channel and three soluble domains. The periplasmic N-terminal domain binds chaperone-subunit complexes supplying new subunits for the growing fiber. The middle domain, which is structurally similar to Caf1 and other fimbrial subunits, serves as a plug that regulates the permeability of the usher. Here we describe the identification, characterization, and crystal structure of the Caf1A usher C-terminal domain (Caf1A(C)). Caf1A(C) is shown to be a periplasmic domain with a seven-stranded β-barrel fold. Analysis of C-terminal truncation mutants of Caf1A demonstrated that the presence of Caf1A(C) is crucial for the function of the usher in vivo, but that it is not required for the initial binding of chaperone-subunit complexes to the usher. Two clusters of conserved hydrophobic residues on the surface of Caf1A(C) were found to be essential for the efficient assembly of surface polymers. These clusters are conserved between the FGL family and the FGS family of chaperone-usher systems.

The application of Prony’s method to time-domain waveform data modeling in the presence of noise

In this paper,the Prony's method is applied to the time-domain waveform data modelling in the presence of noise.The following three problems encountered in this work are studied:(1)determination of the order of waveform;(2)de-termination of numbers of multiple roots;(3)determination of the residues.The methods of solving these problems are given and simulated on the computer.Finally,an output pulse of model PG-10N signal generator and the distorted waveform obtained by transmitting the pulse above mentioned through a piece of coaxial cable are modelled,and satisfactory results are obtained.So the effectiveness of Prony's method in waveform data modelling in the presence of noise is confirmed.

A simple fluid cell for the study of aqueous solutions using THz time-domain spectroscopy

We describe a fluid cell for the measurement of aqueous solutions of biomolecules adapted particularly for the requirements of THz time-domain spectroscopy. The design is simple, requires small-volume samples, avoids cross-contamination and is inexpensive.

Wavelet filtered modelling applied to measurements of a waveguide's THz time domain response

A quasi-optical de-embedding technique for characterizing waveguides is demonstrated using wideband time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time domain responses were discretised and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an ARX as well as with a state space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize signal distortion and the noise propagating in the ARX and subspace models. The model identification procedure requires isolation of the phase delay in the structure and therefore the time-domain signatures must be firstly aligned with respect to each other before they are compared. An initial estimate of the number of propagating modes was provided by comparing the measured phase delay in the structure with theoretical calculations that take into account the physical dimensions of the waveguide. Models derived from measurements of THz transients in a precision WR-8 waveguide adjustable short will be presented.

HR-semantics roadmap: the semantic challenges and opportunities in the Human Resources domain

Purpose: This document identifies the challenges and opportunities in applying the ontology technology in the Human Resources domain. Target users: A reference for both the HR and the ontology communities. Also, to be used as a roadmap for the OOA itself, within the HR domain. Background: During the discussion panel at the OOA kick-off workshop, which was attended by more than 50 HR and ontology experts, the need for this roadmap was realized. It was obvious that the current understanding of the problem of semantics in HR is fragmented and only partial solutions exist. People from both the HR and the ontology communities speak different languages, have different understandings, and are not aware of existing solutions.

Rapid protein domain assignment from amino acid sequence using predicted secondary structure

The elucidation of the domain content of a given protein sequence in the absence of determined structure or significant sequence homology to known domains is an important problem in structural biology. Here we address how successfully the delineation of continuous domains can be accomplished in the absence of sequence homology using simple baseline methods, an existing prediction algorithm (Domain Guess by Size), and a newly developed method (DomSSEA). The study was undertaken with a view to measuring the usefulness of these prediction methods in terms of their application to fully automatic domain assignment. Thus, the sensitivity of each domain assignment method was measured by calculating the number of correctly assigned top scoring predictions. We have implemented a new continuous domain identification method using the alignment of predicted secondary structures of target sequences against observed secondary structures of chains with known domain boundaries as assigned by Class Architecture Topology Homology (CATH). Taking top predictions only, the success rate of the method in correctly assigning domain number to the representative chain set is 73.3%. The top prediction for domain number and location of domain boundaries was correct for 24% of the multidomain set (±20 residues). These results have been put into context in relation to the results obtained from the other prediction methods assessed

Synthesis and incorporation into cyclic peptides of tolan amino acids and their hydrogenated congeners: construction of an array of A–B-loop mimetics of the Cε3 domain of human IgE

The disruption of the human immunolobulin E–high affinity receptor I (IgE–FcεRI) protein–protein interaction (PPI) is a validated strategy for the development of anti asthma therapeutics. Here, we describe the synthesis of an array of conformationally constrained cyclic peptides based on an epitope of the A–B loop within the Cε3 domain of IgE. The peptides contain various tolan (i.e., 1,2-biarylethyne) amino acids and their fully and partially hydrogenated congeners as conformational constraints. Modest antagonist activity (IC50 660 μM) is displayed by the peptide containing a 2,2′-tolan, which is the one predicted by molecular modeling to best mimic the conformation of the native A–B loop epitope in IgE.

On the numerical integration of a class of singular perturbation problems

A three-point difference scheme recently proposed in Ref. 1 for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to a one-sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.