QR factoring to compute the GCD of univariate approximate polynomials

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over /spl Ropf/[x] or /spl Copf/[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9.     

Defect-controlled numerical methods and shadowing for chaotic differential equations

It is well-known that chaotic ODE's are, in the classical sense, unstable or ill-conditioned. It is not clear that variable step-size codes based on local error control can solve such problems in a useful way. In particular, it is usually difficult to show that the apparent chaos in the resulting solution is not a numerical artifact. I show here that a defect-controlled method gives useful solutions for chaotic problems. A pragmatically modified definition of what it means for a dynamical system to be chaotic is also presented.     

Optimal residuals and the Dahlquist test problem

Numerical Algorithms - We show how to compute the optimal relative backward error for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of a general...     

Bandwidth-expandable erbium-doped fiber amplets

A narrow-band optical amplifier (“amplet”) is proposed and demonstrated that can be constructed into an amplifier-based subsystem to perform nonlinear dispersion compensation and to flatten gain while the input level changes in a dense wavelength-division-multiplexed (DWDM) optical networking system. The amplet is designed to inherently provide two networking features: narrow-band accessibility and bandwidth scalability. For a 100-GHz-spaced DWDM application, each amplet can process four channels. The crosstalk between amplets is better than 58 dB. The capability to flatten gain and improve the transient response is experimentally demonstrated when an amplet array subsystem is formed     

Optimal Control of Rigid Body Angular Velocity with Quadratic Cost

In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.     

The nature of collision-induced dissociation processes of doubly protonated peptides: comparative study for the future use of matrix-assisted laser desorption/ionization on a hybrid quadrupole time-of-flight mass spectrometer in proteomics.

Comparative MS/MS studies of singly and doubly charged electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI) precursor peptide ions are described. The spectra from these experiments have been evaluated with particular emphasis on the data quality for subsequent data processing and protein/amino acid sequence identification. It is shown that, once peptide ions are formed by ESI or MALDI, their charge state, as well as the collision energy, is the main parameter determining the quality of collision-induced dissociation (CID) MS/MS fragmentation spectra of a given peptide. CID-MS/MS spectra of singly charged peptides obtained on a hybrid quadrupole orthogonal time-of-flight mass spectrometer resemble very closely spectra obtained by matrix-assisted laser desorption/ionization post-source decay time-of-flight mass spectrometry (MALDI-PSD-TOFMS). On the other hand, comparison of CID-MS/MS spectra of either singly or doubly charged ion species shows no dependence on whether ions have been formed by ESI or MALDI. This observation confirms that, at the time of precursor ion selection, further mass analysis is effectively decoupled from the desorption/ionization event. Since MALDI ions are predominantly formed as singly charged species and ESI ions as doubly charged, the associated difference in the spectral quality of MS/MS spectra as described here imposes direct consequences on data processing, database searching using ion fragmentation data, and de novo sequencing when ionization techniques are changed.     

Polymers for the Cell‐Specific Immobilisation of Megakaryocytic Cell Lines

Primary human megakaryocytes, the precursor cells of platelets, are difficult to collect and cultivate. Polymers that enrich these cells without affecting their regulation or function are of interest for basic research as well as for cord blood transplantation purposes since co‐transplantation of enriched megakaryocyte concentrates increase the success of stem cell therapy. Herein, polymer microarrays were used for the discovery of substrates for MEG‐01 cells, with five polymers identified which selectively bound cells of the megakaryocytic lineage. Flow cytometry and miRNA profiling revealed that immobilisation had only a minor effect on the cellular maturation status, making the identified substrates potential candidates for concentrating megakaryocytes from patients prior to transplantation.

     

Adaptive disturbance transmission decoupling in active vehicle suspensions

With active vehicle suspension, one can tailor a vehicles response to load and inertial without affecting the vehicle response to road disturbances. This decoupling is achieved in [1] and [2] using a filtered combination of measured signals. These filters require exact knowledge of certain vehicle parameters including vehicle mass to achieve the desired decoupling. Here we propose a parameter adaptive version of these filters which does not require knowledge of vehicle parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)