Implicit peer methods for large stiff ODE systems

Implicit two-step peer methods are introduced for the solution of large stiff systems. Although these methods compute s-stage approximations in each time step one-by-one like diagonally-implicit Runge-Kutta methods the order of all stages is the same due to the two-step structure. The nonlinear stage equations are solved by an inexact Newton method using the Krylov solver FOM (Arnoldi??s method). The methods are zero-stable for arbitrary step size sequences. We construct different methods having order p=s in the multi-implicit case and order p=s?1 in the singly-implicit case with arbitrary step sizes and s??5. Numerical tests in Matlab for several semi-discretized partial differential equations show the efficiency of the methods compared to other Krylov codes.     

Plant cystoliths: a complex functional biocomposite of four distinct silica and amorphous calcium carbonate phases

Plant cystoliths are mineralized objects that are formed by specialized cells in the leaves of certain plants. The main mineral component of cystoliths by volume is amorphous calcium carbonate (ACC) and the minor component is silica. We show that the silica stalk is formed first and is essential for ACC formation. Furthermore, the cystolith is shown to be composed of four distinct mineral phases with different chemical properties: an almost pure silica phase grades into a Mg-rich silica phase. This Mg-rich silica is overlaid by a relatively stable ACC phase. A bulky and less stable ACC phase encapsulates the first ACC phase. This architecture poses interesting questions about the role of Mg in the silica phase and suggests a strategy for ACC stabilization that takes advantage of a precise regulation of the mineral-growth microenvironment.     

Attribution of the discrepancy between ELISA and LC-MS/MS assay results of a PEGylated scaffold protein in post-dose monkey plasma samples due to the presence of anti-drug antibodies

High-performance liquid chromatography-tandem mass spectrometry (LC-MS/MS) and enzyme-linked immunosorbent assay (ELISA) methods were developed for the quantification of a PEGylated scaffold protein drug in monkey plasma samples. The LC-MS/MS method was based on the extraction of the therapeutic protein with a water-miscible organic solvent and the subsequent trypsin digestion of the extract followed by the detection of a surrogate peptide. The assay was linear over a range of 10-3,000 ng/mL. The ELISA method utilized a therapeutic target-binding format in which the recombinant target antigen was used to capture the drug in the sample, followed by detection with an anti-PEG monoclonal antibody. The assay range was 30-2,000 ng/mL. A correlation study between the two methods was performed by measuring the drug concentrations in plasma samples from a single-dose pharmacokinetic (PK) study in cynomolgus monkeys following a 5-mg/kg subcutaneous administration (n = 4). In the early time points of the PK profile, the drug concentrations obtained by the LC-MS/MS method agreed very well with those obtained by the ELISA method. However, at later time points, the drug concentrations measured by the LC-MS/MS method were consistently higher than those measured by the ELISA method. The PK parameters calculated based on the concentration data showed that the two methods gave equivalent peak exposure (C(max)) at 24-48 h. However, the LC-MS/MS results exhibited about 1.53-fold higher total exposure (AUC(tot)) than the ELISA results. The discrepancy between the LC-MS/MS and ELISA results was investigated by conducting immunogenicity testing, anti-drug antibody (ADA) epitope mapping, and Western blot analysis of the drug concentrations coupled with Protein G separation. The results demonstrated the presence of ADA specific to the engineered antigen-binding region of the scaffold protein drug that interfered with the ability of the drug to bind to the target antigen used in the ELISA method. In the presence of the ADAs, the ELISA method measured only the active circulating drug (target-binding), while the LC-MS/MS method measured the total circulating drug. The work presented here indicates that the bioanalysis of protein drugs may be complicated owing to the presence of drug-binding endogenous components or ADAs in the post-dose (incurred) samples. The clear understanding of the behavior of different bioanalytical techniques vis-à-vis the potentially interfering components found in incurred samples is critical in selecting bioanalytical strategies for measuring protein drugs.     

Bandwidth scaling and spectral flatness enhancement of optical frequency combs from phase-modulated continuous-wave lasers using cascaded four-wave mixing

We introduce a new cascaded four-wave mixing technique that scales up the bandwidth of frequency combs generated by phase modulation of a continuous-wave (CW) laser while simultaneously enhancing the spectral flatness. As a result, we demonstrate a 10?GHz frequency comb with over 100?lines in a 10?dB bandwidth in which a record 75?lines are within a flatness of 1?dB. The cascaded four-wave mixing process increases the bandwidth of the initial comb generated by the modulation of a CW laser by a factor of five. The broadband comb has approximately quadratic spectral phase, which is compensated upon propagation in single-mode fiber, resulting in a 10?GHz train of 940?fs pulses.     

Restricting Positive Energy Representations of Diff<Superscript>+</Superscript>(<Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>) to the Stabilizer of <Emphasis Type="Italic">n</Emphasis> Points

Let G _n ? Diff⁺(S ¹) be the stabilizer of n given points of S ¹. How much information do we lose if we restrict a positive energy representation \(U^c_h\) associated to an admissible pair (c, h) of the central charge and lowest energy, to the subgroup G _n ? The question, and a part of the answer originate in chiral conformal QFT. The value of c can be easily “recovered” from such a restriction; the hard question concerns the value of h. If c ≤ 1, then there is no loss of information, and accordingly, all of these restrictions are irreducible. In this work it is shown that \(U^c_{h}|_{G_n}\) is always irreducible for n =  1 and, if h =  0, it is irreducible at least up to n ≤  3. Moreover, an example is given for c >  2 and certain values of \(h \neq \tilde{h}\) such that \(U^c_{h}|_{G_1}\simeq U^c_{\tilde{h}}|_{G_1}\) . It is also concluded that for these values \(U^c_{h}|_{G_n}\) cannot be irreducible for n ≥  2. For further values of c, h and n, the question is left open. Nevertheless, the example already shows that, on the circle, there are conformal QFT models in which local and global intertwiners are not equivalent.     

Efficiency in the loading of a sodium magneto-optical trap from alkali metal dispensers

We study the loading of sodium atoms into a magneto-optical trap from current-controlled sodium metal dispensers. Contrary to what was previously reported [V. Wippel, C. Binder, W. Huber, L. Windholz, M. Allegrini, F. Fuso, E. Arimondo, Eur. Phys. J. D 17 (2001) 285] we demonstrate a significantly higher number of trapped atoms that make Na dispensers a feasible source of atoms for cold-atom studies. The inherent rise in pressure that naturally arises from metal dispensers as they are heated to release atoms is partially controlled by placing the metal dispensers near the pumping port where an ion pump is connected. We also study the effects of placing the sodium dispensers at different distances from the main vacuum chamber where the atoms are trapped and the effectiveness of using a Zeeman slower to cool the atoms as they emerge from the dispensers. We observe trapping of up to 1.9 × 10⁸ atoms, which is significantly higher by almost three orders of magnitude than previously reported experiments.     

On the stability of small blocking sets

A stability theorem says that a nearly extremal object can be obtained from an extremal one by “small changes”. In this paper, we study the relation of sets having few 0-secants and blocking sets.     

Reduced variable molecular dynamics

This article describes an extension to previously developed constraint techniques. These enhanced constraint methods will enable the study of large computational chemistry problems that cannot be easily handled with current constrained molecular dynamics (MD) methods. These methods are based on an O(N) solution to the constrained equations of motion. The benefits of this approach are that (1) the system constraints are solved exactly at each time step, (2) the solution algorithm is noniterative, (3) the algorithm is recursive and scales as O(N), (4) the algorithm is numerically stable, (5) the algorithm is highly amenable to parallel processing, and (6) potentially greater integration step sizes are possible. It is anticipated that application of this methodology will provide a 10- to 100-improvement in the speed of a large molecular trajectory as compared with the time required to run a conventional atomistic unconstrained simulation. It is, therefore, anticipated that this methodology will provide an enabling capacity for pursuing the drug discovery process for large molecular systems. © 1995 John Wiley & Sons, Inc.     

Control and Design Principles in Biological Mineralization

The control of crystal formation has been developed to a remarkable degree by many organisms. Oriented nucleation, control over crystal morphology, formation of unique composites of proteins and single crystals, and the production of ordered multicrystal arrays, are all well within the realm of biological capability. Understanding the control and design principles in biomineralization is a fascinating subject that may well contribute to the improved fabrication of synthetic materials on the one hand, and to the solution of many serious pathological problems involving mineralization, on the other.