Stable bundle extensions on elliptic Calabi–Yau threefolds

We construct stable bundle extensions on elliptically fibered Calabi–Yau threefolds. We show that these bundles can solve the topological anomaly constraint in heterotic string theory without the need for invoking background five-branes.     

Classification of Graeco‐Latin Cubes

A q‐ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one‐error‐correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 5³, 3)₅ and (5, 7³, 3)₇ codes and equivalence classes of (5, 8³, 3)₈ codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco‐Latin cubes.     

Towards a synthetic avidin mimic

A series of streptavidin-mimicking molecularly imprinted polymers has been developed and evaluated for their biotin binding characteristics. A combination of molecular dynamics and NMR spectroscopy was used to examine potential polymer systems, in particular with the functional monomers methacrylic acid and 2-acrylamidopyridine. The synthesis of copolymers of ethylene dimethacrylate and one or both of these functional monomers was performed. A combination of radioligand binding studies and surface area analyses demonstrated the presence of selectivity in polymers prepared using methacrylic acid as the functional monomer. This was predicted by the molecular dynamics studies showing the power of this methodology as a prognostic tool for predicting the behavior of molecularly imprinted polymers.

A note on the efficiency of the conjugate gradient method for a class of time‐dependent problems

We discuss the efficiency of the conjugate gradient (CG) method for solving a sequence of linear systems; Auⁿ⁺¹ = uⁿ, where A is assumed to be sparse, symmetric, and positive definite. We show that under certain conditions the Krylov subspace, which is generated when solving the first linear system Au¹ = u⁰, contains the solutions {uⁿ} for subsequent time steps. The solutions of these equations can therefore be computed by a straightforward projection of the right‐hand side onto the already computed Krylov subspace. Our theoretical considerations are illustrated by numerical experiments that compare this method with the order‐optimal scheme obtained by applying the multigrid method as a preconditioner for the CG‐method at each time step. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive energy preserving methods for partial differential equations

A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of unity methods, thereby including finite element methods. The schemes are then extended to accommodate r-, h- and p-adaptivity. To illustrate the ideas, the method is applied to the Korteweg–de Vries equation and the sine-Gordon equation. Results from numerical experiments are presented.     

Rates of redox reactions in basaltic melts determined by Mössbauer spectroscopy

Mössbauer spectroscopy has been widely used for determining the ferric/ferrous ratio in amorphous rock samples to reveal the oxygen pressure in the melt. In the present investigation, Mössbauer spectroscopy in conjunction with melting experiments at controlled oxygen pressures was used to determine the rates of redox reactions in basaltic melts at 1300°C. The samples were kept at a fixed oxygen pressure long enough to reach equilibrium at a well established ferric/ferrous ratio. Then, the oxygen fugacity in the furnace was changed abruptly and the samples were kept for different lengths of time, from 15 min, to 4 hrs, at the new condition. At the end of each run the samples were quenched and the ferric/ferrous ratio analyzed by Mössbauer spectroscopy. A geological corollary of our results is that natural volcanic glasses, representing quenched melts, retain and reflect the oxidation state in the melt immediately prior to eruption, and hence the oxygen fugacity in the magma.     

Dynamics and energetics of the self-assembly of a hydrophobically modified polyelectrolyte: Naphthalene-labeled poly(acrylic acid)

Steady-state and time-resolved fluorescence studies were performed on aqueous solutions of poly(acrylic acid) hydrophobically modified with two very different levels of naphthalene (Np). It is demonstrated that unique information on association phenomena involving hydrophobe-modifed polymers can be obtained from an extended fluorescence study by using data for a less-modified polymer as a reference. For the more highly modified polymer, the presence of excited-state (as well as ground-state) dimers in addition to monomer emission due to locally excited naphthalene gives evidence for hydrophobic association between naphthalene groups. This association becomes, as expected, much less important at higher pH due to the electrostatic repulsion between different chain segments. However, it is noted that even at high pH there is a significant self-association. The coexistence of static and dynamic quenching phenomena of the Np monomer label was also revealed in the time-resolved fluorescence data. The data are compatible with the existence of two types of monomers and one excimer and suggest that the essential contribution to the monomer emission comes from isolated chromophores, whereas excimer formation arises from both a dynamic route (excited Np chromophores able to produce a dynamic excimer) and a static route (excitation of ground-state Np dimers). At room temperature, the dissociative reaction, excimer-to-monomer, can be neglected, and thus the rate constant for excimer formation and decay could be obtained with and without considering the influence of preformed dimers. Temperature has shown to induce different behavior in the polymer photophysics. In the case of the less-labeled polymer, the decays were found to be single-exponential with the fluorescence lifetime decreasing with increasing temperature. From the temperature dependence of the steady-state fluorescence data, the activation energy for excimer formation and the binding energy of the excimer were evaluated at different pH values, through the Stevens-Ban-type plots of the excimer-to-monomer intensity ratio. With the time-resolved data, measured in the temperature range of 5-60 degrees C, it was possible to extract the intrinsic activation energies for excimer formation. The thermodynamic driving force for the intrapolymeric association was found to be dependent on a balance between hydrophobic and electrostatic interactions, which are dependent on the pH, temperature, and hydrophobic content of the polymer.     

An online nano‐LC‐ESI‐FTICR‐MS method for comprehensive characterization of endogenous fragments from amyloid β and amyloid precursor protein in human and cat cerebrospinal fluid

Amyloid precursor protein (APP) is the precursor protein to amyloid β (Aβ), the main constituent of senile plaques in Alzheimer's disease (AD). Endogenous Aβ peptides reflect the APP processing, and greater knowledge of different APP degradation pathways is important to understand the mechanism underlying AD pathology. When one analyzes longer Aβ peptides by low‐energy collision‐induced dissociation tandem mass spectrometry (MS/MS), mainly long b‐fragments are observed, limiting the possibility to determine variations such as amino acid variants or post‐translational modifications (PTMs) within the N‐terminal half of the peptide. However, by using electron capture dissociation (ECD), we obtained a more comprehensive sequence coverage for several APP/Aβ peptide species, thus enabling a deeper characterization of possible variants and PTMs. Abnormal APP/Aβ processing has also been described in the lysosomal storage disease Niemann–Pick type C and the major large animal used for studying this disease is cat. By ECD MS/MS, a substitution of Asp7 → Glu in cat Aβ was identified. Further, sialylated core 1 like O‐glycans at Tyr10, recently discovered in human Aβ (a previously unknown glycosylation type), were identified also in cat cerebrospinal fluid (CSF). It is therefore likely that this unusual type of glycosylation is common for (at least) species belonging to the magnorder Boreoeutheria. We here describe a detailed characterization of endogenous APP/Aβ peptide species in CSF by using an online top‐down MS‐based method. Copyright © 2012 John Wiley & Sons, Ltd.