The equivalence of theories that characterize ALogTime

A number of theories have been developed to characterize ALogTime (or uniform NC ¹, or just NC ¹), the class of languages accepted by alternating logtime Turing machines, in the same way that Buss’s theory characterizes polytime functions. Among these, ALV′ (by Clote) is particularly interesting because it is developed based on Barrington’s theorem that the word problem for the permutation group S ₅ is complete for ALogTime. On the other hand, ALV (by Clote), T ⁰ NC ⁰ (by Clote and Takeuti) as well as Arai’s theory and its two-sorted version VNC ¹ (by Cook and Morioka) are based on the circuit characterization of ALogTime. While the last three theories have been known to be equivalent, their relationship to ALV′ has been an open problem. Here we show that ALV′ is indeed equivalent to the other theories.      

Some fixed point theorems for multivalued mappings concerning <Emphasis Type="Italic">F</Emphasis>-contractions

The aim of this paper is to prove some fixed point theorems for multivalued maps satisfying different inequalities based on Wardowski’s technique in complete metric spaces. Our results extend and generalize several known results in the literature. We also give an application to the existence of fixed points for a class of Lipschitz multivalued mappings with a constant being greater than 1. Examples are also given to illustrate our results.     

On a nonlinear Kirchhoff–Carrier wave equation associated with Robin conditions

This paper is devoted to the study a nonlinear Kirchhoff–Carrier wave equation associated with Robin conditions. Existence and uniqueness of weak solutions are proved by using the Faedo–Galerkin method and the linearization method for nonlinear terms. An asymptotic expansion of high order in many small parameters of solutions is also discussed.     

Electrochemical Oxidation of Ergolines

An electrochemical procedure for the preparation of D -3-alkoxy-halogen-2,3-dihydro-6-methyl-2-oxoergolines-I is described.     

Combined Experimental and Simulation Studies Suggest a Revised Mode of Action of the Anti‐Alzheimer Disease Drug NQ‐Trp

Inhibition of the aggregation of the monomeric peptide β‐amyloid (Aβ) into oligomers is a widely studied therapeutic approach in Alzheimer’s disease (AD). Many small molecules have been reported to work in this way, including 1,4‐naphthoquinon‐2‐yl‐L ‐tryptophan (NQ‐Trp). NQ‐Trp has been reported to inhibit aggregation, to rescue cells from Aβ toxicity, and showed complete phenotypic recovery in an in vivo AD model. In this work we investigated its molecular mechanism by using a combined approach of experimental and theoretical studies, and obtained converging results. NQ‐Trp is a relatively weak inhibitor and the fluorescence data obtained by employing the fluorophore widely used to monitor aggregation into fibrils can be misinterpreted due to the inner filter effect. Simulations and NMR experiments showed that NQ‐Trp has no specific “binding site“‐type interaction with mono‐ and dimeric Aβ, which could explain its low inhibitory efficiency. This suggests that the reported anti‐AD activity of NQ‐Trp‐type molecules in in vivo models has to involve another mechanism. This study has revealed the potential pitfalls in the development of aggregation inhibitors for amyloidogenic peptides, which are of general interest for all the molecules studied in the context of inhibiting the formation of toxic aggregates.     

Investigation of DOTA–Metal Chelation Effects on the Chemical Shift of 129Xe

Recent work has shown that xenon chemical shifts in cryptophane‐cage sensors are affected when tethered chelators bind to metals. Here, we explore the xenon shifts in response to a wide range of metal ions binding to diastereomeric forms of 1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid (DOTA) linked to cryptophane‐A. The shifts induced by the binding of Ca²⁺, Cu²⁺, Ce³⁺, Zn²⁺, Cd²⁺, Ni²⁺, Co²⁺, Cr²⁺, Fe³⁺, and Hg²⁺ are distinct. In addition, the different responses of the diastereomers for the same metal ion indicate that shifts are affected by partial folding with a correlation between the expected coordination number of the metal in the DOTA complex and the chemical shift of ¹²⁹Xe. These sensors may be used to detect and quantify many important metal ions, and a better understanding of the basis for the induced shifts could enhance future designs.     

Dihedral angle principal component analysis of molecular dynamics simulations

It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and interpretation of the free energy landscape of a biomolecule undergoing large structural rearrangements. To account for the circular statistics of angular variables, a transformation from the space of dihedral angles {phi(n)} to the metric coordinate space {x(n)=cos phi(n),y(n)=sin phi(n)} was employed. To study the validity and the applicability of the approach, in this work the theoretical foundations underlying the dihedral angle principal component analysis (dPCA) are discussed. It is shown that the dPCA amounts to a one-to-one representation of the original angle distribution and that its principal components can readily be characterized by the corresponding conformational changes of the peptide. Furthermore, a complex version of the dPCA is introduced, in which N angular variables naturally lead to N eigenvalues and eigenvectors. Applying the methodology to the construction of the free energy landscape of decaalanine from a 300 ns molecular dynamics simulation, a critical comparison of the various methods is given.     

Water sorption by poly(tetrahydrofurfuryl methacrylate‐co‐2‐hydroxyethyl methacrylate). I. A mass‐uptake study

Cylindrical samples (≈5 mm × 20 mm) of poly(2‐hydroxyethyl methacrylate) and copolymers of 2‐hydroxyethyl methacrylate and furfuryl methacrylate were prepared, and the sorption of water into these cylinders was studied by the mass‐uptake method and by the measurement of the volume change at equilibrium. The equilibrium water content and volume change for the cylinders both varied systematically with the copolymer composition. The diffusion of water into the cylinders followed Fickian behavior, with the diffusion coefficients, dependent on the copolymer composition, varying from 2.00 × 10⁻¹¹ m²s⁻¹ for poly(2‐hydroxyethyl methacrylate) to 5.00 × 10⁻¹² m²s⁻¹ for poly(2‐hydroxyethyl methacrylate‐co‐tetrahydrofurfuryl methacrylate) with a 1 : 4 composition. The polymers that were rich in 2‐hydroxyethyl methacrylate were characterized by a water‐sorption overshoot, which was attributed to a slow reorientation of the polymer chains in the swollen rubbery regions formed after water sorption. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1939–1946, 2000