Wavelet Approach to Nonlinear Problems, II. Metaplectic Wavelets

this paper we continue the application of powerful methods of wavelet analysis to polynomial approximations of mechanical and physical problems. In part 1 we considered general approach for constructing wavelet representation. But now we need take into account the Hamiltonian or symplectic structure of our problems. Therefore, we need to consider instead of compactly supported wavelet representation from part 1 the generalized wavelets, which allow us to consider the corresponding symplectic structures [1]-[5]. By using the orbit method and constructions from the geometric quantization theory we consider the symplectic and Poisson structures associated with Weyl-- Heisenberg wavelets by using metaplectic structure and the corresponding polarization. In wavelet analysis the following three concepts are used now: a square integrable representation U of a group G, coherent states over G, wavelet transform associated to U. We have three important particular cases: the affine (ax + b) group, which yields usual wavelet analysis [ß(b; a)f](x)

Benzothienoiodolium Cations Doubly Bonded to Anions via Halogen-Chalcogen and Halogen-Hydrogen Supramolecular Synthons

The simultaneous binding of a molecular entity through two interactions is a frequently pursued recognition mode due to the advantages it offers in securing molecular self-assembly. Here, we report how the planarity of the benzothienoiodolium (BTI) cation allows for preorganizing in the cation plane the hydrogen, halogen, and chalcogen bonds (HBs, XBs, and ChBs, respectively) formed by the phenyl hydrogen, iodolium iodine, and thienyl sulfur. Crystallographic analyses of some BTI salts show how this interaction coplanarity enables their coupling to point toward a single anion that is coordinated via the supramolecular and heteroditopic synthon XB/HB or XB/ChB, the latter observed here for the first time. These synthons adopt a Janus-like arrangement around iodine. Crystallographic information suggests that interactions of the synthons act synergistically, e.g., when resulting in the unusually short ChBs formed by the thienyl sulfur. Determination of the molecular electrostatic potential, Bader's quantum theory of "atoms-in-molecules" analysis, and natural bond orbital investigations give information on the nature and energetic aspects of the short contacts observed in crystals

Review conformation, self-aggregation, and membrane interaction of peptaibols as studied by pulsed electron double resonance spectroscopy

Pulsed EPR methods, in particular pulsed electron double resonance (PELDOR) [or double electron-electron resonance (DEER)], are very sensitive to the dipole \ub7\ub7\ub7 dipole interaction between electron spins in a pair of free radicals. Using PELDOR, the conformations of a number of double radical-containing biomolecules have been determined. In this review article, we focused our attention on the application of this spectroscopy to nitroxide-labeled peptaibols. This is an emerging class of naturally occurring, relatively short, linear, helical peptide molecules endowed with hydrophobic character, capability to interact with and to alter the structure of membranes, and antibiotic activity. We extracted detailed information on the secondary structures of specifically site-directed, double nitroxide-labeled peptaibols under a variety of experimental conditions, including biologically relevant environments. Moreover, we examined in-depth peptaibol clustering, related to the marked propensity of these molecules to undergo self-association in model and whole-cell membrane systems, using mainly mono-nitroxide-containing synthetic analogs. Finally, based on the PELDOR data accumulated, we proposed models of supramolecular (quaternary) structures of peptaibols and their binding modes to membranes

Impact of diet on adult hippocampal neurogenesis

Research over the last 5 years has firmly established that learning and memory abilities, as well as mood, can be influenced by diet, although the mechanisms by which diet modulates mental health are not well understood. One of the brain structures associated with learning and memory, as well as mood, is the hippocampus. Interestingly, the hippocampus is one of the two structures in the adult brain where the formation of newborn neurons, or neurogenesis, persists. The level of neurogenesis in the adult hippocampus has been linked directly to cognition and mood. Therefore, modulation of adult hippocampal neurogenesis (AHN) by diet emerges as a possible mechanism by which nutrition impacts on mental health. In this study, we give an overview of the mechanisms and functional implications of AHN and summarize recent findings regarding the modulation of AHN by diet