Binomial Cycle Bases on Koszul Homology Modules

Let I be a principal p-Borel ideal of the polynomial ring S in variables x over a field. Then the Koszul homology module H ₃(x;S/I) has binomial cycle bases.     

Quasiperiodic spectra and orthogonality for iterated function system measures

We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension. Moreover, the spectrum is then typically quasi-periodic, but non-periodic, i.e., the spectrum is a “small perturbation” of a lattice. Due to earlier research on IFSs, there are known results on certain classes of spectral duality-pairs, also called spectral pairs or spectral measures. It is known that some duality pairs are associated with complex Hadamard matrices. However, not all IFSs X admit spectral duality. When X is given, we identify geometric conditions on X for the existence of a Fourier spectrum, serving as the second part in a spectral pair. We show how these spectral pairs compose, and we characterize the decompositions in terms of atoms. The decompositions refer to tensor product factorizations for associated complex Hadamard matrices. Research supported in part by a grant from the National Science Foundation DMS-0704191.     

Is it biologically relevant to measure the structures of small peptides in the gas-phase?

Recent developments in sample introduction of biologically relevant molecules have heralded a new era for gas-phase methods of structural determination. One of the biggest challenges is to relate gas-phase structures, often measured in the absence of water and counter ions, with in vivo biologically active structures. An advantage of gas-phase based techniques is that a given peptide can be analysed in a variety of different forms, for example, as a function of charge state, or with additional water molecules. Molecular modelling can provide insight into experimental findings and help elucidate the differences between structural forms. Combining experiment and theory provides a thorough interrogation of candidate conformations. Here two important naturally occurring peptide systems have been examined in detail and results are assessed in terms of their biological significance.The first of these is gonadotropin-releasing hormone (GnRH), a decapeptide which is the central regulator of the reproductive system in vertebrates. We have examined several naturally occurring variants of this peptide using Ion Mobility Mass Spectrometry and Electron Capture Dissociation (ECD) in conjunction with Fourier Transform Ion Cyclotron Mass Spectrometry (FT-ICR-MS). Candidate conformations are modelled using the AMBER force field. Single amino acid changes, for example Gly6 → Ala6, or Ala6 → D-Ala6, have observable effects on the gas phase structure of GnRH. It has been shown that evolutionary primary sequence variations are key to the biological activity of GnRH, and it is thought that this is due to different binding affinities at target receptors. This work provides strong evidence that this activity is structurally based. The second system examined is the relationship between the quaternary structure and activity of two novel β-defensins. FT-ICR mass spectrometry has been employed to characterize di-sulphide bridging and dissociation based experiments utilised to investigate their structural core. Defr1, with five cysteines, exists as a covalently bound disulphide linked dimer; Defr1 Y5C with six cysteines also is observed as a dimer, but non-covalently bound, suggesting that this defensin has a tendency to aggregate. The activity of Defr1 is 10 times higher than that of Defr1 Y5C when tested against the pathogen Pseudomonas aeruginosa. The results from these studies could inform future design of novel GnRH type ligands and anti-microbial agents, and illustrate the power of gas-phase based techniques for solving peptide structures.     

Synthesis of platinum nanowheels using a bicellar template

Disk-like surfactant bicelles provide a unique meso-structured reaction environment for templating the wet-chemical reduction of platinum(II) salt by ascorbic acid to produce platinum nanowheels. The Pt wheels are 496 +/-55 nm in diameter and possess thickened centers and radial dendritic nanosheets (about 2-nm in thickness) culminating in flared dendritic rims. The structural features of the platinum wheels arise from confined growth of platinum within the bilayer that is also limited at edges of the bicelles. The size of CTAB/FC7 bicelles is observed to evolve with the addition of Pt(II) complex and ascorbic acid. Synthetic control is demonstrated by varying the reaction parameters including metal salt concentration, temperature, and total surfactant concentration. This study opens up opportunities for the use of other inhomogeneous soft templates for synthesizing metals, metal alloys, and possibly semiconductors with complex nanostructures.     

Intrinsic Fluorescence of Metabolite Amyloids Allows Label‐Free Monitoring of Their Formation and Dynamics in Live Cells

The formation of apoptosis‐inducing amyloidal structures by metabolites has significantly extended the “amyloid hypothesis” to include non‐proteinaceous, single metabolite building blocks. However, detection of metabolite assemblies is restricted compared to their larger protein‐based counterparts owing to the hindrance of external labelling and limited immunohistochemical detection tools. Herein, we present the detection of the formation, dynamics, and cellular distribution of metabolite amyloid‐like structures and provide mechanistic insights into the generation of supramolecular chromophores. Moreover, the intrinsic fluorescence properties allow the detection of metabolite assemblies in living cells without the use of external dyes. Altogether, this intrinsic fluorescence of metabolite assemblies further verifies their amyloidal nature, while providing an important tool for further investigation of their pathological role in inborn error of metabolism disorders.     

Betti numbers for p -stable ideals

Abstract

All Riemannian algebras of dimension ≤3 are classified in this paper.     

Heat‐treatment influence on the microstructure and magnetic properties of rare‐earth substituted SrFe12O19

Rare‐earth substituted strontium ferrite nanopowders SrFe_12‐xR_xO₁₉ (R = La, Gd and Er; x = 0.2, 0.5 and 1) were prepared by sol‐gel‐autocombustion method and subsequent heat treatments. Structural and magnetic properties of SrFe_12‐xR_xO₁₉ powders heat treated at 800, 900 and 1000⁰C, for various times, were characterized with an X‐ray diffractometer, a vibrating sample magnetometer and a scanning electron microscope. The results of X‐ray diffraction measurements showed the M‐type hexagonal structure formation by heat treatments. Magnetic properties, such as specific saturation magnetization σ_s, specific remanent magnetization σ_r and coercivity H_c, as well as microstructure depend on the heat treatment conditions (temperature and time). The coercivity H_c exhibits a great increase after a critical heat treatment time. When the heat treatment time increases, one obtains an increase in H_c after a shorter heat treatment time. This jump of H_c was explained by a transition from the superparamagnetic state to normal state of the single domain nanoparticles. The occurrence of an agglomerated structure composed of magnetically interacting ultrafine crystallites also contributes to the increase of H_c.The heat treatment determines a reduced grain growth due to the internal stress generated by R ions. With increasing R content the σ_s and σ_r decrease due to the dissolution of R ions into the hexaferrite lattice. We believe that by selecting the time and temperature of the heat treatment, microstructure and magnetic properties suitable for magnetic recording media application can be obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)