A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

Zeros of the Zak transform on locally compact Abelian groups

Let be a locally compact abelian group. The notion of Zak transform on extends to . Suppose that is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for , we then prove that if is such that its Zak transform is continuous on , then has a zero.

     

Identification of phosphoproteins and determination of phosphorylation sites by zirconium dioxide enrichment and SELDI-MS/MS

Reversible protein phosphorylation mediated by protein kinases and phosphatases is the most studied post-translational modification. Efficient characterization of phosphoproteomes is hampered by (1) low stoechiometry, (2) the dynamic nature of the phosphorylation process and (3) the difficulties of mass spectrometry to identify phosphoproteins from complex mixtures and to determine their sites of phosphorylation. Combination of the phosphopeptide enrichment method with MALDI-TOFMS, or alternatively, with HPLC-ESI-MS/MS and MS(3) analysis was shown to be a step forward for the successful application of MS in the study of protein phosphorylation. In our study we used phosphopeptide enrichment performed in a simple single-tube experiment using zirconium dioxide (ZrO(2)). A simple protein mixture containing precipitated bovine milk caseins was enzymatically digested and the mixture of tryptic fragments was analysed before and after enrichment using nanoflow HPLC-ESI-MS/MS and surface-enhanced laser desorption/ionization (SELDI)-MS/MS on QqTOF instruments to compare the efficiency of the two methods in the determination of phosphorylation sites. Both approaches confirm the high selectivity obtained by the use of batch-wise, ZrO(2)-based protocol using di-ammonium phosphate as the eluting buffer. More phosphorylation sites (five for beta-casein and three for alpha(S1)-casein) were characterized by SELDI-MS/MS than by nanoflow HPLC-ESI-MS/MS. Therefore, ZrO(2)-based phosphopeptide enrichment combined with SELDI-MS/MS is an attractive alternative to previously reported approaches for the study of protein phosphorylation in mixtures of low complexity with the advance of fast in situ peptide purification. The method was limited to successful analysis of high-abundance proteins. Only one phosphorylation site was determined for the minor casein component alpha(S2)-casein by ESI-MS/MS and none for kappa-casein. Therefore an improvement in enrichment efficiency, especially for successful phosphoproteomic applications, is needed.     

Quantitative Comparison of Tandem Mass Spectra Obtained on Various Instruments

The similarity between two tandem mass spectra, which were measured on different instruments, was compared quantitatively using the similarity index (SI), defined as the dot product of the square root of peak intensities in the respective spectra. This function was found to be useful for comparing energy-dependent tandem mass spectra obtained on various instruments. Spectral comparisons show the similarity index in a 2D “heat map”, indicating which collision energy combinations result in similar spectra, and how good this agreement is. The results and methodology can be used in the pharma industry to design experiments and equipment well suited for good reproducibility. We suggest that to get good long-term reproducibility, it is best to adjust the collision energy to yield a spectrum very similar to a reference spectrum. It is likely to yield better results than using the same tuning file, which, for example, does not take into account that contamination of the ion source due to extended use may influence instrument tuning. The methodology may be used to characterize energy dependence on various instrument types, to optimize instrumentation, and to study the influence or correlation between various experimental parameters.

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Graphical Abstract ?

     

Ambiguity functions, Wigner distributions and Cohen's class for LCA groups

In this paper we construct a general class of time-frequency representations for LCA groups which parallel Cohen's class for the real line. For this, we generalize the notion of ambiguity function and Wigner distribution to the setting of general LCA groups in such a way that the Plancherel transform of the ambiguity function coincides with the Wigner distribution. Furthermore, properties of the general ambiguity function and Wigner distribution are studied. In detail we characterize those groups whose ambiguity functions and Wigner distributions vanish at infinity or are square-integrable. Finally, we explicitly construct Cohen's class for the group of p-adic numbers, p prime.     

Amino acid cluster formation studied by electrospray ionization mass spectrometry

The association properties of natural and non-natural amino acids were studied in detail using electrospray ionization mass spectrometry. The results show a highly diverse cluster formation behavior of amino acids. There are differences regarding the degree of clustering (average cluster size), the presence or absence of one or several 'magic' clusters of special stability and the influence of chirality on cluster stability. Cluster formation does not show a good correlation with simple physico-chemical properties (such as solubility), indicating that it is a specific process and not only a simple aggregation during evaporation/ionization. A systematic study of cluster formation of serine derivatives reveals that all functional groups play a prominent role in the binding of the magic octamer. The results support the idea of the zwitterionic character of the octamer. Electrospray ionization of the side-chain acetylated serine shows the formation of a very stable tetramer with a strong preference for homochirality. The results suggest that Ser8 is made up of two tetramer subunits, held together by hydrogen bonds of the side-chain.     

Biomimetic oxidation of 3,5-di-tert-butylcatechol by dioxygen via Mn-enhanced base catalysis

The 6-coordinate dioximatomanganese(II) complex [Mn(HL)(CH3OH)]+ (2, where H2L is [HON=C(CH3)C(CH3)=NCH2CH2]2NH), formed by instant solvolysis of [Mn2(HL)2](BPh4)2 (1) in methanol, accelerates the triethylamine (TEA)-catalyzed oxidation of 3,5-di-tert-butylcatechol (H2dtbc) by O2 to the corresponding o-benzoquinone. Significantly, 2 alone has no catalytic effect. The observed rate increase can be explained by the interaction of 2 with the hydroperoxo intermediate HdtbcO2- formed from Hdtbc- and O2 in the TEA-catalyzed oxidation. The kinetics of the TEA-catalyzed and Mn-enhanced reaction has been studied by gas-volumetric monitoring of the amount of O2 consumed. The initial rate of O2 uptake (V(in)) shows a first-order dependence on the concentration of 2 and O2 and saturation kinetics with respect to both H2dtbc and TEA. The observed kinetic behavior is consistent with parallel TEA-catalyzed and Mn-enhanced oxidation paths. The 3,5-di-tert-butylsemiquinone anion radical is an intermediate detectable by electron spin resonance (ESR) spectroscopy. The dimeric catalyst precursor has been characterized by X-ray diffraction and electrospray ionization mass spectrometry and the monomeric catalyst by ESR spectroscopy.     

Affine Density,Frame Bounds,and the Admissibility Condition for Wavelet Frames

For a large class of irregular wavelet frames we derive a fundamental relationship between the affine density of the set of indices, the frame bounds, and the admissibility constant of the wavelet. Several implications of this theorem are studied. For instance, this result reveals one reason why wavelet systems do not display a Nyquist phenomenon analogous to Gabor systems, a question asked in Daubechies' Ten Lectures book. It also implies that the affine density of the set of indices associated with a tight wavelet frame has to be uniform. Finally, we show that affine density conditions can even be used to characterize the existence of wavelet frames, thus serving, in particular, as sufficient conditions.     

Irregular Shearlet Frames: Geometry and?Approximation Properties

Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few construction strategies for discrete shearlet systems are known so far.