Respiratory noise correction using phase information

Respiratory noise is a confounding factor in functional magnetic resonance imaging (MRI) data analysis. A novel method called Respiratory noise Correction using Phase information is proposed to retrospectively correct for the respiratory noise in functional MRI (fMRI) time series. It is demonstrated that the respiratory movement and the phase of functional MRI images are highly correlated in time. The signal fluctuation due to respiratory movements can be effectively estimated from the phase variation and removed from the functional MRI time series using a Wiener filtering technique. In our experiments, this new method is compared with RETROICOR, which requires recording respiration signal simultaneously in an fMRI experiment. The two techniques show comparable performance with respect to the respiratory noise correction for fMRI time series. However, this technique is more advantageous because there is no need for monitoring the subjects’ respiration or changing functional MRI protocols. This technique is also potentially useful for correcting respiratory noise from abnormal breathing or when the respiration is not periodic.     

On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its fourier series

In a recent paper Lal and Yadov [4] obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.     

Pluripotential Energy

We discuss a notion of the energy of a compactly supported measure in \mathbbCⁿ \mathbb{C}^n for n > 1 which we show is equivalent to that defined by Berman, Boucksom, Guedj and Zeriahi. This generalizes the classical notion of logarithmic energy of a measure in the complex plane \mathbbC \mathbb{C} ; i.e., the case n = 1.     

PubChemSR: A search and retrieval tool for PubChem

Background  

Recent years have seen an explosion in the amount of publicly available chemical and related biological information. A significant step has been the emergence of PubChem, which contains property information for millions of chemical structures, and acts as a repository of compounds and bioassay screening data for the NIH Roadmap. There is a strong need for tools designed for scientists that permit easy download and use of these data. We present one such tool, PubChemSR.     

Lagrangean Structure and Propagation of Singularities in Multidimensional Compressible Flow

We study the propagation of singularities in solutions of the Navier–Stokes equations of compressible, barotropic fluid flow in two and three space dimensions. The solutions considered are in a fairly broad regularity class for which initial densities are nonnegative and essentially bounded, initial energies are small, and initial velocities are in certain fractional Sobolev spaces. We show that, if the initial density is bounded below away from zero in an open set V, then each point of V determines a unique integral curve of the velocity field and that this system of integral curves defines a locally bi-Hölder homeomorphism of V onto its image at each positive time. This “Lagrangean structure” is then applied to show that, if the initial density has a limit at a point of such a set V from a given side of a continuous hypersurface in V, then at each later time both the density and the divergence of the velocity have limits at the transported point from the corresponding side of the transported hypersurface, which is also a continuous manifold. If the limits from both sides exist, then the Rankine–Hugoniot conditions hold in a strict pointwise sense, showing that the jump in the divergence of the velocity is proportional to the jump in the pressure. This leads to a derivation of an explicit representation for the strength of the jump in the logarithm of the density, from which it follows that discontinuities persist for all time, convecting along fluid particle paths, and in the case that the pressure is strictly increasing in density, having strengths which decay exponentially in time.     

Resolving and assigning N-linked glycan structural isomers from ovalbumin by IMS-MS

Ion mobility-mass spectrometry (IMS-MS) and molecular modeling techniques have been used to characterize ovalbumin N-linked glycans. Some glycans from this glycoprotein exist as multiple isomeric forms. The gas-phase separation makes it possible to resolve some isomers before MS analysis. Comparisons of experimental cross sections for selected glycan isomers with values that are calculated for iterative structures generated by molecular modeling techniques allow the assignment of sharp features to specific isomers. We focus here on an example glycan set, each having a m/z value of 1046.52 with formula [H₅N₄+2Na]²⁺, where H corresponds to a hexose, and N to a N-acetylglucosamine. This glycan appears to exist as three different isomeric forms that are assignable based on comparisons of measured and calculated cross sections. We estimate the relative ratios of the abundances of the three isomers to be in the range of ∼1.0:1.35:0.85 to ∼1.0:1.5:0.80. In total, IMS-MS analysis of ovalbumin N-linked glycans provides evidence for 19 different glycan structures corresponding to high-mannose and hybrid type carbohydrates with a total of 42 distinct features related to isomers and/or conformers.     

Structural analysis of leukotriene C<Subscript>4</Subscript> isomers using collisional activation and 157 nm photodissociation

The fragmentation of 5-hydroxy-6-glutathionyl-7,9,11,14-eicosatetraenoic acid [leukotriene C4 or LTC4 (5, 6)] and its isomeric counterpart LTC4 (14, 15) were studied by low and high-energy collisional induced dissociation (CID) and 157 nm photofragmentation. For singly charged protonated LTC4 precursors, photodissociation significantly enhances the signal intensities of informative fragment ions that are very important to distinguish the two LTC4 isomers and generates a few additional fragment ions that are not usually observed in CID experiments. The ion trap enables MSn experiments on the fragment ions generated by photodissociation. Photofragmentation is found to be suitable for the structural identification and isomeric differentiation of cysteinyl leukotrienes and is more informative than low or high-energy CID. We describe for the first time the structural characterization of the LTC4 (14, 15) isomer by mass spectrometry using CID and 157 nm light activation methods.     

Asymptotics for Christoffel functions of planar measures

We prove a version of asymptotics of Christoffel functions with varying weights for a general class of sets E in, and measures μ on the complex plane ℂ. This class includes all regular measures μ in the sense of Stahl-Totik [18] on regular compact sets E in ℂ and even allows varying weights. Our main theorems cover some known results for subsets of the real line ℝ. In particular, we recover information in the case of E = ℝ with Lebesgue measure dx and weight w(x) = exp(−Q(x)) where Q(x) is a nonnegative even degree polynomial having positive leading coefficient. Supported in part by an NSERC of Canada grant     

A diffractive optical element for shaping arbitrary beams

A design method is presented for an optical element that shapes an arbitrary collimated beam. The optical element consists of a pair of diffractive optical elements (DOEs). The outgoing beam is also collimated, and can have any desired intensity profile. The phase functions of the DOEs are computed by minimizing an appropriate cost function under an energy conservation constraint.     

Iron(III) p-toluenesulfonate catalyzed synthesis of homoallyl ethers from acetals and aldehydes

Iron(III) p-toluenesulfonate, Fe(OTs)₃·6H₂O, is an inexpensive, versatile and commercially available catalyst for the allylation of acetals using allyltrimethylsilane to yield homoallyl ethers in moderate to good yields. The one-pot conversion of aldehydes to homoallyl ethers using alkoxysilanes has also been accomplished using Fe(OTs)₃·6H₂O as a catalyst. The use of mild reaction conditions and a relatively non-corrosive catalyst make this method an attractive option for the synthesis of a range of homoallyl ethers.