Einstein metrics and quaternionic Kähler manifolds

The research is partially suported by a grant from the Natural Sciences and Engineering Research Council of Canada     

Single P and As dopants in the Si(001) surface

Using first-principles density functional theory, we discuss doping of the Si(001) surface by a single substitutional phosphorus or arsenic atom. We show that there are two competing atomic structures for isolated Si-P and Si-As heterodimers, and that the donor electron is delocalized over the surface. We also show that the Si atom dangling bond of one of these heterodimer structures can be progressively charged by additional electrons. It is predicted that surface charge accumulation as a result of tip-induced band bending leads to structural and electronic changes of the Si-P and Si-As heterodimers which could be observed experimentally. Scanning tunneling microscopy (STM) measurements of the Si-P heterodimer on a n-type Si(001) surface reveal structural characteristics and a bias-voltage dependent appearance, consistent with these predictions. STM measurements for the As:Si(001) system are predicted to exhibit similar behavior to P:Si(001).     

Arithmetic of Finite Ordered Sets: Cancellation of Exponents, I

Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying A ^P B ^P , then A B. We show that this is true in case P is dismantlable to each of its points, or P is connected and each of A and B is dismantlable to each of its covering pairs.     

Discrete Lie Advection of Differential Forms

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.     

Erratum to: Discrete Lie Advection of Differential Forms

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.     

Faster,More Reproducible DESI-MS for Biological Tissue Imaging

A new, more robust sprayer for desorption electrospray ionization (DESI) mass spectrometry imaging is presented. The main source of variability in DESI is thought to be the uncontrolled variability of various geometric parameters of the sprayer, primarily the position of the solvent capillary, or more specifically, its positioning within the gas capillary or nozzle. If the solvent capillary is off-center, the sprayer becomes asymmetrical, making the geometry difficult to control and compromising reproducibility. If the stiffness, tip quality, and positioning of the capillary are improved, sprayer reproducibility can be improved by an order of magnitude. The quality of the improved sprayer and its potential for high spatial resolution imaging are demonstrated on human colorectal tissue samples by acquisition of images at pixel sizes of 100, 50, and 20 μm, which corresponds to a lateral resolution of 40–60 μm, similar to the best values published in the literature. The high sensitivity of the sprayer also allows combination with a fast scanning quadrupole time-of-flight mass spectrometer. This provides up to 30 times faster DESI acquisition, reducing the overall acquisition time for a 10 mm × 10 mm rat brain sample to approximately 1 h. Although some spectral information is lost with increasing analysis speed, the resulting data can still be used to classify tissue types on the basis of a previously constructed model. This is particularly interesting for clinical applications, where fast, reliable diagnosis is required.

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Graphical Abstract ?

     

Profiling of the secretome of human cancer cells: Preparation of supernatant for proteomic analysis

Secretomic analysis requires removal of serum proteins from cell‐culture media. We evaluate the proteins washed from cells prepared in bovine serum‐supplemented medium. PBS and serum‐free‐medium (SFM) were the washing solutions. A Bradford assay was used for total protein concentration and a 1D gel and LC‐MS/MS, to assign the protein to human or bovine origin. For both wash solutions, all bovine protein had been removed by the third wash, without compromising the number of living cells. Further washes reduced the number of living cells, especially when using PBS. Proteomic analysis of wash supernatant showed that SFM induced greater lysis of dead cells. Three washes were sufficient to minimize the effects on cell viability, while still removing serum proteins. Washing in SFM resulted in contamination of the wash supernatant with lysed dead cell proteins. Washed cells were incubated in SFM and exposed to ionizing radiation. Analysis of the supernatant showed an increase in human cytoplasmic, plasma membrane, and nuclear protein following irradiation. Secreted proteins were also detected, but in smaller quantities. The significance of these findings extend to in vitro studies of bystander phenomena, since the proteins of lysed dead cells may participate in driving bystander responses.