A note on Taylor boundary conditions for accurate image restoration

In recent years, several efforts were made in order to introduce boundary conditions for deblurring problems that allow to get accurate reconstructions. This resulted in the birth of Reflective, Anti-Reflective and Mean boundary conditions, which are all based on the idea of guaranteeing the continuity of the signal/image outside the boundary. Here we propose new boundary conditions that are obtained by suitably combining Taylor series and finite difference approximations. Moreover, we show that also Anti-Reflective and Mean boundary conditions can be attributed to the same framework. Numerical results show that, in case of low levels of noise and blurs able to perform a suitable smoothing effect on the original image (e.g. Gaussian blur), the proposed boundary conditions lead to a significant improvement of the restoration accuracy with respect to those available in the literature.     

Leading order asymptotics in the Goldbeter–Koshland switch

An asymptotic analysis at leading order of the Goldbeter–Koshland switch, the simplest futile cycle, is carried out in detail. After a nondimensionalization of the problem, we find the leading order uniform expansions of the reactants, identifying the proper time scales in a total setting. Comparison with numerical integration confirms the goodness of our analysis.     

Synthesis of cananodine by intramolecular epoxide opening

Cananodine is a guaipyridine alkaloid with activity against liver cancer. Cananodine was synthesized using a remarkable intramolecular opening of a trisubstituted epoxide as the key step in construction of the seven-membered carbocycle of the target. The epoxide opening strategy allows all four stereoisomers of cananodine to be prepared.     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Glycoproteomic characterization of carriers of the CD15/Lewis<Superscript>x</Superscript> epitope on Hodgkin's Reed-Sternberg cells

Background  

The Lewis^x trisaccharide, also referred to as the CD15 antigen, is a diagnostic marker used to distinguish Hodgkin's lymphoma from other lymphocytic cancers. However, the role of such fucosylated structures remains poorly understood, in part because carriers of Lewis^x structures on Hodgkin's Reed-Sternberg cells have not been identified.     

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.