An Optimal Dimensionality Sampling Scheme on the Sphere for Antipodal Signals In Diffusion Magnetic Resonance Imaging

We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.Comment: Will be published in the proceedings of the International Conference Acoustics, Speech and Signal Processing 2015 (ICASSP'2015

Firm Strategy and Foreign Direct Investment: An Examination of the Economic Performance of U.S. Multinational Firms

International Relations/Trade, Production Economics,

Meningiomas occurring during long-term survival after treatment for childhood cancer

Childhood cancer is rare but improvements in treatment over the past five decades have resulted in a cohort of more than 30,000 long-term survivors of childhood cancer in the UK with more added annually. These long-term survivors are at risk of late effects of cancer treatment which replace original tumour recurrence as the leading cause of premature death. Second neoplasms are a particular risk and in the central nervous system meningiomas occur increasingly with increased radiation dose to central nervous system tissue and length of time after exposure, resulting in a 500-fold increase above that expected in the normal population by 40 years of follow up. This multidisciplinary author group and others met to discuss the issue. Our pooled information, and consensus that screening should only follow symptoms, was published online by the Royal College of Radiologists in 2013. We outline here the current knowledge and management of these neoplasms secondary to childhood cancer treatment

A Selected Ion Flow Tube Study of the Reactions of Several Cations with the Group 6B Hexafluorides SF6, SeF6, and TeF6

The first investigation of the ion chemistry of SeF$_6$ and TeF$_6$ is presented. Using a selected ion flow tube, the thermal rate coefficients and ion product distributions have been determined at 300 K for the reactions of fourteen atomic and molecular cations, namely H$_3$O$^+$, CF$_3^+$, CF$^+$, CF$_2^+$, H$_2$O$^+$, N$_2$O$^+$, O$^+$, CO$_2^+$, CO$^+$, N$^+$, N$_2^+$, Ar$^+$, F$^+$ and Ne$^+$ (in order of increasing recombination energy), with SeF$_6$ and TeF$_6$. The results are compared with those from the reactions of these ions with SF$_6$, for which the reactions with CF$^+$, CF$_2^+$, N$_2$O$^+$ and F$^+$ are reported for the first time. Several distinct processes are observed amongst the large number of reactions studied, including dissociative charge transfer, and F$^-$, F, F$_2^-$ and F$_2$ abstraction from the neutral reactant molecule to the reagent ion. The dissociative charge transfer channels are discussed in relation to vacuum ultraviolet photoelectron and threshold photoelectron-photoion coincidence spectra of XF$_6$ (X = S, Se, and Te). For reagent ions whose recombination energies lie between the first dissociative ionisation limit, XF$_6$ $\rightarrow$ XF$_5^+$ + F + e$^-$, and the onset of ionisation of the XF$_6$ molecule, the results suggest that if dissociative charge transfer occurs, it proceeds via an intimate encounter. For those reagent ions whose recombination energies are greater than the onset of ionisation, long-range electron transfer may occur depending on whether certain physical factors apply, for example non-zero Franck-Condon overlap. From the reaction kinetics, limits for the heats of formation of SeF$_4$, SeF$_5$, TeF$_4$ and TeF$_5$ at 298 K have been obtained; $\Delta_f$H$^o$(SeF$_4$) < -369 kJ mol$^{-1}$, $\Delta_f$H$^o$(SeF$_5$) < -621 kJ mol$^{-1}$, $\Delta_f$H$^o$(TeF$_4$) > -570 kJ mol$^{-1}$, and $\Delta_f$H$^o$(TeF$_5$) < -822 kJ mol$^{-1}$