Compression and reconstruction of MRI images using 2D DCT.

In magnetic resonance imaging (MRI), the original data are sampled in the spatial frequency domain. The sampled data thus constitute a set of discrete Fourier transform (DFT) coefficients. The image is usually reconstructed by taking inverse DFT. The image data may then be compressed using the discrete cosine transform (DCT). We present here a method of treating the data that combines two procedures, image reconstruction and data compression. This method may be particularly useful in medical picture archiving and communication systems (PACS) where both image reconstruction and compression are important issues.     

Hamilton cycles in prisms

The prism over a graph G is the Cartesian product G □ K₂ of G with the complete graph K₂. If G is hamiltonian, then G□K₂ is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian. In this article, we examine classical problems on hamiltonicity of graphs in the context of having a hamiltonian prism. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 249–269, 2007     

Edge partitions of the complete symmetric directed graph and related designs

We show that the edges of the complete symmetric directed graph onn vertices can be partitioned into directed cycles (or anti-directed cycles) of lengthn−1 so that any two distinct cycles have exactly one oppositely directed edge in common whenn=p ^e>3, wherep is a prime ande is a positive integer. When the cycles are anti-directedp must be odd. We then consider the designs which arise from these partitions and investigate their construction. We would like to thank the Mathematics Department of the University of Arizona for their hospitality during January 1979 when this work was begun. Partial support was provided for this research by the Natural Sciences and Engineering Research Council of Canada under Grant A-4792.     

Additivity of melting curves

Universality of some melting indicators, in the context of two successful models of the solid and the liquid, gives rise to simple semi-empirical melting equations that describe additivity of melting curves. Computer inverse power melting results are used to reproduce the melting characteristics of argon to a good accuracy.     

Synthesis and reactivity of [(silox)2Mo=NR]2Hg (R=tBu, tAmyl; silox=OSitBu3): unusual thermal stability and ready nucleophilic cleavage rationalized by electronic factors

Treatment of (DME)Cl2Mo(=NR)2 (R=tBu, (1-tBu), tAmyl (1-tAmyl)) with 2 equiv of tBu3SiOH (siloxH) and 1 equiv of HCl produced (silox)2Cl2Mo=NR (R=tBu, (3-tBu), tAmyl (3-tAmyl)); subsequent reduction by Na/Hg afforded the Mo(V) chloride, (silox)2ClMo=NtBu (4-tBu), and the Mo(IV) mercury derivatives, [(silox)2Mo=NR]2Hg (R=tBu ((5-tBu)2Hg), tAmyl ((5-tAmyl)2Hg)). Reductions of 3-tBu and 3-tAmyl in the presence of L (L=PMe3, pyridine, 4-picoline) led to the isolation of adducts (silox)2(Me3P)Mo=NR (R=tBu (6-tBu), tAmyl (6-tAmyl)) and (silox)2L2Mo=NtBu (L=py (7-py), 4-pic (7-4-pic)). Single-crystal X-ray structural investigations of pseudo-tetrahedral 4-tBu, Hg-capped, pseudo-trigonal planar (5-tBu)2Hg, pseudo-tetrahedral 6-tBu, and trigonal bipyramidal 7-4-pic reveal that all possess a closed O-Mo-O angle when compared to the N=Mo-O angles. A molecular orbital rationale and supporting calculations suggest that this is a manifestation of the greater pi-donating ability of the imido relative to that of the siloxides. While the D(Mo-Hg) of [(HO)2Mo=NH]2Hg ((5')2Hg) was calculated to be 22.4 kcal/mol, (5-R)2Hg (R=tBu, tAmyl) are remarkably stable; (5-tBu)2Hg degraded in a first-order fashion with DeltaG=31.9(1) kcal/mol. In the presence of strong (L=PMe, pyridine, S8) or weak (L=2-butyne, ethylene, N2O, 1,4,7,10-tetrathiacyclododecane, 1,4,7,10,13,16-hexathiacyclooctadecane) nucleophiles, an enhanced rate of Mo-Hg bond cleavage was noted, with some of the former group generating adducts in <5 min; the products were 6-tBu, 7-py, (silox)2(S)Mo=NtBu (10-tBu), (silox)2Mo=NtBu(C2Me2) (8-tBu), (silox)2(C2H4)Mo=NtBu (11-tBu), (silox)2(O)Mo=NtBu (9-tBu), and a mixture of 10-tBu and 11-tBu, respectively. Some of these were independently prepared via substitution of 6-tBu. According to calculations and a molecular orbital rationale, dissociation of the Mo-Hg bond in (5-R)2Hg (R=tBu, tAmyl) is orbitally forbidden, and the addition of a nucleophile to the terminus of the Mo-Hg-Mo linkage mitigates the symmetry requirements. The mechanism of thermal degradation was studied with mixed success. NMR spectroscopy revealed imido exchange between (5-tBu)2Hg and (5-tAmyl)2Hg during an initial induction period and a subsequent rapid exchange period that implicated free 5-R (R=tBu, tAmyl). Further crossover studies revealed siloxide exchange as an additional complication.     

Quantum memories

We perform a review of various approaches to the implementation of quantum memories, with an emphasis on activities within the quantum memory sub-project of the EU integrated project “Qubit Applications”. We begin with a brief overview over different applications for quantum memories and different types of quantum memories. We discuss the most important criteria for assessing quantum memory performance and the most important physical requirements. Then we review the different approaches represented in “Qubit Applications” in some detail. They include solid-state atomic ensembles, NV centers, quantum dots, single atoms, atomic gases and optical phonons in diamond. We compare the different approaches using the discussed criteria.     

Synchrotron X‐ray microbeam dosimetry with a 20 micrometre resolution scintillator fibre‐optic dosimeter

Cancer is one of the leading causes of death worldwide. External beam radiation therapy is one of the most important modalities for the treatment of cancers. Synchrotron microbeam radiation therapy (MRT) is a novel pre‐clinical therapy that uses highly spatially fractionated X‐ray beams to target tumours, allowing doses much higher than conventional radiotherapies to be delivered. A dosimeter with a high spatial resolution is required to provide the appropriate quality assurance for MRT. This work presents a plastic scintillator fibre optic dosimeter with a one‐dimensional spatial resolution of 20 µm, an improvement on the dosimeter with a resolution of 50 µm that was demonstrated in previous work. The ability of this probe to resolve microbeams of width 50 µm has been demonstrated. The major limitations of this method were identified, most notably the low‐light signal resulting from the small sensitive volume, which made valley dose measurements very challenging. A titanium‐based reflective paint was used as a coating on the probe to improve the light collection, but a possible effect of the high‐Z material on the probes water‐equivalence has been identified. The effect of the reflective paint was a 28.5 ± 4.6% increase in the total light collected; it did not affect the shape of the depth‐dose profile, nor did it explain an over‐response observed when used to probe at low depths, when compared with an ionization chamber. With improvements to the data acquisition, this probe design has the potential to provide a water‐equivalent, inexpensive dosimetry tool for MRT.