Discrete tomography: Determination of finite sets by X-rays

We study the determination of finite subsets of the integer lattice , , by X-rays. In this context, an X-ray of a set in a direction gives the number of points in the set on each line parallel to . For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory and convexity, we prove that there are four prescribed lattice directions such that convex subsets of (i.e., finite subsets with ) are determined, among all such sets, by their X-rays in these directions. We also show that three X-rays do not suffice for this purpose. This answers a question of Larry Shepp, and yields a stability result related to Hammer's X-ray problem. We further show that any set of seven prescribed mutually nonparallel lattice directions in have the property that convex subsets of are determined, among all such sets, by their X-rays in these directions. We also consider the use of orthogonal projections in the interactive technique of successive determination, in which the information from previous projections can be used in deciding the direction for the next projection. We obtain results for finite subsets of the integer lattice and also for arbitrary finite subsets of Euclidean space which are the best possible with respect to the numbers of projections used.

     

Development of practical syntheses of the marine anticancer agents discodermolide and dictyostatin

Initially isolated in trace quantities from deep-sea sponges, the structurally related polyketides discodermolide and dictyostatin share the same microtubule-stabilizing antimitotic mechanism as Taxol. Discodermolide has been the focus of intense research activity in order to develop a practical supply route, and these efforts ultimately allowed its large-scale synthesis and the initiation of clinical trials as a novel anticancer drug. Similarly, the re-isolation and synthesis of dictyostatin continues to stimulate the biological and chemical communities in their quest for the development of new chemotherapeutic agents. This comprehensive review chronicles the synthetic endeavours undertaken over the last 15 years towards the development and realization of practical chemical syntheses of discodermolide and, more recently, dictyostatin, focusing on the methods and strategies employed for achieving overall stereocontrol and key fragment unions, as well as the design and synthesis of novel hybrid structures.     

Development and validation of an LC-MS assay for finasteride and its application to prostate cancer prevention trial sample analysis

An analytical method is developed and validated for the quantitative determination of finasteride, a potent 5 alpha-reductase inhibitor, in human plasma. Calibration curves are linear in the concentration range of 1 to 100 ng/mL. Sample pretreatment involves a liquid-liquid extraction with ethyl acetate using 0.2 mL aliquots of plasma. Finasteride and the internal standard (beclomethasone) are separated on a Waters Symmetry Shield RP18 column (50 x 2.1 mm, 3.5 microm) and eluted using a gradient mobile phase composed of acetonitrile and 10mM ammonium acetate with 0.1% formic acid. The column eluant is monitored by mass spectrometry with electrospray ionization. A complete validation of the method is performed. For quality control samples at three different concentrations that were analyzed in quintuplicate, on six separate occasions, the accuracy and precision range from 95.2% to 101% and 3.4% to 7.3%, respectively. The developed method is subsequently applied to measure the steady state finasteride concentration of patients who participated in the Prostate Cancer Prevention Trial.     

Impact of proline and aspartic acid residues on the dissociation of intermolecularly crosslinked peptides

The dissociation of intermolecularly crosslinked peptides was evaluated for a series of peptides with proline or aspartic acid residues positioned adjacent to the crosslinking sites (lysine residues). The peptides were crosslinked with either disuccinimidyl suberate (DSS) or disuccinimidyl L-tartrate (DST), and the influence of proline and aspartic acid residues on the fragmentation patterns were investigated for precursor ions with and without a mobile proton. Collisionally activated dissociation (CAD) spectra of aspartic acid-containing crosslinked peptide ions, doubly-charged with both protons sequestered, were dominated by cleavage C-terminal to the Asp residue, similar to that of unmodified peptides. The proline-containing crosslinked peptides exhibited a high degree of internal ion formation, with the resulting product ions having an N-terminal proline residue. Upon dissociation of the doubly-charged crosslinked peptides, twenty to fifty percent of the fragment ion abundance was accounted for by multiple cleavage products. Crosslinked peptides possessing a mobile proton yielded almost a full series of b- and y-type fragment ions, with only proline-directed fragments still observed at high abundances. Interestingly, the crosslinked peptides exhibited a tendency to dissociate at the amide bond C-terminal to the crosslinked lysine residue, relative to the N-terminal side. One could envision updating computer algorithms to include these crosslinker specific product ions--particularly for precursor ions with localized protons--that provide complementary and confirmatory information, to offer more confident identification of both the crosslinked peptides and the location of the crosslink, as well as affording predictive guidelines for interpretation of the product-ion spectra of crosslinked peptides.     

Decongestion of methylene spectra in biological and non-biological systems using picosecond 2DIR spectroscopy measuring electron-vibration–vibration coupling

Methylene is found in the repeat units of many polymers including proteins. In some cases it appears to be a useful reporter of variation in local environment whilst in other contexts average behaviour seems to dominate. In this paper we apply a particular 2DIR technique to a range of systems containing methylene groups, showing that mode frequencies, linewidths and splittings can be easily extracted even when the infrared absorption bands are too congested to allow reliable analysis. 2DIR spectra of polyethylene and several liquid alkanes are compared and it is shown for the case of l-arginine that the methylene scissor modes are split and that this can be resolved by tracking the 2DIR spectrum as a function of time. Calculations from first principles reveal that for most of the methylene modes studied, electrical anharmonicity is the dominant contributor to the 2DIR cross-peak intensity, with the mechanical anharmonicity making only a small contribution.     

Assessment of the UVR protection provided by different tree species

In recent years, SunSmart campaigns have emphasized the importance of the use of shade as a strategy in the reduction of human exposure to solar UV radiation (UVR), particularly in early life with the provision of shade in schools. Trees can play an important role in shade provision, either as the main shade provider or to augment shade structures and increase UVR protection provided to the general population. A study to measure the protection provided by a range of trees common in Australian urban environments was undertaken during the summers of 2004/2005 and 2005/2006. Solar UVR beneath the trees was measured using UVR sensitive polysulphone badges positioned horizontally within the shaded area and were compared with those in full sunshine to give an indication of the protection provided. Measurements made on sunny days during the months of October to April indicated that the shade cover provided by the trees depended upon the tree species and changed with season as a result of changing foliage and sun angles. Measured protection factors ranged from 5 to 10 and were generally a maximum in the height of summer when the sun was highest in the sky and the foliage was densest.     

Reinvestigation of the electronic spectroscopy of the Au-Ar complex

The Au-Ar complex is reinvestigated employing resonance-enhanced multiphoton ionization spectroscopy. Spectra are reported, corresponding to the atomic transition Au(6p<--6s). This electronic excitation yields (2)Pi and (2)Sigma(+) states of Au-Ar, which interact under the influence of spin-orbit coupling. The spectra are consistent with strong sigma-pi mixing induced by the large spin-orbit coupling of Au, leading to strong interaction of the two Omega=12 states, which arise from the Ar((1)S(0))+Au((2)P(12,32)) asymptotes, and the consequent formation of a "shelf" on the outer wall of the lowest Omega=12 state. In addition, high-level ab initio calculations are reported on the ground electronic state, X (2)Sigma(+), including extrapolation to the basis set limit.     

Oxygen dynamics in epitaxial YBa2Cu3O7-δ thin films

We have investigated epitaxial YBCO films by Perturbed γγ-Angular Correlation Spectroscopy (PAC) using ¹¹¹In probe atoms. The probes substitute on the yttrium lattice site and hyperfine parameters have been determined unambiguously. Excellent agreement is achieved with full potential electric field gradient (efg) calculations. Good reproducibility has been achieved by our preparation method allowing us to study the influence of oxygen motion on the structural orthorhombic to tetragonal phase transition. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multi-gigabit WDM optical networking for next generation avionics system communications

It is envisaged that photonic networking will play a significant role in improving performance and reliability in both civil and military avionics systems. Of all the available photonic multiplexing technologies, wavelength-division multiplexing (WDM) has been the primary focus of attention within mainstream telecommunications offering increased throughput at a reasonable cost, with scope for enhanced routing flexibility, connectivity and network survivability. A direct mapping of techniques and devices from the maturing telecommunications sector is, however, not possible because of the stringent requirements of systems operating in the hostile aerospace environment. This paper gives an outline of these requirements and discusses, in detail, the design and development of a multi-gigabit, broadband optical WDM network architecture, specifically for use on aerospace platforms. The paper will also discuss a key element in the system, the arrayed-waveguide grating (AWG) wavelength multiplexing component, which has been designed to allow operation over the full military temperature specification without environmental conditioning.     

Unravelling overlaps and torsion-facilitated coupling using two-dimensional laser-induced fluorescence

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is employed to identify contributions to fluorescence excitation spectra that arise from both overlapping bands and coupling between zero-order states (ZOSs). Evidence is found for the role of torsional motion in facilitating the coupling between vibrations that particularly involves the lowest-wavenumber out-of-plane vibrational modes. The experiments are carried out on jet-cooled p-fluorotoluene, where the molecules are initially in the lowest two torsional levels. Here we concentrate on the 390–420?cm^?1 features in the S₁?←?S₀ excitation spectrum, assigning the features seen in the 2D-LIF spectrum, aided by separate dispersed fluorescence spectra. The 2D-LIF spectra allow the overlapping contributions to be cleanly separated, including some that arise from vibrational-torsional coupling. Various coupling routes open up because of the different symmetries of the lowest two torsional modes; these combine with the vibrational symmetry to provide new symmetry-allowed vibration-torsion (‘vibtor’) interactions, and the role of the excited m?=?1 torsional level is found to be significant.