Magnetic resonance imaging screening in women at genetic risk of breast cancer: imaging and analysis protocol for the UK multicentre study. UK MRI Breast Screening Study Advisory Group

The imaging and analysis protocol of the UK multicentre study of magnetic resonance imaging (MRI) as a method of screening for breast cancer in women at genetic risk is described. The study will compare the sensitivity and specificity of contrast-enhanced MRI with two-view x-ray mammography. Approximately 500 women below the age of 50 at high genetic risk of breast cancer will be recruited per year for three years, with annual MRI and x-ray mammography continuing for up to 5 years. A symptomatic cohort will be measured in the first year to ensure consistent reporting between centres. The MRI examination comprises a high-sensitivity three-dimensional contrast-enhanced assessment, followed by a high-specificity contrast-enhanced study in equivocal cases. Multiparametric analysis will encompass morphological assessment, the kinetics of contrast agent uptake and determination of quantitative pharmacokinetic parameters. Retrospective analysis will identify the most specific indicators of malignancy. Sensitivity and specificity, together with diagnostic performance, diagnostic impact and therapeutic impact will be assessed with reference to pathology, follow-up and changes in diagnostic certainty and therapeutic decisions. Mammography, lesion localisation, pathology and cytology will be performed in accordance with the UK NHS Breast Screening Programme quality assurance standards. Similar standards of quality assurance will be applied for MR measurements and evaluation.     

Jahn—Teller effects in substituted benzene cations. V. Quadratic coupling

A calculation model is derived for taking into account quadratic, in addition to linear, coupling Jahn—Teller effects in determining vibronic energy levels and transitions. Procedures are developed for analysis of Jahn—Teller electronic spectra on this basis and the new features, with respect to the linear coupling approximation, brought about by introduction of quadratic coupling, are discussed. Vibronic analyses of the B?² A″₂-X?²E″ transitions of 1,3,5-C₆F₃H⁺₃, 1,3,5-C₆F₃D⁺₃ and 1,3,5-C₆Cl₃H⁺₃ are carried out, in particular for bands involving excitation of the mode 6 vibration. Experimental evidence for quadratic Jahn—Teller effects is obtained for the sym-trifluorobenzene ions and the linear coupling parameters D₆, ω₆ and quadratic coupling parameter q₆ are derived. Two possible orders of magnitude of the quadratic coupling strength are found to be compatible with the spectra of 1,3,5-C₆Cl₃H⁺₃. The analyses are consistent between the three ions and are not in contradiction with the general findings based on the linear approximation alone.     

Jahn—Teller effects in substituted benzene cations. IV. Intermode interactions and intensity anomalies in sym-trifluorobenzene ions

A theoretical treatment of coupling between Jahn—Teller modes is given which includes both linear and quadratic Jahn—Teller coupling. Effects of two and three mode interactions on the B?²A″₂ → X?²E″ transition of the sym-trifluorobenzene ions are studied, within the linear coupling approximation, for modes 6, 7, 8 and 9. Quadratic coupling effects are considered in a companion paper (part V). The results show that discrepancies previously noted between observed relative band intensities and those calculated on the basis of single Jahn—Teller modes cannot be accounted for by multimode interactions or by Fermi resonance effects operating in conjunction with Jahn—Teller effects. Jahn—Teller combination bands are shown to have several components, the most intense of which are assigned. Particular attention is paid to various possible assignments of the 8^0,0_{1,$\text{1}\text{2}$} and 6^0,0_{3,$\text{1}\text{2}$} vibronic transitions in the light of the multimode interaction analyses.     

Nondisconnecting disentanglements of amalgamated 2‐factorizations of complete multipartite graphs

In this paper necessary and sufficient conditions are found for an edge‐colored graph H to be the homomorphic image of a 2‐factorization of a complete multipartite graph G in which each 2‐factor of G has the same number of components as its corresponding color class in H. This result is used to completely solve the problem of finding hamilton decompositions of K_a,b ? E(U) for any 2‐factor U of K_a,b. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 460–467, 2001     

X-ray Crystallographic Structures of Neuroprotective Pyrimidine Derivatives: (I) the Mesylate Salt of BW1003C87 and (II) Sipatrigine Base

Abstract Drugs based on 5-phenyl-2,4 diamino pyrimidine and 6-phenyl-1,2,4 triazine derivatives are well known for their effects on the central nervous system. The study presented here provides detailed crystal structures of two pyrimidine derivatives which have neuroprotective properties in models of both grey and white matter ischemia. Recently published studies suggest that the compounds lamotrigine (a triazine derivative), and the two pyrimidines BW1003C87 (I) and sipatrigine (II) mediate their primary in vivo mode of action by inhibiting voltage-gated Na⁺ channels. The X-ray crystal structures will contribute valuable data for applications involving binding and modelling studies of the biological actions of these drugs. Graphical Abstract X-ray crystallographic structures of neuroprotective pyrimidine derivatives: (I) the mesylate salt of BW1003C87 and (II) sipatrigine base Rex A. Palmer*, Brian S. Potter, Michael J. Leach and Babur Z. Chowdhry Surface representations, [20] are a useful tool with respect to considerations employed for the purposes of drug design. Shown here are the neuroprotective drug molecules (a) BW1003C87 and (b) Sipatrigine Base (BW619C89) derived from their solid state structures reported in this paper. The molecules are viewed edge on to ring B with the two adjacent Cl atoms uppermost on the left.      

Concerning electronegativity as a basic elemental property and why the periodic table is usually represented in its medium form

Electronegativity, described by Linus Pauling described as “The power of an atom in a molecule to attract electrons to itself” (Pauling in The nature of the chemical bond, 3rd edn, Cornell University Press, Ithaca, p 88, 1960), is used to predict bond polarity. There are dozens of methods for empirically quantifying electronegativity including: the original thermochemical technique (Pauling in J Am Chem Soc 54:3570–3582, 1932), numerical averaging of the ionisation potential and electron affinity (Mulliken in J Chem Phys 2:782–784, 1934), effective nuclear charge and covalent radius analysis (Sanderson in J Chem Phys 23:2467, 1955) and the averaged successive ionisation energies of an element’s valence electrons (Martynov and Batsanov in Zhurnal Neorganicheskoi Khimii 5:3171–3175, 1980), etc. Indeed, there are such strong correlations between numerous atomic parameters—physical and chemical—that the term “electronegativity” integrates them into a single dimensionless number between 0.78 and 4.00 that can be used to predict/describe/model much of an element’s physical character and chemical behaviour. The design of the common and popular medium form of the periodic table is in large part determined by four quantum numbers and four associated rules. However, adding electronegativity completes the construction so that it displays the multi-parameter periodic law operating in two dimensions, down the groups and across the periods, with minimal ambiguity.     

High mass accuracy and high mass resolving power FT-ICR secondary ion mass spectrometry for biological tissue imaging

Biological tissue imaging by secondary ion mass spectrometry has seen rapid development with the commercial availability of polyatomic primary ion sources. Endogenous lipids and other small bio-molecules can now be routinely mapped on the sub-micrometer scale. Such experiments are typically performed on time-of-flight mass spectrometers for high sensitivity and high repetition rate imaging. However, such mass analyzers lack the mass resolving power to ensure separation of isobaric ions and the mass accuracy for elemental formula assignment based on exact mass measurement. We have recently reported a secondary ion mass spectrometer with the combination of a C₆₀ primary ion gun with a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) for high mass resolving power, high mass measurement accuracy, and tandem mass spectrometry capabilities. In this work, high specificity and high sensitivity secondary ion FT-ICR MS was applied to chemical imaging of biological tissue. An entire rat brain tissue was measured with 150 μm spatial resolution (75 μm primary ion spot size) with mass resolving power (m/Δm _50%) of 67,500 (at m/z 750) and root-mean-square measurement accuracy less than two parts-per-million for intact phospholipids, small molecules and fragments. For the first time, ultra-high mass resolving power SIMS has been demonstrated, with m/Δm _50%?>?3,000,000. Higher spatial resolution capabilities of the platform were tested at a spatial resolution of 20 μm. The results represent order of magnitude improvements in mass resolving power and mass measurement accuracy for SIMS imaging and the promise of the platform for ultra-high mass resolving power and high spatial resolution imaging.

Entangled optical vortex links

Optical vortices are lines of phase singularity which percolate through all optical fields. We report the entanglement of linked optical vortex loops in the light produced by spontaneous parametric down-conversion. As measured by using a Bell inequality, this entanglement between topological features extends over macroscopic and finite volumes. The entanglement of photons in complex three-dimensional topological states suggests the possibility of entanglement of similar features in other quantum systems describable by complex scalar functions, such as superconductors, superfluids, and Bose-Einstein condensates.     

The role of structural heat exchange and heat loss in the design of efficient silicon micro-combustors

The performance of millimeter-scale combustors intended for miniaturized power and propulsion systems is strongly influenced by heat exchange to and within the combustor structure. Accordingly, a one-dimensional model with full chemistry that includes heat exchange to and within the combustor wall has been developed. It is used to study the effects of axial heat transfer from the post-flame to the pre-flame via wall conduction in a silicon micro-channel combustor with planar symmetry. The simulations show that axial heat transfer widens stability limits, increases the burning rate, and can enable the construction of smaller, higher power density combustors. Axial heat transfer also enhances the benefits of operating at elevated pressures. The simulations also show that heat loss to the environment places a lower bound on the combustor volume. Maximum power density combustor configurations are identified under adiabatic and non-adiabatic conditions. The maximum power density tends to increase with increasing pressure while the micro-channel length and height associated with the maximum tend to decrease.     

Pattern formation in a 2D simple chemical system with general orders of autocatalysis and decay

In this paper, we investigate pattern formation in a coupledsystem of reaction–diffusion equations in two spatialdimensions. These equations arise as a model of isothermal chemicalautocatalysis with termination in which the orders of autocatalysisand termination, m and n, respectively, are such that 1 <n < m. We build on the preliminary work by Leach & Wei(2003, Physica D, 180, 185–209) for this coupled systemin one spatial dimension, by presenting rigorous stability analysisand detailed numerical simulations for the coupled system intwo spatial dimensions. We demonstrate that spotty patternsare observed over a wide parameter range.