On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

Isotopic composition of Murchison organic compounds: Intramolecular carbon isotope fractionation of acetic acid. Simulation studies of cosmochemical organic syntheses

Recently, in our laboratories, samples of Murchison acetic acid were decarboxylated successfully and the carbon isotopic composition was measured for the methane released by this procedure. These analyses showed significant differences in C-13/C-12 ratios for the methyl and carboxyl carbons of the acetic acid molecule, strongly suggesting that more than one carbon source may be involved in the synthesis of the Murchison organic compounds. On the basis of this finding, laboratory model systems simulating cosmochemical synthesis are being studied, especially those processes capable of involving two or more starting carbon sources

Sand in the wheels, or oiling the wheels, of international finance? : New Labour's appeal to a 'new Bretton Woods'

Tony Blair’s political instinct typically is to associate himself only with the future. As such, his explicit appeal to ‘the past’ in his references to New Labour’s desire to establish a “new Bretton Woods” is sufficient in itself to arouse some degree of analytical curiosity (see Blair 1998a). The fact that this appeal was made specifically in relation to Bretton Woods is even more interesting. The resonant image of the international economic context established by the original Bretton Woods agreements invokes a style and content of policy-making which Tony Blair typically dismisses as neither economically nor politically consistent with his preferred vision of the future (see Blair 2000c, 2001b)

Validity and practical utility of accelerometry for the measurement of in-hand physical activity in horses

Background: Accelerometers are valid, practical and reliable tools for the measurement of habitual physical activity (PA). Quantification of PA in horses is desirable for use in research and clinical settings. The objective of this study was to evaluate a triaxial accelerometer for objective measurement of PA in the horse by assessment of their practical utility and validity. Horses were recruited to establish both the optimal site of accelerometer attachment and questionnaire designed to explore owner acceptance. Validity and cut-off values were obtained by assessing PA at various gaits. Validation study- 20 horses wore the accelerometer while being filmed for 10 min each of rest, walking and trotting and 5 mins of canter work. Practical utility study- five horses wore accelerometers on polls and withers for 18 h; compliance and relative data losses were quantified. Results: Accelerometry output differed significantly between the four PA levels (P <0•001) for both wither and poll placement. For withers placement, ROC analyses found optimal sensitivity and specificity at a cut-off of <47 counts per minute (cpm) for rest (sensitivity 99.5 %, specificity 100 %), 967–2424 cpm for trotting (sensitivity 96.7 %, specificity 100 %) and ≥2425 cpm for cantering (sensitivity 96.0 %, specificity 97.0 %). Attachment at the poll resulted in optimal sensitivity and specificity at a cut-off of <707 counts per minute (cpm) for rest (sensitivity 97.5 %, specificity 99.6 %), 1546–2609 cpm for trotting (sensitivity 90.33 %, specificity 79.25 %) and ≥2610 cpm for cantering (sensitivity 100 %, specificity 100 %) In terms of practical utility, accelerometry was well tolerated and owner acceptance high. Conclusion: Accelerometry data correlated well with varying levels of in-hand equine activity. The use of accelerometers is a valid method for objective measurement of controlled PA in the horse

Multiple scattering of matter waves: an analytic model of the refractive index for atomic and molecular gases

We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines a WKB treatment of the long range attraction with the Fraunhofer model treatment of the short range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two dimensional "hard core" of the potential, is essential for obtaining a correct imaginary part of the refractive index.Comment: 5 pages, 1 figure, 2 table

National registry for sudden unexpected deaths of infants and children in England: why do we need one and do families want one?

The sudden and unexpected death of an infant or child is devastating. An inability to explain why an infant or child died is difficult to accept for both families and professionals. No reliable national dataset exists to estimate precisely how many infants and children die unexpectedly each year in England. This lack of accurate epidemiological data belies the scale of this public health problem. Detailed controlled observational studies of infant deaths identifying risk factors and providing evidence-based advice for parents has seen a dramatic reduction in incidence over the last 30 years by almost 80% but greater knowledge is needed if future deaths of infants and older children are to be prevented and families optimally supported. We propose that a national registry of sudden unexpected deaths in infancy and childhood would accurately determine incidence, identify unknown risk factors and highlight good care practices, ensuring these can be standardised nationally. For such a project to be successful, however, parents must be at the heart of it. We held a consultation day between families, professionals and supporting charities (The Lullaby Trust, Child Bereavement UK, SUDC UK and CRY) to seek opinion on the desire for a registry and how best to ensure families are engaged. Here, we summarise our rationale for a registry and the feedback we received from attendees regarding their views of the proposal and the practical aspects of administering it