Box splines and the equivariant index theorem

In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distributions, on the dual of the group G or on the dual of its Lie algebra. The morphism from K-theory to cohomology is analyzed and the multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semidiscrete convolution with a box spline. Finally, the multiplicities of the index of a G-transversally elliptic operator on M are determined using the infinitesimal index of the symbol.Comment: 44 page

From geometric quantization to Moyal quantization

We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by ``doubling'' the phase space.Comment: 7 two-column pages, RevTeX, UCR--FM--03--9

Vector partition functions and index of transversally elliptic operators

Let G be a torus acting linearly on a complex vector space M, and let X be the list of weights of G in M. We determine the equivariant K-theory of the open subset of M consisting of points with finite stabilizers. We identify it to the space DM(X) of functions on the lattice of weights of G, satisfying the cocircuit difference equations associated to X, introduced by Dahmen--Micchelli in the context of the theory of splines in order to study vector partition functions. This allows us to determine the range of the index map from G-transversally elliptic operators on M to generalized functions on G and to prove that the index map is an isomorphism on the image. This is a setting studied by Atiyah-Singer which is in a sense universal for index computations

Experimental pig-to-pig transmission dynamics for African swine fever virus, Georgia 2007/1 strain

African swine fever virus (ASFV) continues to cause outbreaks in domestic pigs and wild boar in Eastern European countries. To gain insights into its transmission dynamics, we estimated the pig-to-pig basic reproduction number (R 0) for the Georgia 2007/1 ASFV strain using a stochastic susceptible-exposed-infectious-recovered (SEIR) model with parameters estimated from transmission experiments. Models showed that R 0 is 2·8 [95% confidence interval (CI) 1·3–4·8] within a pen and 1·4 (95% CI 0·6–2·4) between pens. The results furthermore suggest that ASFV genome detection in oronasal samples is an effective diagnostic tool for early detection of infection. This study provides quantitative information on transmission parameters for ASFV in domestic pigs, which are required to more effectively assess the potential impact of strategies for the control of between-farm epidemic spread in European countries.ISSN:0950-2688ISSN:1469-440

Joint inversion of teleseismic and GOCE gravity data: application to the Himalayas

Our knowledge and understanding of the 3-D lithospheric structure of the Himalayas and the Tibetan Plateau is still challenging although numerous geophysical studies have been performed in the region. The GOCE satellite mission has the ambitious goal of mapping Earth's gravity field with unprecedented precision (i.e. an accuracy of 1-2 mGal for a spatial resolution of 100 km) to observe the lithosphere and upper-mantle structure. Consequently, it gives new insights in the lithospheric structure beneath the Himalayas and the Tibetan Plateau. Indeed, the GOCE gravity data now allow us to develop a new strategy for joint gravimetry-seismology inversion. Combined with teleseismic data over a large region in a joint inversion scheme, they will lead to lithospheric velocity-density models constrained in two complementary ways. We apply this joint inversion scheme to the Hi-CLIMB (Himalayan-Tibetan Continental Lithosphere during Mountain Building) seismological network which was deployed in South Tibet and the Himalayas for a 3-yr period. The large size of the network, the high quality of the seismological data and the new GOCE gravity data set allow us to image the entire lithosphere of this active area in an innovative way. We image 3-D low velocity and density structures in the middle crust that fit the location of discontinuous low S-velocity zones revealed by receiver functions in previous geophysical studies. In the deeper parts of our velocity model we image a positive anomaly interpreted to be the heterogenous Indian lithosphere vertically descending beneath the centre of the Tibetan Platea

Identification of serine/threonine kinase and nucleotide-binding site–leucine-rich repeat (NBS-LRR) genes in the fire blight resistance quantitative trait locus of apple cultivar ‘Evereste’

Fire blight is the most destructive bacterial disease affecting apple (Malus×domestica) worldwide. So far, no resistance gene against fire blight has been characterized in apple, despite several resistance regions having been identified. A highly efficacious resistance quantitative trait locus (QTL) was localized on linkage group 12 (LG12) of the ornamental cultivar ‘Evereste’. A marker previously reported to be closely linked to this resistance was used to perform a chromosome landing. A bacterial artificial chromosome (BAC) clone of 189 kb carrying the fire blight resistance QTL was isolated and sequenced. New microsatellite markers were developed, and the genomic region containing the resistance locus was limited to 78 kb. A cluster of eight genes with homologies to already known resistance gene structures to bacterial diseases was identified and the corresponding gene transcription was verified. From this cluster, two genes were recognized in silico as the two most probable fire blight resistance genes showing homology with the Pto/Prf complex in tomato

Polarimetry of an Intermediate-age Open Cluster: NGC 5617

We present polarimetric observations in the UBVRI bands of 72 stars located in the direction of the medium age open cluster NGC 5617. Our intention is to use polarimetry as a tool membership identification, by building on previous investigations intended mainly to determine the cluster's general characteristics rather than provide membership suitable for studies such as stellar content and metallicity, as well as study the characteristics of the dust lying between the Sun and the cluster. The obsevations were carried out using the five-channel photopolarimeter of the Torino Astronomical Observatory attached to the 2.15m telescope at the Complejo Astron\'omico El Leoncito (CASLEO; Argentina. We are able to add 32 stars to the list of members of NGC 5617, and review the situation for others listed in the literature. In particular, we find that five blue straggler stars in the region of the cluster are located behind the same dust as the member stars are and we confirm the membership of two red giants. The proposed polarimetric memberships are compared with those derived by photometric and kinematical methods, with excellent results. Among the observed stars, we identify 10 with intrinsic polarization in their light. NGC 5617 can be polarimetrically characterized with $P_{max}= 4.40$ and $\theta_{v}= 73^\circ.1$. The spread in polarization values for the stars observed in the direction of the cluster seems to be caused by the uneven distribution of dust in front of the cluster's face. Finally, we find that in the direction of the cluster, the interstellar medium is apparently free of dust, from the Sun's position up to the Carina-Sagittarius arm, where NGC 5617 seems to be located at its farthest border