On natural and conformally equivariant quantizations

The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in \cite{DLO} for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold $M$, that depends on a pseudo-Riemannian metric, is natural and is invariant with respect to a conformal change of the metric. The existence of such a procedure was conjectured by P. Lecomte in \cite{Leconj} and proved by C. Duval and V. Ovsienko in \cite{DO1} for symbols of degree at most 2 and by S. Loubon Djounga in \cite{Loubon} for symbols of degree 3. In two recent papers \cite{MR,MR1}, we investigated the question of existence of projectively equivariant quantizations using the framework of Cartan connections. Here we will show how the formalism developed in these works adapts in order to deal with the conformally equivariant quantization for symbols of degree at most 3. This will allow us to easily recover the results of \cite{DO1} and \cite{Loubon}. We will then show how it can be modified in order to prove the existence of conformally equivariant quantizations for symbols of degree 4.Comment: 19 page

Projectively equivariant quantizations over the superspace Rp∣q\R^{p|q}

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.Comment: 19 page

Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page

Conformal geometry of the supercotangent and spinor bundles

We study the actions of local conformal vector fields X∈conf(M,g) on the spinor bundle of (M,g) and on its classical counterpart: the supercotangent bundle M of (M,g). We first deal with the classical framework and determine the Hamiltonian lift of conf(M,g) to M. We then perform the geometric quantization of the supercotangent bundle of (M,g), which constructs the spinor bundle as the quantum representation space. The Kosmann Lie derivative of spinors is btained by quantization of the comoment map. The quantum and classical actions of conf(M,g) turn, respectively, the space of differential operators acting on spinor densities and the space of their symbols into conf(M,g)-modules. They are filtered and admit a common associated graded module. In the conformally flat case, the latter helps us determine the conformal invariants of both conf(M,g)-modules, in particular the conformally odd powers of the Dirac operator.Peer reviewe

Mapping of Submerged Aquatic Vegetation in Rivers From Very High Resolution Image Data, Using Object Based Image Analysis Combined with Expert Knowledge

The use of remote sensing for monitoring of submerged aquatic vegetation (SAV) in fluvial environments has been limited by the spatial and spectral resolution of available image data. The absorption of light in water also complicates the use of common image analysis methods. This paper presents the results of a study that uses very high resolution (VHR) image data, collected with a Near Infrared sensitive DSLR camera, to map the distribution of SAV species for three sites along the Desselse Nete, a lowland river in Flanders, Belgium. Plant species, including Ranunculus aquatilis L., Callitriche obtusangula Le Gall, Potamogeton natans L., Sparganium emersum L. and Potamogeton crispus L., were classified from the data using Object-Based Image Analysis (OBIA) and expert knowledge. A classification rule set based on a combination of both spectral and structural image variation (e.g. texture and shape) was developed for images from two sites. A comparison of the classifications with manually delineated ground truth maps resulted for both sites in 61% overall accuracy. Application of the rule set to a third validation image, resulted in 53% overall accuracy. These consistent results show promise for species level mapping in such biodiverse environments, but also prompt a discussion on assessment of classification accuracy

Inactivation of genes coding for mitochondrial Nd7 and Nd9 complex I subunits in Chlamydomonas reinhardtii. Impact of complex I loss on respiration and energetic metabolism.

In Chlamydomonas, unlike in flowering plants, genes coding for Nd7 (NAD7/49kDa) and Nd9 (NAD9/30kDa) core subunits of mitochondrial respiratory-chain complex I are nucleus-encoded. Both genes possess all the features that facilitate their expression and proper import of the polypeptides in mitochondria. By inactivating their expression by RNA interference or insertional mutagenesis, we show that both subunits are required for complex I assembly and activity. Inactivation of complex I impairs the cell growth rate, reduces the respiratory rate, leads to lower intracellular ROS production and lower expression of ROS scavenging enzymes, and is associated to a diminished capacity to concentrate CO2 without compromising photosynthetic capacity.Peer reviewe

Inactivation of genes coding for mitochondrial Nd7 and Nd9 complex I subunits in Chlamydomonas reinhardtii. Impact of complex I loss on respiration and energetic metabolism.

In Chlamydomonas, unlike in flowering plants, genes coding for Nd7 (NAD7/49kDa) and Nd9 (NAD9/30kDa) core subunits of mitochondrial respiratory-chain complex I are nucleus-encoded. Both genes possess all the features that facilitate their expression and proper import of the polypeptides in mitochondria. By inactivating their expression by RNA interference or insertional mutagenesis, we show that both subunits are required for complex I assembly and activity. Inactivation of complex I impairs the cell growth rate, reduces the respiratory rate, leads to lower intracellular ROS production and lower expression of ROS scavenging enzymes, and is associated to a diminished capacity to concentrate CO2 without compromising photosynthetic capacity.Peer reviewe

Supersymmetric QCD corrections to e+e−→tbˉH−e^+e^-\to t\bar{b}H^- and the Bernstein-Tkachov method of loop integration

The discovery of charged Higgs bosons is of particular importance, since their existence is predicted by supersymmetry and they are absent in the Standard Model (SM). If the charged Higgs bosons are too heavy to be produced in pairs at future linear colliders, single production associated with a top and a bottom quark is enhanced in parts of the parameter space. We present the next-to-leading-order calculation in supersymmetric QCD within the minimal supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD corrections. In addition to the usual approach to perform the loop integration analytically, we apply a numerical approach based on the Bernstein-Tkachov theorem. In this framework, we avoid some of the generic problems connected with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.

Clinical anticancer drug development: targeting the cyclin-dependent kinases

Cell division involves a cyclical biochemical process composed of several step-wise reactions that have to occur once per cell cycle. Dysregulation of cell division is a hallmark of all cancers. Genetic and epigenetic mechanisms frequently result in deranged expression and/or activity of cell-cycle proteins including the cyclins, cyclin-dependent kinases (Cdks), Cdk inhibitors and checkpoint control proteins. The critical nature of these proteins in cell cycling raises hope that targeting them may result in selective cytotoxicity and valuable anticancer activity