Discovery of a large set of SNP and SSR genetic markers by high-throughput sequencing of pepper (Capsicum annuum)

Genetic markers based on single nucleotide polymorphisms (SNPs) are in increasing demand for genome mapping and fingerprinting of breeding populations in crop plants. Recent advances in high-throughput sequencing provide the opportunity for whole-genome resequencing and identification of allelic variants by mapping the reads to a reference genome. However, for many species, such as pepper (Capsicum annuum), a reference genome sequence is not yet available. To this end, we sequenced the C. annuum cv. "Yolo Wonder" transcriptome using Roche 454 pyrosequencing and assembled de novo 23,748 isotigs and 60,370 singletons. Mapping of 10,886,425 reads obtained by the Illumina GA II sequencing of C. annuum cv. "Criollo de Morclos 334" to the "Yolo Wonder" transcriptome allowed for SNP identification. By setting a threshold value that allows selecting reliable SNPs with minimal loss of information, 11,849 reliable SNPs spread across 5919 isotigs were identified. In addition, 853 single sequence repeats were obtained. This information has been made available online

Gradient Representations and Affine Structures in AE(n)

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.Comment: 43 page

Symmetries,Singularities and the De-Emergence of Space

Recent work has revealed intriguing connections between a Belinsky-Khalatnikov-Lifshitz-type analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the `maximally extended' hyperbolic Kac--Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(-time) at the Planck scale, and hence -- via an effective `de-emergence' of space near a singularity -- to a novel mechanism for achieving background independence in quantum gravity.Comment: 10 page

Quantum State Engineering with Continuous-Variable Post-Selection

We present a scheme to conditionally engineer an optical quantum system via continuous-variable measurements. This scheme yields high-fidelity squeezed single photon and superposition of coherent states, from input single and two photon Fock states respectively. The input Fock state is interacted with an ancilla squeezed vacuum state using a beam-splitter. We transform the quantum system by post-selecting on the continuous-observable measurement outcome of the ancilla state. We experimentally demonstrate the principles of this scheme using displaced coherent states and measure experimentally fidelities that are only achievable using quantum resources.Comment: 4 pages, 5 figures, publishe

The influence of bond-rigidity and cluster diffusion on the self-diffusion of hard spheres with square-well interaction

Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength

Conditional quantum-state engineering using ancillary squeezed-vacuum states

We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\leq4$, and conjecture that this can be generalized for an arbitrary $n$ Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.Comment: 10 pages, 14 figures, use pdf version, high quality figures available on reques

Relativistic entanglement of two massive particles

We describe the spin and momentum degrees of freedom of a system of two massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.Comment: 17 pages, 4 figure

Supersymmetric quantum cosmological billiards

D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.Comment: 4 pages. v2: Added ref. Version to be published in PR

Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories

We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated to SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the `broken phase' can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged non-linear sigma model based on SL(D-2,R)/SO(D-2), while the metric appears in a purely topological Chern-Simons form.Comment: 23 pages, minor changes, v3: published versio

Photon creation in a spherical oscillating cavity

We study the photon creation inside a perfectly conducting, spherical oscillating cavity. The electromagnetic field inside the cavity is described by means of two scalar fields which satisfy Dirichlet and (generalized) Neumann boundary conditions. As a preliminary step, we analyze the dynamical Casimir effect for both scalar fields. We then consider the full electromagnetic case. The conservation of angular momentum of the electromagnetic field is also discussed, showing that photons inside the cavity are created in singlet states.Comment: 14 pages, no figure