QSD VI : Quantum Poincar\'e Algebra and a Quantum Positivity of Energy Theorem for Canonical Quantum Gravity

We quantize the generators of the little subgroup of the asymptotic Poincar\'e group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy operator is densely defined on an appropriate Hilbert space, symmetric and essentially self-adjoint. Moreover, we prove a quantum analogue of the classical positivity of energy theorem due to Schoen and Yau. The proof uses a certain technical restriction on the space of states at spatial infinity which is suggested to us given the asymptotically flat structure available. The theorem demonstrates that several of the speculations regarding the stability of the theory, recently spelled out by Smolin, are false once a quantum version of the pre-assumptions underlying the classical positivity of energy theorem is imposed in the quantum theory as well. The quantum symmetry algebra corresponding to the generators of the little group faithfully represents the classical algebra.Comment: 24p, LATE

Characterization of autonomous Dart1 transposons belonging to the hAT superfamily in rice

An endogenous 0.6-kb rice DNA transposon, nDart1-0, was found as an active nonautonomous element in a mutable virescent line, pyl-v, displaying leaf variegations. Here, we demonstrated that the active autonomous element aDart in pyl-v corresponds to Dart1-27 on chromosome 6 in Nipponbare, which carries no active aDart elements, and that aDart and Dart1-27 are identical in their sequences and chromosomal locations, indicating that Dart1-27 is epigenetically silenced in Nipponbare. The identification of aDart in pyl-v was first performed by map-based cloning and by detection of the accumulated transposase transcripts. Subsequently, various transposition activities of the cloned Dart1-27 element from Nipponbare were demonstrated in Arabidopsis. Dart1-27 in Arabidopsis was able to excise nDart1-0 and Dart1-27 from cloned sites, generating footprints, and to integrate into new sites, generating 8-bp target site duplications. In addition to Dart1-27, Nipponbare contains 37 putative autonomous Dart1 elements because their putative transposase genes carry no apparent nonsense or frameshift mutations. Of these, at least four elements were shown to become active aDart elements in transgenic Arabidopsis plants, even though considerable sequence divergence arose among their transposases. Thus, these four Dart1 elements and Dart1-27 in Nipponbare must be potential autonomous elements silenced epigenetically. The regulatory and evolutionary implications of the autonomous Dart1 elements and the development of an efficient transposon-tagging system in rice are discussed