Spinors in the hyperbolic algebra

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.Comment: 9 pages Latex2

Gravitoelectromagnetism in a complex Clifford algebra

A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford algebra.Comment: 10 pages Latex2

A spinor approach to Walker geometry

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski (2002) and Plebanski (1975) in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.Comment: 41 pages. Typos which persisted into published version corrected, notably at (2.15

A single amino acid substitution in ORF1 dramatically decreases L1 retrotransposition and provides insight into nucleic acid chaperone activity

L1 is a ubiquitous interspersed repeated sequence in mammals that achieved its high copy number by autonomous retrotransposition. Individual L1 elements within a genome differ in sequence and retrotransposition activity. Retrotransposition requires two L1-encoded proteins, ORF1p and ORF2p. Chimeric elements were used to map a 15-fold difference in retrotransposition efficiency between two L1 variants from the mouse genome, TFC and TFspa, to a single amino acid substitution in ORF1p, D159H. The steady-state levels of L1 RNA and protein do not differ significantly between these two elements, yet new insertions are detected earlier and at higher frequency in TFC, indicating that it converts expressed L1 intermediates more effectively into new insertions. The two ORF1 proteins were purified and their nucleic acid binding and chaperone activities were examined in vitro. Although the RNA and DNA oligonucleotide binding affinities of these two ORF1 proteins were largely indistinguishable, D159 was significantly more effective as a nucleic acid chaperone than H159. These findings support a requirement for ORF1p nucleic acid chaperone activity at a late step during L1 retrotransposition, extend the region of ORF1p that is known to be critical for its functional interactions with nucleic acids, and enhance understanding of nucleic acid chaperone activity

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

Genome-wide association study identifies 30 loci associated with bipolar disorder.

Bipolar disorder is a highly heritable psychiatric disorder. We performed a genome-wide association study (GWAS) including 20,352 cases and 31,358 controls of European descent, with follow-up analysis of 822 variants with P < 1 × 10-4 in an additional 9,412 cases and 137,760 controls. Eight of the 19 variants that were genome-wide significant (P < 5 × 10-8) in the discovery GWAS were not genome-wide significant in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity. In the combined analysis, 30 loci were genome-wide significant, including 20 newly identified loci. The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene sets, including regulation of insulin secretion and endocannabinoid signaling. Bipolar I disorder is strongly genetically correlated with schizophrenia, driven by psychosis, whereas bipolar II disorder is more strongly correlated with major depressive disorder. These findings address key clinical questions and provide potential biological mechanisms for bipolar disorder

Gag Mutations Strongly Contribute to HIV-1 Resistance to Protease Inhibitors in Highly Drug-Experienced Patients besides Compensating for Fitness Loss

Human immunodeficiency virus type 1 (HIV-1) resistance to protease inhibitors (PI) results from mutations in the viral protease (PR) that reduce PI binding but also decrease viral replicative capacity (RC). Additional mutations compensating for the RC loss subsequently accumulate within PR and in Gag substrate cleavage sites. We examined the respective contribution of mutations in PR and Gag to PI resistance and RC and their interdependence using a panel of HIV-1 molecular clones carrying different sequences from six patients who had failed multiple lines of treatment. Mutations in Gag strongly and directly contributed to PI resistance besides compensating for fitness loss. This effect was essentially carried by the C-terminal region of Gag (containing NC-SP2-p6) with little or no contribution from MA, CA, and SP1. The effect of Gag on resistance depended on the presence of cleavage site mutations A431V or I437V in NC-SP2-p6 and correlated with processing of the NC/SP2 cleavage site. By contrast, reverting the A431V or I437V mutation in these highly evolved sequences had little effect on RC. Mutations in the NC-SP2-p6 region of Gag can be dually selected as compensatory and as direct PI resistance mutations, with cleavage at the NC-SP2 site behaving as a rate-limiting step in PI resistance. Further compensatory mutations render viral RC independent of the A431V or I437V mutations while their effect on resistance persists