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

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

Novel integrative genomic tool for interrogating lithium response in bipolar disorder

We developed a novel integrative genomic tool called GRANITE (Genetic Regulatory Analysis of Networks Investigational Tool Environment) that can effectively analyze large complex data sets to generate interactive networks. GRANITE is an open-source tool and invaluable resource for a variety of genomic fields. Although our analysis is confined to static expression data, GRANITE has the capability of evaluating time-course data and generating interactive networks that may shed light on acute versus chronic treatment, as well as evaluating dose response and providing insight into mechanisms that underlie therapeutic versus sub-therapeutic doses or toxic doses. As a proof-of-concept study, we investigated lithium (Li) response in bipolar disorder (BD). BD is a severe mood disorder marked by cycles of mania and depression. Li is one of the most commonly prescribed and decidedly effective treatments for many patients (responders), although its mode of action is not yet fully understood, nor is it effective in every patient (non-responders). In an in vitro study, we compared vehicle versus chronic Li treatment in patient-derived lymphoblastoid cells (LCLs) (derived from either responders or non-responders) using both microRNA (miRNA) and messenger RNA gene expression profiling. We present both Li responder and non-responder network visualizations created by our GRANITE analysis in BD. We identified by network visualization that the Let-7 family is consistently downregulated by Li in both groups where this miRNA family has been implicated in neurodegeneration, cell survival and synaptic development. We discuss the potential of this analysis for investigating treatment response and even providing clinicians with a tool for predicting treatment response in their patients, as well as for providing the industry with a tool for identifying network nodes as targets for novel drug discovery

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

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

Synapsin II Is Involved in the Molecular Pathway of Lithium Treatment in Bipolar Disorder

Bipolar disorder (BD) is a debilitating psychiatric condition with a prevalence of 1–2% in the general population that is characterized by severe episodic shifts in mood ranging from depressive to manic episodes. One of the most common treatments is lithium (Li), with successful response in 30–60% of patients. Synapsin II (SYN2) is a neuronal phosphoprotein that we have previously identified as a possible candidate gene for the etiology of BD and/or response to Li treatment in a genome-wide linkage study focusing on BD patients characterized for excellent response to Li prophylaxis. In the present study we investigated the role of this gene in BD, particularly as it pertains to Li treatment. We investigated the effect of lithium treatment on the expression of SYN2 in lymphoblastoid cell lines from patients characterized as excellent Li-responders, non-responders, as well as non-psychiatric controls. Finally, we sought to determine if Li has a cell-type-specific effect on gene expression in neuronal-derived cell lines. In both in vitro models, we found SYN2 to be modulated by the presence of Li. By focusing on Li-responsive BD we have identified a potential mechanism for Li response in some patients