Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

A sigma model field theoretic realization of Hitchin's generalized complex geometry

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.Comment: 28 pages, Plain TeX, no figures, requires AMS font files AMSSYM.DEF and amssym.tex. Typos in eq. 6.19 and some spelling correcte

Calibrated cycles and T-duality

For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane energy in type II string theories, involving both so-called NS-NS- and R-R-fields. Further, we investigate the behaviour of calibrated cycles under T-duality and construct non-trivial examples.Comment: 43 pages. v4: formalism and T-duality part considerably expande

Energy-Sensitive and "Classical-like" Distances Between Quantum States

We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script

Mirror duality and noncommutative tori

In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence on generalized complex tori and generalize the mirror duality on complex tori to the case of noncommutative complex tori.Comment: 22pages, no figure

Towards mirror symmetry \`a la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and \hat{M}. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3)xSU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.Comment: 30 pages, 3 figures, LaTeX; v2: references adde

Generation of Functional CLL-Specific Cord Blood CTL Using CD40-Ligated CLL APC

PMCID: PMC3526610This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Some Properties of R\'{e}nyi Entropy over Countably Infinite Alphabets

In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties shown parallel those known in the finite alphabet case, while others illustrate a quite different behaviour of R\'enyi entropy in the infinite case. In particular, it is shown that, for any distribution $\mathcal P$ and any $r\in[0,\infty]$, there exists a sequence of distributions $\mathcal{P}_n$ converging to $\mathcal{P}$ with respect to the total variation distance, such that $\lim_{n\to\infty}\lim_{\alpha\to{1+}} H_\alpha(\mathcal{P}_n) = \lim_{\alpha\to{1+}}\lim_{n\to\infty} H_\alpha(\mathcal{P}_n) + r$.Comment: 13 pages (single-column

Upregulation of the cell-cycle regulator RGC-32 in Epstein-Barr virus-immortalized cells

Epstein-Barr virus (EBV) is implicated in the pathogenesis of multiple human tumours of lymphoid and epithelial origin. The virus infects and immortalizes B cells establishing a persistent latent infection characterized by varying patterns of EBV latent gene expression (latency 0, I, II and III). The CDK1 activator, Response Gene to Complement-32 (RGC-32, C13ORF15), is overexpressed in colon, breast and ovarian cancer tissues and we have detected selective high-level RGC-32 protein expression in EBV-immortalized latency III cells. Significantly, we show that overexpression of RGC-32 in B cells is sufficient to disrupt G2 cell-cycle arrest consistent with activation of CDK1, implicating RGC-32 in the EBV transformation process. Surprisingly, RGC-32 mRNA is expressed at high levels in latency I Burkitt's lymphoma (BL) cells and in some EBV-negative BL cell-lines, although RGC-32 protein expression is not detectable. We show that RGC-32 mRNA expression is elevated in latency I cells due to transcriptional activation by high levels of the differentially expressed RUNX1c transcription factor. We found that proteosomal degradation or blocked cytoplasmic export of the RGC-32 message were not responsible for the lack of RGC-32 protein expression in latency I cells. Significantly, analysis of the ribosomal association of the RGC-32 mRNA in latency I and latency III cells revealed that RGC-32 transcripts were associated with multiple ribosomes in both cell-types implicating post-initiation translational repression mechanisms in the block to RGC-32 protein production in latency I cells. In summary, our results are the first to demonstrate RGC-32 protein upregulation in cells transformed by a human tumour virus and to identify post-initiation translational mechanisms as an expression control point for this key cell-cycle regulator