Holomorphic Koszul-Brylinski Homology

In this note, we study the Koszul-Brylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinski homology is nondegenerate. Finally we compute the Koszul-Brylinski homology for Poisson structures on \CP^1\times\CP^1.Comment: 14 page

Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle $A\to X$ is shown to be equivalent to a matched pair of complex Lie algebroids $(T^{0,1}X,A^{1,0})$, in the sense of Lu. The holomorphic Lie algebroid cohomology of $A$ is isomorphic to the cohomology of the elliptic Lie algebroid $T^{0,1}X\bowtie A^{1,0}$. In the case when $(X,\pi)$ is a holomorphic Poisson manifold and $A=(T^*X)_\pi$, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold.Comment: 29 pages, v2: paper split into two, part 1 of 2, v3: two references added, v4: final version to appear in International Mathematics Research Notice

Allogeneic hematopoietic cell transplantation as curative therapy for patients with non-Hodgkin lymphoma: Increasingly successful application to older patients

AbstractNon-Hodgkin lymphoma (NHL) constitutes a collection of lymphoproliferative disorders with widely varying biological, histological, and clinical features. For the B cell NHLs, great progress has been made due to the addition of monoclonal antibodies and, more recently, other novel agents including B cell receptor signaling inhibitors, immunomodulatory agents, and proteasome inhibitors. Autologous hematopoietic cell transplantation (auto-HCT) offers the promise of cure or prolonged remission in some NHL patients. For some patients, however, auto-HCT may never be a viable option, whereas in others, the disease may progress despite auto-HCT. In those settings, allogeneic HCT (allo-HCT) offers the potential for cure. Over the past 10 to 15 years, considerable progress has been made in the implementation of allo-HCT, such that this approach now is a highly effective therapy for patients up to (and even beyond) age 75 years. Recent advances in conventional lymphoma therapy, peritransplantation supportive care, patient selection, and donor selection (including the use of alternative hematopoietic cell donors), has allowed broader application of allo-HCT to patients with NHL. As a result, an ever-increasing number of NHL patients over age 60 to 65 years stand to benefit from allo-HCT. In this review, we present data in support of the use of allo-HCT for patients with diffuse large B cell lymphoma, follicular lymphoma, and mantle cell lymphoma. These histologies account for a large majority of allo-HCTs performed for patients over age 60 in the United States. Where possible, we highlight available data in older patients. This body of literature strongly supports the concept that allo-HCT should be offered to fit patients well beyond age 65 and, accordingly, that this treatment should be covered by their insurance carriers

Clinicopathologic consensus study of gray zone lymphoma with features intermediate between DLBCL and classical HL

Gray zone lymphoma (GZL) is described as sharing features with classical Hodgkin lymphoma (cHL) and diffuse large B-cell lymphoma (DLBCL). However, there remains complexity in establishing diagnosis, delineating prognosis, and determining optimum therapy. Sixty-eight cases diagnosed as GZL across 15 North American academic centers were evaluated by central pathology review to achieve consensus. Of these, only 26 (38%) were confirmed as GZL. Morphology was critical to GZL consensus diagnosis (eg, tumor cell richness); immunohistochemistry showed universal B-cell derivation, frequent CD30 expression, and rare Epstein-Barr virus (EBV) positivity (CD20(+), 83%; PAX5(+), 100%; BCL6(+), 20%; MUM1(+), 100%; CD30(+), 92%; EBV(+), 4%). Forty-two cases were reclassified: nodular sclerosis (NS) cHL, n = 27 (including n = 10 NS grade 2); lymphocyte predominant HL, n = 4; DLBCL, n = 4; EBV(+) DLBCL, n = 3; primary mediastinal large BCL n = 2; lymphocyte-rich cHL and BCL-not otherwise specified, n = 1 each. GZL consensus-confirmed vs reclassified cases, respectively, more often had mediastinal disease (69% vs 41%; P = .038) and less likely more than 1 extranodal site (0% vs 25%; P = .019). With a 44-month median follow-up, 3-year progression-free survival (PFS) and overall survival for patients with confirmed GZL were 39% and 95%, respectively, vs 58% and 85%, respectively, for reclassified cases (P = .19 and P = .15, respectively). Interestingly, NS grade 2 reclassified patients had similar PFS as GZL consensus-confirmed cases. For prognostication of GZL cases, hypoalbuminemia was a negative factor (3-year PFS, 12% vs 64%; P = .01), whereas frontline cyclophosphamide, doxorubicin, vincristine, and prednisone +/- rituximab (CHOP+/-R) was associated with improved 3-year PFS (70% vs 20%; P = .03); both factors remained significant on multivariate analysis. Altogether, accurate diagnosis of GZL remains challenging, and improved therapeutic strategies are needed

Nonlocal regularization of abelian models with spontaneous symmetry breaking

We demonstrate how nonlocal regularization is applied to gauge invariant models with spontaneous symmetry breaking. Motivated by the ability to find a nonlocal BRST invariance that leads to the decoupling of longitudinal gauge bosons from physical amplitudes, we show that the original formulation of the method leads to a nontrivial relationship between the nonlocal form factors that can appear in the model.Comment: 11 pages, uses amsart. To appear in Mod. Phys. Lett

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

The quantization of the symplectic groupoid of the standard Podles sphere

We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic groupoid. By using a complex polarization we recover the convolution algebra on the space of polarized sections. We stress the role of the modular class in the definition of the scalar product in order to get the correct quantum space.Comment: 33 pages; minor correction

Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde