Jacobi Structures in R3\mathbb{R}^3

The most general Jacobi brackets in $\mathbb{R}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed

Generalized n-Poisson brackets on a symplectic manifold

On a symplectic manifold a family of generalized Poisson brackets associated with powers of the symplectic form is studied. The extreme cases are related to the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can be obtained in a similar way.Comment: Latex, 10 pages, to appear in Mod. Phys. Lett.

Poisson sigma models and symplectic groupoids

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a general class of two-dimensional Poisson domains is constructed.Comment: 34 page

Poisson Geometry in Constrained Systems

Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson manifolds associated to the system, forming a symplectic dual pair with respect to the original, unconstrained phase space. We provide sufficient conditions so that the reduced phase space of the constrained system may be identified with a symplectic leaf in one of those. In the second class case the original constrained system may be reformulated equivalently as an abelian first class system in an extended phase space by these methods. Inspired by the relation of the Dirac bracket of a general second class constrained system to the original unconstrained phase space, we address the question of whether a regular Poisson manifold permits a leafwise symplectic embedding into a symplectic manifold. Necessary and sufficient for this is the vanishing of the characteristic form-class of the Poisson tensor, a certain element of the third relative cohomology.Comment: 41 pages, more detailed abstract in paper; v2: minor corrections and an additional referenc

Integration of Dirac-Jacobi structures

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.Comment: 10 pages. Brief changes in the introduction. References update

Adoptive immunotherapy monitored by micro-MRI in experimental colorectal liver metastasis

In this study we used the colon carcinoma DHDK12 cell line and generated single metastasis after subcapsular injection in BDIX rats as an experimental tumor model. The aim of the work was to set up in vitro experimental conditions to prepare immune effector cells and in vivo conditions for monitoring the effects of such cells injected as adoptive immunotherapy. Dendritic cells can process tumor cell antigens, induce a T-cell response and be used ex vivo to prepare activated lymphocytes. Lymphocytes were harvested from mesenteric lymph nodes and cocultured with bone marrow-derived autologous dendritic cells previously loaded with irradiated tumor cells. In vitro, the coculture: 1) induced the proliferation of lymphocytes, 2) expanded a preferential subpopulation of T CD8 lymphocytes, and 3) was in favor of lymphocyte cytotoxic activity against the DHDK12 tumor cell line. Activated lymphocytes were injected in the tumor-bearing rat portal vein. Parameters could be set to monitor tumor volume by micro MRI. This monitoring before and after treatment and immunohistochemical examinations revealed that: 1) micro MRI is an appropriate tool to survey metastasis growth in rat, 2) injected lymphocytes increase lesional infiltration with T CD8 cells even 15 days after treatment, 3) a dose of 50 millions lymphocytes is not sufficient to act on the course of the tumor

Is magnetic resonance imaging texture analysis a useful tool for cell therapy in vivo monitoring?

Assessment of anti-tumor treatment efficiency is usually done by measuring tumor size. Treatment may however induce changes in the tumor other than tumor size. Magnetic Resonance Imaging Texture Analysis (MRI-TA) is presently used to follow activated lymphocyte cell therapy. We used a 7T microimager to acquire high-resolution MR images of an experimental liver metastasis from colon carcinoma in rats treated (n = 4) or not (n = 3) with a cell therapy product. MRI-TA was then performed with Linear Discriminant Analysis and showed: i) a significant variation of tumor texture with tumor growth and ii) a significant modification in the texture of tumors treated with activated lymphocytes compared with untreated tumors. T2-weighted images or volume calculation did not evidence any difference. MRI-TA appears as a promising method for early detection and follow-up of response to cell therapy