Nonholonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 200

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

Poisson-Jacobi reduction of homogeneous tensors

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential operators on a closed submanifold $N$ of codimension 1 such that $\Delta$ is transversal to $N$. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on $M$ to the Schouten-Jacobi bracket of first-order polydifferential operators on $N$ and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can be also understood as a sort of reduction; in the standard case -- a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between $\Delta$-homogeneous symplectic structures on $M$ and contact structures on $N$.Comment: 19 pages, minor corrections, final version to appear in J. Phys. A: Math. Ge

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

Prevalence of impairments, disabilities, handicaps and quality of life in the general population: a review of recent literature

International audienc

Quantized reduction as a tensor product

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with correspondences between von Neumann algebras. Further analogies are drawn with categories of groupoids (of algebraic, measured, Lie, and symplectic type). In all cases, the arrows are isomorphism classes of appropriate bimodules, and their composition may be seen as a tensor product. Hence in suitable categories reduction is simply composition of arrows, and Morita equivalence is isomorphism of objects.Comment: 44 pages, categorical interpretation adde

Lie algebroid foliations and E1(M){\cal E}^1(M)-Dirac structures

We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid $A$ over $M$ and the leaves of the Lie algebroid foliation on $M$ associated with $A$. Using these results, we show that a ${\cal E}^1(M)$-Dirac structure $L$ induces on every leaf $F$ of its characteristic foliation a ${\cal E}^1(F)$-Dirac structure $L_F$, which comes from a precontact structure or from a locally conformal presymplectic structure on $F$. In addition, we prove that a Dirac structure $\tilde{L}$ on $M\times \R$ can be obtained from $L$ and we discuss the relation between the leaves of the characteristic foliations of $L$ and $\tilde{L}$.Comment: 25 page