73 research outputs found
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 ,
homogeneous with respect to a vector field on , and first-order
polydifferential operators on a closed submanifold of codimension 1 such
that is transversal to . This correspondence relates the
Schouten-Nijenhuis bracket of multivector fields on to the Schouten-Jacobi
bracket of first-order polydifferential operators on 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 -homogeneous symplectic structures on and
contact structures on .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 -Dirac structures
We prove some general results about the relation between the 1-cocycles of an
arbitrary Lie algebroid over and the leaves of the Lie algebroid
foliation on associated with . Using these results, we show that a
-Dirac structure induces on every leaf of its
characteristic foliation a -Dirac structure , which comes
from a precontact structure or from a locally conformal presymplectic structure
on . In addition, we prove that a Dirac structure on can be obtained from and we discuss the relation between the leaves of
the characteristic foliations of and .Comment: 25 page
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