Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method

The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to derive explicit Hamiltonian formulations for the guiding-center and gyrokinetic Vlasov-Maxwell equations that have important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov-Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.Comment: 39 page

On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality

A gyro-gauge independent minimal guiding-center reduction by Lie-transforming the velocity vector field

International audienceWe introduce a gyro-gauge independent formulation of a simplified guiding-center reduction, which removes the fast time-scale from particle dynamics by Lie-transforming the velocity vector field. This is close to Krylov-Bogoliubov method of averaging the equations of motion, although more geometric. At leading order, the Lie-transform consists in the generator of Larmor gyration, which can be explicitly inverted, while working with gauge-independent coordinates and operators, by using the physical gyro-angle as a (constrained) coordinate. This brings both the change of coordinates and the reduced dynamics of the minimal guiding-center reduction order by order in a Larmor radius expansion. The procedure is algorithmic and the reduction is systematically derived up to full second order, in a more straightforward way than when Lie-transforming the phase-space Lagrangian or averaging the equations of motion. The results write up some structures in the guiding-center expansion. Extensions and limitations of the method are considered

Multiplexed Immunofluorescence Analysis and Quantification of Intratumoral PD-1+ Tim-3+ CD8+ T Cells

Immune cells are important components of the tumor microenvironment and influence tumor growth and evolution at all stages of carcinogenesis. Notably, it is now well established that the immune infiltrate in human tumors can correlate with prognosis and response to therapy. The analysis of the immune infiltrate in the tumor microenvironment has become a major challenge for the classification of patients and the response to treatment. The co-expression of inhibitory receptors such as Program Cell Death Protein 1 (PD1; also known as CD279), Cytotoxic T Lymphocyte Associated Protein 4 (CTLA-4), T-Cell Immunoglobulin and Mucin Containing Protein-3 (Tim-3; also known as CD366), and Lymphocyte Activation Gene 3 (Lag-3; also known as CD223), is a hallmark of T cell exhaustion. We developed a multiparametric in situ immunofluorescence staining to identify and quantify at the cellular level the co-expression of these inhibitory receptors. On a retrospective series of frozen tissue of renal cell carcinomas (RCC), using a fluorescence multispectral imaging technology coupled with an image analysis software, it was found that co-expression of PD-1 and Tim-3 on tumor infiltrating CD8 T cells is correlated with a poor prognosis in RCC. To our knowledge, this represents the first study demonstrating that this automated multiplex in situ technology may have some clinical relevance