Numerical algorithms based on variational and symplectic integrators exhibit
special features that make them promising candidates for application to general
relativity and other constrained Hamiltonian systems. This paper lays part of
the foundation for such applications. The midpoint rule for Hamilton's
equations is examined from the perspectives of variational and symplectic
integrators. It is shown that the midpoint rule preserves the symplectic form,
conserves Noether charges, and exhibits excellent long--term energy behavior.
The energy behavior is explained by the result, shown here, that the midpoint
rule exactly conserves a phase space function that is close to the Hamiltonian.
The presentation includes several examples.Comment: 11 pages, 8 figures, REVTe

Bruehl, H.

Csernok, E.

Erdmann, A.

Feller, A. C.

Gross, W. L.

Holl-Ulrich, K.

Lamprecht, P.

Mueller, A.

Reinhold-Keller, E.

English

arXiv

J. David Brown

M. Henneaux

P. Dirac

A. Taflove

A. Lew

J. Sanz-Serna

H. Goldstein

Crossref

Midpoint rule as a variational-symplectic integrator: Hamiltonian systems

Memory T cells display phenotypic heterogeneity. Surface antigens previously regarded as exclusive markers of naive T cells, such as L-selectin ( CD62L), can also be detected on some memory T cells. Moreover, a fraction of CD45RO(+) ( positive for the short human isoform of CD45) memory T cells reverts to the CD45RA(+) ( positive for the long human isoform of CD45) phenotype. We analyzed patients with biopsy-proven localized Wegener's granulomatosis (WG) (n = 5), generalized WG (n = 16) and age- and sex-matched healthy controls ( n = 13) to further characterize memory T cells in WG. The cell-surface expression of CD45RO, CD45RA, CD62L, CCR3, CCR5 and CXCR3 was determined on blood-derived T cells by four-color flow cytometric analysis. The fractions of CCR5(+) and CCR3(+) cells within the CD4(+) CD45RO(+) and CD8(+) CD45RO(+) memory T cell populations were significantly expanded in localized and generalized WG. The mean percentage of Th1-type CCR5 expression was higher in localized WG. Upregulated CCR5 and CCR3 expression could also be detected on a fraction of CD45RA(+) T cells. CD62L expression was seen on approximately half of the memory T cell populations expressing chemokine receptors. This study demonstrates for the first time that expression of the inducible inflammatory chemokine receptors CCR5 and CCR3 on CD45RO(+) memory T cells, as well as on CD45RA(+) T cells ('revertants'), contributes to phenotypic heterogeneity in an autoimmune disease, namely WG. Upregulated CCR5 and CCR3 expression suggests that the cells belong to the effector memory T cell population. CCR5 and CCR3 expression on CD4(+) and CD8(+) memory T cells indicates a potential to respond to chemotactic gradients and might be important in T cell migration contributing to granuloma formation and vasculitis in WG

Open Access LMU ( Ludwig-Maximilians-Univ. München)

Heterogeneity of CD4(+) and CD8(+) memory T cells in localized and generalized Wegener's granulomatosis

Peter Lamprecht

Anika Erdmann

Antje Mueller

Elena Csernok

Eva Reinhold-Keller

Konstanze Holl-Ulrich

Alfred C Feller

Hilke Bruehl

Wolfgang L Gross

Springer - Publisher Connector

Universität München: Elektronischen Publikationen