Optimal prediction of underresolved dynamics

A method is presented for computing the average solution of problems that are too complicated for adequate resolution, but where information about the statistics of the solution is available. The method involves computing average derivatives by interpolation based on linear regression, and an updating of a measure constrained by the available crude information. Examples are given.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Preferential induction of a Th1 immune response and inhibition of specific IgE antibody formation by plasmid DNA immunization.

We compared the antigen-specific antibody isotypes and lymphokine secretion by CD4+ T cells in BALB/c mice immunized intradermally with either Escherichia coli beta-galactosidase (beta-gal) or plasmid DNA (pDNA) encoding beta-gal in a cytomegalovirus-based expression vector (pCMV-LacZ). pCMV-LacZ induced mainly IgG2a, whereas beta-gal in saline or alum induced IgG1 and IgE beta-gal-specific antibodies. In addition, splenic CD4+ T helper (Th) cells isolated from pDNA-immunized mice secreted interferon-gamma but not interleukin (IL)-4 and IL-5, whereas Th cells from beta-gal-injected mice secreted IL-4 and IL-5 but not interferon-gamma after in vitro stimulation with antigen. Together these data demonstrate that pDNA immunization induced a T helper type 1 (Th1) response, whereas protein immunization induced a T helper type 2 (Th2) response to the same antigen. Interestingly, priming of mice with pCMV-LacZ prevented IgE antibody formation to a subsequent i.p. beta-gal in alum injection. This effect was antigen-specific, because priming with pCMV-LacZ did not inhibit IgE anti-ovalbumin antibody formation. Most importantly, intradermal immunization with pCMV-LacZ (but not pCMV-OVA) of beta-gal in alum-primed mice caused a 66-75% reduction of the IgE anti-beta-gal titer in 6 weeks. Also, pCMV-LacZ induced specific IgG2a antibody titers and interferon-gamma secretion by Th cells in the beta-gal in alum-primed mice. The data demonstrate that gene immunization induces a Th1 response that dominates over an ongoing protein-induced Th2 response in an antigen-specific manner. This suggests that immunization with pDNA encoding for allergens may provide a novel type of immunotherapy for allergic diseases.