A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Equidistribution of Fekete Points on the Sphere

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.

Mouse mammary tumor virus superantigens and murine autoimmune gastritis.

BACKGROUND/AIMS: Neonatal thymectomy induces autoimmune gastritis in BALB/c (minor lymphocyte-stimulating antigen [Mls]-1b) mice, whereas DBA/2 (Mls-1a) mice are resistant. Resistance has been linked to the Mls-1a locus, which encodes a retroviral superantigen, and to superantigen reactive T cells that express V beta 6+ T-cell receptors. V beta 6+ T cells are known to be deleted in mice expressing Mls-1a superantigens. METHODS: Neonatal thymectomized BALB/c and Mls-1a congenic BALB.D2.Mls-1a mice were analyzed to examine directly the role of Mls-1a self-superantigens and V beta 6+ T cells in autoimmune gastritis. RESULTS: Autoimmune gastritis was detected in thymectomized BALB.D2.Mls-1a mice with high incidence. Autoantibodies to the gastric H+,K(+)-adenosine triphosphatase were present independent of the Mls phenotype in sera of gastritic mice. Severe gastritis had already appeared 1 month after thymectomy in BALB.D2.Mls-1a mice. V beta 6+ T cells were deleted in the stomach lymph nodes of 1-month-old gastritic BALB.D2.Mls-1a mice but could be detected by immunocytochemistry in the stomach lesions. CONCLUSIONS: Endogenous Mls-1a self-superantigens and Mls-1a reactive V beta 6+ T cells are not involved in resistance to autoimmune gastritis in BALB.D2 mice.

Peripheral T cell activation and deletion induced by transfer of lymphocyte subsets expressing endogenous or exogenous mouse mammary tumor virus.

Murine T cell reactivity with products of the minor lymphocyte stimulatory (Mls) locus correlates with the expression of particular variable (V) domains of the T cell receptor (TCR) beta chain. It was recently demonstrated that Mls antigens are encoded by an open reading frame (ORF) in the 3' long terminal repeat of either endogenous or exogenous mouse mammary tumor virus (MMTV). Immature thymocytes expressing reactive TCR-V beta domains are clonally deleted upon exposure to endogenous Mtv's. Mature T cells proliferate vigorously in response to Mls-1a (Mtv-7) in vivo, but induction of specific anergy and deletion after exposure to Mtv-7-expressing cells in the periphery has also been described. We show here that B cells and CD8+ (but not CD4+) T cells from Mtv-7+ mice efficiently induce peripheral deletion of reactive T cells upon transfer to Mtv-7- recipients, whereas only B cells stimulate specific T cell proliferation in vivo. In contrast to endogenous Mtv-7, transfer of B, CD4+, or CD8+ lymphocyte subsets from mice maternally infected with MMTV(SW), an infectious homologue of Mtv-7, results in specific T cell deletion in the absence of a detectable proliferative response. Finally, we show by secondary transfers of infected cells that exogenous MMTV(SW) is transmitted multidirectionally between lymphocyte subsets and ultimately to the mammary gland. Collectively our data demonstrate heterogeneity in the expression and/or presentation of endogenous and exogenous MMTV ORF by lymphocyte subsets and emphasize the low threshold required for induction of peripheral T cell deletion by these gene products.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.