2,363 research outputs found
On the Whitham Hierarchies: Reductions and Hodograph Solutions
A general scheme for analyzing reductions of Whitham hierarchies is
presented. It is based on a method for determining the -function by means of
a system of first order partial differential equations. Compatibility systems
of differential equations characterizing both reductions and hodograph
solutions of Whitham hierarchies are obtained. The method is illustrated by
exhibiting solutions of integrable models such as the dispersionless Toda
equation (heavenly equation) and the generalized Benney system.Comment: 24 page
Recycling probability and dynamical properties of germinal center reactions
We introduce a new model for the dynamics of centroblasts and centrocytes in
a germinal center. The model reduces the germinal center reaction to the
elements considered as essential and embeds proliferation of centroblasts,
point mutations of the corresponding antibody types represented in a shape
space, differentiation to centrocytes, selection with respect to initial
antigens, differentiation of positively selected centrocytes to plasma or
memory cells and recycling of centrocytes to centroblasts. We use exclusively
parameters with a direct biological interpretation such that, once determined
by experimental data, the model gains predictive power. Based on the experiment
of Han et al. (1995b) we predict that a high rate of recycling of centrocytes
to centroblasts is necessary for the germinal center reaction to work reliably.
Furthermore, we find a delayed start of the production of plasma and memory
cells with respect to the start of point mutations, which turns out to be
necessary for the optimization process during the germinal center reaction. The
dependence of the germinal center reaction on the recycling probability is
analyzed.Comment: 30 pages, 8 figure
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