7,208 research outputs found
Optimal randomized incremental construction for guaranteed logarithmic planar point location
Given a planar map of segments in which we wish to efficiently locate
points, we present the first randomized incremental construction of the
well-known trapezoidal-map search-structure that only requires expected preprocessing time while deterministically guaranteeing worst-case
linear storage space and worst-case logarithmic query time. This settles a long
standing open problem; the best previously known construction time of such a
structure, which is based on a directed acyclic graph, so-called the history
DAG, and with the above worst-case space and query-time guarantees, was
expected . The result is based on a deeper understanding of the
structure of the history DAG, its depth in relation to the length of its
longest search path, as well as its correspondence to the trapezoidal search
tree. Our results immediately extend to planar maps induced by finite
collections of pairwise interior disjoint well-behaved curves.Comment: The article significantly extends the theoretical aspects of the work
presented in http://arxiv.org/abs/1205.543
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
Approximating Edit Distance Within Constant Factor in Truly Sub-Quadratic Time
Edit distance is a measure of similarity of two strings based on the minimum
number of character insertions, deletions, and substitutions required to
transform one string into the other. The edit distance can be computed exactly
using a dynamic programming algorithm that runs in quadratic time. Andoni,
Krauthgamer and Onak (2010) gave a nearly linear time algorithm that
approximates edit distance within approximation factor .
In this paper, we provide an algorithm with running time
that approximates the edit distance within a constant
factor
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