5,799 research outputs found
On the Oß-hull of a planar point set
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We study the Oß-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle ß. Given a set P of n points in the plane, we show how to maintain the Oß-hull of P while ß runs from 0 to p in T(n log n) time and O(n) space. With the same complexity, we also find the values of ß that maximize the area and the perimeter of the Oß-hull and, furthermore, we find the value of ß achieving the best fitting of the point set P with a two-joint chain of alternate interior angle ß.Peer ReviewedPostprint (author's final draft
Ultrametric spaces of branches on arborescent singularities
Let be a normal complex analytic surface singularity. We say that is
arborescent if the dual graph of any resolution of it is a tree. Whenever
are distinct branches on , we denote by their intersection
number in the sense of Mumford. If is a fixed branch, we define when and
otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of
surfaces, by proving that whenever is arborescent, then is an
ultrametric on the set of branches of different from . We compute the
maximum of , which gives an analog of a theorem of Teissier. We show that
encodes topological information about the structure of the embedded
resolutions of any finite set of branches. This generalizes a theorem of Favre
and Jonsson concerning the case when both and are smooth. We generalize
also from smooth germs to arbitrary arborescent ones their valuative
interpretation of the dual trees of the resolutions of . Our proofs are
based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has
a new section 4.3, accompanied by 2 new figures. Several passages were
clarified and the typos discovered in the meantime were correcte
Optimally fast incremental Manhattan plane embedding and planar tight span construction
We describe a data structure, a rectangular complex, that can be used to
represent hyperconvex metric spaces that have the same topology (although not
necessarily the same distance function) as subsets of the plane. We show how to
use this data structure to construct the tight span of a metric space given as
an n x n distance matrix, when the tight span is homeomorphic to a subset of
the plane, in time O(n^2), and to add a single point to a planar tight span in
time O(n). As an application of this construction, we show how to test whether
a given finite metric space embeds isometrically into the Manhattan plane in
time O(n^2), and add a single point to the space and re-test whether it has
such an embedding in time O(n).Comment: 39 pages, 15 figure
Shape and holography: studies of dual operators to giant gravitons
In this paper we study the conjectured dual operators to a near maximal giant
graviton and their open string fluctuations in the large limit. Using
matrix model estimates we show that the spectrum of states near the D-brane
operator is consistent with a Fock space of open plus closed string states. We
also give an argument that these operators, in spite of having large R charge
of order N, are amenable to being studied with standard perturbative
techniques, which organize themselves in a 1/N expansion. Also the spectrum of
operators dual to massless fluctuations on the D-brane is shown to be protected
from weak to strong coupling at leading order, so it is possible to read the
shape of the dual operator by understanding how the spherical harmonics of the
D-brane fluctuations appear.Comment: 27 pages. v2: Added reference
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