35,553 research outputs found
On the reconstruction of planar lattice-convex sets from the covariogram
A finite subset of is said to be lattice-convex if is
the intersection of with a convex set. The covariogram of
is the function associating to each u \in
\integer^d the cardinality of . Daurat, G\'erard, and Nivat and
independently Gardner, Gronchi, and Zong raised the problem on the
reconstruction of lattice-convex sets from . We provide a partial
positive answer to this problem by showing that for and under mild extra
assumptions, determines up to translations and reflections. As a
complement to the theorem on reconstruction we also extend the known
counterexamples (i.e., planar lattice-convex sets which are not
reconstructible, up to translations and reflections) to an infinite family of
counterexamples.Comment: accepted in Discrete and Computational Geometr
Effective Classification using a small Training Set based on Discretization and Statistical Analysis
This work deals with the problem of producing a fast and accurate data classification, learning it from a possibly small set of records that are already classified. The proposed approach is based on the framework of the so-called Logical Analysis of Data (LAD), but enriched with information obtained from statistical considerations on the data. A number of discrete optimization problems are solved in the different steps of the procedure, but their computational demand can be controlled. The accuracy of the proposed approach is compared to that of the standard LAD algorithm, of Support Vector Machines and of Label Propagation algorithm on publicly available datasets of the UCI repository. Encouraging results are obtained and discusse
A Chandra view of the clumpy reflector at the heart of the Circinus galaxy
We present a spectral and imaging analysis of the X-ray reflecting structure
at the heart of the Circinus galaxy, investigating the innermost regions
surrounding the central black hole. By studying an archival 200 ks Chandra
ACIS-S observation, we are able to image the extended clumpy structure
responsible for both cold reflection of the primary radiation and neutral iron
Ka line emission. We measure an excess of the equivalent width of the iron Ka
line which follows an axisymmetric geometry around the nucleus on a hundred pc
scale. Spectra extracted from different regions confirm a scenario in which the
dominant mechanism is the reflection of the nuclear radiation from
Compton-thick gas. Significant differences in the equivalent width of the iron
Ka emission line (up to a factor of 2) are found. It is argued that these
differences are due to different scattering angles with respect to the line of
sight rather than to different iron abundances.Comment: 6 pages, 4 figures, accepted for publication on MNRA
Symmetrization in Geometry
The concept of an -symmetrization is introduced, which provides a
convenient framework for most of the familiar symmetrization processes on
convex sets. Various properties of -symmetrizations are introduced and the
relations between them investigated. New expressions are provided for the
Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual
relationship between them. Characterizations of Steiner, Minkowski and central
symmetrization, in terms of natural properties that they enjoy, are given and
examples are provided to show that none of the assumptions made can be dropped
or significantly weakened. Other familiar symmetrizations, such as Schwarz
symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several
typos have been corrected. This version has been accepted for publication on
Advances in Mathematic
Planar Duality in WZW Models
We show how to generalize the WZW models to allow for open and
unoriented sectors. The construction exhibits some novel patterns of Chan-Paton
charge assignments and projected spectra that reflect the underlying current
algebra.Comment: 13 pages, latex, 1 figure
String amplitudes in the Hpp-wave limit of AdS3xS3
We compute string amplitudes on pp-waves supported by NS-NS 3-form fluxes and
arising in the Penrose limit of AdS3xS3xM. We clarify the role of the
non-chiral accidental SU(2) symmetry of the background. We comment on the
extension of our results to the superstring and propose a holographic formula
in the BMN limit of the AdS3/CFT2 correspondence valid for any correlator.Comment: Latex,no figures, 47 p
X-ray reprocessing in Seyfert Galaxies: simultaneous XMM-Newton/BeppoSAX observations
We selected a sample of eight bright unobscured (at least at the iron line
energy) Seyfert Galaxies observed simultaneously by XMM-Newton and BeppoSAX,
taking advantage of the complementary characteristics of the two missions. The
main results of our analysis can be summarized as follows: narrow neutral iron
lines are confirmed to be an ubiquitous component in Seyfert spectra; none of
the analyzed sources shows unambiguously a broad relativistic iron line; all
the sources of our sample (with a single exception) show the presence of a
Compton reflection component; emission lines from ionized iron are observed in
some sources; peculiar weak features around 5-6 keV (possibly arising from
rotating spots on the accretion disk) are detected in two sources. The scenario
emerging from these results strongly requires some corrections for the
classical model of reprocessing from the accretion disk. As for materials
farther away from the Black Hole, our results represent a positive test for the
Unification Model, suggesting the presence of the torus in (almost) all
sources, even if unobscured.Comment: Accepted for publication in A&
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