693 research outputs found
Connectivity and tree structure in finite graphs
Considering systems of separations in a graph that separate every pair of a
given set of vertex sets that are themselves not separated by these
separations, we determine conditions under which such a separation system
contains a nested subsystem that still separates those sets and is invariant
under the automorphisms of the graph.
As an application, we show that the -blocks -- the maximal vertex sets
that cannot be separated by at most vertices -- of a graph live in
distinct parts of a suitable tree-decomposition of of adhesion at most ,
whose decomposition tree is invariant under the automorphisms of . This
extends recent work of Dunwoody and Kr\"on and, like theirs, generalizes a
similar theorem of Tutte for .
Under mild additional assumptions, which are necessary, our decompositions
can be combined into one overall tree-decomposition that distinguishes, for all
simultaneously, all the -blocks of a finite graph.Comment: 31 page
Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
We prove general comparison theorems for eigenvalues of perturbed Schrodinger
operators that allow proof of Lieb--Thirring bounds for suitable non-free
Schrodinger operators and Jacobi matrices.Comment: 11 page
On the negative spectrum of two-dimensional Schr\"odinger operators with radial potentials
For a two-dimensional Schr\"odinger operator
with the radial potential , we study the behavior of
the number of its negative eigenvalues, as the coupling
parameter tends to infinity. We obtain the necessary and sufficient
conditions for the semi-classical growth and for
the validity of the Weyl asymptotic law.Comment: 13 page
Localization criteria for Anderson models on locally finite graphs
We prove spectral and dynamical localization for Anderson models on locally
finite graphs using the fractional moment method. Our theorems extend earlier
results on localization for the Anderson model on \ZZ^d. We establish
geometric assumptions for the underlying graph such that localization can be
proven in the case of sufficiently large disorder
Lieb-Thirring inequalities for geometrically induced bound states
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of
Schr\"odinger operators in wave guides with local perturbations. The estimates
are optimal in the weak-coupling case. To illustrate their applications, we
consider, in particular, a straight strip and a straight circular tube with
either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page
The Thresher : lucky imaging without the waste
JAH acknowledges funding from the Science and Technology Facilities Council of the United Kingdom.In traditional lucky imaging (TLI), many consecutive images of the same scene are taken with a high frame-rate camera, and all but the sharpest images are discarded before constructing the final shift-and-add image. Here, we present an alternative image analysis pipeline – The Thresher – for these kinds of data, based on online multi-frame blind deconvolution. It makes use of all available data to obtain the best estimate of the astronomical scene in the context of reasonable computational limits; it does not require prior estimates of the point-spread functions in the images, or knowledge of point sources in the scene that could provide such estimates. Most importantly, the scene it aims to return is the optimum of a justified scalar objective based on the likelihood function. Because it uses the full set of images in the stack, The Thresher outperforms TLI in signal-to-noise ratio; as it accounts for the individual-frame PSFs, it does this without loss of angular resolution. We demonstrate the effectiveness of our algorithm on both simulated data and real Electron-Multiplying CCD images obtained at the Danish 1.54-m telescope (hosted by ESO, La Silla). We also explore the current limitations of the algorithm, and find that for the choice of image model presented here, non-linearities in flux are introduced into the returned scene. Ongoing development of the software can be viewed at https://github.com/jah1994/TheThresher.Publisher PDFPeer reviewe
Simulator for Microlens Planet Surveys
We summarize the status of a computer simulator for microlens planet surveys.
The simulator generates synthetic light curves of microlensing events observed
with specified networks of telescopes over specified periods of time.
Particular attention is paid to models for sky brightness and seeing,
calibrated by fitting to data from the OGLE survey and RoboNet observations in
2011. Time intervals during which events are observable are identified by
accounting for positions of the Sun and the Moon, and other restrictions on
telescope pointing. Simulated observations are then generated for an algorithm
that adjusts target priorities in real time with the aim of maximizing planet
detection zone area summed over all the available events. The exoplanet
detection capability of observations was compared for several telescopes.Comment: Proc. IAU Symp. No. 293 "Formation, detection, and characterization
of extrasolar habitable planets", ed. by N. Haghighipour. 4 pages, in pres
On non-local variational problems with lack of compactness related to non-linear optics
We give a simple proof of existence of solutions of the dispersion manage-
ment and diffraction management equations for zero average dispersion,
respectively diffraction. These solutions are found as maximizers of non-linear
and non-local vari- ational problems which are invariant under a large
non-compact group. Our proof of existence of maximizer is rather direct and
avoids the use of Lions' concentration compactness argument or Ekeland's
variational principle.Comment: 30 page
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