29,528 research outputs found
Embedding Stacked Polytopes on a Polynomial-Size Grid
A stacking operation adds a -simplex on top of a facet of a simplicial
-polytope while maintaining the convexity of the polytope. A stacked
-polytope is a polytope that is obtained from a -simplex and a series of
stacking operations. We show that for a fixed every stacked -polytope
with vertices can be realized with nonnegative integer coordinates. The
coordinates are bounded by , except for one axis, where the
coordinates are bounded by . The described realization can be
computed with an easy algorithm.
The realization of the polytopes is obtained with a lifting technique which
produces an embedding on a large grid. We establish a rounding scheme that
places the vertices on a sparser grid, while maintaining the convexity of the
embedding.Comment: 22 pages, 10 Figure
Assessing old-age long-term care using the concepts of healthy life expectancy and care duration: the new parameter "Long-Term Care-Free Life-Expectancy (LTCF)"
Achieving old ages is also connected with prevalence of illness and long-term care. With the introduction of the statutory long-term care insurance in 1996 and the long-term care statistics in 1999 research data of about 2.3 million people receiving long-term care benefits is available. Average life expectancy can be qualitatively divided into lifetime spent in good health and lifetime spent in long-term care dependence (average care duration). In Germany women’s and men’s average care duration amount 3.6 years respectively 2.1 years.Germany, ageing, laboratories, life expectancy
Mott law as lower bound for a random walk in a random environment
We consider a random walk on the support of a stationary simple point process
on , which satisfies a mixing condition w.r.t.the translations
or has a strictly positive density uniformly on large enough cubes. Furthermore
the point process is furnished with independent random bounded energy marks.
The transition rates of the random walk decay exponentially in the jump
distances and depend on the energies through a factor of the Boltzmann-type.
This is an effective model for the phonon-induced hopping of electrons in
disordered solids within the regime of strong Anderson localization. We show
that the rescaled random walk converges to a Brownian motion whose diffusion
coefficient is bounded below by Mott's law for the variable range hopping
conductivity at zero frequency. The proof of the lower bound involves estimates
for the supercritical regime of an associated site percolation problem
Dynamical Ne K Edge and Line Variations in the X-Ray Spectrum of the Ultra-compact Binary 4U 0614+091
We observed the ultra-compact binary candidate 4U 0614+091 for a total of 200
ksec with the high-energy transmission gratings onboard the \chandra X-ray
Observatory. The source is found at various intensity levels with spectral
variations present. X-ray luminosities vary between 2.0 \ergsec
and 3.5 \ergsec. Continuum variations are present at all times
and spectra can be well fit with a powerlaw component, a high kT blackbody
component, and a broad line component near oxygen. The spectra require
adjustments to the Ne K edge and in some occasions also to the Mg K edge. The
Ne K edge appears variable in terms of optical depths and morphology. The edge
reveals average blue- and red-shifted values implying Doppler velocities of the
order of 3500 \kms. The data show that Ne K exhibits excess column densities of
up to several 10 cm. The variability proves that the excess is
intrinsic to the source. The correponding disk velocities also imply an outer
disk radius of the order of cm consistent with an ultra-compact binary
nature. We also detect a prominent soft emission line complex near the \oviii
L position which appears extremely broad and relativistic effects from
near the innermost disk have to be included. Gravitationally broadened line
fits also provide nearly edge-on angles of inclination between 86 and
89. The emissions appear consistent with an ionized disk with
ionization parameters of the order of 10 at radii of a few 10 cm. The
line wavelengths with respect to \oviiia\ are found variably blue-shifted
indicating more complex inner disk dynamics.Comment: 24 pages, 8 figures, submitted to the Astrophyscial Main Journa
Bounds on the maximum multiplicity of some common geometric graphs
We obtain new lower and upper bounds for the maximum multiplicity of some
weighted and, respectively, non-weighted common geometric graphs drawn on n
points in the plane in general position (with no three points collinear):
perfect matchings, spanning trees, spanning cycles (tours), and triangulations.
(i) We present a new lower bound construction for the maximum number of
triangulations a set of n points in general position can have. In particular,
we show that a generalized double chain formed by two almost convex chains
admits {\Omega}(8.65^n) different triangulations. This improves the bound
{\Omega}(8.48^n) achieved by the double zig-zag chain configuration studied by
Aichholzer et al.
(ii) We present a new lower bound of {\Omega}(12.00^n) for the number of
non-crossing spanning trees of the double chain composed of two convex chains.
The previous bound, {\Omega}(10.42^n), stood unchanged for more than 10 years.
(iii) Using a recent upper bound of 30^n for the number of triangulations,
due to Sharir and Sheffer, we show that n points in the plane in general
position admit at most O(68.62^n) non-crossing spanning cycles.
(iv) We derive lower bounds for the number of maximum and minimum weighted
geometric graphs (matchings, spanning trees, and tours). We show that the
number of shortest non-crossing tours can be exponential in n. Likewise, we
show that both the number of longest non-crossing tours and the number of
longest non-crossing perfect matchings can be exponential in n. Moreover, we
show that there are sets of n points in convex position with an exponential
number of longest non-crossing spanning trees. For points in convex position we
obtain tight bounds for the number of longest and shortest tours. We give a
combinatorial characterization of the longest tours, which leads to an O(nlog
n) time algorithm for computing them
Counting Carambolas
We give upper and lower bounds on the maximum and minimum number of geometric
configurations of various kinds present (as subgraphs) in a triangulation of
points in the plane. Configurations of interest include \emph{convex
polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also
consider related problems for \emph{directed} planar straight-line graphs.Comment: update reflects journal version, to appear in Graphs and
Combinatorics; 18 pages, 13 figure
Stripes on a 6-Leg Hubbard Ladder
While DMRG calculations find stripes on doped n-leg t-J ladders, little is
known about the possible formation of stripes on n-leg Hubbard ladders. Here we
report results for a 7x6 Hubbard model with 4 holes. We find that a stripe
forms for values of U/t ranging from 6 to 20. For U/t ~ 3-4, the system
exhibits the domain wall feature of a stripe, but the hole density is very
broadened.Comment: 4 pages, 5 figure
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