16,092 research outputs found
Strong inapproximability of the shortest reset word
The \v{C}ern\'y conjecture states that every -state synchronizing
automaton has a reset word of length at most . We study the hardness
of finding short reset words. It is known that the exact version of the
problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and
complete for the DP class, and that approximating the length of the shortest
reset word within a factor of is NP-hard [Gerbush and Heeringa,
CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly
improve on these results by showing that, for every , it is NP-hard
to approximate the length of the shortest reset word within a factor of
. This is essentially tight since a simple -approximation
algorithm exists.Comment: extended abstract to appear in MFCS 201
Early Term Effects of rhBMP-2 on Pedicle Screw Fixation in a Sheep Model: Histomorphometric and Biomechanical Analyses
Background: The effects of recombinant human bone morphogenetic protein-2 (rhBMP-2) on pedicle screw pullout force and its potential to improve spinal fixation have not previously been investigated. rhBMP-2 on an absorbable collagen sponge (ACS) carrier was delivered in and around cannulated and fenestrated pedicle screws in a sheep lumbar spine instability model. Two control groups (empty screw and ACS with buffer) were also evaluated. We hypothesized that rhBMP-2 could stimulate bone growth in and around the cannulated and fenestrated pedicle screws to improve early bone purchase.
Methods: Eight skeletally mature sheep underwent destabilizing laminectomies at L2–L3 and L4–L5 followed by stabilization with pedicle screw and rod constructs. An ACS carrier was used to deliver 0.15 mg of rhBMP-2 within and around the cannulated and fenestrated titanium pedicle screws. Biomechanics and histomorphometry were used to evaluate the early term results at 6 and 12 postoperative weeks.
Results: rhBMP-2 was unable to improve bony purchase of the cannulated and fenestrated pedicle screws compared to both control groups. Although rhBMP-2 groups had pullout forces that were less than both control groups, both rhBMP-2 groups had pullout force values exceeding 2,000 N, which was comparable to previously published results for unmodified pedicle screws. Significant differences in the percentages of bone in peri-screw tissues was not observed amongst the four treatment groups. Microradiography and quantitative histomorphometry showed that at 6 weeks, rhBMP-2 induced peri-screw remodeling regions containing peri-implant bone which was hypodense with respect to surrounding native trabeculae. A moderate correlation between biomechanical pullout variables and histomorphometry data was observed.
Conclusions: The design of the cannulated and fenestrated pedicle screw was able to facilitate new bone formation to achieve high pullout forces. However, delivery of rhBMP-2 should be carefully controlled to prevent excessive bone remodeling which could cause early screw loosening
Growth kinetics effects on self-assembled InAs/InP quantum dots
A systematic manipulation of the morphology and the optical emission
properties of MOVPE grown ensembles of InAs/InP quantum dots is demonstrated by
changing the growth kinetics parameters. Under non-equilibrium conditions of a
comparatively higher growth rate and low growth temperature, the quantum dot
density, their average size and hence the peak emission wavelength can be tuned
by changing efficiency of the surface diffusion (determined by the growth
temperature) relative to the growth flux. We further observe that the
distribution of quantum dot heights, for samples grown under varying
conditions, if normalized to the mean height, can be nearly collapsed onto a
single Gaussian curve.Comment: 2 figure
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
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