1,714 research outputs found
A combinatorial smoothness criterion for spherical varieties
We suggest a combinatorial criterion for the smoothness of an arbitrary
spherical variety using the classification of multiplicity-free spaces,
generalizing an earlier result of Camus for spherical varieties of type .Comment: 14 pages, 2 table
Mechatronic design of a fast and long range 4 degrees of freedom humanoid neck
This paper describes the mechatronic design of a humanoid neck. To research human machine interaction, the head and neck combination should be able to approach the human behavior as much as possible. We present a novel humanoid neck concept that is both fast, and has a long range of motion in 4 degrees of freedom (DOFs). This enables the head to track fast objects, and the neck design is suitable for mimicking expressions. The humanoid neck features a differential drive design for the lower 2 DOFs resulting in a low moving mass and the ability to use strong actuators. The performance of the neck has been\ud
optimized by minimizing backlash in the mechanisms, and by using gravity compensation. Two cameras in the head are used for scanning and interaction with the environment
Spherical orbit closures in simple projective spaces and their normalizations
Let G be a simply connected semisimple algebraic group over an algebraically
closed field k of characteristic 0 and let V be a rational simple G-module of
finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its
closure, then we describe the orbits of X and those of its normalization. If
moreover the wonderful completion of G/H is strict, then we give necessary and
sufficient combinatorial conditions so that the normalization morphism is a
homeomorphism. Such conditions are trivially fulfilled if G is simply laced or
if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation
Groups. Simplified some proofs and corrected minor mistakes, added
references. v3: major changes due to a mistake in previous version
Classification of double flag varieties of complexity 0 and 1
A classification of double flag varieties of complexity 0 and 1 is obtained.
An application of this problem to decomposing tensor products of irreducible
representations of semisimple Lie groups is considered
The Rise Times of High and Low Redshift Type Ia Supernovae are Consistent
We present a self-consistent comparison of the rise times for low- and
high-redshift Type Ia supernovae. Following previous studies, the early light
curve is modeled using a t-squared law, which is then mated with a modified
Leibundgut template light curve. The best-fit t-squared law is determined for
ensemble samples of low- and high-redshift supernovae by fitting simultaneously
for all light curve parameters for all supernovae in each sample. Our method
fully accounts for the non-negligible covariance amongst the light curve
fitting parameters, which previous analyses have neglected. Contrary to Riess
et al. (1999), we find fair to good agreement between the rise times of the
low- and high-redshift Type Ia supernovae. The uncertainty in the rise time of
the high-redshift Type Ia supernovae is presently quite large (roughly +/- 1.2
days statistical), making any search for evidence of evolution based on a
comparison of rise times premature. Furthermore, systematic effects on rise
time determinations from the high-redshift observations, due to the form of the
late-time light curve and the manner in which the light curves of these
supernovae were sampled, can bias the high-redshift rise time determinations by
up to +3.6/-1.9 days under extreme situations. The peak brightnesses - used for
cosmology - do not suffer any significant bias, nor any significant increase in
uncertainty.Comment: 18 pages, 4 figures, Accepted for publication in the Astronomical
Journal. Also available at http://www.lbl.gov/~nugent/papers.html Typos were
corrected and a few sentences were added for improved clarit
Hilbert Series for Flavor Invariants of the Standard Model
The Hilbert series is computed for the lepton flavor invariants of the
Standard Model with three generations including the right-handed neutrino
sector needed to generate light neutrino masses via the see-saw mechanism. We
also compute the Hilbert series of the quark flavor invariants for the case of
four generations.Comment: 6 page
Polarizations and Nullcone of Representations of Reductive Groups
The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.
Perturbations in the relaxation mechanism for a large cosmological constant
Recently, a mechanism for relaxing a large cosmological constant (CC) has
been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates
at late times without fine-tuning. The setup is implemented in the LXCDM
framework, and we found a reasonable cosmological background evolution similar
to the LCDM model with a fine-tuned CC. In this work we analyse analytically
the perturbations in this relaxation model, and we show that their evolution is
also similar to the LCDM model, especially in the matter era. Some tracking
properties of the vacuum energy are discussed, too.Comment: 18 pages, LaTeX; discussion improved, accepted by CQ
Combined Anterior-Posterior Surgery Versus Posterior Surgery for Thoracolumbar Burst Fractures: A Systematic Review of the Literature
Abstract: Study Design: A systematic quantitative review of the literature.
Objective: To compare combined anterior-posterior surgery versus posterior surgery for thoracolumbar fractures in order to identify better treatments.
Summary of Background Data: Axial load of the anterior and middle column of the spine can lead to a burst fracture in the vertebral body. The management of thoracolumbar burst fractures remains controversial. The goals of operative treatment are fracture reduction, fixation and decompressing the neural canal. For this, different operative methods are developed, for instance, the posterior and the combined anterior-posterior approach. Recent systematic qualitative reviews comparing these methods are lacking.
Methods: We conducted an electronic search of MEDLINE, EMBASE, LILACS and the Cochrane Central Register for Controlled Trials.
Results: Five observational comparative studies and no randomized clinical trials comparing the combined anteriorposterior approach with the posterior approach were retrieved. The total enrollment of patients in these studies was 755 patients. The results were expressed as relative risk (RR) for dichotomous outcomes and weighted mean difference (WMD) for continuous outcomes with 95% confidence intervals (CI). Conclusions: A small significantly higher kyphotic correction and improvement of vertebral height (sagittal index)
observed for the combined anterior-posterior group is cancelled out by more blood loss, longer operation time, longer
hospital stay, higher costs and a possible higher intra- and postoperative complication rate requiring re-operation and the
possibility of a worsened Hannover spine score. The surgeons’ choices regarding the operative approach are biased: worse
cases tended to undergo the combined anterior-posterior approach
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