18,840 research outputs found
A contour integral approach to the computation of invariant pairs
We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thümmler [6]. Invariant pairs extend the notion of eigenvalue–eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. We compute formulations for the condition numbers and the backward error for invariant pairs and solvents. We then adapt the Sakurai–Sugiura moment method [1] to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues. Numerical refinement via a variant of Newton's method is also studied. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials
Object Edge Contour Localisation Based on HexBinary Feature Matching
This paper addresses the issue of localising object
edge contours in cluttered backgrounds to support robotics
tasks such as grasping and manipulation and also to improve
the potential perceptual capabilities of robot vision systems. Our
approach is based on coarse-to-fine matching of a new recursively
constructed hierarchical, dense, edge-localised descriptor,
the HexBinary, based on the HexHog descriptor structure first
proposed in [1]. Since Binary String image descriptors [2]–
[5] require much lower computational resources, but provide
similar or even better matching performance than Histogram
of Orientated Gradient (HoG) descriptors, we have replaced
the HoG base descriptor fields used in HexHog with Binary
Strings generated from first and second order polar derivative
approximations. The ALOI [6] dataset is used to evaluate
the HexBinary descriptors which we demonstrate to achieve
a superior performance to that of HexHoG [1] for pose
refinement. The validation of our object contour localisation
system shows promising results with correctly labelling ~86% of edgel positions and mis-labelling ~3%
Black hole pair creation in de Sitter space: a complete one-loop analysis
We present an exact one-loop calculation of the tunneling process in
Euclidean quantum gravity describing creation of black hole pairs in a de
Sitter universe. Such processes are mediated by gravitational
instantons giving an imaginary contribution to the partition function. The
required energy is provided by the expansion of the universe. We utilize the
thermal properties of de Sitter space to describe the process as the decay of a
metastable thermal state. Within the Euclidean path integral approach to
gravity, we explicitly determine the spectra of the fluctuation operators,
exactly calculate the one-loop fluctuation determinants in the -function
regularization scheme, and check the agreement with the expected scaling
behaviour. Our results show a constant volume density of created black holes at
late times, and a very strong suppression of the nucleation rate for small
values of .Comment: 63 pages, 4 eps figures, references and thanks added, to appear in
Nucl.Phys.
Schwinger pair production in AdS2
We analyze the pair production of charged particles in two-dimensional
Anti-de Sitter space (AdS_2) with a constant, uniform electric field. We
compute the production rate both at a semi-classical level, viewing Schwinger
pair production as a tunneling event, and at the full quantum level, by
extracting the imaginary part of the one-loop amplitude. In contrast to the
usual Schwinger pair production in flat space, pair production in AdS_2
requires a sufficiently large electric field E^2> M^2+1/4 in order to overcome
the confining effect of the AdS geometry -- put in another way, the presence of
an electric field E raises the Breitenlohner-Freedman bound to M^2 > -1/4 +
E^2. For E greater than this threshold, the vacuum is unstable to production of
charged pairs in the bulk. We expect our results to be helpful in constructing
supersymmetric AdS_2 X S^2 perturbative string vacua, which enter in the
near-horizon limit of extremal charged black holes. Although the generalized
Breitenlohner-Freedman bound is obeyed in these cases, production of BPS
particles at threshold is possible and relevant for AdS_2 fragmentation.Comment: 23 pages, 4 figures, v2:important revision, discussion of one-loop
amplitude extended, several references adde
- …