1,029 research outputs found
Uncertainty in phylogenetic tree estimates
Estimating phylogenetic trees is an important problem in evolutionary
biology, environmental policy and medicine. Although trees are estimated, their
uncertainties are discarded by mathematicians working in tree space. Here we
explicitly model the multivariate uncertainty of tree estimates. We consider
both the cases where uncertainty information arises extrinsically (through
covariate information) and intrinsically (through the tree estimates
themselves). The importance of accounting for tree uncertainty in tree space is
demonstrated in two case studies. In the first instance, differences between
gene trees are small relative to their uncertainties, while in the second, the
differences are relatively large. Our main goal is visualization of tree
uncertainty, and we demonstrate advantages of our method with respect to
reproducibility, speed and preservation of topological differences compared to
visualization based on multidimensional scaling. The proposal highlights that
phylogenetic trees are estimated in an extremely high-dimensional space,
resulting in uncertainty information that cannot be discarded. Most
importantly, it is a method that allows biologists to diagnose whether
differences between gene trees are biologically meaningful, or due to
uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical
Statistic
Time Discrete Geodesic Paths in the Space of Images
In this paper the space of images is considered as a Riemannian manifold
using the metamorphosis approach, where the underlying Riemannian metric
simultaneously measures the cost of image transport and intensity variation. A
robust and effective variational time discretization of geodesics paths is
proposed. This requires to minimize a discrete path energy consisting of a sum
of consecutive image matching functionals over a set of image intensity maps
and pairwise matching deformations. For square-integrable input images the
existence of discrete, connecting geodesic paths defined as minimizers of this
variational problem is shown. Furthermore, -convergence of the
underlying discrete path energy to the continuous path energy is proved. This
includes a diffeomorphism property for the induced transport and the existence
of a square-integrable weak material derivative in space and time. A spatial
discretization via finite elements combined with an alternating descent scheme
in the set of image intensity maps and the set of matching deformations is
presented to approximate discrete geodesic paths numerically. Computational
results underline the efficiency of the proposed approach and demonstrate
important qualitative properties.Comment: 27 pages, 7 figure
Causality and Micro-Causality in Curved Spacetime
We consider how causality and micro-causality are realised in QED in curved
spacetime. The photon propagator is found to exhibit novel non-analytic
behaviour due to vacuum polarization, which invalidates the Kramers-Kronig
dispersion relation and calls into question the validity of micro-causality in
curved spacetime. This non-analyticity is ultimately related to the generic
focusing nature of congruences of geodesics in curved spacetime, as implied by
the null energy condition, and the existence of conjugate points. These results
arise from a calculation of the complete non-perturbative frequency dependence
of the vacuum polarization tensor in QED, using novel world-line path integral
methods together with the Penrose plane-wave limit of spacetime in the
neighbourhood of a null geodesic. The refractive index of curved spacetime is
shown to exhibit superluminal phase velocities, dispersion, absorption (due to
\gamma \to e^+e^-) and bi-refringence, but we demonstrate that the wavefront
velocity (the high-frequency limit of the phase velocity) is indeed c, thereby
guaranteeing that causality itself is respected.Comment: 16 pages, 11 figures, JHEP3, microcausality now shown to be respected
even when the Kramers-Kronig relation is violate
Low-latency compression of mocap data using learned spatial decorrelation transform
Due to the growing needs of human motion capture (mocap) in movie, video
games, sports, etc., it is highly desired to compress mocap data for efficient
storage and transmission. This paper presents two efficient frameworks for
compressing human mocap data with low latency. The first framework processes
the data in a frame-by-frame manner so that it is ideal for mocap data
streaming and time critical applications. The second one is clip-based and
provides a flexible tradeoff between latency and compression performance. Since
mocap data exhibits some unique spatial characteristics, we propose a very
effective transform, namely learned orthogonal transform (LOT), for reducing
the spatial redundancy. The LOT problem is formulated as minimizing square
error regularized by orthogonality and sparsity and solved via alternating
iteration. We also adopt a predictive coding and temporal DCT for temporal
decorrelation in the frame- and clip-based frameworks, respectively.
Experimental results show that the proposed frameworks can produce higher
compression performance at lower computational cost and latency than the
state-of-the-art methods.Comment: 15 pages, 9 figure
Human Motion Capture Data Tailored Transform Coding
Human motion capture (mocap) is a widely used technique for digitalizing
human movements. With growing usage, compressing mocap data has received
increasing attention, since compact data size enables efficient storage and
transmission. Our analysis shows that mocap data have some unique
characteristics that distinguish themselves from images and videos. Therefore,
directly borrowing image or video compression techniques, such as discrete
cosine transform, does not work well. In this paper, we propose a novel
mocap-tailored transform coding algorithm that takes advantage of these
features. Our algorithm segments the input mocap sequences into clips, which
are represented in 2D matrices. Then it computes a set of data-dependent
orthogonal bases to transform the matrices to frequency domain, in which the
transform coefficients have significantly less dependency. Finally, the
compression is obtained by entropy coding of the quantized coefficients and the
bases. Our method has low computational cost and can be easily extended to
compress mocap databases. It also requires neither training nor complicated
parameter setting. Experimental results demonstrate that the proposed scheme
significantly outperforms state-of-the-art algorithms in terms of compression
performance and speed
Black hole-neutron star mergers and short GRBs: a relativistic toy model to estimate the mass of the torus
The merger of a binary system composed of a black hole and a neutron star may
leave behind a torus of hot, dense matter orbiting around the black hole. While
numerical-relativity simulations are necessary to simulate this process
accurately, they are also computationally expensive and unable at present to
cover the large space of possible parameters, which include the relative mass
ratio, the stellar compactness, and the black hole spin. To mitigate this and
provide a first reasonable coverage of the space of parameters, we have
developed a method for estimating the mass of the remnant torus from black
hole-neutron star mergers. The toy model makes use of an improved relativistic
affine model to describe the tidal deformations of an extended tri-axial
ellipsoid orbiting around a Kerr black hole and measures the mass of the
remnant torus by considering which of the fluid particles composing the star
are on bound orbits at the time of the tidal disruption. We tune the toy model
by using the results of fully general-relativistic simulations obtaining
relative precisions of a few percent and use it to extensively investigate the
space of parameters. In this way we find that the torus mass is largest for
systems with highly spinning black holes, small stellar compactnesses, and
large mass ratios. As an example, tori as massive as ~1.33 solar masses can be
produced for a very extended star with compactness of ~0.1 inspiralling around
a black hole with dimensionless spin equal to 0.85 and mass ratio of about 0.3.
However, for a more astrophysically reasonable mass ratio of ~0.14 and a
canonical value of the stellar compactness of ~0.145, the toy model sets a
considerably smaller upper limit to the torus mass of less than ~0.34 solar
masses.Comment: Added new figure and new table to confirm agreement with simulations;
matches version accepted for publication in Ap
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