12,242 research outputs found
Early structure formation from cosmic string loops
We examine the effects of cosmic strings on structure formation and on the
ionization history of the universe. While Gaussian perturbations from inflation
are known to provide the dominant contribution to the large scale structure of
the universe, density perturbations due to strings are highly non-Gaussian and
can produce nonlinear structures at very early times. This could lead to early
star formation and reionization of the universe. We improve on earlier studies
of these effects by accounting for high loop velocities and for the filamentary
shape of the resulting halos. We find that for string energy scales G\mu >
10^{-7} the effect of strings on the CMB temperature and polarization power
spectra can be significant and is likely to be detectable by the Planck
satellite. We mention shortcomings of the standard cosmological model of galaxy
formation which may be remedied with the addition of cosmic strings, and
comment on other possible observational implications of early structure
formation by strings.Comment: 22 pages, 10 figures. References adde
Minimality and mutation-equivalence of polygons
We introduce a concept of minimality for Fano polygons. We show that, up to
mutation, there are only finitely many Fano polygons with given singularity
content, and give an algorithm to determine the mutation-equivalence classes of
such polygons. This is a key step in a program to classify orbifold del Pezzo
surfaces using mirror symmetry. As an application, we classify all Fano
polygons such that the corresponding toric surface is qG-deformation-equivalent
to either (i) a smooth surface; or (ii) a surface with only singularities of
type 1/3(1,1).Comment: 29 page
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
A Posteriori Error Control for the Binary Mumford-Shah Model
The binary Mumford-Shah model is a widespread tool for image segmentation and
can be considered as a basic model in shape optimization with a broad range of
applications in computer vision, ranging from basic segmentation and labeling
to object reconstruction. This paper presents robust a posteriori error
estimates for a natural error quantity, namely the area of the non properly
segmented region. To this end, a suitable strictly convex and non-constrained
relaxation of the originally non-convex functional is investigated and Repin's
functional approach for a posteriori error estimation is used to control the
numerical error for the relaxed problem in the -norm. In combination with
a suitable cut out argument, a fully practical estimate for the area mismatch
is derived. This estimate is incorporated in an adaptive meshing strategy. Two
different adaptive primal-dual finite element schemes, and the most frequently
used finite difference discretization are investigated and compared. Numerical
experiments show qualitative and quantitative properties of the estimates and
demonstrate their usefulness in practical applications.Comment: 18 pages, 7 figures, 1 tabl
Quantifying identifiability in independent component analysis
We are interested in consistent estimation of the mixing matrix in the ICA
model, when the error distribution is close to (but different from) Gaussian.
In particular, we consider independent samples from the ICA model , where we assume that the coordinates of are independent
and identically distributed according to a contaminated Gaussian distribution,
and the amount of contamination is allowed to depend on . We then
investigate how the ability to consistently estimate the mixing matrix depends
on the amount of contamination. Our results suggest that in an asymptotic
sense, if the amount of contamination decreases at rate or faster,
then the mixing matrix is only identifiable up to transpose products. These
results also have implications for causal inference from linear structural
equation models with near-Gaussian additive noise.Comment: 22 pages, 2 figure
K-orbit closures and Barbasch-Evens-Magyar varieties
We define the Barbasch-Evens-Magyar variety. We show it is isomorphic to the
smooth variety defined in [D. Barbasch-S. Evens '94] that maps finite-to-one to
a symmetric orbit closure, thereby giving a resolution of singularities in
certain cases. Our definition parallels [P. Magyar '98]'s construction of the
Bott-Samelson variety [H. C. Hansen '73, M. Demazure '74]. From this
alternative viewpoint, one deduces a graphical description in type A,
stratification into closed subvarieties of the same kind, and determination of
the torus-fixed points. Moreover, we explain how these manifolds inherit a
natural symplectic structure with Hamiltonian torus action. We then prove that
the moment polytope is expressed in terms of the moment polytope of a
Bott-Samelson variety.Comment: 26 pages, 4 figure
- …