1,475 research outputs found
Chiral dynamics and peripheral transverse densities
In the partonic (or light-front) description of relativistic systems the
electromagnetic form factors are expressed in terms of frame-independent charge
and magnetization densities in transverse space. This formulation allows one to
identify the chiral components of nucleon structure as the peripheral densities
at transverse distances b = O(M_pi^{-1}) and compute them in a parametrically
controlled manner. A dispersion relation connects the large-distance behavior
of the transverse charge and magnetization densities to the spectral functions
of the Dirac and Pauli form factors near the two-pion threshold at timelike t =
4 M_pi^2. Using relativistic chiral effective field theory in the leading-order
approximation, we (a) derive the asymptotic behavior (Yukawa tail) of the
isovector transverse densities in the "chiral" region b = O(M_pi^{-1}) and the
"molecular" region b = O(M_N^2/M_pi^3); (b) perform the heavy-baryon expansion;
(c) explain the relative magnitude of the peripheral charge and magnetization
densities in a simple mechanical picture; (d) include Delta intermediate states
and study the densities in the large-N_c limit of QCD; (e) quantify the spatial
region where the chiral components are numerically dominant; (f) calculate the
chiral divergences of the b^2-weighted moments of the transverse densities
(charge and magnetic radii) and determine their spatial support. Our approach
provides a concise formulation of the spatial structure of the nucleon's chiral
component and offers new insights into basic properties of the chiral
expansion. It relates the information extracted from low-t elastic form factors
to the generalized parton distributions probed in peripheral high-energy
scattering processes.Comment: 52 pages, 13 figure
Distribution of Flux Vacua around Singular Points in Calabi-Yau Moduli Space
We study the distribution of type IIB flux vacua in the moduli space near
various singular loci, e.g. conifolds, ADE singularities on P1, Argyres-Douglas
point etc, using the Ashok- Douglas density det(R + omega). We find that the
vacuum density is integrable around each of them, irrespective of the type of
the singularities. We study in detail an explicit example of an Argyres-Douglas
point embedded in a compact Calabi-Yau manifold.Comment: 27 pages, 1 figure; v2: minor change, references added ; v3:
references added, published versio
Towards underlying quantum gravity constraints on string inflation
Inflation is a widely accepted concept in cosmology proposing an accelerated expansion of the very early universe. For the class of large-field inflation models the energy driving the expansion arises from a scalar inflaton field that traverses trans-Planckian distances in a suitable potential. This thesis aims to discuss whether there exist underlying string theory or quantum gravity principles constraining/forbidding large-field inflation.
Our framework is axion inflation and its interplay with moduli stabilization in string theory. Axionic inflaton fields appear naturally in string compactifications and are protected from UV corrections due to their shift symmetry. The thesis is basically organized as follows: first, attempting to engineer a fully-fledged model of large-field inflation within string theory and second, analyzing possible underlying quantum gravity reasons to explain the ubiquitous control issues.
More precisely, we investigate aligned inflation in the vicinity of a conifold in the complex structure moduli space as well as axion monodromy inflation for a D7-brane position modulus. The ultimate failure of all scenarios boils down to the violation of a sophisticated mass hierarchy that is required to justify the employed effective field theories. These obstacles can be traced back to the swampland conjectures which had been claimed to hold generically for effective theories deduced from quantum gravity. In order to gather more evidence for these conjectures we investigate geodesic distances in moduli spaces of various Calabi-Yau manifolds.
Our results strongly support one of the swampland conjectures that predicts a break down of the effective theory of inflation as soon as one moves trans-Planckian distances. If true, parametrically controllable models of large single field inflation seem to be impossible in string theory
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
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