52,368 research outputs found
Pixel area variations in sensors: a novel framework for predicting pixel fidelity and distortion in flat field response
We describe the drift field in thick depleted silicon sensors as a
superposition of a one-dimensional backdrop field and various three-dimensional
perturbative contributions that are physically motivated. We compute
trajectories for the conversions along the field lines toward the channel and
into volumes where conversions are confined by the perturbative fields. We
validate this approach by comparing predictions against measured response
distributions seen in five types of fixed pattern distortion features. We
derive a quantitative connection between "tree ring" flat field distortions to
astrometric and shape transfer errors with connections to measurable wavelength
dependence - as ancillary pixel data that may be used in pipeline analysis for
catalog population. Such corrections may be tested on DECam data, where
correlations between tree ring flat field distortions and astrometric errors -
together with their band dependence - are already under study. Dynamic effects,
including the brighter-fatter phenomenon for point sources and the flux
dependence of flat field fixed pattern features are approached using
perturbations similar in form to those giving rise to the fixed pattern
features. These in turn provide drift coefficient predictions that can be
validated in a straightforward manner. Once the three parameters of the model
are constrained using available data, the model is readily used to provide
predictions for arbitrary photo-distributions with internally consistent
wavelength dependence provided for free.Comment: 17 pages, 7 figures, submitted to "Precision Astronomy with Fully
Depleted CCDs" - conference proceedings to be published by JINS
Intersubject Regularity in the Intrinsic Shape of Human V1
Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic
alternative to the Laplacian for spectral geometry processing and shape
analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator,
cannot capture the spatial embedding of a shape up to rigid motion, and many
previous extrinsic methods lack theoretical justification. Instead, we consider
the Steklov eigenvalue problem, computing the spectrum of the
Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable
property of this operator is that it completely encodes volumetric geometry. We
use the boundary element method (BEM) to discretize the operator, accelerated
by hierarchical numerical schemes and preconditioning; this pipeline allows us
to solve eigenvalue and linear problems on large-scale meshes despite the
density of the Dirichlet-to-Neumann discretization. We further demonstrate that
our operators naturally fit into existing frameworks for geometry processing,
making a shift from intrinsic to extrinsic geometry as simple as substituting
the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde
Intermittency in crystal plasticity informed by lattice symmetry
We develop a nonlinear, three-dimensional phase field model for crystal
plasticity which accounts for the infinite and discrete symmetry group G of the
underlying periodic lattice. This generates a complex energy landscape with
countably-many G-related wells in strain space, whereon the material evolves by
energy minimization under the loading through spontaneous slip processes
inducing the creation and motion of dislocations without the need of auxiliary
hypotheses. Multiple slips may be activated simultaneously, in domains
separated by a priori unknown free boundaries. The wells visited by the strain
at each position and time, are tracked by the evolution of a G-valued discrete
plastic map, whose non-compatible discontinuities identify lattice
dislocations. The main effects in the plasticity of crystalline materials at
microscopic scales emerge in this framework, including the long-range elastic
fields of possibly interacting dislocations, lattice friction, hardening,
band-like vs. complex spatial distributions of dislocations. The main results
concern the scale-free intermittency of the flow, with power-law exponents for
the slip avalanche statistics which are significantly affected by the symmetry
and the compatibility properties of the activated fundamental shears.Comment: 13 pages, 4 figure
Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
It is well known that Shannon's rate-distortion function (RDF) in the colored
quadratic Gaussian (QG) case can be parametrized via a single Lagrangian
variable (the "water level" in the reverse water filling solution). In this
work, we show that the symmetric colored QG multiple-description (MD) RDF in
the case of two descriptions can be parametrized in the spectral domain via two
Lagrangian variables, which control the trade-off between the side distortion,
the central distortion, and the coding rate. This spectral-domain analysis is
complemented by a time-domain scheme-design approach: we show that the
symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma
modulation and differential pulse-code modulation. Specifically, two source
prediction loops, one for each description, are embedded within a common noise
shaping loop, whose parameters are explicitly found from the spectral-domain
characterization.Comment: Accepted for publications in the IEEE Transactions on Information
Theory. Title have been shortened, abstract clarified, and paper
significantly restructure
Crystal image analysis using synchrosqueezed transforms
We propose efficient algorithms based on a band-limited version of 2D
synchrosqueezed transforms to extract mesoscopic and microscopic information
from atomic crystal images. The methods analyze atomic crystal images as an
assemblage of non-overlapping segments of 2D general intrinsic mode type
functions, which are superpositions of non-linear wave-like components. In
particular, crystal defects are interpreted as the irregularity of local
energy; crystal rotations are described as the angle deviation of local wave
vectors from their references; the gradient of a crystal elastic deformation
can be obtained by a linear system generated by local wave vectors. Several
numerical examples of synthetic and real crystal images are provided to
illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure
Shadows of rotating five-dimensional charged EMCS black holes
Higher dimensional theories admit astrophysical objects like supermassive
black holes, which are rather different from standard ones, and their
gravitational lensing features deviate from general relativity. It is well
known that a black hole shadow is a dark region due to the falling geodesics of
photons into the black hole and, if detected, a black hole shadow could be used
to determine which theory of gravity is consistent with observations.
Measurements of the shadow sizes around the black holes can help to evaluate
various parameters of the black hole metric. We study the shapes of the shadow
cast by the rotating five-dimensional charged Einstein-Maxwell-Chern-Simons
(EMCS) black holes, which is characterized by the four parameters, i.e., mass,
two spins, and charge, in which the spin parameters are set equal. We integrate
the null geodesic equations and derive an analytical formula for the shadow of
the five-dimensional EMCS black hole, in turn, to show that size of black hole
shadow is affected due to charge as well as spin. The shadow is a dark zone
covered by a deformed circle, and the size of the shadow decreases with an
increase in the charge when compared with the five-dimensional Myers-Perry
black hole. Interestingly, the distortion increases with charge . The effect
of these parameters on the shape and size of the naked singularity shadow of
five-dimensional EMCS black hole is also discussed.Comment: 27 pages, 9 figures, matches with published versio
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